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Hard amorphous (diamond-like) carbons
/~n~g. $o//d St. C/ram. Vol. 21, pp. 199-333, 1991 Prlnt~l in O r ~ t Britain. All dlhts r,~rvod.
0079-6786/91 $0.00 + ..TO @ 199"2Persamoa Prm~ Lid
HARD AMORPHOUS (DIAMOND-LIKE) CARBONS John Robertson National Power Laboratory, ~atl~rlm~ Surrey, KT22 7SE, U. FL
ABSTRACT The hard forms of amorphous carbon and hydrogenated amorphous carbon, also known as diamond-like carbon, have recently aroused considerable interest as coating materials. This paper reviews their preparation, structure and properties. These carbons contain both sp 2 and sp3 sites. A chemical bonding model is developed which describes the arrangement of these sites and which accounts for many of the electronic and mechanical properties, The review covers the various deposition methods and the deposition mechanisms, the characterisation of amorphous carbons by techniques such as diffraction, electron energy loss, Raman, infra-red, nuclear magnetic resonance, and thermal stability, their electronic structure, optical properties and electronic spectra, and their mechanical properties such as elastic modulus, hardness, wear rate, friction and film adhesion. The dependence of electronic and mechanical properties on deposition methods and conditions is studied, to assess which methods are most valuable for applications. CONTENTS 1 Introduction
201
Deposition Methods 2.1 Ion Beam Methods 2.2 Sputtering 2.3 Plasma Deposition 2.4 Laser Methods 3 Atomic Structure 3.1 Techniques 3.2 Structure o f a - C 3.3 Structure o f M S I B a-C 3.4 Structural Modelling of a-C 3.5 EXAFS 3.6 Structure ofa-C:H 3.7 Real Space Studies JPSSC 21:4°A
205 205 208 209 213
199
213 213 218 222 224 228 228 230
200
4
J. Robertson
3.8
Infrared and Raman Spectra
3.9
C-H Vibrational Modes
Atomic Structure
7
8
249 250 254
Coordination Huckel Calculations
4.3 4.4 4.5
Band Gaps a - n Mixing Electronic Structure Simulations
260
4.6
Photoemission
263
4.7
Optical Spectra
4.8
Electron Energy Loss Spectra
268 271
258
275
,5.1 A-C:H
275
5.2
Role of Hydrogen
279
5.3
A-C
283
Localized States
288
6.1
Origin of Localized States
288
6.2
Localization
290
6.3
Electrical Conductivity
293
6.4
Doping
6.5
Defect Densities
295 299
6.6
Luminescence
6.7
Defect Equilibria
303 304
7.1
Plasma Deposition - case ofa-Si:H
306 306
7.2
Plasma Depsoition ofa-C:t!
3O8
7.3
Ion-Solid Interactions
310
7.4
Ion Beam Deposition
311
Deposition Mechanisms
Mechanical Properties 8.1
9
249
4.1 4.2
,5 Properties ofa-C and a-C :lI
6
236 247
Survey
313 313
8.2 Constraint Model
314
8.3
Elastic Moduli -Comparison with Experiment
316
8.4
ttardness
317
8.5
Friction
8,6
Wear
321 322
8.7
Internal Stress
322
8.8
Adhesion
323
Conclusions
324
References
325
Diamond-Like Carbons
201
1 INTRODUCTION There have recently been two important advances in the science of crystalline carbon - the discovery that diamond can be readily grown by vapour deposition (1-3) and the discovery of a third allotrope of carbon, a molecular crystal of the fullerene molecule (4,5), 'buckyball' C6o .: There has been a parallel advance in effort in disordered carbons. The range of disordered carbons is wide, covering soots, chars, carbon fibres, glassy carbon and evaporated amorphous carbon. These carbons are basically sp 2 bonded. A range of new preparation methods has produced forms of amorphous carbon (a-C) and hydrogenated amorphous carbon (a-C:H) which are mechanically hard, infra-red transparent and chemically inert. They are finding immediate applications as hard coating materials for magnetic disc drives or as antireflective coatings for infra-red windows (6-15). Their beneficial properties arise from the sp 3 component of their bonding and these carbons are frequently called diamond-like carbon (DLC). In general, such carbons can be fully amorphous or contain crystalline inclusions. This field of noncrystalline carbons is of interest both technologically to materials scientists and also at a more fundamental level to solid state chemists and physicists. A carbon atom can exert three different hybridizations, sp 3 , sp 2 and sp t (Fig. I). In the sp3: configuration, as in diamond, each of a carbon atom's four valence electrons is assigned to a tetrahedrally directed sp 3 hybrid orbital, which makes a strong tr bond with an adjacent atom (7). In the 3-fold coordinated sp ~ configuration as in graphite, three of the four valence electrons are assigned to trigonally directed sp ~ hybrid orbitals which form strong intra-layer tr bonds. The fourth electron lies in a pn orbital which lies normal to this bonding plane. This orbital forms weak rr bonds with neighbouring ~t orbitals, rt bonding is also called unsaturated bonding. In the sp ~ configuration as found in acetylene, two valence electrons are assigned to linearly directed sp ~ hybrids which form a bonds and the other two electrons are placed in each of the py~ and Pz, orbitals. The physical properties of the various non-crystalline forms of carbon are compared with those of diamond, graphite and C~0 in Table I. In diamond, the strong, directional tr bonds give it a wide 5.5 eV band gap, and the highest hardness, elastic modulus and room temperature thermal conductivity of any solid (I,16,17). Graphite consists of hexagonal layers of sp ~ sites, weakly
z Z
sP 3 Fig. 1.
sp2
sp
Schematic representation of sp s, sp 2 and sp ~ hybridized carbon.
J. Robeamn
202
Table 1. Properties of various forms of carbon Density gm cm -3
Hardness GPa
% sip
Diamond
3.515
100
Graphite
2,267
C~o
Gap eV
Ref.
100
5.5
16
0
-0.04
0
at.% H
0
275
1.8
5
Glassy C
1.3-1.55
2-3
-~0
0.01
83
a-C, evap.
1.9-2.0
2-5
1
0.4-0.7
90
a-C, MSIB
3.0
30-130
90 -t- 5
<9
0.5-1.5
39
PD a-C:H, hard
1.6-2,2
10-20
30-60
10-40
0.8-1.7
9
PD a-C:H, soft
0.9-1.6
<5
50-80
40-65
1.6-4
9,141
Polyethylene
0.92
0.01
100
67
6
292
bonded together by Van der Waals forces in an ABAB stacking sequence along its c axis. This bonding anisotropy produces a high conductivity and strength within the basal plane but low values in the c direction. In C60 each carbon is 3-fold coordinated in a slightly distorted siP configuration. The various non-crystalline carbons can be considered to be intermediate between diamond, graphite and hydrocarbon polymers, in that they can contain variable amounts of sip and sip sites and hydrogen. The long-known forms of non-crystalline carbon such as soot, glassy carbon and evaporated carbon consist almost totally of sip sites. The first diamond-like carbons were produced by ion beam deposition by Aisenberg and Chabot (10). It is now recognised that a wide variety of methods can be used in their preparation, such as plasma-deposition, sputtering, magnetron sputtering, ion plating, and laser plasma deposition (18-48). These deposition methods are reviewed in section 2. A common theme of these methods is that the film is subjected to ion bombardment during growth which promotes siP bonding. Nevertheless the precise deposition mechanism responsible for the promotion of sip bonding is a matter of contention, as discussed in detail in section 8. A wide variety of methods have been used to characterise the structure of amorphous carbons, using both structural and electronic probes. These are described in section 3. Characterisation of diamond-like carbons has been held back because of their mixed bonding character and the absence of unhydrogenated, highly sip form of a-C, analogous to a-Si. It is now recognised that such a form of a-C can be prepared by mass-selected ion beam deposition (MSIB) in which a mass-filtered beam of C ~ or C- ions is condensed on a substrate. The process was originally developed by Akensov et al (37) and the structural characterization was carried out by McKenzie et al (39,40) and Gaskeil et al (41). Weissmantel et al (30) and Angus et al (6) observed that the properties of amorphous carbons deposited under ion bombardment conditions tend to pass through three regimes as a function of ion energy (Fig. 2). Unhydrogenated a-C deposited at low ion energy is essentially graphitic and similar to evaporated a-C. It changes to hard a-C at moderate ion energies and it then becomes less hard again at high energies as its structure adopts a highly disordered, defected graphitic structure. A-C:II is soft and polymeric at low ion energies due to the predominance
Diamond-Like Ca.,'bon~
GRAPHITIC a-C
I000
>
I00
0ENSE CARBON
HARD a-C:H
v
>.. L~ r,, tU
Z
LU
I-U <
13.
I($OF POLYMERIC T) a-C:H
I0
p'J/
m
kMORPHOUc, CARBON ($pZ)
CARBON sOURCES Fig. 2.
PLASMA POLYMERS
.IYDROCARBON SOURCES
Schematic variation of bonding character on ion energy during deposition for a-C and a-C:H (6).
of = CH2 groups. Its hardness passes through a maximum at moderate ion energies as its hydrogen content drops and finally the hardness declines at high ion energies when it also adopts a defected graphitic structure (9). Angus (1,49) has proposed a valuable means of classifying the various carbons and hydrocarbons in terms of their atom density and hydrogen content as shown in Fig. 3. The atom number density is the total number of atoms per unit volume divided by the Avogadro's number. This plot emphasises that the diamond-like forms of a-C:H are unique in that they have a much higher atom density than conventional hydrocarbon polymers. Diamond is seen
204
J. Robertmn
0.30 DIAMOND •
b
o.oo
o.oo
Atom Fraction Hydrogen Fig. 3.
Atom number density versus atomic fraction of hydrogen content for solid carbons and hydrocarbons, after Angus (I). a-C:H points are full cicles and triangles. Amorphous carbon refers to evaporated C, while a-C refers to a-C deposited by sputtering or ion beam methods.
to have the highest atom density, and indeed has the highest atom density of any solid at ambient pressure. Graphite has a lower density and lower atom density than diamond. Amorphous carbon formed by evaporation and many sputtering processes consists largely of sp~ carbon and has a density just less than graphite. The various conventional hydrocarbon polymers included are the alkanes such as polyethylene, the polyacetylenes and the polynuclear aromatics. The atom densities of diamond-like hydrocarbons are above 0.19 gram-atom cm -3, indicating the effect that network cross-linking has on raising the density. The hard amorphous carbons formed from filtered ion beams or from laser plasmas are seen to have densities and atomic densities above graphite and below diamond. The atomic structure and the electronic structure are very closely related in amorphous car. bons, as they are in all amorphous semiconductors (7). Of particular interest is the presence
Diamond-Like Carbons
filled valence states
205
empty conduction stotes
Energy Fig. 4.
Schematic band structure of amorphous carbons (7).
of n states and the effect of disorder on them. Since the rt states are more weakly bound, they lie closer to the Fermi level Er than the ¢r states, as shown in Fig. 4. The filled n states form the valence band and the empty n * states form the conduction band in all amorphous carbons, and so they control the size of the optical gap. Many aspects of the local bonding in a-C can be deduced from quantum chemistry. It is found that a mixed phase of sp s and sp2 sites tends to segregate into sp2 bonded clusters. These clusters have a pronounced effect of the electronic properties of a-C which are of considerable fundamental interest, as described in more detail in section 5. The major technical interest in diamond-like carbons is as a thin film coating material. This has led to significant work on their mechanical properties such as hardness, elastic modulus, adhesion, friction and wear rate. Recently the author developed a microscopic model of the mechanical propeties. This relates the elastic modulus to the underlying chemical bonding and composition of the film. This is then extended to treat hardness, wear properties and film adhesion, as described in section 8. The adhesion of hard carbon films to their substrates is a major concern in their application. 2 DEPOSITION METHODS 2.1 Ion Beam Methods
A wide variety of deposition methods have been used to prepare diamond-like carbon.
A
common feature of each method is the exposure of the growing film to bombardment by ions of medium energy, 20-500 V, which appears to promote sp 3 bonding (6,9,50). The various methods and their growth rates are summarised in Table 2. The first ion beam device of Aisenberg (10) generated carbon ions by sputtering carbon electrodes in an Ar atmosphere in a magnetically confined plasma. A bias voltage extracts the ions and directs them at the substrate. Higher growth rates were found to be possible if the ions are generated from a hydrocarbon source gas. The resulting films may have contained both a-C and diamond microcrystallites. The results were confirmed by Spencer et al (11), and Vora and
206
J. Robezt.mn
Table 2.
Methods for the deposition of Diamond-like Carbon Precursor
ypical Growth Rate,
ref.
sec.
ion beam
graphite
1.3
10
ion beam
methane
2
51
PD
methane
I
9
PD
benzene
15
9
Ar beam sputtering
graphite
3
22
Magnetron sputtering
graphite
3
23
Ion plating
benzene
I0
30
Laser plasma
graphite
<3
22
Cascade arc
Ar/methane
300
34
Mass selected ion beam
graphite
0.I-6
40
Moravec (19), while Mori and Namba (18) investigated the dependence of film properties on deposition conditions. A very popular ion source is that due to Kaufmann (51), shown in Fig. 5. In this source, electrons from a thermionic cathode are used with an axial magnetic field to generate a plasma. This gives high ionization rates in a source gas such as methane. Positive ions are extracted from the source by a bias electrode and are directed at a substrate.
Anode grid Ion box Filament k
Ion source Accelerator grid Neutralizer wire
II II | | ~ i _ _
o
Ill II''JI I ~
Fig. 5.
• |--"
•
" °
-*
*'"
Schematic ion beam deposition apparatus (51).
•
~' *
Diamond-LikeCarbons
207
The ions generated in a carbon source are of the form Cm-' while those from a gas source are of the form CmH,~. In both cases the substrate also receives a large flux of neutral species such as un-ionized Ar or methane from the background gas. This reduces the ion/neutral mass flux ratio to of order 0.02 (50,52). A high ionization ratio and a relatively high deposition rate can be achieved by using a cathodic arc as carbon ion source (37,39) A further increase in deposition rate is achieved by using a cascade arc source (53). A highly ionized thermal plasma of methane and Ar is created in an arc and the pumping conditions and design are such that the plasma expands supersonically into a high vacuum towards the substrate. This expansion causes a high degree of ionization of the plasma. Deposition of a single ion species is possible if the ion beam is passed through a magnetic mass analyser for e/m selection. The analyzer filters neutrals, cluster species, graphitic fragments and impurities from the beam and allows only a pure beam of C ~ (or C-) ions to reach the substrate. This MSIB method was first used by Aksenov et al (37), who believed that a new crystalline phase of C was formed. The method has now been used by a number of groups (38-48). Structural studies summarised later indicate that the resulting material is fully amorphous with the highest fraction of sp3 bonding of those from any present deposition process. The deposition rate for this method can be maximised by using the carbon arc as an ion source (Fig. 6). Typical rates are now 400 A/min. The arc is confined magnetically for stability. The main practical problem with this method is the high compressive stress in the films, which limits their adhesion and thereby the maximum stable film thickness.
B
H: To vacuum pump ~ I: High current power supply J: Viewing ports
Fig. 6.
[ ~i
\
H
Apparatus for Mass Selected Ion Beam deposition by magnetic filter, using a cathode arc source, after McKenzie et al (39)
J. Robertson
208 2.2 Sputtering
Various sputtering methods can be used to produce hard carbons. In ion beam sputtering, a beam of typically 1 kV Ar ions is directed at a graphite target (22,28). An angle of incidence of 30-45 ° is used to maximise the yield. The sputtered carbon is condensed onto a nearby substrate. A second Ar ion beam can be directed at the substrate to provide the ion bombardment of the growing film. A disadvantage of ion beam sputtering is its low deposition rates due to the low sputtering rate of graphite.
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Magnetron sputtering source, after Savvides (23).
Diamond-LikeCarbons
209
zo
2
10
100
500
Power ( W ) Fig. 8.
Variation of Ar m and C atom arrival rates with sputtering power for magnetron sputtering, after Savvides (23).
Higher deposition rates can be achieved by magnetron sputtering (23,26,27). Here an Ar plasma is used to both sputter from the target and bombard the growing film, as shown in Fig. 7. Growth rates vary linearly with rf. power and are typically 3A/sec (23). Ion energies are of order 20 eV and these decline slowly with increasing power or gas pressure. A mixture of Ar and carbon ions and atoms reaches the substrate. Savvides noted that the ion/atom ratio in the beam increases with decreasing sputtering power because the ion yield decreases less quickly than the neutral atom flux (23), Fig. 8. This is the opposite dependence to that in plasma deposition where ion bombardment effectively increases with plasma power. A d c bias can be applied separately to the substrate if it is desired to raise the mean ion energy. The general advantage of sputtering methods is their good process control and their ability to be scaled up for manufacturing. A disadvantage is that the hardest films seem to be prepared under conditions of low power and low gas pressure, where deposition rates are lower. 2.3 Plasma Deposition
The most popular deposition method involves the rf. plasma decomposition of a hydrocarbon source gas onto negatively self-biased substrates. Plasma deposition (PD) or strictly plasmaassisted chemical vapour deosition (PACVD) was pioneered for a-C:tt by ttolland and Ojha (20), and it is also widely used to deposit a-Si:H. Self-biasing is prefered to dc biasing for a-C:H because the films are insulating (9,21,54-56). In this method, Fig. 9, the rf. power is capacitively coupled to the substrate electrode and the counter electrode is either a second electrode or just the grounded walls of the deposition chamber. This gives a large difference between the electrode sizes. If the r£ frequency is greater than the ion plasma frequency, of order 2-5 MHz, the electrons can follow the rf voltage but the ions cannot. The large difference in electrode size and also in the electron and ion mobilities produces a negative dc. self-bias on the powered
210
J. Robertson
Vacuum gauge Pump Y
Substrote,
-VMatching box
~
Needle valve
souJg. E
RF P°wermeterLI~J 2~r
Voltmeter. c
RF Generator Fig. 9.
Schematic of capacitively-coupled RF plasma deposition apparatus, with substrate attached to the powered electrode (cathode) (9).
electrode, making it the cathode. The ion current is now largely dc while the compensating electron current flows in short bursts each rf. cycle (Fig. I0). The dischage now consists of a glow region, in which the ions are generated by collisions with electrons, and a space charge region or ion sheath, across which the ions are accelerated to reach the cathode. The equivalent electrical circuit for the plasma is a resistance for the plasma glow in series with a capacitance for the sheath (54,57). The dc. bias is largely dropped across the sheath (Fig. 10). The bias voltage, -Vb, varies with rf. power W and operating pressure P as (21,54), W
Vb = k(--f-)
112
[l]
where k depends on factors such as the electrode areas. Catherine and Couderc (54) have shown that this is the dependence expected for an ohmic plasma and a sheath thickness proportional to p-in. The ion energy Eu depends on Vb and the ion mean free path in the sheath, At low pressures in the absence of collisions
Diamond-Like Carbons
Distribution of time-averaged potential within discharge
f i l l
'
211
Rf modulation of plasma and cathode potential
I i
I I I I
0
.! 4~
C @ 0
o. @ 01 0 L_
,,C
"~
>-
2_1
0 I q)
_E k-
Distance cathode (small electrode) Fig. 10.
t anode (large electrode)
Time
(a) Average potential distribution and (b) waveforms in a capacitively coupled plasma reactor, after Koidl et al (9).
Ei-~eVb while at higher, typical operating pressures there is a spectrum of ion energies with a mean value of Vb E i -~ k '
pi12
[2]
or about E, = 0.6Vb for typical pressures of 3 Pa (9). Ion energy spectra have been measured for Ar discharges by Wild et al (58). The deposition rate varies with the ionization potential and molecular weight of the source gas as shown in Fig. ! I, with low ionization potentials and large molecular weights giving higher growth rates (59-61). The deposition rate v for a given gas has been found to vary with bias voltage and gas pressure as v -----k " V b P
['3]
by Koidl et al (9,21), Catherine and Couderc (54), and Zou et al (60,61), for various different source gases (methane, acetylene and benzene). The deposition rate can saturate or decline for
J. Robertmn
212
1000
--
I
n-hexane~"' ne _Butane " ~ P r o p a n e Ethene *
~
100
.o Methane
W 0 e~ 0
a
10
I
9
Fig. 11.
I
I0
I
I
I
I
11 12 lonlzation potential, eV
I
13
Plasma deposition rates versus ionization potential of precursor gas, for a gas pressure of 3 Pa and a self-bias voltage of-400V, after Koidl et al (9). Data for acetylene from Zou et al (61).
biases over 1.2-1.5 kV as the incoming ions begin to sputtered the film. The total deposition flux again consists of both ions and neutral species from un-ionized background gas. Some of the neutral species can be energetic, as they are formed by charge exchange reactions with energetic ions. Catherine (55) found the ion/neutral flux ratio to be 0.1-0.2 for methane plasmas on the basis of ion flux measurements, while Locher et al (62) found a ratio closer to 0.5 for benzene plasmas by comparing with ion-beam deposited films. The advantage of plasmadeposition is its simplicity and high deposition rates with the appropriate gases. A problem with PD is in the scaling up to larger systems as film properties depend mainly on bias voltage and thereby electrode areas rather than directly on process parameters like RF power and gas pressure. The properties of PI) a-C:tl depend strongly on the ion energies, as discussed in detail in section 5.1. I.ow ion energies only weakly dissociate the source gas and give a highly hydrogenated or polymeric form of a-C:H. This regime is similar to that of plasma polymerisation, reviewed by Yatsuda (63). Plasma deposition is also a popular method of preparing a-Si:ll and polycrystalline diamond (3), but the conditions are considerably different in each case, as summarised in Table 3. Hard
213
Diamond-Lik~Carbons
Table 3.
Conditions for plasma polycrystalline diamond.
deposition
of a-C:H,
electronic
a-C: H
a- Si:! I
diamond
RF power density, W/cm -~
!
0.01
10
Gas pressure, Pa
3
10
3
Substrate electrode
cathode
anode
Td , °C
25
250
Dilution
grade
a-Si:H
and
800 It~/CI-t4--- 100
a-(':H is obtained if there is ion bombardment during deposition, and these conditions are favoured by a cathodic substrate (to receive positive ions), a high RF power (for a high bias voltage), low gas pressure (for high ionisation) and low substrate temperatures (to minimise self-annealling). Electronic grade a-Si:tt is deposited from silane plasmas under conditions which minimise the concentration of defect states due to Si dangling bonds. Sufficient hydrogen must be retained to passivate the dangling bonds but not so much that polymeric SiI-t2 groups are common. This requires gentle conditions orlow RF power density, a moderate gas pressure, an anodic substrate (to minimise ion bombardment) and a substrate temperature of about 250 °C to give optimum self-annealling (64). Diamond growth is favoured by using hydrogendiluted source gases, a high power density and a higher substrate temperature. These conditions generate atomic hydrogen which suppresses the deposition of graphite and a-C by various mechanisms such as preferential etching (2). There are also a variety of hybrid deposition methods such as ion plating in which the plasma is created by an RF plasma and then the ions are accelerated by a separate field from a grid electrode to the substrate (29-31,65). More highly ionised plasmas can be produced by using microwave discharges, particularly if operated at the electron cyclotron resonance (66,67). This method produces high ion densities even at low gas pressures. The absence of electrodes and ability to control the shape and position of the plasma make this method technically attractive. Control of both ionisation and ion energy can be achieved by using a microwave ion source and a rf. self-biasing accelerator. 2.4 Laser Methods
A carbon ion plasma can also be produced by the laser ablation or graphite (33-35), Fig. 12. The resulting plasma probably resembles that formed by a cathodic arc (36). The resulting a-C is found to have a diamond-like character if the laser power density exceeds a threshold value. 3 ATOMIC STRUCTURE 3.1 Techniques
This section describes the structures of the various forms of a-C and critically reviews the various structural characterisation methods. The principal requirement from a structural study of a-C or a-C:H is to find the fraction o f s p 2 and sp 3 sites and the hydrogen content. A secondary
214
J. Robertson
LASER INPUT
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o"
useful deposition 6roph/le
Laser-plasma deposition apparatus, after Collins (34).
requirement, particularly in the more sp 2 bonded carbons, is to find the degree of medium range ordering (MRO), which can be expressed as whether there is a local layer structure and whether it is dominated by planar 6-fold rings. The principal techniques wbich have been used to characterise the structure have been electron, X-ray and neutron diffraction, nuclear magnetic resonance (NMR), electron energy loss spectroscopy (EEl.S), X-ray near edge absorption spectroscopy (XANES), X-ray absorption fine structure (EXAFS), Rutherford Backscattering (RBS), optical spectroscopy, infra-red (IR) spectroscopy, Raman and Auger. The hydrogen content can be found by proton NMR, nuclear reaction analysis (NRA), elastic recoil detection (ERD), combustion analysis or by thermal evolution. The relative merits of the characterisation methods are summarised in Table 4 and are discussed in more detail below. The most direct and valuable probes of fraction of sp ~ and sp3 sites are C ~3 N M R and XANES spectroscopies. N M R has been used to charcterise a wide variety of carbons, from polymers to coal (68,69) The advantage of N M R is that each different hybridization gives rise to a chemically shifted peak whose area is directly proportional to its concentration (68-76). The
Diamond-Like Carbons
Table 4.
215
Comparison of structural characterisation methods.
C I~ N M R
Strengths
Weakness
quantitative, detects sp ~ and sp2 sites
sensitivity (cost, time)
XANES
quantitative
best for sp2 sites
Diffraction
detailed
long interpretation
IR of C-H modes
cheap
only detects C-H sites, variable matrix element
Raman
sensitive to M R O
weak sp 3 scattering, interpretation
EXAFS
low Z, contamination
Density
indirect
limitations of the technique are the large sample sizes needed to detect the C 13 N M R because of the isotope's low natural abundance and the time needed for data acquistion. A certain
sp 2 sp 3
'
' 4(~0
'
'
CHEMICAL Fig. 13. JPSSC 21;4-B
' 200'
'
'
()
'
'
'-200
S H I F T F R O M T M S ~PPM)
N M R spectra of sputtered a-C, after Pan et al (76), and a sample ofplasma-deposited a-C:H after Petrich et al (68).
216
J. Robertson
density of unpaired nuclear or electronic spins helps to give a short enough coherence time T~ to collect the NMR signals. The nuclear spins can be either C ~3nuclei or protons. On the other hand, interactions with other spins and also chemical shift anisotropy will broaden the N M R peaks. Magic angle spinning (MAS) can be used to reduce this peak broadening. In a-C:H, because of the H-C interaction, an additional 'proton decoupling' signal will align the proton spins and so it considerably sharpens the peaks. A typical example of this is shown in Fig. 13. The H-C interaction can also be used to distinguish between hydrogenated and unhydrogenated sites, whenever it is the predominant source of line broadening, as is the case in a-C:H. The tt-C interaction is dipolar and decays rapidly with distance as r -3 , so turning off the proton decoupling signal broadens the spectra of the hydrogenated sites into the baseline. The remaining spectral peaks now correspond to the unhydrogenated sites. The spectrum with decoupling includes all sites. XANES gives direct evidence of the existence of sp 2 sites (77,78). The photoexcitation of a core electron of an atom gives rise to an x-ray absorption spectrum. The part of this spectrum near the edge is called XANES and the oscillating components at higher energy are called the EXAFS. The XANES spectrum reflects the conduction band density of states, Fig. 4. The XANES of carbon consists of a broad step at 290 eV due to excitations from the C Is core level to the empty a * states and a prepeak at 285 eV due to excitations to the n* states of any sp2 or sp ~ sites present (7). The XANES spectra of the major types of a-C are shown in Fig. 14. The absence of a n* peak at 285 eV in diamond is quite clear. The differences in the shapes of the n* and a* features do not allow for a simple analysis of sp~ content. Additionally, the n* is likely to be enhanced and red-shifted by the interaction of the excited electron and the core hole. Nevertheless, this effect is relatively constant, so that it is possible to extract the sp~ content from the relative areas of the n* peak and the leading edge of the a* step, by using the spectrum of graphite for normalisation, as shown by Berger et al (77). Jarman et al (70) found a reasonable correspondance between sp2 site fractions derived by XANES and NMR. One should note that the n* peak is strongly anisotropic and energy dependent in graphite (79,80). Hence care should be taken to directionally average this peak in the graphite spectrum or in any anisotropic form of a-C. XANES can be measured using photons, on a dedicated electron energy loss spectrometer or by an EEI.S attachment to an electron microscope. The density also gives very useful indirect information on the likely sp s content of a-C due to the large difference in density of graphite (2.267) and diamond (3.515). The sp3 content can be infered by extrapolation. Density is less meaningfkd for a-C:H as its polymeric component can give rise to densities down to 0.92, that of polythene, but nevertheless high densities are a good indication of favourable mechanical properties. Densities can be measured by floatation, weight gain measurement during deposition, Rutherford backscattering (RBS), or be inferred from the low energy EELS. The low energy EE1.S of carbons shows a peak around 20-35 eV due to the plasma oscillations of all the valence electrons known as the o + n plasmon. Its energy is proportional to the square root of the valence electron density (28), as discussed in section 5. This allows the derivation of the density if the electrons due to any hydrogen are allowed for. Wang et al (81) found reasonable agreement between densities determined by EELS with those determined directly. Diffraction studies give the most detailed information on local structure. The diffraction pattern of an object, the diffraction intensity l(k) is given by the product
Diamond-LikeCarbons I
I
II
217 I
I
(I"* ~/
~RAPHITE DIAMOND
) m
¢h
Z IZ
I,M
EVAP a-C
m
PD a-C:H
MSIB a-C 280 Fig. 14.
ENERGY, eV
300
XANES spectra of graphite, diamond, evaporated a-C, PD a-C :H and MSIB a-C:H, after Berger et al (77) and Fink et al (78).
l(k) = S(k)Nle(k)
[4]
where k is the scattered wavevector, S(k) is tile structure factor, N is the number of atoms and f(k) is the atomic form factor for of a single (bonded) atom by electrons, X-rays or neutrons. The k dependence of f(k) is significant for electrons, particularly because C has few core electrons to dominate scattering. The k dependence is minimal for neutrons, except for the case of H. The structure factor is related to the radial distribution function (RDF), J(r), by S(k) =
{J(r)/r - 4npor } sin(kr)dr
[5]
J. Robertson
218
The R D F is the probability of finding another atom at a distance r from a given atom. The R D F consists of a series of peaks and tends to a parabolic curve J(r) = 4nr2p0r at large r, where p0 is the microscopic density. The first peak lies at the average nearest neighbour distance or bond length r~ and its area equals the coordination number n~. The second peak lies at the second neighbor distance r2 from which the bond angle 0 is found, r 2 = 2r I sin(0/2)
[6]
The R D F is also often plotted in the reduced form G(r)= J(r)/r - 4 nrpo so that G(r)--*0 as r oo. The peak widths of an R D F equal their natural width plus the resolution of the experiment, which depends on kmtffl, where km,~ is the highest value of k used. kmu limitations are significant for carbon because of the short bond length rl. The wide band optical spectra have also been used to deduce sp 3 fractions. This method is described later. Auger is also used to give the sp3 fraction (82). The IR and Raman spectra give information on the C-H bonding and medium range ordering, as discussed shortly. 3.2 Structure of a-C.
We first consider the structure of the various forms of unhydrogenated a-C. Table 5 gives the peak positions in measured structure factors for various types of a-C. Table 6 gives some structural values deduced from their RDFs, compared to those of diamond and graphite. The four parameters n~, r~ 0 and p0 are generally sufficient to establish the character of any a-C. It is also of interest to know the degree of longer range order in graphitic carbons. Ideal graphite consists of hexagonal layers of atoms arranged in an ABAB.. stacking sequence with unit cell dimensions a=2.461A and c=6.708A, corresponding to a bond length of 1.421A, an interplanar spacing of d = 3.354A and a density of 2.267gm.cm -3. The most ordered form of synthetic graphite is called highly oriented pyrolytic graphite (HOPG). The structure of microcrystaUine graphites follows the turbostratic model in which graphite layers are stacked
Table 5.
Peak positions in S(k) of various forms of a-C, compared to the indexed reflections of graphite and diamond Peak position, A -j
glassy C
1.8
2.98
5.11
a-C (evap)
1.0
2.9
a-C (sput)
1.6
a-C (MSIB)
Ref. 8.8
10.2
83
5.1
8.7
10.3
90
2.95
5.5
8.7
10.5
92
1.2
2.9
5.4
8.7
10.3
41
a-C:H
1.2
3.0
5.4
8.5
10.4
113
Graphite (hkl)
(002) 1.88
(100) 2.95
(110) 5.11
(200) 5.90
(210) (300) (220) 7.82 8.86 10.2
(220) 5.00
(311) 5.86
(331) 7.71
Diamond (hkl)
(100) 3.06
(200) 3.53
5.96
7.8
Diamond-Like Carbons
Table 6.
219
Inter-atomic distance(r), coordination number(n) and density of various forms of C r~, A
n~
r2, A
n~
Graphite
1.42
3
2.45
6
2.267
Diamond
!.544
4
2.512
12
3.515
16
glassy C
!.425
2.99
2.45
6. I
1.49
83
a-C (evap)
1.43
3.3
2.53
8.8
2.0
90
1.46
3.34
2.49
6.7
2.44
92
1.526
3.9
2.52
8.9-10.9
3.0
41
a-C (sput) a-C (MSIB) a-C:H
1.39,1.52
2.5
local density, gm.cm-S
ref
i.5-1.8 113
in an arbitrary sequence and orientation. Their diffraction patterns retain only the interlayer (hk0) peaks and the intralayer (002) peaks. Mildner and Carpenter (82,83) measured the structure factor of glassy C by neutron diffraction to k,,,~ = 25A -1 (Fig. 15). The RDF in Fig. 16 shows a strong retention of graphitic local order (82-86). with a bond length of !.425A a coordination number of 2.99 atoms and a bond angle of 120 °, consistent with 100% sp~ sites. The peaks of S(k) can be indexed according to the turbostratic model, and the peak widths indicate an in-plane correlation length Lo-~50A and an inter-plane correlation length of Lc-~30A. This indicates that glassy C possesses too high a degree of ordering to be classified as amorphous. numerous microvoids.
Its low density of 1.5gm.cm-~ arises from its
The XANES spectrum of evaporated a-C indicates that it contains about 99% sp 2 sites (Fig. 14). Its structure has also been measured by electron diffraction by Kakinoki et al (88), Boiko et al (89) and McKenzie et al (90,91). Kakinoki (88) concluded that evaporated a-C contained of order 50% sp 3 sites but the Boiko (89) and McKenzie (90,91) data indicate about 5% or fewer sp 3 sites. The structure of sputtered a-C has recently been studied by static and magic angle spinning N M R by Pan et al (7,5). The static NMR spectrum is shown in Fig. 13. This material was prepared by condensation onto substrates cooled by liquid nitrogen, to minimise any heatinginduced graphitisation. ]'hey found 6% sp~ sites. The structure of this same sputtered a-C was studied by neutron diffraction by Li and Lannin (92) with kmax -- 30A -1. Tile RDF in Fig. 16 gives a coordination number of 3.3 and a bond length of 1.46A. These are both consistent with 10-20% sp 3 sites. This is higher than found by NMR but of the same order. The second neighbor peak at 2.49A gives a bond angle of 117 ° and its coordination of 6.9 compared to values of 120 ° and 6 for sp~ bonding. The a-C had a macroscopic density of 2.0gm.cm 3, and a microscopic density of 2.4gm.cm-3 from the RDF, the latter being 5% higher than graphite. The first peak was found to be relatively broad, indicating a range of bond lengths, as expected from the hybridization. It also shows a tail at high r, suggesting that the existence of some quasi-sp 3 sites with a fourth, weakly bonded neighbour. This configuration also occurs in the high pressure transformation of graphite lattice to diamond (93).
220
J. Robert.son
evaporated a-C
g
U)
I
0
Fig. 15.
2
4
6
8 10 k, ~-1
12
14
16
Structure factors of glassy C after Mildner and Carpenter(84), evaporated a-C after Green et al (90), sputtered a-C after Li and Lannin (92), MSIB a-C after Gaskell et al (41) and PD a-C:lt after Newport et al (I 10).
The R D F also gives information on more long-range structure. The R D F of an ideal graphite layer would possess a peak at 2r, --- 2.84A, the third neighbour cross-ring distance. This peak
Diamond-Like Carbons
|
I
l
A
•
221
I
,
I
glassy
C
, .a J_AA a-C
A
A
sputtered a-C
,o ..c:, -
0 Fig. 16.
I
1
-
v ~ , , j
I
2
I
3
I
4"
I
5
-6
R,~
Radial distribution fimctions of glassy C (Mildner and Carpenter(84)) evaporated a-C (Green et al (90)), sputtered a-C (Li and l.annin (92)), MSIB a-C (Gaskell et al (41)), and PD a-C:H (Newport et al (I 10)).
222
J. Robertson
Fig. 17.
Core structure of a graphite layer dislocation with a Burger's vector (1120)a/3.
is absent in the RDF of sputtered and evaporated a-C and indicates the presence of intra-layer disorder. However, the peak only contains 2 atoms, compared to the 6 under most intra-layer peaks. It can therefore be washed out by relatively little disorder, such as the presence of a small fraction of adjacent 5- and 7-fold rings. This configuration can be constructed from an ideal layer as the core of an edge dislocation (94) of Burgers vector < 1120> a/3, as shown in Fig. 17. This ring-pair is the unit oftopolgicai disorder in a hexagonal layer. It can be used to introduce topological disorder progressively into the perfect layer (95,96). A conversion of under 10% of rings to 5- and 7-fold rings has been found to be sufficient to wash out the 2.84A peak and the other third neighbor peak at 4.25A. A similar situation exists in 4-fold coordinated a-Ge where odd-membered rings wash out the third neighbour peak of its R D F (97). Further modelling of the R D F would clearly be useful. It is interesting that the S(k) of the various forms of a-C show very similar peak positions, despite their diffferent coordinations, as emphasised by the data in Table 5. This emphasises the potential danger of using crude diffraction patterns to characterise the diamond-like character. 3.3 Structure of M S I B a-C
A highly sp ,1 bonded form of a-C can be prepared by mass selected ion beam deposition (MSIB).
Dismond-LikeCarbons
223
A magnetic filter removes neutral species and graphitic fragments given off by an evaporation or sputtering source which are believed to increase the amount of graphitic bonding in a growing film (33,39).: The verification of the highly sp ~ character of MSIB a-C has been crucial to the field of hard carbons, as it shows that a purely sp 3 bonded random network can exist, even when chemistry allows other coordinations to co-exist. The structure of MSIB a-C has been studied by EELS, electron diffraction and neutron diffraction (39-41,77,90,91). A macroscopic density of 2.85 gm.cm -3 was found by floatation (90), while the valence plasmon energy of 32 eV in low energy EELS indicates a microscopic density of 3.1, approaching that of diamond (39). Its high energy EELS spectrum in Fig. 14 shows only a small peak at 285 eV from n* states, consistent with about 85% sp a bonding (77). The S(k) of MSIB a-C measured by neutron diffraction (41) is shown in Fig. 15, and the R D F is shown in Fig. 16. The k,,~ was limited to 8A-' because of the small sample size. The first neighbour distance of 1.53A and a bond angle of 11 I* indicates a s p 3 content of 90_5%, consistent with other estimates. The absolute values of the peak areas are less reliable indicators of coordinations in this material, due to the large scattering by a small amount (-~9%) of unbonded hydrogen. This hydrogen appears to be present as H~ molecules at voids, rather than as C-H bonds, as the latter interpretation would give a poorer fit to the RDF. The first and second coordination numbers are related by n2 = n l ( n , -
!)
[73
for a network without 4-membered rings (as here). Their ratio in MSIB a-C suggests a lower sp '~ fraction of below 80%. However, this value depends on the assignment of atoms around 3.0A to second or third neighbor peaks, which needs further study. A comparison of the R D F with that of a-Ge, normalized to the same bond length (Fig. 18), shows that the first neighbor peak is wider that in a-Ge, which is consistent with the mixed coordination (40). On the other hand, the second neighbor peak is narrower than in a-Ge, due to the greater relative stiffness of bond bending forces in diamond than in Ge. Note that the
8 6
A
- - MSIB a-C
4 A
2
G(r)
"" a-Ge
0 -2 -4 0.5
Fig. 18. JPSSC 21:4-C
1
1.5 2 2.5 r (Reduced Units)
3
3.5
R D F of MSIB a-C and a-Ge normalised to the same bond length (40).
J. Robemon
224
R D F displays a flat region between the second and third peaks which is characteristic of all tetrahedrally bonded networks and is caused by the uniform distribution of dihedral angles and third neighbor distances. We can therefore concluded that an essentially fully sp3 bonded form of a-C, analogous to a-Si, does exist, despite the greater bond bending stiffness of C. Some workers have doubted this was possible. 3.4 Structural Modelling of a-C There are numerous ways of modelling the structure of a-C. Some analyses of a-C have consisted of blending functions of S(k) of graphite and diamond in order to estimate the fractions of sp 2 and sp 3 bonding (98,87). The:structure of amorphous solids is also often studied using random network models (99). These can be built by hand or on a computer by, for instance, making topological rearrangements of crystalline lattices. A continuous randon network (CRN) has no broken (dangling) bonds and its average bond lengths and bond angles are set to the chemical determined values. The networks can be further refined by relaxing their structure under a valence force field (VFF) in which the distortions of bond length (Ar) and bond angle (A0) give an elastic energy of AE ffi I
I k°rlA0 2 2 + -~I kj,rlA# 2 2 krAr 2 + "T
E83
The VFF of sp 3 sites consists of a bond stretching force kr and a bond bending force ko. The VFF of graphite and sp ~ sites must also include a four-body out-0f-plane force k, which opposes the puckering of the layers (100). The values of force constants are found by fitting data such as the IR and Raman modes, elastic constants, and the phonon dispersion curves found by neutron scattering. They are kr= 270Nm -~, ke--25Nm-' for sp3 sites and k , = 363Nm-' , k0--- 36Nm -I k~ = 134Nm-' for graphite. In simple systems like a-Si, the values of Kr and Ke give a small bond length distortion and a A0"~I0 ° . Beeman and others (101,102) have hand-built C R N models of a-C, containing varying fractions of sp2 and sp 3 sites. Their characteristics are summarised in Table 7, and their RDFs are shown in Fig. 19(a). The C1120 model consists of four warped layers of sp 2 sites. The C340 model contains 9.1% sp 3 sites, and the C356 model contains 51.4%sp 3 sites. The C519 model contains only sp 3 sites and is the Polk (99) model of a-Ge rescaled to the C sp3 bond length. The bond lengths are set to those appropriate for the hybridization. The density of the models increases with the sp ~ fraction. The sp" bonded models have a low density because of their large interlayer space. All models contain a sizeable fraction of odd-membered rings. The author believes that these models contain a much higher fraction • of odd-membered rings of sp3 sites than is probably realistic, in that they do not take into account the lower stability of odd-membered rings of sp ~ sites, as discussed in section 4.2. Beeman et al (101) compared the RDFs of the models to the P,DF of evaporated a-C of Kakinoki et al (88) and Boiko et al (89). He concluded that the C340 model with 9% sp 3 sites ftted the experimental structure most closely. The interference functions of all four Beeman models are shown in Fig. 19(b). All four models
225
Diamond-LikeCarbons Table 7.
Structural characteristics o f the Beeman random network models (104) %sp 3
rl, ,~
nt
r2, A
n2
density, gm.cm -3
6
2. I I
C I 120
0
1.42
3
2.44
C340
9.1
1.42
3.28
2.43
2.69
C356
51.4
1.51
3.53
2.5,5
3.21
C519
100
1.55
4
2.52
(a)
,~,
I
I
I'll
~
I
I
I
12 I
I
3.39
I~J
J
I
II
I
,
I
_ ,__ •.4,,,..;,OvoU;orate d (KQkinoki) ....... glassy (Mildner) C 1120 .._.,~--" ; |00% sp2... ~.,...__....~
4O 2O
o 40 C340 20 8
0 40
r~
c3
6
o
49°1o ~ / ' ~ " . . .
i:5 2 O
'e o
n'-
0
40
C519 0 % sP2
20
.. _.....-" -'""
/-,,,,,,..._~..~.._. ./.;)'~.. ~ _ ~ . . - - . ? e.e
i
0
I
I
I
[~
• ° °.%. o
I ~ / I , I t 2
I r"; 3
R (~)
oot °
i , , Ill, 4
I
5
J. R o b e m o n
'J "1
(b)
I
I
i A'l
I
I
I
I .... I
I
'1
C340
A
91% sp2
A
4o
o m
C356 4 9 % sp2
2 o ~
.0 0 t_
v, V
C519 0 % sp 2
0
Fig. 19.
2
4
6
8 k (~,-11
t0
t2
14
16
(a) Radial distribution functions and (b) structure factors of the random network models of Beeman et al (101).
produce a peak around 3A-' and a main pe~tk around 5.5A-' The C! 120 and to a lesser extent the C340 model possess a pre-peak around 1.8A-L Such a pre-peak is charcteristie of layered structures and is the analogous of the (002) peak of graphite. It is interesting that this survives the introduction of some sp 3 sites in the C340 model, in which the more obvious layering charcter is lost. A noticeable feature is the similarity of the peak positions of all four models, despite the change from 3-fold to 4-fold bonding. This emphasises that structural differences produce quite subtle changes in the S(k).
Diamond-Like Carbons r
,
.
~
|
~
1
~ .~,
t ....
~..
~l '~
-
1
,,fT
i v
A
~
.
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i
.
;
.
i
.
~
C~}
[! i~|
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/i
~-
;'
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2
i
:!
"
Exp {D} I
/t \ ,,'?
...
I
',,
~
i
iiii
F" 8 ~"
IL
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Cb)
-
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-
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/ Il
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"""
/" /!
2
0
,dr
8
~ll
,
--
-
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r.,..o.
!
-
..............
i
"",
m
co~
!
I
/ ~,
6 4
i
//','l/-
Beeman
C340
2
F,,,
0
,..I,,,
, I..........
I
2 r
Fig. 20.
, ,ll
li,,
0 ,,,
o
,
!,,
3
.....
t , ,
4
(A)
Comparison of the radial distribution function of sputtered a-C (Li and Lannin (92)) (solid line) with the simulations of Galli et al (103) and Tersoff (105) and the C340 random network model of Beeman (101) (dashed lines).
228
J. Robe~'umn
Li and I.annin (92) have compared the R D F of sputtered a-C with those of the simulations of Galli (103,104) and of Tersoff(105), and of the C340 Beeman model (Fig. 20). They found that both the Galli and Beeman models reproduced the significant bond length disorder found experimentally. They found that the models of Tersoff and Galli placed the second neighbor peak too distant, thereby overestimating the bond angle. The Beeman model was found to reproduce well the shape and position of the second peak, and in addition the relatively fiat region between the second and third peaks due to topological disorder. 3.5 EXAFS
Extended X-ray Absorption Fine Structure (EXAFS) are the small oscillations in absorption intensity occuring above the X-ray absorption edge. They are caused by an interference between the outgoing wave of the photoelectron and the back-reflections from the surrounding atoms, which causes variations in the absorption cross-section for the photon. The EXAFS intensity is given by 0t ----- ~,i0ti sin(kr i 4- r/) exp( -2o~k 2) exp(-2ri/2e(k))
[9]
Here k is the wavevector of the photoelectron, n is the distance from the excited atom and the i-th atom, al is the width of the n distribution, ,t, is the electron mean free path and ,/ is the phase shift. The effect of 2 is to damp out the effects of neighbors more distant than about 5 A. In disordered solids, the effects of second and higher order neighbors tend to be damped out by their larger static broadening ai. EXAFS is often the method of choice for determining local structure, because of its chemical selectivity and its sensitivity to bond lengths, ttowever, their are two problems with EXAFS in a-C(:H); the low atomic number causes problems in setting the phase shift and secondly EXAFS is unable to detect hydrogen. There have been numerous measurements of the EXAFS on a-C, by Batson and Craven (106), Denley et al (107), and Fink et al (78). Fink (78) compared the EXAFS of diamond, graphite, evaporated a-C and PD a-C:H (Fig. 21). The EXAFS of diamond and graphite extended to about 100 eV above the absorption edge. In contrast, the EXAFS of evaporated a-C are highly damped, decaying within 40 eV of the edge. This is due to the variation in bond length aj = 0.1 - 0.2A. Lannin (92) found a similar variation in bond length in sputtered a-C. This variation does not arise from hybrdization disorder, as both forms of a-C are over 95% sp 2 bonded. Oddly, Fink (78) found that the EXAFS of PD a-C:H were less damped that a-C, as a-C:}t has more coordination disorder. Comelli et al (108) observed a relatively undamped EXAFS for an a-C sample. This sample was created by Ar ion bombardment o f P I ) a-C:H. Its EXAFS were found to decay at a similar rate to those of graphite and to have about 2/3 of their intensity. They corresponded to a coordination number of about 2 and a bond length of 1.44A. It is difficult to accept such a low value of coordination for a-C, which conflicts with all other data on this system, but it is difficult to find the source of the problem. 3.6 Structure of a-C:H
The determination of the structure of a-C:H is more difficult than that of a-C because the hydrogen cannot be treated as a minor constituent, The minimum requirement of a structural determination is a value for the hydrogen content and the carbon coordination number. One
Diamond-Like Carbons
,
i'i
,
,'
I
I
'
i
229
J
,
I
I
J
i
graphite
a-C:H
"~- Jl./ \
~ - ~ ' ~
W
TQ:
r,,
a-C:H
2oc
-o_c
'~;o'
'"
'~'o'
' ' '~'oo'
'
Energy (eV) Fig. 21.
Extended X-ray absorption fine structure of graphite, annealled PD a-C:H, PD a-C:H, evaporated a-C and diamond, after Fink et al (78).
230
J. Robettson
should emphasise that there is no unique structure of a-C:H, it depends very strongly on deposition conditions. The hydrogen content can be determined by nuclear reaction analysis (NRA), elastic recoil detection (ERD), spin counting in proton NMR, thermal evolution and combustion analysis. Thermal evolution is the simplest method, and is most commonly used in a-Si:H. Care should be taken in a-C:H because some hydrogen can evolve as hydrocarbons, particularly from highly hydrogenated forms of a-C:H. The relative merits of the various techniques of determining sp3 fraction were summarised in Table 4. N M R (68-75) and XANES (78) are particularly valuable for a-C:H. Extensive NMR, IR and hydrogen evolution studies of PD a-C:H have been carried out as a function of preparation conditions and are summarised later. McKenzie et al (109) studied the structure of a-C:H by electron diffraction. The difficulty in applying electron or X-ray diffraction to a-C:H is that they do not detect hydrogen, so they give only the partial C-C coordination not the total C coordination. It is therefore unclear whether coordinations below 4 arise from C-H bonds or sp2 bonding. This is a non-trivial issue for H contents of 30-60%. Neutron diffraction detects hydrogen strongly. The S(k) of a-C:ll deposited from acetylene has been measured by Newport et al (i 10) to k,,,~ = 50A -~ . The sample had a hydrogen content of 32% and a density of 1.51 gm.cm -3. The low k region of S(k) is shown in Fig. 15 and the associated R D F is shown in Fig. 16. The total R D F of a-C:H is the sum of the three partial RDFs, weighted by the relevant elemental scattering lengths. The total R D F is dominanted by the C-C and C-H terms in a-C:tl, with the C-It peaks being negative going because of the negative scattering length o f H I. The first peak of the R D F at 0.8 A is due to H-H bonds. This is due to either Its molecules at voids or H-H clustering of CH, groups. 1t2 molecules have been detected by neutron scattering from their rotational spectrum. The second (negative) peak at 1.05A is due to C-H bonds. The third peak is found to be a split peak at 1.39 and 1.52A, which can be ascribed to sp 2 and sp 3 sites respectively. A s p 3 fraction of 80% was estimated from the relative sizes of these components, equivalent to a mean C coordination of 3.8. The area under this peak-pair is 2.5 atoms, equivalent to a total C coordination of 3.0 atoms for 3 2 0 H content, but much smaller than that deduced from the sp3 fraction. 3.7 Real Space Studies.
Hard carbons can Show various degrees of longer range order. There appears to be two forms of this, inhomogeneities and sp ~ site clustering. It was noted in section 1 that ion beam deposition could produce hard carbon which was a mixture of amorphous C and microcrystalline diamond inclusions. The inclusions typically have a 100A grain size and can be detected by real space imaging processes such as transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM)and scanning tunneling microscopy (STM). On the other hand, many deposition methods such as sputtering and plasma depostion produce films which are fully amorphous and show no crystailinity at the 10-100A scale, as evidenced by TEM (90,91,111,112). There is a degree of medium range order in these films which shows up as the zero k peak in S(k), which can arise from residual layering or Sl~ clustering described shortly. In particular, Li and Lannin (92) noted that evaporated C may contain graphitic fragments originating from the evaporation source.
Diamond-Like C~bons
,
,
•¢
,,
¢
,
';
,;
4
'¢', t
231
4. ~i
t<,
#
, ~,,11
(aJ ,i,l
(b:
(cJ
f/.zm Fig. 22.
Scanning tunnelling microscope images of (a) evaporated C, (b) ion beam deposited C and (c) laser plasma deposited C, after Collins (35).
232
Fig. 23.
J. Robertson
Transmission electron micrograph of laser plasma C sample of Collins et al (35), after J. C. Pivin (CSNSM, Orsay) with thanks.
Collins et al (35) have compared carbon produced by evaporation, ion beams (IB) and laser plasma (LP) deposition by TEM and STM. STM images such as those in Fig. 22 were interpreted as showing that evaporated carbon consisted of a s p 2 matrix, as expected, IB carbon consisted of a series of diamond-like grains lying as ribbons in a s p 2 bonded matrix, and LP carbon consisted on a dense three-dimensional mesh of diamond-like grains. The diamond-like grains are further seen in the TEM picutre of LP carbon shown in Fig. 23. This material in clearly not amorphous. Medium range ordering is expected in PD a-C:H, but on a much smaller 4-10A scale. Electronic structure calculations in section 4.2 suggest that the sp 2 and sp a sites in this material tend to segregate into sp~-bonded graphitic clusters embedded in a sp a bonded matrix. The clusters are typically 4-10A wide and theory suggests that they should be compact rather than elongated. Raman spectra descibed in section 3.8 provide strong indirect evidence for their existance. It is possible that graphitic clusters have been directly observed in sputtered a-C by STM by Marchon et al (I 13), Fig. 24. This image o f a 28x12A area shows some 6-fold and 5-fold rings of atoms; the 6-fold rings may correspond to graphitic bonding. Nevertheless, care is needed
Diamond-Like Carbons
233
(a)
(b)
Fig. 24.
(c)
Scanning tunnelling microscope image of (a) 28x12A area of sputtered a-C, with close-ups of (b) left- and (c) right-hand parts of the image below, showing possible 6- and 5-fold rings of atoms, after Marchon et ai (113).
in using STM in graphitic systems because the weak interlayer bonding may not support a layer against the STM probe tip. Fig. 25 shows topographical images of a flake of MSIB a-C taken by energy filtered scanning transmission electron microscopy (STEM) by Juan et al (112). Each image is taken for electrons which have lost the indicated energy passing through the specimen. The images therefore represent real space electron energy loss (EELS) images of the local bonding. The losses in this case occur by the excitation of valence plasmons (see section 4.7), The 7r electrons of sp 2 sites produce losses at 5-7 eV and their cr+~t electrons produce losses at 20-24 eV, The electrons of sp 3 sites produce losses at 30-33 eV. While a specimen of a-C can have a
234
J. Robertsou
> ¢,q t~
N
e~
0
p..
i 0
O~
t'q
O0
t,q p,.
t~ r~
i~i!~i~i~i!~~ii~il!!~!~ ~i~i~~~ ~' i~~~ ,~!~~
t,.., 0
.E r~ t_.
> t'q 04
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2,35
Diamond-Like Carbons
diamond
graphite
5 e
~
01
glassy
._=
g E a-C:H,
¢r
25C
t_
0
sput, 25 C
ol L_
o
~
LL
evap, 25 C , S----
0
I
500
I
,
i
1000
1500
,
%.
2000
Wavenumber (cm-1) Fig. 26.
First order Raman spectra of diamond, highly oriented pyrolytic graphite (hopg), microcrystalline graphite, glassy C, PD a-C:H, sputtered a-C and evaporated a-C, after Shroder et al (! 14), Nemanich and Solin (116) and Wagner et al (130).
236
J. Robertson
macroscopic loss from 20 to 33 eV, depending on its sp 3 content, one might expect that the loss locally would be either that of sp 2 or sp 3 bonding. This behaviour is indeed seen in the figure, bright regions at 6 eV are bright at 22 eV but dark at 32 eV. However, there are strong losses at 28 eV, perhaps indicating the presence of mixed bonding. This technique has great potential in hard carbons, with perhaps the highest ultimate resolution of 5 A. Losses due to C is excitations at 285-290 eV can also be used to distinquish between sp ~ and sp 3 sites. 3.8 Infrared and Raman S p e c t r a
The infrared (IR) and Raman activity of crystals is restricted by symmetry and k conservation to a series of sharp lines. In diamond, there is one Raman active mode at 1332cm -~ and no IR active modes (114). In graphite (100), four atoms per unit cell, there are two IR active modes, the main E~u longitudinal optic mode at 1585cm-' and the out-of-plane A2u mode at 868cm -t. There are two Raman active modes both of E2s symmetry, the main 'G' mode at 1580cm -~ and the rigid layer mode at 50 cm -t. A 'D ~mode around 1350 cm -j is also found in microcrystalline and disordered graphites but not in highly crystalline graphite (I 15,116), as seen in Fig. 26.
t/.I Fig. 27.
1
Mechanism of infra-red activity in a random covalent network (I 17).
~s
Diamond-Like Carbons
237
The k conservation rule no longer holds in amorphous solids because of the loss of periodicity, and all vibrational modes can have IR or Raman activity. The most common IR activity arises from the vibration of ions in ionic crystals like NaCI. IR activity can also occur in a network of purely covalent bonds if there is no center of inversion symmetry. The simplest example of this is trigonal Se. The most simple, localized mechanism of IR activity in a covalent network is the creation of an induced dipole by charge flow from extended bonds to contracted bonds, as proposed by Albert et al (117), Fig. 27. The resulting IR spectrum resembles the phonon DOS, but with greater contributions from the higher lying modes of LO character. The phonon spectra of a covalent network can be calculated using the valence force field {8}. Fig. 28 shows the resulting phonon DOS for diamond, graphite and the four Beeman models (I01). These phonon DOS do not show sharp van Hove singularities because the equation of motion method used there causes a smoothing. The graphite spectrum shows a large peak at o9 = 1 3 5 0 - 1 5 5 0 c m -~ due to bond stretching modes, two lower peaks around 300 and 600 cm -~ due to modes of bond bending character, and a large peak around oJ = 0 due to rigid layer translational modes (118-123). The diamond spectrum shows a large peak at 1100-1300 cm -~ due to bond stretching modes and again two lower peaks at 600 and 900 cm -t (118). In general, the random networks show a gradual evolution of features and peak shifting with changing sp 3 content. In particular, the band maximum falls with increasing sp3 content, from about 1600 cm -~ in graphite and the Cl120 model to about 1350 cm -~ in diamond and the C519 model. Fig. 28 compares these DOS with the IR absorption of evaporated a-C found by Knoll and Geiger (124). Raman spectroscopy is a popular tool for characterising both the crystalline quality of diamond films and the nature of a-C(:H) films (114,125,126,9). Fig. 26 compares the Raman spectra of a diamond thin film, highly crystalline graphite (HOPG), microcrystalline graphite and some amorphous carbons (114,116,9). The Raman spectrum of a good diamond film consists of a single sharp line at 1332 cm --j with no background. Highly crystalline graphite has a single Raman peak at 1580 cm -~ known as the G peak. This is a zone center mode of E2s symmetry, whose eigenvector is shown in Fig. 29. An additional feature occurs in microcrystaUine and disordered graphites known as the D peak and centered on 1350 cm-L This mode is inactive for an infinite layer and is activated by the absence of k conservation. It is a common feature of disordered carbons. Tuinstra and Koenig (115) associated the D peak with the A~, mode at the K point of the Brillouin zone, whose eigenvector is also shown in Fig. 29. The intensity of the D mode relative to the G mode is found to vary with the crystallite size as (I 15) I(D)/I(G) = k/I.~
{10-I
While the Raman activity of the D mode can be found to cancel about each atom for an infinite layer, there is no cancellation at the perimeter sites of a crystallite, leading to the proportionality given in [10]. More generally, Nemanich and Solin (116) attributed the D mode to the large DOS around the K point, which arise from the nearby fiat bands, as seen in the calculated phonon dispersion curves of Lespade et al (123) in Fig. 30. The Raman spectra ofa-C and a-C:lI should in principle give considerable information on their local bonding. The loss of k conservation allows each mode to become Raman active to some degree. The Raman spectrum of a highly disordered solid will resemble the phonon DOS but weighted by a matrix element which tends to vary as o92 at low phonon frequency, o9. The Raman spectra of the various amorphous carbons have similarities to microcrystaUine graphite
J. Robertson
238
I
>,, e
I
l
~
I
l
l
l
I
i
;
]
~
J
i
j
Infra-red oborption
m
C c-
Roman
scottering
rheor.y
~)
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Cl120
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'4--
C 340
0 >, .4..# II) c-
f
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C 356
C 519
0
500 Wove
Fig. 28.
I
1000 number
I
1500
w
I
t
~1
2000
(cm -1)
Calculated phonon DOS of diamond, graphite and Beeman random networks for a nearst neighbor valence force field (104), compared to experimental IR absorption spectrum of evaporated a-C of Knoll and Geiger (124) and the Raman spectrum of sputtered a-C.
(Fig. 26). This is because the Raman cross-section of graphite is 30-60 times that of diamond, so the siC bonded regions tend to dominate the spectrum (127,128).
Diamond-Like Carbons
239
AIg disorder mode
E2g Roman mode at r
Fig. 29.
Eigenvectors o f t h e E2t zone center G mode and the A~ disorder (D) Raman mode.
I-
I
t
M
K Wavevector
160C
J200
400
0
Fig. 30.
r'
r DOS
Phonon dispersion curves and DOS for single layer of graphite, after l.espade et al (123).
We now consider the experimental situation in more detail (128-138). Fig. 31(a) shows the Raman spectrum of plasma-deposited hard a-C:lI, as a function of excitation frequency, v (129). Fig. 31(b) shows the spectrum of a-C:H annealed at 600°C, which is now essentially sp ~ a-C. JP$SC 21:4-D
J, Robomon
240
o-C "H as deposited
o-C:H
G
hVL= J2.188V
>.
2.sTe
~
IJJ I-Z_
i I,
vii
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z
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I00--012~00-1400 1600 1800 RAMAN SHIFT(cm "11 Fig. 31
I
1000 1200 1400 1600 1800 RAHAN SHtFT(cm "1)
Raman spectra of(a) PD a-C:H and (b) a-C:H annealed at 600°C, vs. excitation frequency, after Wagner et al (I 30). t~
m
m
!m
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m
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---t4O0
.
tim
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(c=-I)
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"
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190 tOO 0 li~0
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Fig. 31
It00
t000
141100
13~0
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1000
Ram,m sh/ft (¢ma)
(c) Raman Spectra of sputtered a-C for different RF sputtering powers, after Cho et al (27).
Dimnond-Like Carbons
1600
(a)
241
Graphite
-2"
1580 A
G" 1560
I
A'
•g
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E
•
U
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o
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459 nm 515 nm 628nm
"A
1500
I
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I
,
I
I
I
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0
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•
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s
4.0
m
o6L
2.0 A
e~
~
500
1000
S
@
o
0.0
0
1500
2000
Bias Voltage (V)
Fig. 32.
Variation of (a) the ratio of D and G mode intensities I(D)/I(G) and (b) the G mode frequency with excitation frequency and bias voltage for PD a-C:H, after Tamor et al (130).
The spectrum of as-deposited a-C:fl at hv = 2.18 eV is seen to consist of a broad peak centered on 1520 cm -m and a shoulder around 1300cm -~, perhaps related to the G and D modes of
242
J. Robertson
graphite. On annealing, the upper peak sharpens into a well defined G peak, and the D peak develops around 1350 cm -I. This behaviour is consistent with a transformation of a-C:H into graphitic a-C by annealling. Fig 32(c) shows the Raman spectrum of sputtered a-C as a function of sputtering power. Each spectrum has been decolvolved into two peaks, a D and a G peak. Note that the D peak has a much greater area than the G peak in some samples. Note also that the D peak is much wider than the D peak in microcrystalline graphite (Fig. 26), so that this spectra is not simply attributable to microcrystalline graphite inclusions. The intensity of the D peak in a-C and a-C:H varies with deposition conditions. It is tempting to assume that the D and G peaks arise from graphitic clusters and so deduce a value of Lo from [10]. Tamor et al (134) studied the variation of I(D)/I(G) for PD a-C:H as a function of bias voltage Vb, as seen in Fig. 32(a). They found that I(D)/I(G) increases with Vb, which would imply that Lo decreased with increasing bias. ttowever, the optical gap also depends on the size of graphitic clusters, varying as Eg = k/L~
as shown in section 4.3. As the gap decreases strongly with increasing bias, we would expect L, to increase with bias, the opposite way. Tamor (134) therefore suggested that eqn [10] fails at low values of I.~ and that I(D)/I(G) varies instead, as shown in Fig. 33, reaching a maximum around L, = 12A. This seems reasonable; I(D) cannot increase without bound at low Lo, as it is bounded above by the DOS in the region of the K point. I(D) is then likely to decrease again in very disordered cases with L, < 12A, as the DOS around K becomes broadened and spreads into modes with lower matrix element.
4
3
1
0
I
0
I
I
I
10
20 L
Fig. 33.
(A)
Proposed variation of I(D)/I(G) vs Sl~ crystallite size I~
30
Diamond-Like Carbons
243
I
glassy C 1600
'mme~e~e
~
graphite (hopg)
a-C:H ~
"\
sputtered a-C
1500
).oo iiim
J:
"\ "\
¢
E
~
"\
sputtered a-C
"\ '\
'\ 1300
"\
"\
glassy C
"\
"\
"\ "\ \
\ \ \
1200 200
Fig. 34.
I 300
J J 400 500 Wavelength, nm
a-C:H
600
tO0
Raman peak shift vs. excitation wavelength, for graphite, glassy C, sputtered a-C (136) and PD a-C:H (130).
The spectra show pronounced changes as a function of excitation frequency. Inspection of Fig. 31 also shows that the G peak shifts upwards with v in the as-deposited film while the D peak moves upwards in the annealed film but the G peak does not (129,130). These movements are
J. Robextmn
244
a common feature of graphitic carbons. Fig. 34 shows the movements of the G and D modes of HOPG, glassy C, sputtered C and a-C:H plotted as a function of excitation wavelength (130,137). The G mode in HOPG does not shift. The G mode in glassy C also does not shift, nor does it in the annealed a-C iti Fig: 31(b). The G mode moves only in the very disordered carbons, a-C and a-C:H, and the movement saturates once a) reaches 1600 cm -t. On the other hand the D mode moves in all forms of carbon. A further factor is that the rate of G peak shift varies with bias voltage for PD a-C:H, as evident in the data of Tamor et al (134), as seen in Fig. 32(b). The parameter controlling the shift rate could be either L, or the sp 3 content. Two types of behaviour are evident in Fig. 34, one in which the G peak remains fixed and one in which it shifts. The distinction between the two behaviours correlates best with whether L, is greater or less than 12A, the critical size in Fig. 33. The G peak shifts only for the more disordered carbons with L, < 12A. The alternative explanation is that the shift arises from a finite sp3 content (132). However, the sp3 in unhydrogenatedsputtered a-C is quite low, about 5%, yet its rate of shift is nearly as great as that o f P D a-C:H. In addition to peak movements, the I(D)/I(G) ratio also varies with excitation frequency v. The spectra in Fig. 31 show that I(D)/I(G) increases at low v. Yoshikawa et al (136) found that the i
I
i
4
o-C:H 3
"
,
o
1600 cm "1
A
1520
o
t
/
cm "1
~ , ,
a 1300 cm"1
~ . .
," " "
== o
1
A
" ~....,O/O'-
o
o .<,:~_._ ...a._ ._a. _,
.....
I
,
1.9
~
,
,
I
,
2.3 PHOTON
Fig. 35.
....
.--'o""""
"
~-
,
I
I
~
2.7 ENERGY
,
I
3.1
I
i
~
I
,
3.5
{eV)
Relative Raman intensities of the D and G modes, after Ramsteiner et al (129).
Diamond-LikeCarbons
245
variation is similar for a-C and glassy C and approximately linear with excitation wavelength. Wagner et al (129-131) studied these changes further by obtaining the absolute variations in Raman intensity of the G and D features in a-C:H as a function of v. Sitting at fixed phonon frequencies, rather than moving with the peaks, they nevertheless found that the intensity ofthe G peak increased strongly with v while the D peak stayed relatively constant (Fig. 35). Wagner et al (129-131,9) noted that the intensity changes of the G and D peaks arose from the Resonant Raman effect. The Raman cross-section L2 arises from the changes in bond polarizability X = ~ - 1 with atomic displacement. ~ results from electronic transitions across the optical gap, so that f~ will vary as ~X 2 n - k(=~=v )
[11]
If the excitation frequency v is below the gap in the transparent region, fl is independent of v. Moving v towards a band edge causes a resonant increase in f 2 , giving the resonant Raman effect. A relatively simple example of this effect is the resonant behaviour of the 1332 cm -~ mode in diamond, found by Wagner et al (131), Wagner et al (129-13 !,9) also interpreted the shifts of the G and D peaks in terms of resonant effects. A more complex two-phase model is now necessary, as the different lmhaviour of the G and D peak intensity in Fig. 28 cannot be expained within a single phase. Phase 1 was assumed to give peaks at 1300 and 1500 cm -t and was attributed to the sp 3 network. Phase 2 was assumed to give a peak at 1600 cm -~ and was attributed to spa clusters. The peak shifts then result from the different dependence of the f2 of each phase on v. This explanation may be partly wrong. The shifting of the G and D peaks is a common feature of disorderd spa carbons, as seen in Fig. 31. In view of the greater Raman cross-section of bonds it seems more likely that essentially all the features of the Raman spectra of a-C:H arise from its spa sites. In the author's opinion, there no satisfactory theory of the Raman effect in amorphous carbons at present. Raman scattering can be modelled as the change in bond polarizability due to atomic displacement. The bond polarizabilities of graphite and diamond are often treated as equal. This would give the same L2 for graphite anddiamond and is wrong. Clearly, an extra contribution to f~ must be included from the ~r bonds, which would be larger due to their smaller gap. Alben (117) noted that there are three basic mechanisms to give changes in bond polarizability in a random network. Mechanism (I) associated with bond stretching is of most interest here as this affects the high frequency part of the spectrum. This gives a Raman tensor of the form
1 where I is the atom index, A is a bond at 1, r is the borid vector and C is the bond compression. Beeman et al (101) used this expression to calculate the Raman spectra of their random network models. However, this form does not allow for the higher bond polarizability of graphite. AI-
246
J. Robertson
though n bonding can be long range, its polarizability is likely to be short range. should be possible to modify 1!2] in the form 0C'
- 1 = Y~a{rAr& - .-~ T}Ca{];I;
c2 2 I,iCl,J
Hence, it
Cn3]
(E, - (E i - Ej)) 2 }
where the sum is over the i electronic valence states and j conduction states of energy E, and E), whose eigenvector component on site 1 is c,.i, etc. This expression would give a resonant Raman effect which varies with the local band gap at each bond. i
q)
CH
/%
a)
STRETCH
|
oc BEND (ROCK OR WAG) i
CH 2
b)
CH 3
SYMMETRIC ASYMMETRIC STRETCH
ROCK
WAG
SYMMETRIC DEGENERATE STRETCH
SCISSORS BEND
TWIST
SYMMETRIC DEGENERATE DEFORMATION
x
c) Fig. 36.
ROCK, WAG
TWIST
Description and symmetries of the C-H I R vibration modes of CH. groups (146).
Diamond-Like Carbons
247
The Raman spectrum has also been used to deduce the sp a fraction. Richter et al (132) noted that the upper limit o f the p h o n o n DOS is lower in diamond than in graphite, and that it moves to lower frequency in the Beeman (101) random networks as the sp ~ content increase (Fig. 26). A fair approximation would therefore be to take the sp "~fraction as proportional to the redshift of the G peak. There are a number o f problems with this approach. The band limit o f a homogeneous random network undoubtedly does shift downwards with sp 3 content. However, if the network is inhomogeneous for Raman as the Wagner 2-phase model implies, and if the Raman cross-section o f sp 2 sites is 30-60 times larger, the Raman scattering o f sp ~ clusters will always dominate the aggregate spectrum. Also, as the G peak appears to shift by similar a m o u n t in sputtered a-C with 5% sp .~ sites or in PD a-C :H with 30-50 sp 3 sites, the sp 3 content is not so obviously the major factor. The author thus concludes that the first necessity is to provide an adequate theoretical model of the peak shifts in sp ~ bonded C, as a function of disorder. 3.9 C-H Vibrational Modes
The C-H vibrational modes produce a series o f infrared (IR) absorption peaks which can provide very detailed information on the local C-H bonding (140-145). It is possible to assign each peak to a different carbon configuration - sp 3, olefinic sp 2, aromatic sp 2 or sp t - and the number o f hydrogen neighbors. The local symmetries and names of the vibrational modes of CH, CH2 and CH3 groups are given in Fig. 36 (these do not depend on the C hybridization). The naming o f the modes is taken from work on a-Si:H (64,146). One may approximate that only the H moves in these modes, due to the large difference in C and tl masses. Each configuration gives rise to one C-H stretching mode per H atom, at around 3000 cm -~, plus two further deformation modes per atom below 1500 cm -~. All modes are IR active, except the A2 twisting modes (146). Dischler (140) assigned each absorption peak, as listed in Table 8, on the basis o f existing assignments in hydrocarbon molecules and from their shifts under deuterium substitution. The assignments for the C-II stretching modes are generally agreed, but the recent neutron scattering data o f t t o n e y b o n e et al suggest different assignments o f some off the deformation modes. Firstly, noting the ordering and spacings of the Si-H modes o f SiH~ groups in a-Si:H (146), scissors at 880 c m -1, wag at 850cm -1, twist at 820cm -I and rock at 630cm -I, we reassign the modes of sp 3 CH2 groups as scissors at 1470cm -t, wagging at 1330cm -t, twist at 1300cm -~ and r o c k i n g at 1030cm-L Secondly, the twisting As mode is IR inactive (146), and cannot be the H I 8 mode at 1180 cm -~. Thirdly, as the Sill bending mode has a similar frequency to the B~ rocking mode of Sill2 (630cm-~), we assign the H I 8 peak at 1180cm -~ instead to sp 3 CH bending. These changes are summarised in the last column of Table 8. The new assignments agree broadly with those of H o n e y b o n e et al (145), but agree less well with those o f T i b b i t t et al 044). They still leave peak HI5 unassigned. Dischler (140) and many others (60,61) have used the peak intensities o f the C-H stretching bands to deduce both the sp 3/sp ~ ratio and the H content of a-C:H films, as a function of bias voltage, source gas, gas pressure and thermal annealling. The IR method has been very popular because o f its wide availability and ease of use. However, it clearly needs a uniform distribution of l-! over the sp 3 and sp ~ sites to give reliable concentrations o f these sites. N M R suggests that this is untrue as tl bonds preferentially to sp 3 sites. The method therefore tends to neglect sp 2 sites, particularly those within clusters.
248
J. Robertson
Table 8.
line 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
C-H infra-red vibrational mode assignments in a-C :H. Modes 1-10 are C-H stretch, lines 11-27 are C-H deformation. s = stretch, ss = symmetric stretch, as--antisymmetric stretch, sd-- symmetric deformation, dd-- degenerate deformation. wavenumber, cm -t hard a-C:tt soft a-C:tt 3300 3300 3045 3060 3025 3000 3000 2970 2945 2920 2920 2920 2875 2850 2850
1440 1435 1370 1290 1170
1030 910 840 755
700
1490 1450 1450 1445 1325 1280 1180 1110 1075 1030 910 840 755 700 700 700
Dischler assignment configuration symmetry spl CH A s arom sp2 Ctt A s olef sp2Ctt2 B~ as olef sp2 CH A s sp3 CIt3 E ds olef sp2 CH2 A~ ss sp3 Ctt2 B~ as sp3 CH At s sp3 CtI3 At ss sp3 CI-I2 At ss sp3 CH3 sp2 CH2 sp3 CIt2 arom sp2 CH sp3 CH sp3 Ct-I3 olef sp2 CH sp3 CH2 olef sp2CH2 sp3 CIt3 sp3 Ctt2 olef sp2 Ctt~ olef sp2 CH arom sp2 CH spl CH olef sp2Cl-12 sp2 Ctt2 olef
E dd As scissors At scissors A bend E bend At sd A bend A, twist B2wag E dd B2 wag A2 twist B bend B bend E bend B, rock B~ rock
New assignment config
unassigned sp3 CH2 B~ wag sp3 CH
E bend
sp3 C1t2 B, rock
C-C Infra, Red vibrational mode assignments for a-C:H, after Dischler (141). line 1 2 3 4 5 6 7 8 9 10
wavenumber, cm-' 2180 1620-1600 1580 1515 1300-1270 1245 1160 970 885-855 840
assignment olef arom mixed mixed mixed olef arom
spl sp2 sp2 sp2/sp3 sp2/sp3 sp2/sp3 sp3 sp2 sp3 sp2
Tamer et al (147,148) in particular noted these problems. They found that a-C:H deposited from benzene at low bias voltage had an increasing fraction of 'pendant benzene' groups, sidechain phenyl groups which were undissociated by the plasma and which do not contribute to the band gap or rigidity of the main network, but serve only to change its density. It could even
Diamond-Like Carbons
249
be suggested that the hydrogens of the pendant phenyls would dominate the IR spectra, and overshadow any Sl~-H sites in the main network. In this way the IR method might be of little use for finding the sp ~ content of the extended network. 4 ELECTRONIC STRUCTURE 4.1 Coordination This section considers the bonding configurations likely to be found in amorphous carbons and their electronic structures. Let us first consider the coordination number. Typical group IV elements like Si and Ge are most stable in the 4-fold coordinated diamond structure than in the 3-fold coordinated graphite structure or the more highly coordinated metallic structures like simple cubic or//-Sn. Si and Ge transform to the higher coordination structures under pressure or on melting. Carbon is different (149-151). It is most stable in the 3-fold coordinated graphite structure. This difference in stability of graphite and diamond is actually very small at NTP, 0.03 eV. C~0 is estimated to be a further 0.4 eV less stable (167). Higher coordination structures are not favoured for carbon at high pressures because they have atomic volumes which are no smaller than that of diamond. Additionally, experiments and simulations suggest that liquid carbon has a lower coordination than the solid, nearer 2. Carbon is atypical because it is a first row element. It has no p core electrons. Its 2p electrons feel the full core potential, while its 2s electrons feel a pseudopotential in which the short range part is screened out. This causes carbon's 2p orbitals to be relatively more tightly bound than
15 t0
T >
A
(D e-
uJ
t5
5 0
£voc
£F
-5
-10 -15 -2C
-25 K Fig. 37.
A
F
~
LL
A
F
A
X
T.
F
Tight binding band structure of (a) single layer of graphite and (b) diamond (7).
250
J. Robertson
its 2s orbitals, compared to the 3s and 3p orbitals in Si. This effect stabilizes carbon's sp2 bonds compared to its sp' bonds. It also reduces the stability of higher coordinations, dependent on p-like bonding. 4.2 Huckel Calculations The key to understanding the electronic structure of all amorphous carbons is to realise that this is controlled by the rt states of the sp~ sites (7,152,153) as these lie closest to the Fermi level EF. This is seen in Figs. 37 and 38, which show the density of states (DOS) and band structures of diamond and a single layer of graphite. The sp3 hybridisation of diamond leads to a wide band gap between the valence band of occupied bonding (o) states and a conduction band of empty antibonding (o*) states. In graphite the o and o* states lie at similar positions to this and the n states form a band which lies across the or-o* gap, with a minimum in the DOS at EF.
A standard approximation is to decouple the o and n states and to treat them separately. This is possible because the orbitals lie perpendicular to each other for planar Sl~ sites (Fig. 1) and because their states tend to lie in different energy ranges (Fig. 4), which minimizes their coupling. The o and n states behave very differently. The o states are the 2-center bonds which form the back-bone of the network. Their bonding is very localized and their bonding energy can be expressed as the sum of the energies of each bond, as for instance in bond orbital approximation of Harrison. Their energetics can also be expressed as a short range valence force field (cf [8]). This causes the a electrons to control the Short-Range Order ( S R O ) o f the network, iv its bond lengths and bond angles, but it leaves the longer range order undefined. The n states are more complex in that they can form both localized 2-center bonds as in ethylene and multicenter or resonant bonds as in benzene or graphite. Their bonding energy is longer range and non-local. It cannot in general be subdivided into the contributions from individual bonds. In this way n electrons may introduce Medium Range Order (MRO) into the structure. A key feature of the n states is that they form a half-filled band. Creating a gap in their spectrum at Er will lower the energy of the occupied states and stabilize the resulting structure. These effects can be analyzed using the Huckel model. This is a simplified tight-binding Hamiltonian which retains only the n orbitals and their nearest neighbor interaction, B = V(pTt). The absence of n states on sp3 sites blocks the n interaction passing through that site. The Huckel model therefore maps the original network of C and H sites into a series of separate n-bonded clusters. Finding the stable structure is reduced to maximizing the total n binding energy per site Etot of each cluster. The possible configurations of these clusters are of course similar to those of the analogous organic molecules (154). We have investigated the binding energy and band gap of a wide range of possible structures. Some of their normalized n binding energies Etot/fl are given in Table 9 and their electronic spectra are given in Fig. 39. This leads to the following observations; (a) Clusters tend to planar. This aligns the 7t orbitals on adjacent sites parallel and maximizes their interaction. (b) There should be an even number of sites in each cluster. Otherwise a half-filled state exists near E = 0 with low binding energy which reduces Etot. as N --) co.
Diamond-LikeCarbons
graphite
251
~
I/} (1} 4.a
0
.l.a {/}
o .ca (/} e-
o l
(D
(:3
-25 -20 -15 -10 -5 0 Energy (eV) Fig. 38.
5
t0
5
Tight-binding density or states of graphite, diamond, and the Beeman random network models of a-C (152). Their sp 3 fractions are given.
252
J. Robertmn
Table 9. Total n binding energies per site of various C configurations.
('~")n
G
# I
•
group
gtot/~
ethylene
1
polyacetylene
1.273
~ benzene
1.333
~napthalene
1.368
azulene
1.336
quinoid
1.240
polyacene
1.403
graphite
1.616
(c) The simplest configuration is the ethylenic double bond C = C which has E~o,/fl = 1. E,oJP of a row of double bonds as in alternant polyacetylene is also 1 in this model, so such olefinic chains are not particularly favoured. (d) E,o, is dramatically increased by combining three C = C bonds into a planar 6-fold (benzene) 1 ring by -~fl per site. Such rings are called aromatic. (e) Etot is further increased by fusing benzene rings into aromatic layers. In this way aromatic clusters are built up. Thus graphitic clusters are favoured over acenic clusters. (f) Compact clusters are favoured over row (acenic) clusters because of their fewer edge sites. (g) Quinoid groups are not favoured. They have a low band gap and a low E~. They would tend to dissociate into separate aromatic and olefinic groups if allowed. (h) 5,7 and 8-fold rings are unfavoured as these give states at or close to E--0. 4-fold rings are unfavoured because they have too much bond angle distortion. The behaviour of oddmembered ring combinations is more complex (! 55,156).
Diamond-Like Carbons
253
(i) A quadrupole of two 5-fold and two 7-fold rings can be created in a perfect graphite layer by rotating two sites by 90 ° and rejoining the bonds (Fig 39 e). This configuration gives quite a high density of states near E = 0 and so is unfavoured. However, an adjacent pair of 5-fold and 7-fold rings as in azulene has states well away from E = 0. Its F~otis only slightly lower than that of naphthalene (Table 9) and it can be considered to be an excited state of the basic structure. The configuration was also found in simulation of Galli et al (106).
ethylene N-fold rings N=5
II
II
I
N=6
.=7 I II . =8 III
II
I II
II
II
fused rings
~ c~
I II III II Ii II
:5
2
I
~111 II I IIIII I! I
0
-1
-2
-3
Energy (/~) Fig. 39.
Electron states and spectra of carbon bonding configurations (152).
254
J. Robertson
A value of /~ = 1.35 eV
[14]
has been found by fitting the bond energies of C = C, benzene and graphite, Such comparisons also show that the Huckel model overestimates aromatic stabilisation - E,ot/B~ 1.19 for benzene rather than the theoretical value of 1.33 given in Table 9, and 1.37 for graphite rather than 1.616. Summarising, rt bonding strongly favours aromatic rings over olefinic chains and also favours the the clustering of separate rings into graphitic sheets. Hence we expect aromatic ring clusters to be the dominant species of sp 2 sites. The o binding energy is independent of the degree of clustering, llence, for a given fraction of sp 2 and sp3 sites, rt bonding favours the formation of the sp2 sites forming sizeable graphitic clusters rather than being spread homogeneously through the sample.
Table 10. 2-phase model of amorphous carbons.
sp2 phase
sp s phase
evap. a-C
sheets
sheet rims
a-C:H
small clusters
sp3 or polymeric matrix
control
electronic properties
mechanical properties
We are therefore led to a 2-phase model of amorphous carbons, Table 10. The first phase is the n bonded clusters. These determine the optical properties. This phase is embedded in a second phase. This second phase can exist as a rim of sp3 sites around the clusters when sp 3 sites are few, as in sputtered a-C. In a-C:H the second phase is the major sp3-bonded phase, which can be either a highly cross-linked as in hard a-C:H, or a more polymeric hydrogenated phase as in softer a-C:H. This phase largely determines the mechanical propeties as shown later. 4.3 Band Gap
The band gap (LUMO-HOMO gap, lowest unoccupied molecular orbital to highest occupied molecular orbital) in all amorphous carbons is controlled by the n states because these states lie closest to E~ as shown in Fig. 4. The familiar amorphous semiconductors like a-Si are o bonded. Their band gap is given by the o-o* gap and this depends mainly on short range order (SRO), such as the coordination number, the bond length and the bond angles. These are conserved in the amorphous phase, so the band gap tends to be unchanged. The band gap of n-bonded systems is very different. It depends mainly on the medium range order (MRO), the degree of clustering (7). This is seen clearly in the Huckel model (152). The band gap of both ethylene and benzene is calculated to be
Eg = 2# The gap of olefinic chains can be found from their eigenvalues
[15]
Diamond-Like Carbons
10 "~////////// a - C : H
-
i
0.11
1
-
o--C~
I
10
0.01
-
I
I0(
go
EL
-1.0 >
•
(!;
uJ 0.1-
M-g
0.1 0.01 1
10
100
Number of rings (M) Fig. 40.
Calculated band gap vs. number of rings, for planar clusters of fused 6-fold rings of sp 2 sites (152). Inset shows likely ring orders for a-C and a-C:[t. ~n
t = 2p c o s ( ~ ) ,
n = I..N
[16]
This gives 2p,~
Eg -~
N
[17]
for N large and even. Fig. 40 shows the gap or compact (upper line) and acenic (lower line) aromatic clusters as a function of M the number of rings. The gap of compact clusters, the most stable sort, declines slowly and irregularly with M, according to the approximate relation
P
Eg ~ 2 MI/-----T JPSSC 21:4-E
[18]
I. Robertmn
256 or
[19]
Eg --6/M ~/2 eV where p--- -2.9eV. It can also be expressed as Eg "-, 7.7/La eV
[20]
where L,(A) is the cluster diameter or in-plane correlation length. The gap of acenic clusters falls off more rapidly, as roughly 60 eV Eg --- (M + 2.16) 2
[21]
The band gap is measured experimentally optically. In the absence of a sharp band edges in an amorphous semiconductor, the optical gap is defined empirically as either as the Eo4 gap, the energy at which the optical absorption coefficient a = 104cm-I, or the Tauc gap given by fitting a to the Tauc formula
[22]
(aE) 1/2 = B ( E " F~r)
s s
J"
..,,"~//"
J
5 10
sputtered a-C
MSIB a-C
Eo ~o4
I
PDa-C:H//~~/
.~, lo 3
/
10 2
/ /
/.-.,.
10
0
1
2
3
4
5
Energy, eV Fig. 41.
Experimental optical absorption spectra of a hard PD a-C:I] (158), a sputtered a-C (157), MSIB a-C (40), and a-Si:H (64).
Diamond-Lii
Carbons
257
for a = 104- lO%~rn-~.The Taut approximation found to be obeyed with fair accuracy by a wide This and other approximations are discussed by Cody range of amorphous semiconductors. (213). The absorption edges of sputtered a-C (157) and a hard PD a-CA-1 (158) are shown in Fig. 41 and can be interpreted within the above model. The edges are quite broad compared to that of a-Si:H which would indicate that a range of cluster sizes are present, each with its local band gap. The observed gap will correspond to that of the largest significant spJ cluster, rather than the average cluster size. For sputtered a-C with E,= 0.5 eV this is M = 140 for a large cluster and perhaps M = 35 for a typical cluster, coresponding to an in-plane correlation length of L. = 9A . For the hard a-C:H, a typical gap of 1.2 eV give M = 25 for the large clusters and perhaps M = 6 for average clusters, or L, = 3.8A. For a soft a-C:H, a gap of 2.5 eV gives M = 5 and perhaps M = 2 for a typical cluster size.
Table 11, A binding energies per site
E,Llt/P
WP
1.407
0.445
1.400
0.520
1.399
0.568
1.352
0.422
1.385
0.295
1.367
0.523
1.352
0.456
1.345
q.31a
1.326
0.097
258
J. Robertson
The relatively small size of the band gap in a-C and much a-C :H is one ofthe reasons why the aromatic cluster model was first proposed for these materials. Bredas and Street (153) indpeendently also reached the same conclusion using more sophisticated calculations. One should note that the E0, gap probably has a firmer theoretical foundation than the Tauc gap, because it is related to a definite density of states. While the E~ gap and Tauc gap are reasonably close in a-Si:H, E04 is 1.25-1.4 greater than the Tauc gap in a-C:tt because of its broad absorption edge. Other arrangements of rings within the clusters give band gaps lying between these limits. Table 11 shows the values of Eto, and band gap for various configurations with M = 5. Interestingly, the unsymmetric configurations tend to have energies and gaps similar to the compact clusters rather than the acenic clusters which have low gaps. Similar results are found for other M values. Thus, the compact clusters are actually fairly typical of unsymmetric clusters. Table 11 also gives Etot and band gap of aromatic clusters with quinoid spurs. The quinoid spurs are seen to strongly reduce the band gap. The band edge states are localized on the quinoid bonds. It is possible that the broad optical absorption edges in Fig .38 arise not from a wide distribution of M values, but a narrower range of M values plus a variety ofquinoid spurs. This might be particularly true of the broad edges which occur after thermal annealling, where the quinoid bonds arise from hydrogen elimination.
4.4 6 - n Mixing n interactions tend to keep n states on adjacent sites parallel and sp 2 clusters planar. This jus-
graphite
------
u) 0r~
puckered graphite
-20
Fig. 42.
S
-10
0 Energy (ev)
10
Calculated TB DOS for a planar and puckered graphite layer. Full line - total DOS, dashed line - s-like DOS.
Diamond-LikeCarbons
a
ii
J
259
/ \
b
(a) Staggered biphenyl molecule (b) Cross-linked sp 2 layers.
titles the convenience o f treating a and n states separately and necessary for the Huckel model. However, any warping or cross connection o f sp 2 layers may create a - n mixing. Their effects can be studied in terms of two limiting cases. The first case is the distortion o f a graphite layer by puckering. The new DOS is shown in Fig. 42. The puckering causes a hybridisation o f s states into the pn states, so the n states become sp lone pairs. This produces a finite s state density around Ev. It gives a second order reduction in the band gap of sp 2 clusters. The second case concerns when the n states on adjacent sites are orthogonal. A simple example o f this is staggered biphenyl, consisting o f two benzene rings with orthogonally oriented planes, Fig. 43(a). This distortion essentially decouples the n systems on each benzene ring. It causes a slight spn mixing and a slight narrowing of the gap. Hardness data (27) discussed in section 8 suggest that the largely sp ~ networks o f sputtered a-C are considerably cross-linked. The present model of n bonding emphasises the planarity o f the n clusters, and needs to be modified to allow cross-linking by sp ~ sites. Cross linking between n bonded planes by sp ~ sites can be analysed by considering the n states in different planes separately. In the network shown in Fig. 42(b), the n,. states o f the extended network form one n system and the n~ states o f sites 1 and 2 form a separate n system associated with a single C = C bond. Their energetics are again roughly separable. There is clearly some distortion o f either the o network or the rt network when sp ~ sites cross-link.
J. RobinSon
260
The presence of s,pn mixing can be seen in the spectral band structure of ion-beam deposited a-C. The retention of a band structure or momentum energy relationship may seem odd in disordered solid in which momentum k is not a good quantum number. However, the disorder in k, Ak, is only large in specfic parts ofthe band structure, such as near EF. The band structure of a-Si has been calculated by Hickey (159). It is found to be essentially parabolic (in an extended zone) and crosses EF at the 'zone boundary', as expected for a semiconductor. The band structure o f I B a-C has been measured by energy loss by Gao et al (160), Fig. 44. Two bands are found, as in graphite, a parabolic band due to a states a n d a higher band attributed to r~ states. The n band is curved in graphite, but is found to be fiat in a-C, for as yet unknown reasons (160-162). (Note that the energy resolution is only 8 eV). The spectral intensity of the fiat band does not fall to zero at k = 0, as it should by symmetry for a n band, indicating a s-like admixture in this band, which is attributed to warping. 4.5 Electronic Structure Simulations
The most sophisiticated simulation to date is that of Galli et al (103,104) who used first principles atomic pseudopotentials, the local density approximation for the electronic screening and
Spectral intensity (Arb. units)
EF
Momentum (~-I) I .o ,rM 2.0
:).o /
i
T
/
I
I
l /
20
3.0 I
l
J I
!
~QFwHM
Fig. 44.
Experimental spectral b a n d structure of ion-beam deposited a-C, measured by electron energy loss (I 81).
Diamond-Like Carbons
261
the Car-Parrinello molecular dynamics algorithm to treat both the electronic and nuclear degrees of freedom at the same time. A small sample of 54 atoms was placed in a periodic fcc lattice with a density set at 2 gm.cm-3 and was given a particular quenching sequence. It was found to consist of 85% sp 3 sites and 15% sp3 sites, with an RDF given in Fig. 20. The sp2 sites were found to be clustered into highly warped largely graphitic layers, which also contained some of the adjacent 5- and 7-fold ring configurations mentioned above. The sp3 sites were also found to be slightly clustered. Fig. 45 shows their calculated density of states. It shows the .w
(7"
(:7"
A
7r
71-~"
I/}
c
S
.6
A
F
•
L_
0
f,r)
o C3 LIJ
/UV
,
~EF ' I
,] ,T TI,T I,
-2o Fig. 45.
-~o o Energy (eV)
~o
Caculated DOS ofa-C from the simulation ofGalli et al (106)
262
J. Robertson
expected features with a small band gap of 0.5 eV lying between the n and the n* states. Their results generally support the model developed above from quantum chemical arguments. In practice, their sample size is too small to study MRO effects properly and their effect on the band gap. Indeed, the band gap in the simulation may arise purely from the model's periodicity. Tersoff (105) investigated the structure of a-C and liquid C. He used an elaborate valence force field which allowed coordination changes in addition to the usual bond length and bond angle changes. Its force constants were fitted to the calculated total energies of C in the graphite, diamond and cubic structure. With a larger cell of 216 atoms, he found a-C to consist of about 91% sp2 sites, with an RDF given in Fig. 20. These were arranged in a more recognisable graphitic structure. The Tersoff method uses only short range valence potentials and excludes the electronic states. It presumably derives a graphitic structure on the basis of the imposed density and the constraints on the possible bond angles. The density of states of a-C(:H) has also been calculated by the tight-binding method by Robertson and O'Reilly (152). It used a sp3s* basis and mainly nearest neighbor interactions. The interactions for C-C bonds were found by fitting the band structures of graphite and diamond (163-165). The parameters are given in Table 12, E(s) etc are the orbital energies and V(ss) ere are the bond parameters. It was found possible to use a single set of parameters for both C-C and C = C bonds, despite their slightly different bond lengths. V(p,n) is the interaction between n states which are treated separately to n interactions between o states. The interactions for C-H bonds were found by fitting the molecular orbital levels of methane. A number of other tight-binding parameterisations of the C-C bond are available. All use a sp 3 basis and nearest neighbor interactions. The early parameters of Chadi (166) are only suitable for the valence band. The parameters of Drchal and Malek (102) use separate interactions for C-C and C = C bonds, but the large difference in their orbital energies for sp3 and sp2 sites will cause trouble. The recent parameters of Tomanek and Schluter (167) are reasonably close to those in Table 12, given that they omitted the s* state.
"Fable 12. Tight-binding parameters, in eV. V(ss)
V(sp)
V(ppo)
V(pn)
V(p,n) V(ps*)
C-C
4.55
5.2
5.45
1.6
2.9
II-C
7.5
8.9
Bond
E(s)
E(p)
E(s*)
C
-5.3.5
0.
14.0
H
-2.3 4.5
Fig. 38 shows the calculated DOS of diamond, graphite and the Beeman (I01) random network models. The valence band of diamond consists of s-like states at -22 to -10 eV and a peak of po states centered on -7 eV. The conduction band consists of a* states above 2 eV. The C519 network with only sp 3 sites, the Polk network, has a DOS which resembles that of diamond. Its gap is slightly lower than that of diamond due to the effects of bond angle distortions. The states of graphite have a similar disposition, with the n states lying across the a-a* gap, as atrowed. The other three networks each have sp2 sites. These introduce n states. Unfortunately, the networks contain many odd-membered rings and these give rise to peaks at E =0, rather than giving an semiconductor.
Diamond-Like Carbons
1
i
I
I
263
I
i
I
a
b
= C - H in graphite
J
ID
C
- ~ C - H in graphite
0
0 °
~
m ¢-
(CH) n layer
(CH2) n chain
-25
Fig. 46.
-,; Energy(eV)
A'
I
5
1 t0
t
Calculated local II DOS for various C-tl bonding configurations (152)
Fig, 46 shows the states calculated for various C-It bond configurations in a random network. Each configuration gives rise to states only well away from the gap. Thus C-H bonds are electrically passive. 4.6 Photoemission
Photoemission spectroscopy gives the valence band DOS weighted by the appropriate cross section (168-173). The spectra are dominated by carbon states because the cross section of H ls states is lower than that of C 2s and 2p states at all photon energies of interest. Varying the
J. R ob e r ~ n
264
i i ii
.,
i.,
UPS
diamond
~l
-25 - 2 0
ii • i ii
-t5
-t0
-5
0
Energy (eV) Fig, 47.
Photoemission spectra of diamond, graphite, a-C (annealed a-C:H) and PD a-C:H, for 120 eV photons, after Wesner et al (169)
photon energy varies the relative cross section of the C 2s and 2p states. The ultraviolet photoemission spectra (UPS) with 20 or 40 eV photons are dominated by the C 2p states, while the X-ray photoemission spectra (XPS) with 1486 eV photons are dominated by the C 2s states, and photoemission spectra at around 100 eV using a synchroton source gives a similar weighting to 2s and 2p states. Fig. 47 shows the 120 eV photoemission spectrum of Wesner et al (169) for diamond, graphite, a-C and a-C:H. Their a-C:H sample was plasma deposited below 100° C while their 'a-C' sample consists of the a-C:H sample annealed to 5000C. The spectra can becompared with the
265
Ditmoad-Like C='oo,,=
calculated valence band DOS in Fig. 38. The upper peak in the photoemission DOS at 0-12 eV is due to p states and the lower peak at 12-22 eV due to s states. The upper peak contains both ~ and ~ states. The ~ states are apparent as a shoulder at 2 eV in the graphite spectrum and as a weak shoulder in the a-C spectrum, but no shoulder is visible in the a-C:H spectrum. Fig. 48 shows the UPS spectra of a-C:H as a function of annealling temperature T,. The ~z states are more visible in the more recent UPS spectra of Ugolini and Oelhafen (171) of a-C:H
ups hv = 40.8 eV
a-C:H
T=25°C U'3 rI -a
Z
T=350°C n" <:
u
O3
T=400°C
Z ILl I-Z m
T=500oC
T=600oC
16
Fig. 48.
12 8 4 BINDING ENERGY (eV, EF-0)
EF=0
Photoemission spectra of a-C:lt and as a function of annealling, after Ugolini and Oelhafen (171), with by-- 20 eV
266
J. Robertson
as a function of annealling temperature. They form a shoulder at 4 eV in the as-deposited sample and an increasing peak in the annealed samples. This spectrum confirms that the valence band edge of a-C:H is n-like. Fig. 49 shows the UPS spectrum of a-C:H samples prepared by ion beam deposition for various source gases as a function of ion beam energy (172,173). The contribution due to n states is again seen as a highlighted shoulder at -4 eV in the spectra of methane-derived films, Fig. 49(a), and as a peak in the other spectra. The shape of the s peak gives information on the topolgy of the network, for both n and a bonded networks. The s peak of a network containing only 6-fold rings consists of two peaks as seen in the calculated DOS of graphite and diamond in Fig. 38. However, introducing isolated 5- and 7-fold rings, as in the C519 model in Fig. 38(e), washes out the dip between the peaks. Thus it is interesting that the s-band shows two peaks for a-C and only one peak for a-C:H. The a-C result is consistent with its dominant n bonding which strongly favours 6-fold rings. On the other hand, a single peak is found for a-C:tt because its sp 3 bonding allows oddmembered rings. The photoemission cross-section of H states is too low for the local DOS at a H site to be visible in the experimental spectra. Nevertheless, the a-C:it spectra may contain features related
i
i
i
i
i
1
i
i
i
i
BenzeflelAu IBD
UPS hv = ~1 ~RV
I
I
n~
16
12
B
4
BINDING ENERGY (eV)
Fig. 49.
0
16
12
8
4
BINDING ENERGY (eV)
0
16
12
8
4
0
BINDING ENERGY (eV~
Photoemission of a-C:lt prepared by ion beam deposition for (a) methane, (b) benzene (c) styrene precursor, versus ion beam energy, after Oelhafen et al (172,173).
Diamond-LikeCarbons
o
267
=CH 2
e l
in ¢:
-CH 3
-25
-20
-15
-10
-5
0
5
t0
t5
~"nercjy (eV) Fig. 50.
Calculated local C DOS for C-H bonding configurations.
to H bonding. The calculated DOS at a s p 3 C site varies strongly with the number of H neighbors (Fig. 50). The s peak is seen to move deeper to larger binding energies, and to become sharper with increasing number of It neighbors. A similar movement is seen in the photoemission spectrum of a-C:lI in Fig. 46, the two s peaks of a-C not only merge into one,
268
I. Robemon
the upper peak also tends t o v a n i s h . Similar effects are found to occur in the spectra of a-SiC:H. Hydrogenation is seen to make the C DOS sharper in Fig. 50. This effect allows photoemission spectra to differentiate between soft a-C:H and hard a-C:H (172,173). The spectra of hard a-C:[t show broad peaks due to band states, as expected for a highly cross-linked solid, while the spectra of soft a-C:H show much sharper peaks with more molecular character. This effect can be seen in the spectra in Fig 49, where the degree of cross-linking increases with ion energy. This is discussed in more detail in section 5.1. 4.7 Optical Spectra
The optical spectra can provide valuable data on' the local structure of amorphous carbons. The complex dielectric function is given in terms of its real and imaginary parts as m el+~2
[233
e I := n 2 _ k 2
[24]
e2 -- 2nk
[25]
k = a/4n2
[26]
Experimentally, ~t and Ea are given by
and
where n is the refractive index and
where a is the optical absorption coefficient, tt and e., are related by the Kramers-Kronig relationship
et(E) = 1 +
-E- '-' - 7E" dE'
[27]
e2 is given by e2(E)----- {(21te2)2/NA}px2(E)J(E)
[28]
where Nt, is the atomic density, and J(E) is the joint valence and conduction band density of states J(E) =
Nv(E')Nc(E + E')dE'
[29]
0
R(E) is the position matrix dipole element and is related to the momentum matrix element by P(E) = [mE/~]R(E)
[30]
The Tauc approximation to the optical gap assumes the band edge DOS to have a parabolic (free electron) form and P(E) to be energy independent. It has been Found to be valid emprically for a wide range of amorphous semiconductors.
81/,
Diamond-Like Carbons
269
6--
2
IL 0
~
0
Fig. 51.
= zo c ~
10
20 eV
30
40
Wide band optical spectra o f diamond, graphite, PD a-C :H and annealled after Fink et al (174)
a-C:H,
The excitations o f a and n electrons show up as two largely ~ p a r a t e contributions in the optical spectra o f carbons (174). This is because a--+ n * and n - + o* transitions are weak for planar sp 2 sites, so that a and = states are also effectively decoupled in the optical spectra. Fig. 51 shows the optical spectra e, o f diamond, graphite for E ± c , a PD a-C :H and an a-C:H annealed at 540°C, the latter curve representing sp 2 a-C (174-177). Each curve consists o f two peaks, a peak at 4-5 eV due to n -+ =* transitions and a peak around 13 eV due to a -+ ~* transitions. Graphite also has a singularity at E = 0 eV as expected for a metal. This suggests that it is possible to estimate the number o f electrons N . . which contribute to each
270
J. Robertson
peak from El to E2 by the sum rule
[3U
• = rcEp/ fo,~Ee2(E)dE 22 with
E~m Ndf = (
[32]
4zee2~2NA )
to give m Netf = ( 2n2NAe2~ 2 )f~aE~'.e.2(E ~' )dE.'
[33]
where N^ is the number of C atoms per unit volume, m is the electron mass and e is the electronic charge. The prefactor takes the value 0.766 for N^ in m ~ and E in eV. N,~ of graphite was found to reach a plateau of one electron per atom by 9 eV and a second plateau of---4 electrons by 30 eV. For diamond, Ne, was found to be very low for E < 8 eV and to plateau at four electrons by 40 eV. It therefore seems possible to assume that all transitions for 0-8 eV i
I
I
I
|
i
|
I
graphite, E.L.C a-C
2
Nff
0
a-C:H
i
~
0
10
20
30
I 40
50
Energy, e V Fig. 52.
Effective number of electrons contributing to the optical spectrum, N,u, for graphite, PD a-C:lt and a-C (180)
Diamond-Like Carbons
271
are due to n electrons and all transitions above 8 eV are due to ~r electrons. In this manner Fink
et al (174) estimated the sp 3 fraction of evaporated a-C and a range of PD a-C:tt samples. The advantage of this N,, method is that it is unaffected by clustering or the presence of hydrogen. However, there are number of possible sources of error in this method. Firstly, Gao et al (160), Sonnenschein et al (178) and Daniels et al (179) have drawn attention to an error in the numerical determination of N~, of graphite by Taft and Phillip (177) resulting in N,~ being reduced by a factor 2/n. Fig. 52 shows the N,, for graphite for E_Lc (corrected), a-C and a sample o f a - C : H (180). N,, no longer reaches 1 at 8 eV nor 4 at 40 eV. Thus, the n and tr + n oscillator strengths are no longer exhausted by the expected energies. This is even more apparent in the E//c spectrum of graphite shown in Daniels et al (179). Thus the fundamental basis of the 8 eV cutoff is removed. A second problem is that the n and o transitions are poorly separated at 8 eV. A separation requires that as ~ 0 in the dip around 8 eV for Ne, to plateau around 8 eV. It is clear from the optical spectra in Fig. 51 and elesewhere that this dip is much weaker in a-C(:H) than in graphite itself. This results in a poor separation and indeed N~, only has an inflexion around 8 eV rather than a plateau in Fig, 52. The cause of this lack of separation are two-fold. The total ~ + ~t* bandwidth is 17 eV, so it is unlikely that the rt oscillator strength would always be exhausted by 8 eV. Also, while diamond has not started to absorb significantly by 8 eV, the loss of k selection in a-C(:It) can allow transitions to occur from a states at lower energies, immediately above the minimum gap. These seem to be the primary factors but the poor separation could also arise from a poor decoupling of ¢r and zt excitations due to the warping of sp~ layers, as suggested by Gao. Nevertheless, we note that the ratio N(o + rt)/N(rt) = Neff(0 - 40eV)/Nerf(0 - 8eV)
[342
is approximately 4 for a-C in Fig. 52, as expected for sp ~ bonding. It is therefore possible to deduce sp ~ contents by this method on an empirical if not fundamental basis. A third source of error in this method is that the density may not be known accurately. This can be circumvented by using ratios, as in eqn [34]. Recently, Tagliaferro et al (181) refined the method of deducing sp 2 fractions and Ne, from optical spectra. They decomposed the e.2 spectrum into two guassians, for n - n * and t r - t r * transitions respectively, which can overlap if necessary. N,, then can be calculated analytically by the sum rule. The method can even be used when optical spectra are only available up to 8 eV. In this case, e, is calculated from e2 by the Kramers-Kronig relation, N(n) is found from the first peak in ~ and then ~., is used to find N(a + n). Finally, the sp ~ fraction is found from the ratio N(~t) to N(n +a), again avoiding the need to know the density explicitly. This formalises the method used by Savvides (24,25) to find sp 2 fractions in sputtered a-C.
4.8 Electron Energy Loss Spectra The electron energy loss function is defined as 1 -lm(-~-) =
£'2 ("e2+ i 2.2)
[35]
where "Im' is the imaginary part of. The loss function can be calculated from the optical spectra or measured directly. The valence loss functions of a-C(:l I) have been oRen measured and are aPSE 21:4-F
272
J. Robertson
4
2 graphite 0 a-C 0 a-C:H E
T. = 650 C
I--I
0
0 -
0 0
~ I A-r-"-
10
diamond I
I
20
I-
30
I
I
40
Energy (ev) Fig. 53.
Electron energy loss spectra of diamond, graphite, evaporated a-C and PD a-C:tt (176,178,78)
frequently used for characterization. Fig. 53 compares the EELS of diamond, graphite, evaporated a-C, sputtered a-C and some PD a-C:H (182,183, 78). The loss function can show both one-elelctron features (band-to-band transitions) and many electron features (plasma oscillations). Plasma oscillations produce a peak in the loss function if the particular plasmon energy occurs where F., is small. Thus, the loss function of carbon consists in general of two peaks, a lower one due to the n plasma oscillations and an upper peak due to all the valence electrons, a + n. ~ is given by
Diamond-Like Carbons
273
4tte2~-2NaNeff I/2 m )
Ep = (
[36]
where N~ is the number of participating electrons per C atom (1 or 4). This equation results. from the sum rule {31} above, with El = 0 and E2 is a cutoff below the core orbital excitation energies. Table 13 compares E, values given by eqn [36] and those found experimentally. The comparison is good for the # + rr plasmon in graphite and diamond. However, the ~t plasmon of graphite lies well below its expected position. This is because its expected energy, 12.5 eV, coincides with the main tr ~ a* band to band transitions, where ra is high (177). This effect Table 13. Plasmon energies in Carbon, in eV. tr A- 7r
7t
Exp Graphite
7.2
Theory
Exp
Theory
Ref
12.5
25.2
25. !
177
30-32
31
175
Diamond a-C.
6
24.9
78
a-C:H
7
20.8-24
78
a-C:H, 1", = 600°C
6
21
78
21
177
glassy C
6° I 50
2:
Methane
4O Benzene
(g
3O
[
.-.._
20
10
I
0
Fig. 54.
I
i
200
i
I
I
I
400 600 Bias voltage (V)
I
I
800
I
J
1000
Hydrogen content vs. bias voltage for PD a-C:H, deposited from methane (75), acetylene (62) and benzene (9)
274
J. Robertmn
40
30 20
0
200
4~
Imll
6~ i im
8~
B
1~0 i
0.8
~sp
2~ •
C3
= 0 0.6
8 m
C3,h 0.4
0
I
polymeric
• C4,h
0.2
o'[ 0
diamond-like 200
400
C4 600
800
1000
Bias voltage, V Fig. 55.
(a) sp s fraction vs. bias voltage for PD a-C:H deposited from methane at 3 Pa, as measured by NMR, from Tamor et al (75) (b) Carbon bonding vs. bias voltage for PD a-C:H deposited from methane, from Tamor et al (75)
Diamond-Like Carbons
275
lowers F~ to its observed position. Consequently, F~ of the a + n is very useful for obtaining the density of a-C(:H). The n plasmon can be used to indicate the presence of sp= sites but it cannot usefully give the n electron density. 5 PROPERTIES OF a-C AND a-C(:H) 5.1 a-C'H
The properties of a-C:H depend primarily on the mean ion energy, E,. In the case of PD a-C:H they depend on the negative substrate bias voltage Vb. Fig. 54 shows the variation of H content for films deposited from methane and benzene at a gas pressure of 3 Pa and at room temperature. The H content was derived from N M R data for the methane films of Tamor et al (75) and by NRA for the benzene films of Koidl et al (9). The H content is seen to decline rapidly with increasing bias. The variation is seen to be similar in each type of film despite the different measurement techniques. Interestingly, a much lower hydrogen content is found for a-C:H deposited from acetylene. The H content again decreases with increasing bias, but at a uniformly lower level. These films were deposited at a gas pressure of 2.6 Pa and measured by ERD by Zou et al (61).
2.2 Acetylene
2.0
1.8
1.6/ 1.4 1.2
Benzene
,
,
, 200
Fig. 56.
I 400
z
, , , 600 800 Bias voltage (V)
,
, 1000
~
, 1200
Density vs. bias voltage for PD a-C:tt, deposited from acetylene, after Zou et al (61), from methane after Tamor et al (75,185), and deposited from benzene, after Koidl et al (9).
276
J. Robertson
Fig. 55 (a) shows the variation of sp a fraction for films deposited from methane, as measured by N M R by Tamor et al (75). The sp a fraction is seen to decline steadily with increasing bias. A similar dependence was found for a-C:H by Jarman et al (71) and Yamamoto et al (73) using NMR. A similar bias dependence is also expected for benzene-derived films, although they have not yet been studied by N M R or XANES, to the author's knowledge. A rather different bias dependence was found by the IR method (60,61,141), with a rather high sp ~ fraction being found at low V~. This emphasises the unreliability of the method and the data are not included in the figure. These variations lead to three regimes of properties (9). At low bias, the bonding is dominated by = CH2 groups and the properties are rather polymeric, giving 'soft' a-C:H. At intermediate bias, the decline in H content gives the films their most "diamond-like' character. This regime of'hard' a-C:H extends from about 100 V to 1 kV for methane films and 200 V to 1.2 kV for benzene films. Finally, sp 2 bonding predominates at the highest bias, where the structure is highly disordered graphitic. These variations are summarised in Fig. 55(b). The mass density of methane-derived a-C:H has been measured by Couderc and Catherine (184), Zou et al (60) and Wang et al (81) with broadly similar results. Fig. 56 shows the variation of mass density with bias, for both the methane-derived films of Tamor (185) and the benzene-derived films of Koidl et al (9). Both were determined by weight gain. The density is seen to increase continuously with bias for the benzene-derived films but to pass through a peak for the methane-derived films. The density of a-C:H deposited from acetylene tends to vary in a similar fashion to methane films with a peak at 200-400V, but to reach much higher values. These densities were measured by RBS by Zou et al (61). These RBS data for acetylene films show more scatter than those found by other methods, but a comparison of RBS and other data
2.3 2.2 Met
2.1 2.o
~1.9 1.8 1.7
Fig. 57.
I
I
200
I
I
I
I
400 600 Bias voltage (V)
I
I
800
I
1000
Refactive index vs. bias voltage for PD a-C:H deposited from methane after Serra et al (186) and benzene after Koidl et al (9).
Diamond-LikeCarbons
277
for methane-derived films shows the RBS data to be moderately reliable, except that they miss the reduction in density at low bias. Fig. 57 shows the variation of refractive index n with bias for methane-derived a-C:H from Serra et al (186) and for benzene-derived a-C:H deposited from Koidl et al (9). The refractive index is seen to vary similarly to the density, passing through a peak for the methane-derived films and increasing progressively for benzene-derived films. The optical gap is found to vary in a very similar fashion for a-C:H derived from both methane (134,185) and benzene (9), as seen in Fig. 58. The gap declines rapidly with bias, from 2.5-3.5 eV for Vb= 0 to 1.0 eV at V~= I kV. [lard a-C:H has E+ < 1.6 eV. Koidl et al (9,56) proposed the useful rule that the properties of hard and graphitic a-C:H were independent of source gas, while those of soft a-C:tl depended on source gas. The foundation of this rule is their observation that the source gas is essentially completely decomposed in the plasma at higher bias voltages, but not at low bias (59,187). Thus, Koidl (9) noted that the H content, sp 3 content as determined by IR, optical gap and refractive index were each very similar for hard a-C:H deposited from methane, benzene, n-hexane and cyclo-hexane at Vb=400 V. In contrast, there are strong differences in film structures of soft a-C:tt, as is seen readily in their
2.8' 2.6 l l t
2.4
\
2.2 ~ Benzene ~---. 2.0
~
~
N
1.8 1.6
~Methane
1.4
1.2
1.0
0.8
Fig. 58.
0
I
I
200
i
I
400
I
I
I
i
600 800 Bias voltage (V)
i
i
1000
t
i
1200
Optical (Tauc) gap vs. bias voltage for PD a-C :H deposited from methane after Tamor et al (134,185) and benzene, after Koidl et al (9).
278
J. Robertson
a) Benzene 600
VB
400
500V
200
'T
a
E
b)
fJ
I.Z LIJ (.3 14. 14.. 14.1 0 (.3
i
',,~;
Benzene
400
n-Hexane .......
m
/
~: t
m
Z
C) I-n n, (:3 Ul
300, 200
i
CD <
100 0 1200
I
i
i
i
I
c)
%
Benzene
•
n - H e x a n e ....... VB,, 1 0 0 V
800
' ,' j, e I e e # #
'
'I
, ',, t t S t t | S
!
/,00 0
|
i
3300
Fig. 59.
i
i
3100 2900 WAVENUMBERS (cm "1)
C-H stretch I R spectra of PD a-C:H deposited from benzene and n-hexane, at various bias voltages, aRer Koidl et al (9).
Diamond-LikeCarbons
279
IR spectra. For instance, Fig. 59 shows that the C-It stretch absorption is similar for films deposited from n-hexane and benzene at a bias of 400V, while there are substantial differences at a bias of 100V. Similar effects were noted between films deposited from methane and benzene by Tamor et al (147), particluarly the presence ofphenyl side-chain groups in low films. More detailed comparisons in Figs. 54-58 above show that electronic properties such as the optical gap follow this rule very well, but that the density, refractive index and hardness do not, remaining quite different at high bias. The cause of this failure is not understood. The difference between the molecular bonding of soft a-C :H and the network bonding of hard a-C:H is perhaps most apparent in the photoemission spectra (172,173) shown in Fig. 49, of a-C:H deposited by ion beam from various source gases. These spectra use a photon energy of 21.2 eV and emphasise the C 2p states. They have a broad peak due to a states and a knee or peak around -4 eV on its leading edge due to r~ states. The network of hard a-C:lt deposited at higher ion energies gives rise to broad spectra, while the molecular bonding of soft a-C:H deposited at lower ion energies produces much sharper spectra. The rr state peak allow this transition to be studied more precisely, and it is found to occur at 300___20 eV for a-C :H deposited from benzene and at 165-t-20 eV in a-C :H deposited from methane. The photoemission spectra therefore support Koidl's general model of soft and hard a-C:H, but note that the threshold ion energy (or bias voltage in PD) does depend on the source gas. This dependence on source gas is further emphasised by the spectra for styrene precursor. Now even the spectra for 1 kV have not lost all their molecular character, indicating that such energies are unable to fully decompose large, aromatic molecules. Indeed, the photoemission spectra of soft a-C:tt prepared from styrene are similar to that of the monomer (173). This emphasises that PD soft a-C:H is very similar to plasma-polymerized hydrocarbon (65). The n electron fraction and sp~ fraction can also be estimated from the UPS spectra, as shown shaded in Fig. 49. The sp2 fraction is found to increase with ion energy for a-C:H deposited from methane, as found by NMR (Fig. 55). The sp2 fraction varies less in a-C:H deposited from benzene. This is significant and suggests that there are many sp~ sites in this soft a-C:lt, presumably at pendant phenyl groups. The ability to vary the optical gap and refractive index of PD a-C:H makes them particularly suitable for protective optical coatings. The films can be prepared at a bias voltage which allows their refractive index to be matched to the substrate. In fact, the dependence on bias and gas pressure P is quite complex. Bubenzer et al (13) found that the gap varies as Vb with only a weak pressure dependence, while the refractive index varies as V,P-~ and the density varies as VbP -1/~. The harder a-C:H films only have low absorption in the far IR, rather than the optical, as seen for a typical film in Fig. 41. The C-H vibrational bands create absorption in the near IR. This absorption can be reduced by using fluorinated a-C:H (a-C:It,F) deposited from fluorinated benzenes, as shown by Sah et al (188). 5.2 Role of Hydrogen
We may summarise that the role of hydrogen is primarily to saturate n bonds, converting sp 2 sites into sp 3 sites. This occurs because the reaction =C=C=
+ tt 2 ~
=CII-(7tt=
[37]
J. Robertson
280 '
t5
I
.
'
I
'
I
'
I
._._._._..,.
I
'
I
',
,,°,
o. ,.s°
I
Io-C:HI
tO
_u. 0.5
'
"x ! ,
I
,
,
,
I
,
I
,•
I
ee
W
le •
•Q
2:1.0
,?.
'~,.. i
o.s
i (b)
Z
0
"~
(c)
'°i o~ 20 I,d O,.
>.
0 0
100
200
300
t,00
500 600
ANNEAL TEHP. (oC) Fig. 60.
Effect of thermal annealling on the sp 2 fraction, I[ content and optical gap for PD a-C:II, aRer Dischler (141)
281
Diamond-Like Carbons
is exothermic. The cluster model suggests that the effect of hydrogen on the band gap is indirect; the reduction in sp~ fraction will tend to reduce the size of the sp 2 clusters and thereby increase the gap. The dependence o f t l content, sp2 content and gap o f P D a-C :H on bias voltage and anneailing temperature generally supports this idea. In rare cases little correlation between Et content and gap is found (74). The addition reaction {37} can be reversed at higher temperatures, by thermal annealing or high temperature deposition. The thermal annealing process is likely to have many similarities to the pyrolysis of hydrocarbons. Pyrolyis occurs in three stages (189); carbonisation with the loss of volatile species, polymerisation with the conversion of olefinic groups into aromatic groups and the graphitisation of aromatic groups into graphitic layers. The first stage of thermal annealing involves largely hydrogen elimination. The simplest reaction is elimination from adjacent sites, the reverse or reaction [37], to form olefinic groups, =CII.CH=
~
=C=C=
+ H2
[38]
The second stage is the conversion of olefinic groups into aromatic rings. We now consider these changes in more detail. The deposition or annealling or a-C:H above about 300°C causes a decline in hydrogen content, and increase in sp~ fraction and a closing of the optical gap. Fig. 60 shows these changes with annealling for a hard a-C:H film deposited at a bias of 1 kV, after Dischler (141). The hydrogen content and sp2 fraction were estimated from the C-H stretching modes around 3000cm-', so the latter is a guide only. The sp~ fraction is seen to reach almost 100% by 600°C, where the gap has closed. The data suggest that lq begins to evolve at 300°C while the sp2 fraction begins to increase at 400°C. Smith (190) observed similar variations of optical gap and hydrogen content. The closing of the optical gap is accompanied by a broadening or the absorption edge (190-192, 142), as discussed in more detail in section 6.2. The C-H modes also show a conversion or olefinic CH groups to aromatic CH groups as temperature is raised, due to polymerisation. ]'he corresponding increases in sp ~ cluster sizes have been observed in the Raman spectra (129,138,139), as noted earlier. In contrast to this, Grill et al (193) studied the behaviour of the 1600 cm -1 IR C = C bond stretching mode and found that the sp~ fraction begins to increase before the onset orhydrogen loss. Grill (193) also noted a reduction in residual stress at higher deposition temperatures. The thermal stability of a-C:H is limited by the loss of hydrogen and the consequent bonding changes (140,194,195). Consider first the simpler case ofa-Si:H. Hydrogen evolves from a-Si:H at two temperatures, roughly 300°C and 550°C (196,197). The low temperature evolution is attributed to weakly bound hydrogen from polymeric or void surface sites. Its evolution rate is limited by the recombination or pairs of H atoms at the internal surface, and the H2 molecule subsequently reaches the film surface by permeation along micropores. The high temperature evolution is due to strongly bound hydrogen from the bulk film. Its evolution rate is limited by the diffusion of atomic tl across the bulk film. These differences were verified by varying film thicknesses and studying isotopic mixing from a-Si:ll/a-Si:D film sandwiches. The peak evolution temperature varies with film thickness for diffusion limited evolution, but not for recombination limited evolution. A sandwich structure evolves 1t5, HD and D2 in the ratio 1:2:1 for diffusion of H in the atomic form, as a complete mixing or the isotopes occurs. In contrast, there is little evolution of tID molecules where evolution occurs by molecular permeation as either H2 or D2 molecules are formed locally.
282
I R nh~'te.nn
Methane
~
I Benzene/.\ ;
~H2
\
+
- - C H3* - - - C 2H/. ÷
!
200V
300V
/
900V
'2''
e,, 0
"6 > uJ
600V
1400V S 2OO
Fig. 61.
400
600
8OO 200 400 Temperature, °C
600
800
i
1000
Thermal evolution spectra of PD a-C:H deposited from methane, after Xiang et al (194), and benzene, after Wild and Koidl (193).
The H evolution from a-C:tI differs in a number of ways. Fig. 61 shows typical evolution spectra for PD a-C:it deposited from methane (195) and benzene (194). The evolution spectra depend primarily on bias voltage and to a lesser extent on precursor gas. Soft a-C:H evolves H over a broad temperature range beginning at 300C, while hard a-C:H evolves H at 600-700* There is little isotopic mixing in evolution from a-C:H/a-(" :D sandwiches (Fig. 62), indicating that evolution occurs by the permeation of It2 rather than atomic H (194,198). Also, the absence of a temperature shift indicates that evolution is limited by H recombination rather than diffusion (194). The recombination rate is found to have an activation energy of 2.7 eV, in benzene-derived films (194). A similar evolution mechanism is found in a-C:H films produced by the proton irradiation of graphite (199-201) These results show that a-C:H has a relatively open network, allowing the relatively easy permeation of H2. This contrasts with the denser networks of a-Si:H which favour transport as atomic H. The network of soft a-C:H is particularly open, being suffiently permeable for evolution from pendant groups as hydrocarbons rather than as I-I2. This is particularly true of benzene-derived films. The technical interest in the density and hydrogen evolution spectra of a-C:H is the indication they give of the network coordination, and thereby of the film's hardness. Hydrogen evolution spectra indicate the hydrogen transport mechanism; an atomic transport mechanism implies a dense network, while a molecular transport mechanism implies an open network. Consider a-Si:H as an example again. The most stable configuration of H in a-Si:H is the Si-H bond. It can also exist at the less stable interstitial sites, such as the bond centered interstitial (202). H diffuses between bonds via these interstitial sites (202,203). A dense network stabilises the interstitial sites, thereby lowering the activation energy of diffusion for atomic H, and favouring atomic H diffusion. On the other hand, molecular H2 is slightly less stable than a Si-H bond.
Diamond-LikeCarbon,
A
" .... o¢ ......... Ho÷
283
/k /,,\ °-c:o 8oov I °-C:H a00v I I si I
P / ,
"\\
'
7i~0
tad i.z !
I a-C:D t,00V a-C:H 400V I
si
ml
~6o
360
'
s6o
TEMPERATURE (oC) Fig. 62.
H evolution spectra from a-C:H/a-C:D sandwich structures after Wild and Koidl (193)
It is immobile in a-Si:H except where it can permeate along micropores associated with voids or (Sill2), groups. Hence, a dense network favours the diffusion of hydrogen as atomic H as seen in the high temperature evolution peak, while an open network favours the permeation of hydrogen as molecular H2, as in the low temperature evolution peak of poorer a-Si:H. A-C:H is expected to behave similarly. The fact that H always transports as Ha shows that the network of all a-C:It prepared to date is still too open. Particle bombardment appears to have a similar effect on a-C:lt as temperature, causing a loss of hydrogen and a reduction in the optical gap. Fig. 63 shows the variation of H content and gap for a-C:H versus ion dose for bombardment with 50 keV C + ions, from Prawer and Kalish (204,205). The reductions in H content and gap are seen to track each other with dose, suggesting that the primary effect of bombardment is to drive off hydrogen, which causes an increase in the sp 2 content and a reduction in the band gap. 5.3 a-C
The properties of sputtered a-C have been studied less intensively than those of PD a-C:H. The
284
J. Robertson I
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2 I 10 14
I 1015
I 10 16'
I 1017
C + ( ions cm "2) Fig. 63.
Variation of tl content, optical gap, and spin density of a-C :tt with dose for 50 keV C ~ ion bombardment, after Prawer et al (204).
dependence of properties of deposition conditions have been studied principally by Cho et al (27), Savvides (24) and Cuomo et al (28). The optical absorption spectrum of a sputtered a-C of Hauser is shown in Fig. 41. Its gap is 0.5 eV. Optical gaps in the range 0.4-0.7 eV have been found by Savvides (24) and Cho (27). The gap increases with decreasing RF power. In Cho's work, the sp3 fraction was deduced by the less reliable Raman peak shift method, but was supported by XANES spectra, and was also found to increase with decreasing RF power (27). The density also increased with decreasing RF power. Rossnagel et al (26) found the gaps and densities to vary inversely with gas pressure. These variations can be attributed to the ion fraction being highest at low gas pressures and RF powers. Cuomo et al (28) sputtered a-C onto a series of increasing well heat-sunk substrates. They estimated the density from low energy EELS and the sp.~ fraction from XANES (high energy EELS). They observed that the sp 3 content increased strongly with the thermal conductivity of the substrate material. The sp"~content was found to vary almost linearly with density (Fig. 64). A peak sp3 content of about 50% was reached. This result is significant in terms of the deposition mechanism because it indicates that high sp3 contents can be produced even by low energy ions. However, the deposition rate was low, 8A/min.
Diamond-Like Carbons
APPARENT DENSITY (g/cm"3) 2.4 2.8 3.2 3.6 4.0
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Density and sp,~content For a-C deposited by sputtering on different substrate materials, after Cuomo et al (28)
The atomic structure or MSIB a-C has been discussed in detail earlier. Fig. 41 shows its optical absorption spectrum from McKenzie et al (39). The spectrum has a strong tail down to I..5 eV, which can only be due to n states at sp~ sites. Fig. 65 shows the absorption replotted in Tauc form as (~E) '2 vs. E. The spectrum does not fit this form well, so that gaps from 1.3 eV to 3.5 eV can be found by extrapolating different parts or the curve. The E~ gap is 3.5 eV, consistent with predominantly sp 3 bonding. The electrical gap appears to be similar. Itowever, the absorption only falls very gradually within the gap. This absorption must be attributed to n states. Lower optical gaps of 0..5-i.5 eV were quoted by Ishikawa (47). The dependence of properties or MSIB a-C on ion energy can be studied by applying a bias voltage to the ion gun. McKenzie et al (39) found that its density passed through a peak at ion energies or order 30 eV, as shown in Fig. 66. They also found that the films were under large compressive strains, which were deduced from substrate curvature. They found the density and strain variations to be strongly correlated (39,40). Koskinen (44) and lshikawa et al (47) also
J. Robertson
286
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Dependence of density on ion beam energy for MSIB a-C, from McKenzieet al (39) and lshikawa et al (47).
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Variation of optical gap with density, for a-C and a-C:H, based on Tamor 047). Data for MSIB a-C from McKenzie (39) and lshikawa (47).
found that the density and other properties passed through a peak with ion energy, although at a much higher energy of 1.50-300 eV. Fig. 66. The reason for this difference to McKenzie's (39) results is not known, lshikawa used C- ions. Tamor (147) noted a clear difference in the behaviour of a-( 2 and a-(" :11 if their optical gaps are plotted against density, Fig. 67. The correlations of atomic densi.ty and hydrogen fraction JPSSC 21:4-G
288
J. Robertson
o f Angus (I) are also relevant, Fig. 3. "File gap o f both a-C and a-C:ll increases with sp s content. I lowever, in a-C increasing the sp a fraction gives a direct increase in both atom and mass density, whereas in a-(':ll increasing the hydrogen fraction increases the sp s fraction, increases the atom density but decreases the mass density, because o f the greater polymeric component. 6 LOCALIZED STATES
6.1 Origins of Localized States The electronic states o f an amorphous semiconductor can be classified as either extended states and localized states. Extended states lie within the bands and conduct electricity at 0°K. The extended states are separated from the localized states by mobility edges, which are analogous to the band edges o f a crystalline semiconductor (Fig. 68). The region o f low DOS between the mobility edges defines a mobility gap which acts like the band gap of a crystalline semiconductor (206). It is convenient to further classify localized states as either band tail states or deep states. Tail states lie adjacent to the mobility edges. Deep states are more localized, lie nearer midgap and are generally associated with specific 'defect' configurations whose bonding differs from that o f bulk sites. The chemistry of amorphous carbon suggests that its defect configurations will be more complicated than those of a-Si (152). The principal defect of a-Si is the dangling bond, a trivalent
-2.1021
TAILS
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Fig. 68.
ENERGY
Schematic picture of electron states near the band gap region o f an amorphous semiconductor, showing localized and extended states, tail and defect states.
Diamond-Like Carbons
289
Si site, formed by breaking a a bond. A defect in a-C can be formed by breaking a a or a n bond. Naturally as n bonding is weaker, we expect n defects to predominate because o f their lower creation energy. A defect will therefore be any configuration o f n states which gives a state near midgap (152). For a more quantitative understanding o f the origins of localized states, we use the I-Iuckel model o f n states. We recall that all states around the gap arise from n states. We set the p orbital energy E , = 0. Within this model, the n electron spectrum tends to be symmetric about E = 0. The tail states are the states o f large clusters. Any cluster with an odd number o f re states automatically gives a state near E = 0 which is half-filled - is a paramagnetic defect level. The simplest olefinic defect is a row o f three n sites and the simplest aromatic defect is cluster o f three fused rings. It is possible to define a defect creation energy Ed for rt defect clusters as (152) Ed = N(EN - EN)
[39]
Here N is the number o f sites, eN is the total n energy per site o f the defect cluster and EN is the n energy o f the equivalent non-defect cluster with a similar number of sites. Fig. 69 shows that Ed decrease rapidly for the olefinic chain defects but only slowly for aromatic clusters. Fig. 69 illustrates two differences between o and n defects. Firstly, Ed is not single valued for n defects.
compact grophitic
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5
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50
100
Number of sites,N(odd) Fig. 69.
Calculated defect creation energies for ~ bonded clusters as a function o f cluster size (I,52)
290
J. Robert,son
Secondly, Ed is much smaller for n defects. The maximum Ea of aromatic defects is about 0.4 eV from Fig. 69, while the Ed of a defects is about half of t h e C-C bond energy or 1.8 eV for a-C. The relatively low creation energies of n defects will give rise to high defect densities on a-C(:H). In a mixed o, n bonded system like a-C, a dangling bond must be defined as an isolated trivalent site (152). Its creation energy is expected to be about 1.8 eV, as noted earlier. It is expected to adopt a planar configuration, by analogy to the methyl radical CH~, and so the unpaired electron will occupy a n orbital. Thus the dangling bond in a-C will have n character, and not sp 3 character as in a-Si. The discussion of electronic structure suggests that tail states in a-C are associated with n states of the larger clusters. Thus tail and defect states have basically the same character in a-C(:H).
6.2 Localization
The optical absorption edge of an amorphous semiconductor such as those shown in Fig. 41 has three regions. The region above about ~ = 104 cm -I corresponds to band to band transitions between extended states (206-209). Below this lies the Urbach tail in which the absorption falls rapidly and often in an exponential manner, due to transitions between localized tail states and band states. The exponential dependence arises from exponential density of states distributions, and the slope represents the slope of the broader of the tails. Finally, there is often an addition step in absorption at the base of the tail, due to absorption by midgap defect states. The empirical definitions of optical gap in an amorphous semiconductor such as the Tauc or Eo, gaps correspond to placing "optical band edges' at a certain density of states near the band
sp 3"
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N(E)
Effect of n bonded clusters on local band gaps, mobility edges and optical band gaps in a-C:H (208)
Diamond-LikeCarbons
291
edges. In o bonded amorphous semiconductors where the potential fluctuations are short range and only moderate in size, the mobility edges also tend to lie at certain density of states, at roughly 1/3 of the corresponding free-electron value (206). Thus, it is possible to define the optical band gap Eo,, to equal the mobility gap E, so that the optical band edges lie at roughly the same energy as the mobility edges. Jackson et al (209) recently thoroughly investigated the sizes of E, and the various optical gaps for a-Si :H. The presence of sp ~ bonded clusters produces large fluctuations in the local band edges (210). These have a profound effect on the localization of states around the gap, particularly in a-C:H which has a similar concentration of sp 2 and sp 3 sites. A schematic band diagram of a-C:H is shown in Fig. 70(a). The n states lie symmetrically about midgap. Their local band gaps vary inversely with cluster size. The gap of the o phase is over 6 eV. It acts as a tunnel barrier between each n cluster and tends to localize n states within each cluster. The 'optical' band edges, depending just on the density of states N(E), will depend primarily on the cluster size distribution. In contrast, the mobility edges also depend strongly on the width of the sp3 barriers. Widening the barriers forces the mobility edges further into the bands, well beyond the optical band edges. Thus, E~ will exceed Eop, in the n states ofa-C:H, Fig. 70(b), in contrast to the case of a-Si:H (210). The potential fluctuations due to clusters also have a strong effect on the optical transitions. There are two types of fluctuations, those in which the band edges move either symmetrically or antisymmetrically about midgap (207,21 i), Fig. 71. The symmetrical fluctuations arise from elastic or deformation potentials such as strained bonds while the antisymmetric fluctuations arise from electrostatic effects such as trapped charges. Fluctuations in amorphous semiconductors are frequently assumed to be of the antisymmetric type, being due to charged defects or ionized dopants. There are four possible types of optical transitions between extended (E) and localized (L) states; extended to extended (EE), LE and EL, and LL. Antisymmetric fluctuations tend to localize the initial and final states of an LL transition in different parts of the sample (Fig 71b)
/ symmetric
Fig. 71.
antisymmetric
Symmetric and antisymmetric band edge fluctuations.
292
J. Robertson
so that LL transitions have only a small matrix element. On the other hand, because of phase randomness, EL and LE transitions tend to have a similar matrix element to EE transitions (208). Thus, EE, EL and LE transitions are allowed but LL transitions are essentially forbiddened for the case of antisymmetric fluctuations, and so they tend to be treated as forbidden in most amorphous semiconductors. This situation is reversed in a-C :It where the clusters create strong symmetric fluctuations, Fig 71(a). LL transitions can now occur between the initial and final states localized in the same cluster. These transitions have a large matrix element and are now strongly allowed. Indeed, the cluster model suggests that optical absorption in a-C:H is due to LL transitions up to well above E04. The consequences of symmetric fluctuations has rarely been studied so the size of the fluctuations in a-C:H makes this an interesting system in this respect. It is interesting that despite the different origins and length scales of the disorder that a-Si:H and a-C:H should each have rather similar optical absorption edges, each displaying a Tauc region and an exponential (Urbach) tail (Fig. 41). Abe and Tozoyawa (211) investigated formally the effect of disorder on the absorption edge. They used a virtual crystal with Guassian site disorder for both the valence and conduction bands, and allowed the disorder to be correlated (symmetric fluctuations), anticorrelated or uncorrelated between the bands. They calculated the optical absorption spectrum in the coherent potential approximation (CPA) within the one-electron approximation. They found that 0t varied in a Tauc-like and Urbachlike manner over different ranges, for both symmetric and antisymmetric fluctuations. Thus, Tauc-like and Urbach behaviour is a fairly widespread behaviour to find in an absorption edge. They also proved that I.L transitions are forbidden for antisymmetric fluctuations but are allowed for symmetric fluctuations, as deduced above. The Urbach slope E, is a measure of the disorder potential. It is given by the sum of the thermal and effective structural disorder (211-213), E0 ~ - O{D(_?_) + l +2X
}
[4o]
where ® is the Debye temperature, D is the Debye function, and X is the mean square value of the structural disorder. Abe and Toyozawa (211) found that the Tauc and Urbach regions each came to a 'focus' about the zero disorder band gap energy. The Urbach focus is a typical feature of the absorption edge ofa-Si:H (212). Cody et al (212,213) studied the variation of Urbaeh slope F~ as a function of measurement temperature and thermal annealling. They found that F~ varied with Tauc gap ET as ET = Bro - CE 0
[41]
whether the changes were due to measurement temperature or to structural disorder (hydrogen loss during annealing). This confirms the equivalence of structural and thermal disorder in the definition of E0 {40}. ET0 would correspond to the zero disordered gap in this model. Datta et al (191) found that the optical edge ofa-C :H also displayed an Urbach focus, They also found a linear variation of E0 with Er, as shown in Fig. 72 Their data was restricted to changes due to the annealing in a wide band gap variety of a-C:H. It is interesting that their Urbach focus was found to be 5.6 eV, close to 2fl, the gap of a single benzene ring and perhaps
Diamond-LikeCarbons
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I
0
1
Vb I
1 2 OPTICAL GAP, eV
3
Dependence of Urbach tail slope E0 on optical gap E~ for a-C:H, as a function of annealling temperature T, for films deposited at low bias (191), and as a function of bias voltage Vb for films deposited at nominally 25°C (158).
the gap of a zero disordered rt band. value.
ttowever, they also found Er0 = 3.5 eV, a much lower
It is possible that a wider range of behaviours may occur in a-C :H. The gap of a-C:It can be varied between 0.5 and 3.0 eV by changing the bias voltage during plasma deposition (9). In this case, using data from Dischler (158), Fig. 72 also shows that E0 tends to vary linearly with E~ as a function of bias, in a very different manner to the thermally-induced changes. This may indicate that two types of disorder occur in a-C:H, with the gross changes in cluster size and band gap caused by bias voltage being analogous to alloying rather than to changing structural disorder.
6.3 Electrical Conductivity The existance of a range of defect centers means that the electronic density of states in the
294
J. Robertson
mobility gap ofa-C(:H) consists of a featureless spectrum, as in Fig. 68. The Fermi level EF lies near midgap in a-C and undoped a-C:H. There are three conduction mechanisms in a-C(:H); hopping between states near EF, thermal activation to a higher density of localized states near a mobility edge, and thermal activation and conduction in extended states above a mobility edge (206). The mechanisms of conductivity a can be distinguished from their temperature dependence which can be expressed in the general form = o 0 exp( - (Tn/T) n)
o
[42]
A regime with n-- 1 indicates thermally activated conduction in states kT, away from EF, where k is Boltzmann's constant. Conduction is in extended states if the prefactor a0 > i0 s ~-~cm-' and in localized states if 00 < 103~-'cm-L If n < 1, this suggests that conduction occurs by
' 10-4
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I
I
~
I
2.5 3.0 IO001T ( K-I)
i
,I 3.5
Temperature dependence of the conductivity of a-C:H, deposited at various temperatures, after Meyerson and Smith (216).
Diamond-Like Carbons
295
variable range hopping in localzied states near Er. n = I/4 is the classic power law for variable range hopping, while n > 1/4 can indicate either a rapidly changing DOS near EF. For n = 1/4,
T4-
16a 3 kN(Er0
[43]
where ~-~ is the decay length o f the localized state (206). For thin films, the hopping distance can exceed the film thickness d, and give a n = I/3 regime, with
T3 -
8a 2 kdN(EF )
[44]
It is conventional to estimate N(EF) from [43] using a-~ = lOAngstroms if only an n = 1/4 regime exists. However, i r a transition from n = 1/4 to n = I/3 can be found with decreasing d, both and N(EF) can be found, tlauser (157) used this method for sputtered a-C to find -1
c~
= 12A
and N(Ev) = 10 is e V - l c m -3 consistent with a defect density of---10r"cm-3 over a mobility gap o f 0.8 eV. Shimakawa (214) noted that the conductivity o f a-C also fitted the relation o = o0(T,/T)" with n = ! 5-17, consistent with a multi-phonon mechanism. A-C:H conducts mainly by hopping in localized states (215-218,142). Fig. 73 shows the conductivity o f PD a-C:H of various deposition temperatures (216). The conductivity does not follow a single power law. It has a simple activated form at high temperatures with n = 1, and the low value o f a0 indicates that conduction occurs by hopping in a band tail. At lower temperatures, conductivity is by hopping near EF, which is confirmed by the low value of the thermopower. The decay length of the defect states in a-C:I| is expected to be much shorter in a-C:H than in a-C because o f the effects o f clustering (Fig. 70). The sp 3 regions are a strong tunnel barrier and cause cc-I < 3A , much lower than is used in a-Si or a-C. This lower value gives an acceptable values of N(E~-) when used with {43} for the low temperature regime (210).
6.4 Doping The Fermi level of an amorphous semiconductor tends to lie near midgap in a low density o f states, giving a low conductivity. E~ o f c-Si can be moved towards a band edge by substitutionally doping with an element of group III or V. Spear and LeComber (219) found that PD a-Si:H could be substitutionally doped by boron and phosphorus by adding diborane or phosphine to the gas stream entering the plasma reactor. Meyerson and Smith (218) discovered that a-C:H could be doped in a similar manner by B~H~ or PH3. Fig. 74 shows typical changes in the electrical conductivity for 1% diborane, phosphine and nitrogen gas doping ratios for a-C:H deposited at 250C from Jones and Stewart (217). Fig. 75 shows typical changes in the activation energy o f conduction at room temperature and compares them with the anal-
296
J. Robertson
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Conductivity ofundoped and doped a-C:H, after Jones and Stewart (217)
ogous changes found for a-Si:H by Spear and LeComber (219). It is clear that a substantial change in conductivity has occured, increasing the room temperature conductivity art from l0 -t2 ~-tcm-I to 10-7 ~--Icm -l for a gas phase doping ratio of 10%. However, it is also clear from Fig. 75 that the doping efficiency is lower than in a-Si:H. A greater doping ratio is needed to produce a large reduction in the activation energy and the conductivity can only be reduced to 10-7 f~-' rather than 10-2 £'-~-Icm-t as in a-Si :H. Meyerson and Smith (218) confirmed that the conductivity changes corresponded to substitutional doping by observing the necessary changes in the sign of the carrier, via the thermopower. There are a number of interesting features of substitutional doping in a-C:H and a-Si:H. Firstly, an element from group V dopes crystalline Si because it is forced to enter a 4-fold coordinated site but only uses four of its valence electrons to form bonds to the neighboring silicons, leaving a free electron (Fig. 76). This free electron lies in a donor level close to the conduction band in
Diamond-Like Carbons
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I 10- 2
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Variation of activation energy of conduction vs. doping ratio for a-C:H (218) and a-Si:H (219).
c-Si which forces EF tO lie there. The absence of periodicity in a-Si means that a group III or V element need no longer enter a 4-fold site, but can instead enter a chemically prefered 3-fold coordinated site in which all the valence states will be filled, so there will be no free carriers. The five phosphorus electrons lie in three bonding states and an s-like lone pair (220), Fig 76. Doping occurs in a-Si:H because a small fraction of dopant atoms enter 4-fold sites, from where they donate carriers. It turns out that these sites have only slightly higher energy than the 3-fold sites, and the doping fraction is found to obey the law of mass action and MaxwellBoltzmann statistics (64). The second factor reducing the efficiency of doping in a-Si is the density of gap states. Doping can only shift EF above midgap by filling up the gap states through which it shifts (Fig. 77). E~ will only shift far if the dopant density exceeds the density of gap states. The passivation of most gap states by hydrogen was therefore an important requirement for the observation of doping in a-Si:H. The gap state DOS is higher in a-C:H (section 6.5) and this is probably the major factor which reduces its doping efficiency. It is interesting that it is possible to dope a-C:H despite its high content of3-fold C sites. There is no forcing of atoms into 3-fold sites, This is further support for the idea that the type of
298
J. Robert.son
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Bonding and electronic configurations at a 4-fold coordinated P site in Si and a 3-fold-coordinated P site in Si. Subscripts denote coordinations.
bonding in a-C is determined by relative site energies and a degree of equilibrium, rather than by strong thermal quenching. It is also possible to dope a-C:H n-type with nitrogen (217). This contrasts with diamond where N forms a deep distorted substitutional level 1.4 eV below Ec. It is possible that 4-fold N sites can dope a-C:tt because their donor level is now above E~ due to the smaller gap of a-C :H. The doping efficiency of N in a-C:l I is low, and there are suggestions that a true substitutional mechanism is not involved (217). It is noted that higher N contents promote sp 2 coordination of carbon (221), so that a-C, xNx alloys become primarily 3-fold coordinated at both sites at high x, and no ordered composition is found at CsN,. Clearly, increased sp~ C bonding will narrow the gap at low x and also increase the conductivity, which could be confused with doping.
Diamond-Like Carbons
299
\
t0 22
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Density o f states near the Fermi level in (a) undoped a-C:tl, (b) n-type a-C:H
6.5 Defect Densities The defect density in a a bonded amorphous solid tends to indicate its degree o f disorder. This in turn depends on the lack of equilibrium during the deposition process and the degree o f any subsequent annealling, lligh defect densities arise from low deposition temperatures, rapid deposition rates or strong ion bombardment. Low defect densities can reflect a gentler growth process or some annealling o f damage. Defect densities of order 10~ cm 4 are typical o f evaporated or sputtered a-Si, and these can be reduced to 10 '9 cm -3 by thermal annealling. Much lower densities such as 10 '6 cm -3 can be achieved in PD a-Si:H, due to passivation o f dangling bonds by hydrogen (64). This line o f argument must be used with care for amorphous carbons where the defects are probably multi-site entities. If the electron correlation energy. (U) is positive, defects are
300
J. Robertson
~,Eo1020
1018 c
\
lo16 0
Fig. 78.
I 500 Bias voltage, V
! 1000
i 200 250 Deposition
i 300
I 350
Temperature, °C
(a) Spin density N, vs. bias voltage for PD a-C:It (224,228,134). Dashed line is the defect density from the weak bond dangling bnod conversion model, eqn {48}. (b) Spin density N, vs. deposition temperature for PD a-C:H deposited at low bias voltage (226).
normally in their paramagnetic (singly occupied) state. Defect densities can then be measured directly by electron spin resonance (ESR). Orzeszko et al (222) found a spin density of about 10~Scm-3 in evaporated a-C which was relatively independent of annealling temperature. A similar value was deduce for sputtered a-C from conductivity data by Hauser (157), as discussed above. Wada et al (128) found 2.1019cm -3 spins in sputtered a-C. A much larger density of 2.102°cm-3 was found in the sputtered a-C of Pan et ai (76), deposited at 77K. The defect densities in a-C:H can be much higher than in PD a-Si:H, tligh values of spin density have been found in reactively sputtered a-C and a-C:H (223) Spin densities ranging from 10'~ to 102' cm --3 have been measured in PD a-C:H, depending on deposition conditions (224-229,134). The data of Reyes-Mena et al (224), Tamor et al (134), Fabisiak et al (228) and Watanabe et al (226) suggest that the spin density N, passes through a maximum as a function of bias voltage for PD a-C:H, as shown in Fig. 78(a). The defect density is low in soft a-C:tt prepared at low bias, presumably because possible defect states are passivated by hydrogen. In a-C:H prepared at ihgh bias, the defect density again becomes low perhaps because of the effects of delocalization in the increasingly graphitic material. Thermal annealling generally increases the density of gap states in a-C:H. This occurs because of the loss of hydrogen, the increase in sp 2 fraction, the narrowing of the band gap and the broadening of the band tails, noted in section 5.2. The spin density of a-C:H of large band gap deposited at low bias is seen to increase with thermal anneaUing above 300C (224-226), and then to decline above 600C, as shown in Fig. 78(b). Note that a different behaviour is found in a-Si:H, because of the absence of sp 2 sites. There thermal annealing up to 300C decreases defect densities and only higher temperature anneals cause an increase in defect density. Singly occupied defect levels can be characterised by electron spin resonance.
Miller and
Diamond-Like Carbons
301
McKenzie (225) and Watanabe and Okumura (227), resolved two different spin signals in a-C:H, a narrow line at g--- 2.003 and a wider line at g= 2.011. Ehrhardt et al (229) resolved a number of lines in their a-C:H, which they attributed to n bonded clusters of different size (230). They found that small defect clusters predominated for films deposited at low ion energy and larger clusters at higher ion energy, in agreement with our cluster model. Structural defects can give rise to electronic states deep within the band gap. In a-Si, dangling bonds give rise to localized defect states near midgap. Transitions from these states to extended conduction band states cause a subgap optical absorption which is seen as an excess absorption above the Urbach tail (231). The excess absorption is found to be proportional to the dangling bond density as measured by electron spin resonance. In amorphous carbons, rc defects are the predominant defects because of their lower creation energies (152). In the graphitic cluster model, any cluster which gives a state at midgap, including all clusters with an odd number of sites, can be defined as a defect configuration. Fig. 79 compares the optical absorption spectra
106
I
I
I
I
l
105
104 "7
a-C:H
103 a-Si:H
/
102
//defects/ 10
I
0
I
1.0
I
2.0 Energy (eV)
Fig. 79.
Optical absorption spectrum ofa-C:H compared to a-Si:H (158,224).
3.0
J. Robertson
302
of a-Si:H with about 10's cm-~ defects (231) to that of a-C:H with a similar spin density (158). No excess absorption is apparent above the a-C:H tail before the C-H stretch band intervenes at 0.4 eV. The absence of defect absorption in a-C:H, first noticed by DasGupta et al (223) in samples of a higher spin density, suggests that the defect excitations have shifted to higher energy. This is also evidence for the cluster model. As defects are relatively rare, on average, band edge states tend to lie on non-defect clusters. Transitions from a defect level to these states on other clusters have low matrix elements and the main transitions from a defect level are to higher levels in the same cluster. Thus, transitions from midgap defect levels will tend to lie well above l/2Eopt and so they will not create subgap absorption.
i
I
~
I
'
I
'
Td(C) @mmm
200.~.~
\
t-
@ m
U ¢-
2
U C/} r-
E
300
1.2
1.6
2.0
Energy(eV) Fig. 80.
Typical luminescence spectra ofa-C:H of various gaps (226)
Diamond-Like Carbons
303
6.6 Luminescence
Optical excitation creates an electron hole pair. These carriers can recombine non-radiatively with the release of heat (phonons) or radiatively with the release of light (luminescence). The process is geminate if the original electron-hole pair recombines and non-geminate if electron and hole recombine after mixing. The various processes occuring in luminescence and recombination have been discussed in detail by Street (64). Non-radiative recombination is favoured by the presence of high defect densities so luminescence has only been found to date in a-C:H (226,232-239). The luminescence spectra depend mainly on the band gap, the defect density, the excitation energy and the temperature. Fig. 80 shows the luminescence spectra of a-C:H samples of different band gaps (233). It is interesting that the peak of the luminescence spectra in the sample of lower gap occurs above its Tauc gap (but still below its E~ gap). The variation of peak luminescence is plotted versus Tauc gap in Fig. 81 for a-C:H from various workers (226,233,238). The luminescence peak is seen to increase only slowly with gap. The luminescence efficiency is high in a-C:H, particularly in samples with a wide gap. Indeed, luminescence can sometimes obscure Raman spectra measurements. The luminescence efficiency is also relatively independent of temperature (234,236), whereas it declines strongly with temperature in a-Si:H (64). Many of these features of luminescence are evidence in favour of the cluster model. We noted earlier that the optical absorption edge originates from states which are strongly localized within
3
!
I
I
I
'
I
I
2-
i
O IJ.I
1
"0
i
0
Fig. 81. dPSgC 2 1 : 4 - X
I
1
,
i
i
2 OPTICAL GAP, eV
I
3
Variation of peak luminesence energy vs. optical gap for a-C :H (226,233,238).
4
304
J. Robertson
1.0
..I ~D % m
m
E L_
0
Z
0 1.6
2.0
2.4
2.8
Photon Energy (eV) Fig. 82.
Luminesence spectra vs. excitation energy for wide gap a-C:H (238). (E,,= 3.5 eV).
clusters. Optical excitation in the region of the edge will create electron hole pairs localized in the same cluster. They will be trapped in the cluster by the surrounding tunnel barrier and so will tend to recombine radiatively. This will produce a luminescence which is relatively independent of temperature and electric fields, as observed (235-238). A temperature dependence generally arises when the electron and hole can hop apart by thermal activation, find some defect center and recombine non-radiatively, as occurs in a-Si:H (64). Fig. 82 shows the luminmescence spectra of a wide gap a-C :I4 (E04= 3,5 eV) as a function of the excitation energy (238). Generally, luminescence is not expected above the excitation energy Eex, shown arrowed in each spectrum. However, closer inspection shows that their is a finite emission above Ee~ in each spectrum. Volkov et al (238) attribute this to a further thermal excitation of the electron or hole while it is trapped in the cluster. They found this so-called Anti-Stokes luminescence to be strong evidence of the presence of clusters, although further details of the mechanism must still be worked out.
6.7 Defect Equilibria The role of hydrogen in a-Si:H is often said to be that of reducing defect densities by passivating dangling bonds, converting them to Si-ll bonds (64). In fact there is a great excess of H in a-Si:H (197). However, even the best a-Si:H still has a defect density ofover 101Scm-3. It is now
Diamond-Like Carbons
305
realised that the defect density in a-Si:H is largely controlled by metastable equilibrium process, which are mediated by the local motion of atomic hydrogen (240-242). In more detail, many workers have noted that an interconversion between weak bonds and dangling bonds can occur. -Si-Si----
~
-Si
+
=Si
[45]
The barrier to interconversion can be lowered by the motion of atomic hydrogen. Although the most stable location of hydrogen is at a Si-H bond, it is also relatively mobile. It moves via interstitial sites such as the bond center site, as also occurs in crystalline Si (202,203). A hydrogen at a weak bond center site is actually more stable than at a normal Si-Si bond (241). This is because the H induces an opening of a weak Si-Si bond towards the configuration of a dangling bond and a Si-tI bond. ---Si-H-Si=-
~
=Si-H
+ .Si-
[46]
In this way, it is possible for the majority of Si-Si bonds to be rigid and to define a random network, while a minority of weak bonds may interconvert with dangling bonds, via the mediation of hydrogen. The hydrogen evolution spectra of a-Si:H verify that atomic H is the dominant transport mode of H in a-Si:Iq (197). It is suggested that the weak bonds form the tail states in a-Si:H, particularly the valence tail, the wider of the two tails (243). Thus, the density of weak bonds with energy E can be written as
N(E) = N Oexp(-E/E0)
[47]
where E0 is the slope of the valence band tail, which equals the slope of the Urbach tail for the case when it is the broader tail. No is the density of states at the top of the tail. The bond strength is proportional to the bonding-antibonding splitting, so the weakest bonds lie at the base of the tail. Stutzmann (244) proposed that all states lying closer to midgap than A are so weak that they would spontaneously convert into d.angling bonds according to reaction [45], thereby releasing an energy A. Treating reaction [45] as an equilibrium and applying the law of mass action, we find that the density of dangling bonds is given by N s = N0E 0 exp( - (Eg/2 - A)/E0)
[48]
A is treated as an adjustable parameter. This weak bond dangling bond conversion model is found to describe the defect density in undoped a-Si:H under a wide range of conditions (244), and also in Si-rich a-SiN~ and a-SiC~ alloys (245-247). This model might be expected to apply to the n defects of a-C:tt, after re-identifying tail states as 'weak clusters' and defect states as defect clusters, llowever, the defect density in a-C:H does not follow eqn [48]. The gap and the Urbach slope decline with increasing bias, so N, should increase monotonically with bias, rather than pass through a maximum as it does in Fig. 78(a). This failure suggests that either the interconversion of tail states and defects is hindered or that their energetics do not follow the equations. Interconversion might be hindered as the reaction now involves multisite clusters rather than single a bonds. However, in principle a tail cluster can become a defect cluster just by changing the number of its sites by one, eg. by the hydrogenation of one of its sp ~ sites or dehydrogenation of an adjacent sp 3 site. The energetics of the model are sound, as they are based on quite general quantum chemical principles, that deeper tail states are more weakly bound and that defect states have even lower stability. The
306
J. Robertson
problem may lie in the multivaluedness of defect and tail state energies (Fig 69), which does not arise for the simpler case of a bond defects, and which would require a more complex analysis than eqns {47,48}. 7 DEPOSITION MECHANISMS 7.1 Plasma Deposition, Case of a-Si
:H It is likely that a range of deposition mechanisms are involved in the production of hard a-C(:H) films in view of the range of processes used. The processes involve aspects of radiation effects, ion-beam modification of materials, and plasma chemistry. We will consider the deposition mechanism of PD a-C:tt, ion-beam a-C and sputtered a-C in detail.: We shall first consider PD a-C:H by using PD a-Si:H as a guide, as this system is now reasonably well understood. It was noted earlier in Table 3 that the process parameters for the deposition of high quality a-Si:H from a silane plasma (low RF power, moderate silane pressure, no ion bombardment, moderate substrate temperature) differ considerably from those used to obtain hard a-C:H from a hydrocarbon plasma (high RF power, lower gas pressure, high ion bombardment, low substrate temperature). In general terms, Tsai et al (248) noted that high quality a-Si:H was deposited under conditions described as chemical vapour deposition (CVD) in which there was conformal surface coverage of slots and steps, rather than under physical vapour deposition (PVD) conditions in which only surfaces in direct line of sight of the source
multipole,
ECR
- - - - > DC or RF discharges
Ar or He d i l u t i o n , d - - - pure S i l l 4 100
. . . . . . . . . . . . . . . . .
•
~_SiH
2
,
. . . . . . . .
H
,
, .
.... + ~ ~iN 3 ~
. . . . . .
.:
1
I
~ "
SJH n m
! , I
= 4
c
1
S| H +
I
~
n m •
0"4
"Fig. 83.
,
•
.=,,i
,
•
•
,
,
==,1
ii " ~ ,
1 0 .3 1 0 "= silane pressure
,
,
.
..=.11
|,
,
•
1 0 "1 (Torr)
Ion to Radical flux ratio in a low power silane plasma (250)
•
,
=.=
10°
Diamond-Like Carbons
307
are covered. CVD conditions arise when the main growth species has multiple surface reflections or high surface mobility, and is relatively weakly bound, In the plasma, electron collisions cause the dissociation of silane molecules (249-256). dominant channels just above the ionisation threshold of silane produce the radicals
The
Sill4 --* SiH~'+ H
1,49]
Sitt4 ~ S i l l 2 + 2 H
1,50]
However, the lowest enthalpy channel Sill 4 ~ S i l l 2 + H a"
[51]
is forbidden because it is a non-vertical transition (250). At lower gas pressures, ions are dominant
1-52]
Sill 4 ~ Sill3 + + 1-1 + eThe ion to radical flux ratio is shown as a function of silane pressure (250) in Fig 83.
The interaction of an incident species with a surface can be defined in terms of r, the reflection coefficient, B the surface reaction probability, s the fraction permanently absorbed (the sticking coefficient) and y the fraction which reacts to form a volatile product (253), Fig. 84. // = l - r
= s+~
1-53]
Incident flux nation (7)
Surface Diffusion
('
Deposition (s) Fig. 84.
Reactions of impinging ions with a surface (253)
308
J. Robertson
with 0 >/~ > 1. The CVD regime corresponds to low values o f p as this allows multiple surface reflections. High quality a-Si:H is formed when Sill3 is the main growth species (250,256). The coefficients for a-Si:H are defined by the fact that the growing surface of a-Si:H is almost fully hydrogenated. Sill and Sills radicals have two or more dangling bonds and can easily insert into a Si-H surface bond, resulting in a low surface mobility,/~-~1, and a low quality (rough, porous) film. In contrast, Sill3 does not insert into a Si-tt bond. It can only physisorb onto Si-H surface bonds as a 3-center bond = Si - H + SiH~ --, - Si.tI.SiH 3
[54]
and diffuse along the surface until it chemisorbs onto a dangling bond = S i + Sill 3 ~
=Si-Silt 3
[55]
or until it recombines to form silane by 1t abstraction -Si-H
+ SiI-I3 -
- - - S i + Sill 4
[56]
This gives a low value of p-0.26 and of s"~0.08 (249). (Atomic H can also cause H abstraction, but atomic H concentrations are relatively low in plasmas for a-Si:H or hard a-C:H growth.) The growth of a-Si:H therefore requires two Sill3 radicals, one to create the dangling bond by H abstraction (257) and the second to chemisorb into the growing film. Note that a closed shell molecule such as silane only physisorbs weakly onto a hydrogenated surface with s~10 -4, while all incident ions with moderate energy will bury themselves and have p = s = 1. In the subsurface region, the highly hydrogenated surface layers must be converted into a-Si:H by hydrogen elimination (249,258). The hydrogen content of a-Si:tt falls with increasing temperature with an apparent activation energy of 0.05-0.1 eV. Hydrogen dilution of a silane plasma tends to produce microcrystalline Si (/~c-Si). The tt atoms are believed to luther hydrogenate the surface and induce a higher surface mobility in Sill3 radicals so that they search out only the most stable sites - those leading to epitaxial growth (255,256). Atomic H is also a key factor in the growth of uc diamond from hydrocarbon plasmas (1-3). This suggests that atomic tt has a number of effects in diamond growth. 7.2 Plasma Deposition of a-C:H
We now consider the growth of a-C:H from methane plasmas. The behaviour of methane and methane/H2 plasmas has been closely studied from the point of view of CVD diamond growth (259,260), but less so for the conditions which give rise to a-C:H growth (261-264). Two additional features must be considered compared to silane plasmas. Firstly, there are many more potential growth species due to carbon's multiple hybridisation. Also, the large bias voltages allow neutrals - radicals and undissociated molecules - to acquire energy by collisional exchange in the plasma, which will increase their sticking coefficients (63). The dominant dissociation channels for a methane plasma produce radicals like CH3 and CH2, ions like CI-t3+ and Ctts ~, and molecules like C~H~ (259-263). The growing surface of a-C:H is also highly hydrogenated. The sticking and p coefficients of the species can be estimated in terms of their unsatisfied valences using silane plasma species as a guide (Table 14). Note that
Diamond-Like Carbons
309
Table 14. Estimated surface reaction probabilties p and sticking coefficients s for PD a-C:H growth species.
Ctt3
0.1
0.3
CI-t~
1
1
CH]
1
I
C[t~
I
1
C~H~
I
1
unsaturated molecules like acetylene can insert directly into C-H bonds. Apart from methane itself, acetylene, CH3 and CH~ are believed to be the main species of interest in the methane plasmas, so this would suggest that these are also the main growth species. Methane molecules are unlikely to contribute much to growth, unless they have acquired kinetic energy, as they have a low sticking coefficient. Indeed, Vandentop et al (265,266) found by mass spectrometry that methyl radicals were the dominant growth species of a-C:H. The general relevance of the weak sticking model to PD a-C :H growth is the observation that the growth rate declines as the temperature increases (50,267). This is ascribed to the thermal activation of either y or of the tI abstraction reaction (253). Strong sticking is likely to give a constant deposition rate. Interestingly, the growth rate of a-Si:tt (in the low power regime though) is temperature independent (253). Ions are likely to become more important growth species in lower pressure plasmas (250). However, Zhang and Catherine (268) found little change in the degree of ionisation at lower pressures. Note that the ion/neutral flux ratio used to compare different sources should exclude closed shell species like methane or Ar, unless they are energetic, as these closed shell molecules have minimal interaction with the surface. We noted earlier that the role of hydrogen in a-C:H was to promote sp3 bonding, but that too high a H content produces many = CIt2 groups and a poorly cross-linked network. The role of ion bombardment in PD a-C:H is to dehydrogenate the subsurface zone and produce this cross-linked network. In a-Si:tl dehydrogenation occurs by H elimination between Si sites on neighboring chains, =Si-H
+ H-Si-=
~
----Si-Si= + I-I2
-5kcals
[57]
This reaction is exothermic (154) so that the equilibrium concentration of Si-It bonds at say 500 °C would be only 10-2. It is only necessary to thermally activate H elimination in a-Si'H to promote this reaction. In contrast, the reaction =(7-tt
+ It-C=
~
-=C-C=+[12
12kcal
[58]
is endothermic, so the equilibrium concentration of C-H bonds in a-C:H would be high. A second H elimination channel exists in a-C:H, in which II atoms leave adjacent sites and produce sp2 sites rather than network cross-linking, =CH-CIt=
~
=C=C=
+ II 2
29kcals
[59]
310
J. Robertson
Although this reaction is endothermic, it has a low activation energy. It is therefore undesireable to use heat to eliminate H from a-C:H to produce a highly cross-linked network. On the other hand ion bombardment will dehydrogenate a-C:H by the preferentially sputtering of hydrogen (268-271). This occurs becuase H is lighter and more weakly bound than C. The radiation studies of Kalish et al (204,205) suggest that the primary effect of ionbombardment on a-C:H is dehydrogenation. This may account for why some studies find that the mean energy deposition rate rather than the mean ion voltage can sometimes control the properties of a-C:H (264,265,272) 7.3 Ion-Solid Interactions We now consider ion-matter interactions in more detail. The stopping power (energy loss per
,~
I02
I Q .J W~
WO
i0 -z
13. (I')
f
102 -I 1,1 >I,Z i,i
=E hi
e,
"
I
I0
Fig. 85.
I02
ENERGY(eV)
103
I04
Sputter yield, displacement yield, and range for C ~ ions in a-C, vs. ion energy (272).
Diamond-LikeCarbons
311
unit path length) equals the product of the atomic cross section and the atomic density of the target (204). The stopping power for a medium energy ion ( < 10 keV) is primarily nuclear, due to interactions with the nuclei rather than the electrons in the target. The overall interaction can be characterised by the ion range, the displacement yield (the number of permanent vacancy-interstitial pairs of the target created per incident ion) and the sputter yield (the number of target atoms emitted from the target surface per incident ion). These parameters can be calculated for an incident C + ion for a-C by the TRIM code, as a function of ion energy (272), as shown in Fig. 85. TRIM assumes an isotropic target of density (set to 2 gm.cm-3) and a displacement threshold of 25 eV, as discussed later. We see that 100 V C + ions have a range of about 7A in a-C, while 1 kV ions have a range of about 30A. As nuclear stopping power dominates at the low ion energies of interest, < 10 kV, the much lower mass of hydrogen means that incident H ~ ions have much less effect than C* ions of similar energy. Also, the lower mass of It and its lower displacement threshold (about the C-It bond strength 4 eV) means that H atoms are much more easily displaced or sputtered than C atoms in a-C:H. This accounts for the preferential sputtering of II by impinging ions. Impingement of muiticenter ions of moderate energy results in their complete dissociation at the surface, with the energy partitioned in proportion to their mass. Acetylene and benzene plasmas are frequently used for a-C :H deposition. The key differences to methane are the different C/t I ratio in the source gases and the great stability of the benzene molecule. Acetylene itself is likely to be a main growth species in its plasmas, with the ions C2I{ + and Ctt ~ being the important ions. Interestingly, the properties of a-C:H deposited from acetylene are relatively similar to those from methane (60,61), suggesting some similarities in their plasmas. In contrast, a-C:H films deposited from benzene are very different overall from those depositied from methane or acetylene, as seen in Figs. 54,56. Wagner et ai (187) studied growth species in benzene plasmas by optical emission spectroscopy. They noted that the CH radical was the dominant species in benzene and methane plasmas for bias voltages of 400 V and above. ttowever, optical emission spectra are misleading in this respect as CIt is a very emissive species while many others do not emit. I.arger radicals and ions may still be dominant growth species at the film surface. This leads to a preponderance of undissociated phenyl groups in films deposited at low bias voltages (147). For higher bias, these species dissociate on striking the surface, with the energy partitioned between each daugther species (272). Thus a C ion will have only 1/6 of the energy of an incident phenyl ion. If this full dissociation occurs mainly at the film surface rather than in the plasma itself, this may explain why the maximum density and hardness of such a-C:H occurs at much higher biases than for a-C:H derived from methane or acetylene. The photoemission spectra of IB a-C:H for a stryene precursor (173) give further strong evidence of the difficulty of dissociating some molecules by impact even at moderate ion energies, Fig. 59. 7.4 Ion Beam Deposition
Different deposition mechanisms must be responsible for the promotion of sp s bonding in unhydrogenated a-C films. Four mechanisms have been proposed for this case, preferential sputtering (11), thermal spike (30), preferential displacement (48,13,272,273) and ion-peening mechanisms (39,40,274). Spencer et al (11) suggested that the sp2 sites had a higher sputtering yield than sp s sites, and this would eventually lead to an increased sp s content. Lifshitz et al
312
J. Robertson
lO
Gra .0
0.1
0.01
I 10
Fig. 86.
I
I 100
I
I
Energy,
eV
I 1000
I
Displacement yield vs. C ~ ion energy for sp 2 and sp 3 sites when the have displacement thresholds of 25 eV and 80 eV respectively (272,13).
(48,273) noted that the sputtering yield of any carbon site is very low, because of its high cohesive energy, so that this mechanism is unlikely. Weissmantei (30) proosed the thermal spike mechanism, that a phase change to sp 3 bonding occured in the pressure front ahead of an incident ion. Lifshitz (48), Moller (273) and others have noted that the ion energies of relevance are quite low, with a relatively low displacement yield, so that the concept of thermal spike is not really relevant. Thermal spikes apply to ion energies above 100 kV where incident ions cause great ion displacement and energy transfer, l.ifshitz et al (48,272) instead proposed that sp3 bonding was promoted by the preferential displacement of sp~ sites. I.ifshitz (48) noted that the quoted displacement yield of sp2 sites in graphite (25-30 eV) was much lower than that for sp3 sites in diamond (275,276). The difference might arise from the lower density and more free space in graphite or sp~ bonded carbon and would therefore carry over into the amorphous phase. The difference causes the displacement yield to be 20 times greater for sp 2 sites than sp3 sites for 100 eV C* ions and about 3 times higher for 1000 eV ions (48), Fig. 86. If, after displacement, the ions settle back into sp3 and sp 2 sites with similar probability, sp 3 sites would tend to be dominant, particularly for ion deposition in the range 100-200 eV which is observed
Diamond-LikeCarbons
313
to be the range which gives the highest density for MSIB a-C according to Ishikawa (47) and Hirovinen et al (45), Fig 65. However, recent analysis (277) suggests that the displacement threshold of diamond is much lower than 80 eV, and closer to the 30 eV value of graphite (the threshold for graphite is well defined from nuclear reactor physics). There would then be little difference in the displacement rates for sp2 and sp 3 sites. McKenzie (39,40) proposed that sp 3 bonding was promoted by an ion peening mechanism. In this, impinging ions cause a build up of compressive stress in the film which moves its conditions into the thermodynamic stability region of diamond, which is only 0.04 eV higher at NTP. This mechanism was supported by the observation that the s ~ content of his MSIB a-C films correlated with this internal stress (40). This mechanism is the ion-peening mechanism proposed by Thornton (278) and analysed in more detail by Windischmann (279,280). Ion peening results from the momentum from the incident ions displacing target atoms which tend to become quenched in position. Windischmann (279,280) noted that the peening effects correlated with the momentum rather than the energy of the incident ion. The ideas are often used in the field of ion-beam modification of materials where it is noted that ion bombardment improves the compaction of deposited films (281). The density and compaction of such films improves when the internal stress is found to change from tensile to compressive (280). Kaukonen and Nieminen (274) have recent carried out a molecular dynamics simulation of this process. They observed the displacemnt and quenching-in of atoms in the interstital positions. They noted that the quenching process set an upper limit to the ion energy and was favoured by a high local thermal conductivity. They observed that the optimum ion energy for promoting sp 3 bonding was about 50 eV, closer to that found experimentally by McKenzie et al (40), as seen in Fig. 66. The work of Cuomo et al (28) is not really consistent with the ion-peening model. They observed that a high fraction of sp 3 sites could be produced for mean ion energies of order 7 eV, provided that the deposition occured onto a substrate of high thermal conductivity. Although the ion energies in this case were low, the ion flux ratio was still very high in this case. There is no adequate theory to the author's knowledge for such low ion energies. 8 MECHANICAL PROPERTIES 8.1 Survey The mechanical properties of diamond-like carbon, its elastic modulus, hardness, friction and wear, are of great interest for its use as a coating. Table 15 compares the mechanical properties of various forms of a-C with those of diamond, graphite, Si and polythene. The strength and rigidity of diamond arises from its strong, directional o bonds. The very high bulk modulus derives largely from its short bond length, because the bulk modulus B of covalent solids tend to vary with bond length R as (282) B = Bo R-'~s
[60]
The sp 3 bonds of diamond are also exceptionally resistant to angular distortions; a reasonable measure of this is the ratio of shear to bulk modulus, S/B, which is twice as high in diamond
314
J. Robertson
Table 15. Mechanical properties. Comparsion of Youngs modulus E, Bulk modulus K, Shear modulus G, Poissons ratio v, Hardness II and Yield stressY. E, GPa
K, GPa
G, GPa
v
H, GPa
Y, GParef.
Diamond
1050
442
478
0.104
103
59
16,289-291
PD a-C:tI, 100 V
145
52
24
0.4
16
9.7
296,297
PD a-C:H 1 kV
55
23
31
0.2
6.3
3.1
296,297
sputtered a-C
140
15
MSIB a-C
20-110
27 12-65
38,44
graphite,//a
686
290
glassy C, GC10
29
12.5
0.15
3.0
1.0
293,294
glassy C, GC20
32
13.5
0.17
2.2
0.73
293,294
polythene
,~0. I
Si
130
a-Si:H
100
0.01 97.8
50.9
292
0.278
10.4
5.0
290
0.32
10.0
4.9
298
as in other diamond-structure crystals like Si and Ge, as seen in Table 15. 8.2 Con~raint Model
The mechanical properties of amorphous carbons clearly depend on the strength of their component bonds. Their mechanical properties are inferior to those of diamond because of their finite sp 2 and H content (Table 1). It is possible to give a firmer theoretical model of these properties, starting with elasticity, the most tractable. The elasticity of amorphous carbons can be related the elasticity of the individual bonds and the connectivity or coordination of the network using the constraint counting model of Phillips (283) and Thorpe (284,285). The energetics of a covalent network can be represented by a valence force field of first neighbour bond stretching and bond bending forces as in eqn {8}. When the mean coordination r is low, there are many ways in which the network can be deformed at zero energy cost, ie. leaving bond lengths and bond angles unchanged. The number of these deformations or zero-frequency vibration modes of a network of N atoms is given by the number of degrees of freedom (3N) minus the number of constraints N~o. The number of constraints varies with the coordination, r. There is one constraint associated with each bond (shared between two atoms) and 2r-3 constraints with the angles of each r-coordinated atom, giving a total of (285,286) Neon(r) = T5 r - 3
1,6U
per site, except for monovalent atoms like hydrogen for which Neon (I) = 1/2
162]
The fraction of zero-frequency modes is then given by f = I - (N~o/3N). Writing f = ~gf,x,, we obtain f = Y~r>l Xr(2- --~r)5 = 2 ---~r 5-
1,,63]
Diamond-LikeCarbons
315
where x, is the concentration of r-fold sites and ~ = ~.Xrr is the mean coordination. Eqn [63] shows that a critical coordination or percolation threshold rp exists rp = 2.4
[64]
below which the network can be deformed a zero energy cost and is called underconstrained or 'floppy'. Above rp the network is called overconstrained or 'rigid'. Its modulus then varies as ( - 0 '.s or
E = Eo(
_f
)
i.s
r-2.4
= Eo( 7o-- :a )
~,s
[65]
where Eo is the modulus of the fully coordinated network, r0 = 4 in our case. Angus and Jansen (287) noted that condition [64] for r~ can still be used for a network containing hydrogen if r now represents only the C-C coordination, the skeletal coordination, found by treating each C-H bond as a broken bond contributing no rigidity. This requiries substituting r ~ r - x~.dx, in [61] and x, - x,/(l - x,) in [63] where xt., is the concentration of hydrogen bonded to r-fold sites, to give
5 [(2---E, 5 r)xr + --ff-x,,,]/[I
f =
- x,]
[66]
Indeed, all pendant groups like - C t h contribute no network rigidity. The constraint model must also be modified to take into account n bonding (13,288). A n bond between two sp 2 sites as in ethylene adds torsional rigidity to that bond. It therefore adds a 1/2 constraint per atom, increasing N~o, from 4.5 to 5 for a s p 2 site. Thus a sp ~ C atom is more constrained than a trivalent P atom. The constraint counting model must clearly be modified to treat graphitic bonding (288). Graphite is a slippery solid with no rigidity between its layers, despite it having a coordination of 3, well above the critical minimum value of r, = 2.4. The model fails for graphite because of its anisotropic bonding. It is strongly bonded in two dimensions but has only weak van der Waals bonding between the layers. In terms of constraints, graphite uses all of its constraints in maintaining rigid layers and none in its interlayer bonding. A graphite layer of N' atoms can be treated as an internally rigid disk with 3N'-3 constraints, 3 for each site minus 3 for its translational degrees of freedom. Such an internally rigid graphite layer or graphitic cluster embedded in a network at N " perimeter sites acts like a N"-fold coordinated site. This adds a further (5N"/2 -3) constraints, to give Neon(3 ) = [(JN' - 3 ) + ( @ N" - 3)]
[67]
and
f3
= 1-T
1
Ne°n =
2 N'
5N" 6N'
[68]
N " is typically much less than N'. For a circular cluster N " ~ T t x / - ~ 2 , and typically N" "-'2.5~N7- for a compact cluster, giving 2.1
[693
316
J. Robertmn
This shows that clustering has the effect of raising rp for sp~ sites and making graphite itself borderline floppy. As clusters tend to be large, we take N'--, oo and fa -~ 0
[70-1
giving finally (288) --f~"
x,t -
-
(1 m
Xl ~ f4 =
4
5
.J
U
[71]
("~-X4---ZX1,4)/(I--XI)
where xt.4 is the fraction of hydrogen bonded to 4-fold sites. We thus reach the important conclusion that both graphitic and polymeric bonding tend to reduce rigidity. The lack of rigidity from graphitic bonding can be confirmed by considering the Youngs modulus of glassy carbon (Table 15). Its modulus is seen to be only about 1/20 of that ofthe in-plane modulus of graphite (293). This is consistent with a modulus derived only from the inter-plane cross links, occurring every L,-~20 rings apart, the observed value (9). 8.3 Ela~ic Moduli - Comparison with Experiment
In the 2-phase model, the network of a-C:H consists of sp2 clusters which control the band gap
0.2
O1 C
= 0.1
0 >-
"O
I
O
Z
0 0
Fig. 87.
500 BIAS VOLTAGE, V
1000
Comparison of experimental (298) and calculated normalised Youngs modulus of a-C:H.
Diamond-Like Carbons
317
embedded in the sp 3 phase whose C-C coordination controls the rigidity (288). Fig. 87 shows the Youngs modulus of PD a-C:H deposited from methane by Jiang et al (296,297) compared with that calculated from eqns [65,71] using the coordination data of Tamor (75) for similar films and with E0 taken from diamond. The agreement is seen to be good, considering the approximations made and the remaning uncertainties in the coordination data. The model shows that E is small at low bias because of the predominance of polymeric groups and declines again at high bias because of the increasing sp ~ content. This decline cannot be reproduced unless the sp2 sites form clusters which contribute little rigidity. The effective C-C coordination may be estimated for these films from equation [65], to give r=2.83 for the 100V film and r=2.63 for the I kV film, Table 15. Clearly, these networks have coordinations well below the ideal limit of 4 but well above rp. Angus and Jansen (287) argued that the H content and sp2 content of a-C:H are optimized during deposition to give ?-,,2.4, as this is the coordination at which the energy gain from increased bond density might balance the increase in network strain energy. The above derivation suggests that the coordination of the network must exceed 2.4 otherwise it would have no rigidity (or hardness). Happily, for the sake of forming hard carbons, it does. Nevertheless, the low Youngs modulus of a-C:H compared to that of diamond serves to emphasise that the C-C coordination of PD a-C:lt is still relatively low. The Youngs modulus of magnetron sputtered a-C has been found to be I15-141 GPa (27), Table 15, as high as that of hard PD a-C:H. This material has at most 5% sp3 sites and little hydrogen. Its rigidity must originate largely from its sp2 sites. An isotropically bonded 3-fold coordinated network with 1.42A bond length would have a modulus of 30% ofthat of diamond, 300 GPa, from eqn [65]. The observed maximum modulus is 45% of this. It is likely that the rigidity of the sp 2 network arises from a significant interlayer cross-linking, giving it a limited form of isotropic bonding. Indeed, E does vary with the Raman D intensity and hence with L, (27). A periodic model with cross-linking and a high modulus is the H-6 structure of Tamor and Hess (299). In contrast, it appears that the sp 2 clusters give little rigidity in a-C :tt because they are well separated and cannot crosslink. 8.4 Hardness
Hardness is the key parameter of diamond-like carbons of technological relevance. It is measured by indentation and is the pressure over the permanently indented area at a given applied load. ttardness is a measure of the yield stress, Y, It is related to Y by an equation of the form H/Y = 0.07 + 0.6 In(E/Y)
[72]
for an isotropic solid. This equation is based on an analysis of tile stress field around the indenter tip. The constants in [72] were found by fitting data for a range of materials - metals, polymers and glasses - which cover a wide range of Y/E ratios (300,301). (The measurements for polymers are most relevant for diamond and a-C in that polymers also have a low Y/E ratios). It can be rearranged to give rl/Y -~ - 0 . 0 4 + 0.77 ln(E/tl)
[73]
l i l y ~ 1.8
[74]
or
318
J. Robet'tson
for materials with low Y/E ratios like diamond and a-C :H (note that this is much lower than the typical factor of 3 used for metals). The yield stress of a metal is controlled by dislocation flow, which gives relatively low values of Y/E. In contrast, dislocation motion is much more difficult in covalent materials like diamond, and yield tends to occur by cleavage, giving a high value of Y/E. The existence of dislocations in amorphous solids is contentious. In any case, they are likely to be pinned by the topological and bond length disorder. Hence yield is also expected to occur by cleavage in a-C(:H). The cleavage stress is the stress needed to separate two adjacent planes of atoms of the solid. This in turn can be related to the Youngs modulus by the Orowan approximation of replacing the interplanar force by a sine function and equating E to the initial slope, to give (290) Y-~E/n
[75]
Combining with eqn [74] gives It-~E/6. The values for diamond in Table 13 show that H/E ~ O.I
[76]
is a better approximation (288). Hardness measurements on a-C and a-C:H films must ensure that the indent depth does not exceed 10% of the film thickness and must allow for elastic recovery. The limit on indent depth is necessary because the substrate often has a lower hardness than the film. On the other hand
3
I
I
I
es °
z E
2 / el
Loading ojO
f10
O ..-I
.,I
:""
0 0
Fig. 88.
'
jLD S
S°
/
/--j
Unloading
--r"/,
..sO
hf
/ /
hp 50 100 Displacement [nml
150
Load vs. depth curve for and indentation measurement, illustrating the elastic recovery (298)
Diamond-LikeCarbons
319
if the penetration is too small, some error arises because of deformation of the indenter tip. The problem of elastic recovery is shown in Fig. 88. Hardness is the average pressure under the indenter, given by the applied load divided by the projected area of contact. In conventional microhardness tests, the indent area is measured by imaging after removing the load. However, if there is significant elastic recovery, the area is underestimated and the hardness overestimated (297). The extreme example is rubber which apparently has high hardness because indents in it recover totally. Many early hardness measurements on a-C(:H) suffered from this error, giving values up to 60 GPa for a-C:H. The true hardness is found by estimating the area in the loaded condition from the load vs. indent depth curve, Fig. 88. A tangent is drawn to the unloading curve at maximum load and extrapolated to zero load. Its slope is proportional to the Youngs modulus and it subtends the elastic depth on the displacement axis. The remainder is the plastic depth, h~, needed for hardness. Elastic recovery is significant when Y/E is not small, such as in covalent solids. Corrected hardness values are typically 30% of uncorrected values. Hardness values for diamond, PD a-C:H, sputtered a-C and MSIB a-C are given in "Fable 15. In each case, H is found to scale with Youngs modulus according to eqn [76]. This scaling holds despite the bonding changes occurring in the a-C:H and despite the changes in Poissons ratio. The validity of eqn [76] in a-C(:tt) allows the previous model of E to be extended to cover hardness. The hardness of MS1B a-C has been found to reach values similar to that of diamond (38). As diamond is the hardest solid, this is perhaps the simplest demonstration of the high sp 3 content of MSIB a-C. The hardness of MSIB a-C has also been studied as a function of ion energy. It is found to peak at a similar energy as its density (44).
I
|
I
I
15
Benzene
m a. ~10 oe-
Z
5
Methane~
O,
0
Fig. 89. JPSSC
21:4-I
200
400
600 800 Bias voltage (V)
1000
1200
Hardness vs. bias for PD a-C:H deposited from methane (298) and benzene (9,30)
320
J. R o b e r t s o n
Fig. 89 shows in more detail the variation of hardness with bias for both the methane films of Jiang et al (297,298) and the benzene films of Koidl et al (9). H is very low at V~= 0 V for soft a-C :H. It then increases and passes through a maximum at around 200 V for the methane films whereas it increases continuously for the benzene films. The data of Weissmantel (30) suggest that H declines again above I-1.5 kV, as shown schematically by a dashed line in Fig. 89. The hardness of a-C:H deposited from acetylene has been measured with a nanoindenter as a function of gas pressure, and by microindenter as a function of bias voltage (61). The measurements as a function of gas pressure suggest that the microindenter overestimates hardness by a constant factor. Thus, Fig. 90 shows the approximate corrected hardness values ofa-C:tt deposited from acetylene as a function of bias. The hardness is seen to vary in a similar fashion to that of methane-derived films (297), but with a substantially higher peak value. Interestingly, the hardness variations for each type of a-C:H are very similar to those of the density. Fig. 91 shows that the hardness increases further as the source gas pressure is reduced (although this reduces deposition rates). These hardness data suggest that acetylene may be the most useful precursor gas for PD a-C:H, combining reasonable deposition rates (Fig. 10) and the highest hardness. Collins et al (35,99,302) have produced hard carbon films by laser-plasma deposition. These films appear to be microscopically inhomogeneous, with apparently highly sp3 bonded possibly diamond grains embedded in a more sp~ bonded matrix of a-C. Fig. 23 showed a TEM micrograph of this material. Its mean hardness has been measured by a nano-indenter to be
30
20
A
o. r3 f~
(g
-r
10-
00
Fig. 90.
a
I
200
,
i
I
i
i
400 600 Bias voltage (V)
I
i
800
i
1000
Approximate micro-hardness vs. bias for PD a-C:H deposited from acetylene (61).
Diamond-LikeCarbons
321
\
30 0
•
~20
• \0
- -
\o
L-0
10
Vb--300 v
0 10-3
Fig. 91.
1 I 10-z 10-1 Pressure of CzHz [rnbor]
\ \
100
Hardness vs. gas pressure, for PD a-C:H deposited from acetylene (61)
30-40GPa, which is particularly high. The indent size is much larger than the grain size, so the hardness respresents an average. Collins (302) noted that the lower modulus of this carbon than diamond could be advantageous, as it lessens the transmission of mechanical shocl~s through such a coating to a weaker substrate. It is also possible that microscopic inhomogeity may raise the stress intensity factor Klc = ~ , by dispersing fractures into microscopic cracks. This could be useful as Kjc of diamond is not so high, its fracture energy y being close to the ideal surface energy value.
8.5 Friction The friction properties of PD a-C:tl deposited from ethylene has been measured by Enke and others (303-307). The coefficient of friction was found to increase strongly with atmospheric humidity, from a low value of 0.05 at 12% relative humidity to 0.30 at 100% humidity. There are basically three regimes of friction on ceramics (308,309). At low loads, friction occurs by the adhesion mechanism, contact is elastic and leaves no permanent groove. At moderate loads, a permanent groove is left by "ploughing" and plastic deformation of the surface. At high loads, a gross cracking and deformation of the surface occurs. Diamond itself has a low friction, due to a combination of its high elastic modulus and its low adhesion (16). This keeps contacts on diamond in the adhesive regime and also minimises their effects (308). The low adhesion arises
322
J. Robertson
from the passivation of its surface with stable C-H bonds. Hard a-C and a-C:H are expected to have generally similar frictional behaviour to diamond, but higher absolute friction coefficients, because they have low adhesion, passivated surfaces but lower elastic moduli. The low friction of a-C:H in dry conditions is consistent with this behaviour, but it is difficult to account for the humidity dependence. Grill et al (193) also observed a friction coefficient of order 0.3. 8.6 Wear
Wear of surfaces can arise from several mechanisms such as adhesion, abrasion and tribochemical (308,309). Adhesive wear occurs by adhesive contact at the asperities where stress magnification causes a local cold-welding of the two surfaces, i f the interface bond is weak, it shears and no wear occurs. If the interface bond is strong, there is shear within the weaker material, transferring material to the tougher surface. The wear rate in volume per unit track length V/L is given by V L
kW 3Y
kW H
177]
where W is the load, Y is the yield stress of the weak surface and H is its hardness (H = 3Y). Abrasive wear occurs at contacts between materials of dissimilar hardness. It occurs by ploughing, by microcracking or local plastic deformation of the softer surface. The wear rate is given the extent of the indented groove, V I-'7 =
Wcot(0) nI-I
1,'78]
where 0 is the indent's pyramidal angle. Thus, adhesive and abrasive wear rates of a surface vary inversely with its hardness. Tribochemical wear is the main form of wear in diamond in air (16). It occurs at high rubbing speeds from a gradual rise in friction coefficient leading to local heating which converts the diamond to graphite which then oxidises to CO2. A number of wear tests have been carried out on amorphous carbons. Abrasive wear has been observed in a-C:H (3 I0) while abrasive and tribochemical wear have been observed in sputtered a-C (311). The abrasive wear rate of a surface varies inversely with its hardness, according to eqn 1,-78]. The abrasive wear rate of a-C:tt was found to increase by a factor of nearly 10~ as the hardness (22) fell as the hydrogen content varied from 0 to 60%, which is consistent with expectations. Marchon et al (311) observed abrasive and tribochemical wear in sputtered a-C. They found that the abrasive wear rate varied inversely with the Raman I(D)/I(G) ratio. This dependence is unexpected as hardness has not been previously correlated with this ratio. Marchon et al (31 I) found the tribochemical wear rate fell for films of lower Raman G mode frequency. Hirvonen et al (45) observed that the wear of MSIB a-C occured by a combination abrasion and cracking. The abrasive wear rate was a factor of 230-290 lower than that of SiC and A1203, and a factor 60 lower than that of WC-Co composite, with only diamond itself being lower. g.7 Internal Stress
A major problem with a-C(:H) films is that they usually possess substantial intrinsic stress. This limits the adhesion of thicker films and their potential applications (308,312). Fig. 92 shows the
Diamond-Like Carbons
323
interface. Evidence of strong bonding was found at Si/C and metal/C interfaces by Raman (317) and photoemission (318-320) respectively.: Adhesive failure of thin films occurs when the internal stress o exceeds a critical value. A film of thickness h delaminates when the mechanical energy density exceeds the energy needed to create two new surfaces (321), o2h 2E
< 2y
[79]
where ~ is the surface/interracial energy. It is preferable to rewrite this in terms of strain t as this is continuous across the interface and to factor out the large variations in Youngs modulus of the films. Eqn 1-79] becomes h <
4yE 2
[80]
for adhesion, where the numerical factor 4 is approximate (321). This sets an upper limit on film thickness. The interracial energy of a-C(:H) films equals the energy needed to break the bonds across a given plane. Its maximum value is that of diamond (16), 5.7 J/m s. Adhesion is measured empirically by the scratch test, in which a stylus in drawn across a surface under continuously increasing normal force, until the film begins to peel off at a critical load W~. The limiting interracial stress c/~ is the sum of the internal stress c/, and the applied stress (322), C/c ----- C/internal +
kl'c
[81]
so the critical load gives an indication of c/c. Metal-containing a-C:H (Me-C:II) films were introduced to improve the adhesion properties of a-C:H (308,323). 9 Conclusions
The hard forms ofa-C and a-C:it can be prepared with significant sp .~contents and much higher atomic densities than other forms of non-crystalline carbon.: The hard carbons can be produced by a range of deposition processes such as ion-beam deposition, plasma deposition, sputtering, laser plasma deposition, cascade arc, and mass selected ion beam deposition. A common factor is the ion bombardment of the growing film. Hard a-C(:H) films tend to have mixed sp ~, sp 3 bonding. Quantum chemical arguments suggest that the sp 2 and sp3 sites will segregate into sp2 aromatic clusters embedded in a s p 3 bonded matrix. The electronic properties depend on tile n states of the sp 2 clusters. The optical gap varies as 6/M 1/~with the cluster size M. The mechanical properties depend on the cross-linking of the sp3 phase in a-C:H, and additional on the warping and cross-linking of the sp2 layers in a-C. Experimental results such as optical absorption, Raman spectra and luminesence spectra support the two-phase model of a-C:H. The sp 3 content of a-C(:H) is best measured by NMR or X-ray near edge spectra. The C-H configurations can be found from infra-red absorption. The Raman spectra reflect mainly the sp~ sites and give information on the degree of clustering. A good theory of Raman is still required.
324
J. Robertson
Hard a-C prepared by RF sputtering has about 95% sp 2 sites, a gap of 0.5-0.7 eV and a true hardness of up to 15 GPa. This hardness indicates a considerable cross-linking of the sp 2 layers. Magnetron sputtering can raise the sp 3 content and optical gap. The most popular preparation method of a-C:H is by RF self-bias plasma-deposition. The properties of PD a-C:H depend primarily on the self-bias voltage. The H content and sp 3 fraction falls steadily with bias, to give three structural regimes. Soft, polymeric films are formed at low bias. Hard, transparent 'diamond-like' films are formed at intermediate bias (100-1000 V depending on source gas) with a highly cross-linked network. Less hard, more graphitic films are formed at high bias. Many properties of hard a-C:tt are independent of source gas, but hardness, density and deposition rate do depend on source g a s . Acetylene seems to give the hardest, highest density a-C:H films, of the commonly available source gases, reaching hardnesses of 30 GPa. A remarkable form of a-C can be prepared by mas selected ion beam deposition, with "~90% sp 3 sites and a low H content. It appears to consist of flakes of sp 3 carbon surrounded by a thin 10A surface layer of sp 2 sites. Its hardness is 30-110 GPa. Laser plasmas can produce a microscopically inhomogeneous form of hard carbon, apparently consisting of small diamond(-like) nodules embedded in a s p 2 matrix. Its hardness is 30-50 GPa. The deposition mechanism needs further study. In PD a-C:tt the major growth species are neutral radicals and ion bombardment is used to dehydrogenate the film and raise netwrok cross-linking. In a-C ion-bombardment is found to promote sp 3 bonding, probably via an ionpeening mechanism, but other mechansims are also active. [lard a-C(:H) has many present applications as a hard, transparent inert coating material. Its low deposition temperature allows it to be applied to a wide range of substrate materials. It is presently used for magnetic disc coatings, protective coatings on optical windows and on orthopaedic implants. The problems of a-C(:tl) coatings concern its high internal stress, lack of adhesion and poor temperature stability.
Acknowledgements The author is very grateful for discussions and information from M. A. Tamor, D. McKenzie, P. Gaskell, G. Gilkes, R. Newport, B. Dischler, J. Fink, J. Perrin, C. B. Collins and J. Prins.
Diamond-LikeCarbons
325
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266. W. Zhang and Y. Catherine, Surface Coat Technol 47 69 (1991) 267. J. D. Warner, J. J. Pouch, S. A. Alterovitz, D. C. Liu, W. A. Lanford, J Vac Sci Technol A 3 900 (1985) 268. W. Moiler, in 'Diamond and Diamond-like Carbon Films', ed R. E. Clausing (Plenum 1991) p229 269. W. Moiler, J Nucl Mats 162 138 (1989) 270. D. Boutard, W. Moiler, J Mater Res 5 2451 (1990) 271. E. Dunlop, J. Haupt, K. Schodt and W. Gissler, Diamond and Related Mats, to be published (1992) 272. Y. Lifshitz, S. R. Kasi, J. W. Rabalais, W. Eckstein, Phys Rev B 41 10468 (1991) 273. W. Moiler, App Phys Lett 59 2391 (1991) 274. H. P. Kaukonen, R. M. Nieminen, Phys Rev Letts 68 620 (1992) 275. B. T. Kelly, 'Physics of Graphite', (Applied Science, London, 1981) 276. E. A. Burgermeister, C. A. J. Ammerlaan, G. J. Davies, J Phys C 13 1,691 (1980) 277. J. Prins, private communication (1991) 278. D. W. Thornton, J Vac Sci Technol (1982) 279. H. Windischmann, J App Phys 62 1800 (1987) 280. H. Windischmann, J Vac Sci Technol A 9 2431 (1991) 281. J. E. Sundgren, in 'Diamond and Diamon-like Carbon Filns', ed R. E. Clausing et al, (Plenum 1991) p 47. 282. M. L. Cohen, Phys Rev B 32 7988 (1985) 283. J. C. Phillips, J Non-Cryst Solids 34 153 (1979) 284. M. F. Thorpe, J Non-Cryst Solids 57 355 (1983) 285. H. He and M. F. Thorpe, Phys Rev Lett 54 2107 (1985) 286. G. H. Dohler, R. Dandoioff, H. Bilz, J Non- Cryst Solids 42 87 (1983) 287. J. C. Angus and F. Jansen, J Vac Sci Technol A 6 1778 (1988) 288. J. Robertson, Phys Rev Letts 68 220 (1992) 289. C. A. Brookes, Phil Mag A 43 529 (1981) 290. A. Kelly and N. H. MacMillan, 'Strong Solids' (Oxford University Press, 1986) 291.1t. J. McSkimin, P. Andreatch, P. Glynn, J App Phys 43 985 (1972) 292. M. F. Ashby, D. R. H. Jones, 'Engineering Materials' (Pergamon, 1980) p58,78 293. J. X. Zhao, R. C. Bradt and P. L. Walker, Carbon 23 15 (1985) 294. H. M. Hawthorne, Carbon 13 215 (1975) 295. V. I. Trefilov and Y. V. Milman, Sov Phys Dokl 8 1240 (1964) 296. X. Jiang, J. W. Zou, K. Reicheit and P. Grunberg, J App Phys 66 4729 (1989) 297. X. Jiang, K. Reichelt and B. Stritzker, J App Phys 66 5805 (1989) 298. X. Jiang, K. Reichelt and B. Stritzker, J App Phys 68 1018 (1990) 299. M. A. Tamor and K. C. Hess, J Mater Res 5 2273 (1990) 300. D. Tabor, Rev Phys Technol 1 145 (1970) 301. S. S. Chiang, D. B. Marshall and A. G. Evans, J App Phys 53 298 (1982) 302. F. Davanloo, T. J. Lee, D. R. Jander, H. Park, J. lq. You, C. B. Collins, J App Phys 71 1446 (1992) 303. K. Enke, Thin Solid Films 80 227 (1981) 304. K. Enke, H. Dimigen and tt. Hubsch, App Phys Lett 36 291 (1980) 305. K. Enke, Mat Sci Forum 52 559 (1990) 306. R. Memming, H. J. Tolle, P. E. Wierenga, Thin Solid Films 143 31 (1986) 307. C. P. Klages, R. Memming, Mat Sci Forum 52 609 (1989)
Diamond-LikeCarbons
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308. D. H. Buckley, K. Miyoshi, Wear 100 33 (1984) 309. A. Sarkar, 'Wear of Metals', (Pergamon Press, 1976) 310. F. Jansen and M. A. Machonkin, Thin Solid Films 140 227 (1986) 311. B. Marchon, N. Heiman, M. R. Khan, A. Lautie, J. W. Ager, D. K. Veirs, J App Phys 69 5748 (1991) 312. A. H. Lettington, Proc EMRS 17 359 (1987) 313. M. Rubin, C. B. Hopper, N. H. Cho, B. Bhushan, J Mater Res 5 2538 (1990) 314. E. T. Prince, J App Phys 70 4903 (1991) 315. D. Nit, Thin Solid Films 146 27 (1987) 316. M Ramsteiner, J Wagner, C. Wild, P. Koidl, Solid State Commun 67 15 (1988) 317. D. Ugolini, P. Oelhafen, Proc EMRS 17 287, 297 (1987) 318. M. Wittmer, D. Ugolini, P. Oelhafen, J Electrochem Soc 137 1256 (1990) 319. D. Ugolini, J Eitle, P. Oeiha['en, J. Wittmer, App Phys A 48 549, 559 (1990) 320. J. Robertson, M. I. Manning, Mat Sci Technol 6 81 (1990) 321. M. Wang, X. Jiang, B. Stritzker, Thin Solid Films 197.57 (1991) 322. H. Dimigen, H. Hubsch, R. Memming, App Phys Lett 50 1056 (1987)
0079-6786/91 $0.00 + ..TO @ 199"2Persamoa Prm~ Lid
HARD AMORPHOUS (DIAMOND-LIKE) CARBONS John Robertson National Power Laboratory, ~atl~rlm~ Surrey, KT22 7SE, U. FL
ABSTRACT The hard forms of amorphous carbon and hydrogenated amorphous carbon, also known as diamond-like carbon, have recently aroused considerable interest as coating materials. This paper reviews their preparation, structure and properties. These carbons contain both sp 2 and sp3 sites. A chemical bonding model is developed which describes the arrangement of these sites and which accounts for many of the electronic and mechanical properties, The review covers the various deposition methods and the deposition mechanisms, the characterisation of amorphous carbons by techniques such as diffraction, electron energy loss, Raman, infra-red, nuclear magnetic resonance, and thermal stability, their electronic structure, optical properties and electronic spectra, and their mechanical properties such as elastic modulus, hardness, wear rate, friction and film adhesion. The dependence of electronic and mechanical properties on deposition methods and conditions is studied, to assess which methods are most valuable for applications. CONTENTS 1 Introduction
201
Deposition Methods 2.1 Ion Beam Methods 2.2 Sputtering 2.3 Plasma Deposition 2.4 Laser Methods 3 Atomic Structure 3.1 Techniques 3.2 Structure o f a - C 3.3 Structure o f M S I B a-C 3.4 Structural Modelling of a-C 3.5 EXAFS 3.6 Structure ofa-C:H 3.7 Real Space Studies JPSSC 21:4°A
205 205 208 209 213
199
213 213 218 222 224 228 228 230
200
4
J. Robertson
3.8
Infrared and Raman Spectra
3.9
C-H Vibrational Modes
Atomic Structure
7
8
249 250 254
Coordination Huckel Calculations
4.3 4.4 4.5
Band Gaps a - n Mixing Electronic Structure Simulations
260
4.6
Photoemission
263
4.7
Optical Spectra
4.8
Electron Energy Loss Spectra
268 271
258
275
,5.1 A-C:H
275
5.2
Role of Hydrogen
279
5.3
A-C
283
Localized States
288
6.1
Origin of Localized States
288
6.2
Localization
290
6.3
Electrical Conductivity
293
6.4
Doping
6.5
Defect Densities
295 299
6.6
Luminescence
6.7
Defect Equilibria
303 304
7.1
Plasma Deposition - case ofa-Si:H
306 306
7.2
Plasma Depsoition ofa-C:t!
3O8
7.3
Ion-Solid Interactions
310
7.4
Ion Beam Deposition
311
Deposition Mechanisms
Mechanical Properties 8.1
9
249
4.1 4.2
,5 Properties ofa-C and a-C :lI
6
236 247
Survey
313 313
8.2 Constraint Model
314
8.3
Elastic Moduli -Comparison with Experiment
316
8.4
ttardness
317
8.5
Friction
8,6
Wear
321 322
8.7
Internal Stress
322
8.8
Adhesion
323
Conclusions
324
References
325
Diamond-Like Carbons
201
1 INTRODUCTION There have recently been two important advances in the science of crystalline carbon - the discovery that diamond can be readily grown by vapour deposition (1-3) and the discovery of a third allotrope of carbon, a molecular crystal of the fullerene molecule (4,5), 'buckyball' C6o .: There has been a parallel advance in effort in disordered carbons. The range of disordered carbons is wide, covering soots, chars, carbon fibres, glassy carbon and evaporated amorphous carbon. These carbons are basically sp 2 bonded. A range of new preparation methods has produced forms of amorphous carbon (a-C) and hydrogenated amorphous carbon (a-C:H) which are mechanically hard, infra-red transparent and chemically inert. They are finding immediate applications as hard coating materials for magnetic disc drives or as antireflective coatings for infra-red windows (6-15). Their beneficial properties arise from the sp 3 component of their bonding and these carbons are frequently called diamond-like carbon (DLC). In general, such carbons can be fully amorphous or contain crystalline inclusions. This field of noncrystalline carbons is of interest both technologically to materials scientists and also at a more fundamental level to solid state chemists and physicists. A carbon atom can exert three different hybridizations, sp 3 , sp 2 and sp t (Fig. I). In the sp3: configuration, as in diamond, each of a carbon atom's four valence electrons is assigned to a tetrahedrally directed sp 3 hybrid orbital, which makes a strong tr bond with an adjacent atom (7). In the 3-fold coordinated sp ~ configuration as in graphite, three of the four valence electrons are assigned to trigonally directed sp ~ hybrid orbitals which form strong intra-layer tr bonds. The fourth electron lies in a pn orbital which lies normal to this bonding plane. This orbital forms weak rr bonds with neighbouring ~t orbitals, rt bonding is also called unsaturated bonding. In the sp ~ configuration as found in acetylene, two valence electrons are assigned to linearly directed sp ~ hybrids which form a bonds and the other two electrons are placed in each of the py~ and Pz, orbitals. The physical properties of the various non-crystalline forms of carbon are compared with those of diamond, graphite and C~0 in Table I. In diamond, the strong, directional tr bonds give it a wide 5.5 eV band gap, and the highest hardness, elastic modulus and room temperature thermal conductivity of any solid (I,16,17). Graphite consists of hexagonal layers of sp ~ sites, weakly
z Z
sP 3 Fig. 1.
sp2
sp
Schematic representation of sp s, sp 2 and sp ~ hybridized carbon.
J. Robeamn
202
Table 1. Properties of various forms of carbon Density gm cm -3
Hardness GPa
% sip
Diamond
3.515
100
Graphite
2,267
C~o
Gap eV
Ref.
100
5.5
16
0
-0.04
0
at.% H
0
275
1.8
5
Glassy C
1.3-1.55
2-3
-~0
0.01
83
a-C, evap.
1.9-2.0
2-5
1
0.4-0.7
90
a-C, MSIB
3.0
30-130
90 -t- 5
<9
0.5-1.5
39
PD a-C:H, hard
1.6-2,2
10-20
30-60
10-40
0.8-1.7
9
PD a-C:H, soft
0.9-1.6
<5
50-80
40-65
1.6-4
9,141
Polyethylene
0.92
0.01
100
67
6
292
bonded together by Van der Waals forces in an ABAB stacking sequence along its c axis. This bonding anisotropy produces a high conductivity and strength within the basal plane but low values in the c direction. In C60 each carbon is 3-fold coordinated in a slightly distorted siP configuration. The various non-crystalline carbons can be considered to be intermediate between diamond, graphite and hydrocarbon polymers, in that they can contain variable amounts of sip and sip sites and hydrogen. The long-known forms of non-crystalline carbon such as soot, glassy carbon and evaporated carbon consist almost totally of sip sites. The first diamond-like carbons were produced by ion beam deposition by Aisenberg and Chabot (10). It is now recognised that a wide variety of methods can be used in their preparation, such as plasma-deposition, sputtering, magnetron sputtering, ion plating, and laser plasma deposition (18-48). These deposition methods are reviewed in section 2. A common theme of these methods is that the film is subjected to ion bombardment during growth which promotes siP bonding. Nevertheless the precise deposition mechanism responsible for the promotion of sip bonding is a matter of contention, as discussed in detail in section 8. A wide variety of methods have been used to characterise the structure of amorphous carbons, using both structural and electronic probes. These are described in section 3. Characterisation of diamond-like carbons has been held back because of their mixed bonding character and the absence of unhydrogenated, highly sip form of a-C, analogous to a-Si. It is now recognised that such a form of a-C can be prepared by mass-selected ion beam deposition (MSIB) in which a mass-filtered beam of C ~ or C- ions is condensed on a substrate. The process was originally developed by Akensov et al (37) and the structural characterization was carried out by McKenzie et al (39,40) and Gaskeil et al (41). Weissmantel et al (30) and Angus et al (6) observed that the properties of amorphous carbons deposited under ion bombardment conditions tend to pass through three regimes as a function of ion energy (Fig. 2). Unhydrogenated a-C deposited at low ion energy is essentially graphitic and similar to evaporated a-C. It changes to hard a-C at moderate ion energies and it then becomes less hard again at high energies as its structure adopts a highly disordered, defected graphitic structure. A-C:II is soft and polymeric at low ion energies due to the predominance
Diamond-Like Ca.,'bon~
GRAPHITIC a-C
I000
>
I00
0ENSE CARBON
HARD a-C:H
v
>.. L~ r,, tU
Z
LU
I-U <
13.
I($OF POLYMERIC T) a-C:H
I0
p'J/
m
kMORPHOUc, CARBON ($pZ)
CARBON sOURCES Fig. 2.
PLASMA POLYMERS
.IYDROCARBON SOURCES
Schematic variation of bonding character on ion energy during deposition for a-C and a-C:H (6).
of = CH2 groups. Its hardness passes through a maximum at moderate ion energies as its hydrogen content drops and finally the hardness declines at high ion energies when it also adopts a defected graphitic structure (9). Angus (1,49) has proposed a valuable means of classifying the various carbons and hydrocarbons in terms of their atom density and hydrogen content as shown in Fig. 3. The atom number density is the total number of atoms per unit volume divided by the Avogadro's number. This plot emphasises that the diamond-like forms of a-C:H are unique in that they have a much higher atom density than conventional hydrocarbon polymers. Diamond is seen
204
J. Robertmn
0.30 DIAMOND •
b
o.oo
o.oo
Atom Fraction Hydrogen Fig. 3.
Atom number density versus atomic fraction of hydrogen content for solid carbons and hydrocarbons, after Angus (I). a-C:H points are full cicles and triangles. Amorphous carbon refers to evaporated C, while a-C refers to a-C deposited by sputtering or ion beam methods.
to have the highest atom density, and indeed has the highest atom density of any solid at ambient pressure. Graphite has a lower density and lower atom density than diamond. Amorphous carbon formed by evaporation and many sputtering processes consists largely of sp~ carbon and has a density just less than graphite. The various conventional hydrocarbon polymers included are the alkanes such as polyethylene, the polyacetylenes and the polynuclear aromatics. The atom densities of diamond-like hydrocarbons are above 0.19 gram-atom cm -3, indicating the effect that network cross-linking has on raising the density. The hard amorphous carbons formed from filtered ion beams or from laser plasmas are seen to have densities and atomic densities above graphite and below diamond. The atomic structure and the electronic structure are very closely related in amorphous car. bons, as they are in all amorphous semiconductors (7). Of particular interest is the presence
Diamond-Like Carbons
filled valence states
205
empty conduction stotes
Energy Fig. 4.
Schematic band structure of amorphous carbons (7).
of n states and the effect of disorder on them. Since the rt states are more weakly bound, they lie closer to the Fermi level Er than the ¢r states, as shown in Fig. 4. The filled n states form the valence band and the empty n * states form the conduction band in all amorphous carbons, and so they control the size of the optical gap. Many aspects of the local bonding in a-C can be deduced from quantum chemistry. It is found that a mixed phase of sp s and sp2 sites tends to segregate into sp2 bonded clusters. These clusters have a pronounced effect of the electronic properties of a-C which are of considerable fundamental interest, as described in more detail in section 5. The major technical interest in diamond-like carbons is as a thin film coating material. This has led to significant work on their mechanical properties such as hardness, elastic modulus, adhesion, friction and wear rate. Recently the author developed a microscopic model of the mechanical propeties. This relates the elastic modulus to the underlying chemical bonding and composition of the film. This is then extended to treat hardness, wear properties and film adhesion, as described in section 8. The adhesion of hard carbon films to their substrates is a major concern in their application. 2 DEPOSITION METHODS 2.1 Ion Beam Methods
A wide variety of deposition methods have been used to prepare diamond-like carbon.
A
common feature of each method is the exposure of the growing film to bombardment by ions of medium energy, 20-500 V, which appears to promote sp 3 bonding (6,9,50). The various methods and their growth rates are summarised in Table 2. The first ion beam device of Aisenberg (10) generated carbon ions by sputtering carbon electrodes in an Ar atmosphere in a magnetically confined plasma. A bias voltage extracts the ions and directs them at the substrate. Higher growth rates were found to be possible if the ions are generated from a hydrocarbon source gas. The resulting films may have contained both a-C and diamond microcrystallites. The results were confirmed by Spencer et al (11), and Vora and
206
J. Robezt.mn
Table 2.
Methods for the deposition of Diamond-like Carbon Precursor
ypical Growth Rate,
ref.
sec.
ion beam
graphite
1.3
10
ion beam
methane
2
51
PD
methane
I
9
PD
benzene
15
9
Ar beam sputtering
graphite
3
22
Magnetron sputtering
graphite
3
23
Ion plating
benzene
I0
30
Laser plasma
graphite
<3
22
Cascade arc
Ar/methane
300
34
Mass selected ion beam
graphite
0.I-6
40
Moravec (19), while Mori and Namba (18) investigated the dependence of film properties on deposition conditions. A very popular ion source is that due to Kaufmann (51), shown in Fig. 5. In this source, electrons from a thermionic cathode are used with an axial magnetic field to generate a plasma. This gives high ionization rates in a source gas such as methane. Positive ions are extracted from the source by a bias electrode and are directed at a substrate.
Anode grid Ion box Filament k
Ion source Accelerator grid Neutralizer wire
II II | | ~ i _ _
o
Ill II''JI I ~
Fig. 5.
• |--"
•
" °
-*
*'"
Schematic ion beam deposition apparatus (51).
•
~' *
Diamond-LikeCarbons
207
The ions generated in a carbon source are of the form Cm-' while those from a gas source are of the form CmH,~. In both cases the substrate also receives a large flux of neutral species such as un-ionized Ar or methane from the background gas. This reduces the ion/neutral mass flux ratio to of order 0.02 (50,52). A high ionization ratio and a relatively high deposition rate can be achieved by using a cathodic arc as carbon ion source (37,39) A further increase in deposition rate is achieved by using a cascade arc source (53). A highly ionized thermal plasma of methane and Ar is created in an arc and the pumping conditions and design are such that the plasma expands supersonically into a high vacuum towards the substrate. This expansion causes a high degree of ionization of the plasma. Deposition of a single ion species is possible if the ion beam is passed through a magnetic mass analyser for e/m selection. The analyzer filters neutrals, cluster species, graphitic fragments and impurities from the beam and allows only a pure beam of C ~ (or C-) ions to reach the substrate. This MSIB method was first used by Aksenov et al (37), who believed that a new crystalline phase of C was formed. The method has now been used by a number of groups (38-48). Structural studies summarised later indicate that the resulting material is fully amorphous with the highest fraction of sp3 bonding of those from any present deposition process. The deposition rate for this method can be maximised by using the carbon arc as an ion source (Fig. 6). Typical rates are now 400 A/min. The arc is confined magnetically for stability. The main practical problem with this method is the high compressive stress in the films, which limits their adhesion and thereby the maximum stable film thickness.
B
H: To vacuum pump ~ I: High current power supply J: Viewing ports
Fig. 6.
[ ~i
\
H
Apparatus for Mass Selected Ion Beam deposition by magnetic filter, using a cathode arc source, after McKenzie et al (39)
J. Robertson
208 2.2 Sputtering
Various sputtering methods can be used to produce hard carbons. In ion beam sputtering, a beam of typically 1 kV Ar ions is directed at a graphite target (22,28). An angle of incidence of 30-45 ° is used to maximise the yield. The sputtered carbon is condensed onto a nearby substrate. A second Ar ion beam can be directed at the substrate to provide the ion bombardment of the growing film. A disadvantage of ion beam sputtering is its low deposition rates due to the low sputtering rate of graphite.
I WATER
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/ \'4k,
MAGNETIC / // FIELD LINESI
\
\
\
\
/
' '
I
¢
/
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MASKING PLATE
L
Fig. 7.
\
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I
/
0=\
\
/
I ,~
/"TARGET /
I
I //~SUBSTRATE
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Magnetron sputtering source, after Savvides (23).
Diamond-LikeCarbons
209
zo
2
10
100
500
Power ( W ) Fig. 8.
Variation of Ar m and C atom arrival rates with sputtering power for magnetron sputtering, after Savvides (23).
Higher deposition rates can be achieved by magnetron sputtering (23,26,27). Here an Ar plasma is used to both sputter from the target and bombard the growing film, as shown in Fig. 7. Growth rates vary linearly with rf. power and are typically 3A/sec (23). Ion energies are of order 20 eV and these decline slowly with increasing power or gas pressure. A mixture of Ar and carbon ions and atoms reaches the substrate. Savvides noted that the ion/atom ratio in the beam increases with decreasing sputtering power because the ion yield decreases less quickly than the neutral atom flux (23), Fig. 8. This is the opposite dependence to that in plasma deposition where ion bombardment effectively increases with plasma power. A d c bias can be applied separately to the substrate if it is desired to raise the mean ion energy. The general advantage of sputtering methods is their good process control and their ability to be scaled up for manufacturing. A disadvantage is that the hardest films seem to be prepared under conditions of low power and low gas pressure, where deposition rates are lower. 2.3 Plasma Deposition
The most popular deposition method involves the rf. plasma decomposition of a hydrocarbon source gas onto negatively self-biased substrates. Plasma deposition (PD) or strictly plasmaassisted chemical vapour deosition (PACVD) was pioneered for a-C:tt by ttolland and Ojha (20), and it is also widely used to deposit a-Si:H. Self-biasing is prefered to dc biasing for a-C:H because the films are insulating (9,21,54-56). In this method, Fig. 9, the rf. power is capacitively coupled to the substrate electrode and the counter electrode is either a second electrode or just the grounded walls of the deposition chamber. This gives a large difference between the electrode sizes. If the r£ frequency is greater than the ion plasma frequency, of order 2-5 MHz, the electrons can follow the rf voltage but the ions cannot. The large difference in electrode size and also in the electron and ion mobilities produces a negative dc. self-bias on the powered
210
J. Robertson
Vacuum gauge Pump Y
Substrote,
-VMatching box
~
Needle valve
souJg. E
RF P°wermeterLI~J 2~r
Voltmeter. c
RF Generator Fig. 9.
Schematic of capacitively-coupled RF plasma deposition apparatus, with substrate attached to the powered electrode (cathode) (9).
electrode, making it the cathode. The ion current is now largely dc while the compensating electron current flows in short bursts each rf. cycle (Fig. I0). The dischage now consists of a glow region, in which the ions are generated by collisions with electrons, and a space charge region or ion sheath, across which the ions are accelerated to reach the cathode. The equivalent electrical circuit for the plasma is a resistance for the plasma glow in series with a capacitance for the sheath (54,57). The dc. bias is largely dropped across the sheath (Fig. 10). The bias voltage, -Vb, varies with rf. power W and operating pressure P as (21,54), W
Vb = k(--f-)
112
[l]
where k depends on factors such as the electrode areas. Catherine and Couderc (54) have shown that this is the dependence expected for an ohmic plasma and a sheath thickness proportional to p-in. The ion energy Eu depends on Vb and the ion mean free path in the sheath, At low pressures in the absence of collisions
Diamond-Like Carbons
Distribution of time-averaged potential within discharge
f i l l
'
211
Rf modulation of plasma and cathode potential
I i
I I I I
0
.! 4~
C @ 0
o. @ 01 0 L_
,,C
"~
>-
2_1
0 I q)
_E k-
Distance cathode (small electrode) Fig. 10.
t anode (large electrode)
Time
(a) Average potential distribution and (b) waveforms in a capacitively coupled plasma reactor, after Koidl et al (9).
Ei-~eVb while at higher, typical operating pressures there is a spectrum of ion energies with a mean value of Vb E i -~ k '
pi12
[2]
or about E, = 0.6Vb for typical pressures of 3 Pa (9). Ion energy spectra have been measured for Ar discharges by Wild et al (58). The deposition rate varies with the ionization potential and molecular weight of the source gas as shown in Fig. ! I, with low ionization potentials and large molecular weights giving higher growth rates (59-61). The deposition rate v for a given gas has been found to vary with bias voltage and gas pressure as v -----k " V b P
['3]
by Koidl et al (9,21), Catherine and Couderc (54), and Zou et al (60,61), for various different source gases (methane, acetylene and benzene). The deposition rate can saturate or decline for
J. Robertmn
212
1000
--
I
n-hexane~"' ne _Butane " ~ P r o p a n e Ethene *
~
100
.o Methane
W 0 e~ 0
a
10
I
9
Fig. 11.
I
I0
I
I
I
I
11 12 lonlzation potential, eV
I
13
Plasma deposition rates versus ionization potential of precursor gas, for a gas pressure of 3 Pa and a self-bias voltage of-400V, after Koidl et al (9). Data for acetylene from Zou et al (61).
biases over 1.2-1.5 kV as the incoming ions begin to sputtered the film. The total deposition flux again consists of both ions and neutral species from un-ionized background gas. Some of the neutral species can be energetic, as they are formed by charge exchange reactions with energetic ions. Catherine (55) found the ion/neutral flux ratio to be 0.1-0.2 for methane plasmas on the basis of ion flux measurements, while Locher et al (62) found a ratio closer to 0.5 for benzene plasmas by comparing with ion-beam deposited films. The advantage of plasmadeposition is its simplicity and high deposition rates with the appropriate gases. A problem with PD is in the scaling up to larger systems as film properties depend mainly on bias voltage and thereby electrode areas rather than directly on process parameters like RF power and gas pressure. The properties of PI) a-C:tl depend strongly on the ion energies, as discussed in detail in section 5.1. I.ow ion energies only weakly dissociate the source gas and give a highly hydrogenated or polymeric form of a-C:H. This regime is similar to that of plasma polymerisation, reviewed by Yatsuda (63). Plasma deposition is also a popular method of preparing a-Si:ll and polycrystalline diamond (3), but the conditions are considerably different in each case, as summarised in Table 3. Hard
213
Diamond-Lik~Carbons
Table 3.
Conditions for plasma polycrystalline diamond.
deposition
of a-C:H,
electronic
a-C: H
a- Si:! I
diamond
RF power density, W/cm -~
!
0.01
10
Gas pressure, Pa
3
10
3
Substrate electrode
cathode
anode
Td , °C
25
250
Dilution
grade
a-Si:H
and
800 It~/CI-t4--- 100
a-(':H is obtained if there is ion bombardment during deposition, and these conditions are favoured by a cathodic substrate (to receive positive ions), a high RF power (for a high bias voltage), low gas pressure (for high ionisation) and low substrate temperatures (to minimise self-annealling). Electronic grade a-Si:tt is deposited from silane plasmas under conditions which minimise the concentration of defect states due to Si dangling bonds. Sufficient hydrogen must be retained to passivate the dangling bonds but not so much that polymeric SiI-t2 groups are common. This requires gentle conditions orlow RF power density, a moderate gas pressure, an anodic substrate (to minimise ion bombardment) and a substrate temperature of about 250 °C to give optimum self-annealling (64). Diamond growth is favoured by using hydrogendiluted source gases, a high power density and a higher substrate temperature. These conditions generate atomic hydrogen which suppresses the deposition of graphite and a-C by various mechanisms such as preferential etching (2). There are also a variety of hybrid deposition methods such as ion plating in which the plasma is created by an RF plasma and then the ions are accelerated by a separate field from a grid electrode to the substrate (29-31,65). More highly ionised plasmas can be produced by using microwave discharges, particularly if operated at the electron cyclotron resonance (66,67). This method produces high ion densities even at low gas pressures. The absence of electrodes and ability to control the shape and position of the plasma make this method technically attractive. Control of both ionisation and ion energy can be achieved by using a microwave ion source and a rf. self-biasing accelerator. 2.4 Laser Methods
A carbon ion plasma can also be produced by the laser ablation or graphite (33-35), Fig. 12. The resulting plasma probably resembles that formed by a cathodic arc (36). The resulting a-C is found to have a diamond-like character if the laser power density exceeds a threshold value. 3 ATOMIC STRUCTURE 3.1 Techniques
This section describes the structures of the various forms of a-C and critically reviews the various structural characterisation methods. The principal requirement from a structural study of a-C or a-C:H is to find the fraction o f s p 2 and sp 3 sites and the hydrogen content. A secondary
214
J. Robertson
LASER INPUT
I
I?°/o//On
Subs/roles
Wilness plole
"°
.
.° ".° °. "°
..J "%
J
. "~,,,
to HV
C/ec/rode
~
L/roll of
' ' . , . .
Q Fig. 12.
o"
useful deposition 6roph/le
Laser-plasma deposition apparatus, after Collins (34).
requirement, particularly in the more sp 2 bonded carbons, is to find the degree of medium range ordering (MRO), which can be expressed as whether there is a local layer structure and whether it is dominated by planar 6-fold rings. The principal techniques wbich have been used to characterise the structure have been electron, X-ray and neutron diffraction, nuclear magnetic resonance (NMR), electron energy loss spectroscopy (EEl.S), X-ray near edge absorption spectroscopy (XANES), X-ray absorption fine structure (EXAFS), Rutherford Backscattering (RBS), optical spectroscopy, infra-red (IR) spectroscopy, Raman and Auger. The hydrogen content can be found by proton NMR, nuclear reaction analysis (NRA), elastic recoil detection (ERD), combustion analysis or by thermal evolution. The relative merits of the characterisation methods are summarised in Table 4 and are discussed in more detail below. The most direct and valuable probes of fraction of sp ~ and sp3 sites are C ~3 N M R and XANES spectroscopies. N M R has been used to charcterise a wide variety of carbons, from polymers to coal (68,69) The advantage of N M R is that each different hybridization gives rise to a chemically shifted peak whose area is directly proportional to its concentration (68-76). The
Diamond-Like Carbons
Table 4.
215
Comparison of structural characterisation methods.
C I~ N M R
Strengths
Weakness
quantitative, detects sp ~ and sp2 sites
sensitivity (cost, time)
XANES
quantitative
best for sp2 sites
Diffraction
detailed
long interpretation
IR of C-H modes
cheap
only detects C-H sites, variable matrix element
Raman
sensitive to M R O
weak sp 3 scattering, interpretation
EXAFS
low Z, contamination
Density
indirect
limitations of the technique are the large sample sizes needed to detect the C 13 N M R because of the isotope's low natural abundance and the time needed for data acquistion. A certain
sp 2 sp 3
'
' 4(~0
'
'
CHEMICAL Fig. 13. JPSSC 21;4-B
' 200'
'
'
()
'
'
'-200
S H I F T F R O M T M S ~PPM)
N M R spectra of sputtered a-C, after Pan et al (76), and a sample ofplasma-deposited a-C:H after Petrich et al (68).
216
J. Robertson
density of unpaired nuclear or electronic spins helps to give a short enough coherence time T~ to collect the NMR signals. The nuclear spins can be either C ~3nuclei or protons. On the other hand, interactions with other spins and also chemical shift anisotropy will broaden the N M R peaks. Magic angle spinning (MAS) can be used to reduce this peak broadening. In a-C:H, because of the H-C interaction, an additional 'proton decoupling' signal will align the proton spins and so it considerably sharpens the peaks. A typical example of this is shown in Fig. 13. The H-C interaction can also be used to distinguish between hydrogenated and unhydrogenated sites, whenever it is the predominant source of line broadening, as is the case in a-C:H. The tt-C interaction is dipolar and decays rapidly with distance as r -3 , so turning off the proton decoupling signal broadens the spectra of the hydrogenated sites into the baseline. The remaining spectral peaks now correspond to the unhydrogenated sites. The spectrum with decoupling includes all sites. XANES gives direct evidence of the existence of sp 2 sites (77,78). The photoexcitation of a core electron of an atom gives rise to an x-ray absorption spectrum. The part of this spectrum near the edge is called XANES and the oscillating components at higher energy are called the EXAFS. The XANES spectrum reflects the conduction band density of states, Fig. 4. The XANES of carbon consists of a broad step at 290 eV due to excitations from the C Is core level to the empty a * states and a prepeak at 285 eV due to excitations to the n* states of any sp2 or sp ~ sites present (7). The XANES spectra of the major types of a-C are shown in Fig. 14. The absence of a n* peak at 285 eV in diamond is quite clear. The differences in the shapes of the n* and a* features do not allow for a simple analysis of sp~ content. Additionally, the n* is likely to be enhanced and red-shifted by the interaction of the excited electron and the core hole. Nevertheless, this effect is relatively constant, so that it is possible to extract the sp~ content from the relative areas of the n* peak and the leading edge of the a* step, by using the spectrum of graphite for normalisation, as shown by Berger et al (77). Jarman et al (70) found a reasonable correspondance between sp2 site fractions derived by XANES and NMR. One should note that the n* peak is strongly anisotropic and energy dependent in graphite (79,80). Hence care should be taken to directionally average this peak in the graphite spectrum or in any anisotropic form of a-C. XANES can be measured using photons, on a dedicated electron energy loss spectrometer or by an EEI.S attachment to an electron microscope. The density also gives very useful indirect information on the likely sp s content of a-C due to the large difference in density of graphite (2.267) and diamond (3.515). The sp3 content can be infered by extrapolation. Density is less meaningfkd for a-C:H as its polymeric component can give rise to densities down to 0.92, that of polythene, but nevertheless high densities are a good indication of favourable mechanical properties. Densities can be measured by floatation, weight gain measurement during deposition, Rutherford backscattering (RBS), or be inferred from the low energy EELS. The low energy EE1.S of carbons shows a peak around 20-35 eV due to the plasma oscillations of all the valence electrons known as the o + n plasmon. Its energy is proportional to the square root of the valence electron density (28), as discussed in section 5. This allows the derivation of the density if the electrons due to any hydrogen are allowed for. Wang et al (81) found reasonable agreement between densities determined by EELS with those determined directly. Diffraction studies give the most detailed information on local structure. The diffraction pattern of an object, the diffraction intensity l(k) is given by the product
Diamond-LikeCarbons I
I
II
217 I
I
(I"* ~/
~RAPHITE DIAMOND
) m
¢h
Z IZ
I,M
EVAP a-C
m
PD a-C:H
MSIB a-C 280 Fig. 14.
ENERGY, eV
300
XANES spectra of graphite, diamond, evaporated a-C, PD a-C :H and MSIB a-C:H, after Berger et al (77) and Fink et al (78).
l(k) = S(k)Nle(k)
[4]
where k is the scattered wavevector, S(k) is tile structure factor, N is the number of atoms and f(k) is the atomic form factor for of a single (bonded) atom by electrons, X-rays or neutrons. The k dependence of f(k) is significant for electrons, particularly because C has few core electrons to dominate scattering. The k dependence is minimal for neutrons, except for the case of H. The structure factor is related to the radial distribution function (RDF), J(r), by S(k) =
{J(r)/r - 4npor } sin(kr)dr
[5]
J. Robertson
218
The R D F is the probability of finding another atom at a distance r from a given atom. The R D F consists of a series of peaks and tends to a parabolic curve J(r) = 4nr2p0r at large r, where p0 is the microscopic density. The first peak lies at the average nearest neighbour distance or bond length r~ and its area equals the coordination number n~. The second peak lies at the second neighbor distance r2 from which the bond angle 0 is found, r 2 = 2r I sin(0/2)
[6]
The R D F is also often plotted in the reduced form G(r)= J(r)/r - 4 nrpo so that G(r)--*0 as r oo. The peak widths of an R D F equal their natural width plus the resolution of the experiment, which depends on kmtffl, where km,~ is the highest value of k used. kmu limitations are significant for carbon because of the short bond length rl. The wide band optical spectra have also been used to deduce sp 3 fractions. This method is described later. Auger is also used to give the sp3 fraction (82). The IR and Raman spectra give information on the C-H bonding and medium range ordering, as discussed shortly. 3.2 Structure of a-C.
We first consider the structure of the various forms of unhydrogenated a-C. Table 5 gives the peak positions in measured structure factors for various types of a-C. Table 6 gives some structural values deduced from their RDFs, compared to those of diamond and graphite. The four parameters n~, r~ 0 and p0 are generally sufficient to establish the character of any a-C. It is also of interest to know the degree of longer range order in graphitic carbons. Ideal graphite consists of hexagonal layers of atoms arranged in an ABAB.. stacking sequence with unit cell dimensions a=2.461A and c=6.708A, corresponding to a bond length of 1.421A, an interplanar spacing of d = 3.354A and a density of 2.267gm.cm -3. The most ordered form of synthetic graphite is called highly oriented pyrolytic graphite (HOPG). The structure of microcrystaUine graphites follows the turbostratic model in which graphite layers are stacked
Table 5.
Peak positions in S(k) of various forms of a-C, compared to the indexed reflections of graphite and diamond Peak position, A -j
glassy C
1.8
2.98
5.11
a-C (evap)
1.0
2.9
a-C (sput)
1.6
a-C (MSIB)
Ref. 8.8
10.2
83
5.1
8.7
10.3
90
2.95
5.5
8.7
10.5
92
1.2
2.9
5.4
8.7
10.3
41
a-C:H
1.2
3.0
5.4
8.5
10.4
113
Graphite (hkl)
(002) 1.88
(100) 2.95
(110) 5.11
(200) 5.90
(210) (300) (220) 7.82 8.86 10.2
(220) 5.00
(311) 5.86
(331) 7.71
Diamond (hkl)
(100) 3.06
(200) 3.53
5.96
7.8
Diamond-Like Carbons
Table 6.
219
Inter-atomic distance(r), coordination number(n) and density of various forms of C r~, A
n~
r2, A
n~
Graphite
1.42
3
2.45
6
2.267
Diamond
!.544
4
2.512
12
3.515
16
glassy C
!.425
2.99
2.45
6. I
1.49
83
a-C (evap)
1.43
3.3
2.53
8.8
2.0
90
1.46
3.34
2.49
6.7
2.44
92
1.526
3.9
2.52
8.9-10.9
3.0
41
a-C (sput) a-C (MSIB) a-C:H
1.39,1.52
2.5
local density, gm.cm-S
ref
i.5-1.8 113
in an arbitrary sequence and orientation. Their diffraction patterns retain only the interlayer (hk0) peaks and the intralayer (002) peaks. Mildner and Carpenter (82,83) measured the structure factor of glassy C by neutron diffraction to k,,,~ = 25A -1 (Fig. 15). The RDF in Fig. 16 shows a strong retention of graphitic local order (82-86). with a bond length of !.425A a coordination number of 2.99 atoms and a bond angle of 120 °, consistent with 100% sp~ sites. The peaks of S(k) can be indexed according to the turbostratic model, and the peak widths indicate an in-plane correlation length Lo-~50A and an inter-plane correlation length of Lc-~30A. This indicates that glassy C possesses too high a degree of ordering to be classified as amorphous. numerous microvoids.
Its low density of 1.5gm.cm-~ arises from its
The XANES spectrum of evaporated a-C indicates that it contains about 99% sp 2 sites (Fig. 14). Its structure has also been measured by electron diffraction by Kakinoki et al (88), Boiko et al (89) and McKenzie et al (90,91). Kakinoki (88) concluded that evaporated a-C contained of order 50% sp 3 sites but the Boiko (89) and McKenzie (90,91) data indicate about 5% or fewer sp 3 sites. The structure of sputtered a-C has recently been studied by static and magic angle spinning N M R by Pan et al (7,5). The static NMR spectrum is shown in Fig. 13. This material was prepared by condensation onto substrates cooled by liquid nitrogen, to minimise any heatinginduced graphitisation. ]'hey found 6% sp~ sites. The structure of this same sputtered a-C was studied by neutron diffraction by Li and Lannin (92) with kmax -- 30A -1. Tile RDF in Fig. 16 gives a coordination number of 3.3 and a bond length of 1.46A. These are both consistent with 10-20% sp 3 sites. This is higher than found by NMR but of the same order. The second neighbor peak at 2.49A gives a bond angle of 117 ° and its coordination of 6.9 compared to values of 120 ° and 6 for sp~ bonding. The a-C had a macroscopic density of 2.0gm.cm 3, and a microscopic density of 2.4gm.cm-3 from the RDF, the latter being 5% higher than graphite. The first peak was found to be relatively broad, indicating a range of bond lengths, as expected from the hybridization. It also shows a tail at high r, suggesting that the existence of some quasi-sp 3 sites with a fourth, weakly bonded neighbour. This configuration also occurs in the high pressure transformation of graphite lattice to diamond (93).
220
J. Robert.son
evaporated a-C
g
U)
I
0
Fig. 15.
2
4
6
8 10 k, ~-1
12
14
16
Structure factors of glassy C after Mildner and Carpenter(84), evaporated a-C after Green et al (90), sputtered a-C after Li and Lannin (92), MSIB a-C after Gaskell et al (41) and PD a-C:lt after Newport et al (I 10).
The R D F also gives information on more long-range structure. The R D F of an ideal graphite layer would possess a peak at 2r, --- 2.84A, the third neighbour cross-ring distance. This peak
Diamond-Like Carbons
|
I
l
A
•
221
I
,
I
glassy
C
, .a J_AA a-C
A
A
sputtered a-C
,o ..c:, -
0 Fig. 16.
I
1
-
v ~ , , j
I
2
I
3
I
4"
I
5
-6
R,~
Radial distribution fimctions of glassy C (Mildner and Carpenter(84)) evaporated a-C (Green et al (90)), sputtered a-C (Li and l.annin (92)), MSIB a-C (Gaskell et al (41)), and PD a-C:H (Newport et al (I 10)).
222
J. Robertson
Fig. 17.
Core structure of a graphite layer dislocation with a Burger's vector (1120)a/3.
is absent in the RDF of sputtered and evaporated a-C and indicates the presence of intra-layer disorder. However, the peak only contains 2 atoms, compared to the 6 under most intra-layer peaks. It can therefore be washed out by relatively little disorder, such as the presence of a small fraction of adjacent 5- and 7-fold rings. This configuration can be constructed from an ideal layer as the core of an edge dislocation (94) of Burgers vector < 1120> a/3, as shown in Fig. 17. This ring-pair is the unit oftopolgicai disorder in a hexagonal layer. It can be used to introduce topological disorder progressively into the perfect layer (95,96). A conversion of under 10% of rings to 5- and 7-fold rings has been found to be sufficient to wash out the 2.84A peak and the other third neighbor peak at 4.25A. A similar situation exists in 4-fold coordinated a-Ge where odd-membered rings wash out the third neighbour peak of its R D F (97). Further modelling of the R D F would clearly be useful. It is interesting that the S(k) of the various forms of a-C show very similar peak positions, despite their diffferent coordinations, as emphasised by the data in Table 5. This emphasises the potential danger of using crude diffraction patterns to characterise the diamond-like character. 3.3 Structure of M S I B a-C
A highly sp ,1 bonded form of a-C can be prepared by mass selected ion beam deposition (MSIB).
Dismond-LikeCarbons
223
A magnetic filter removes neutral species and graphitic fragments given off by an evaporation or sputtering source which are believed to increase the amount of graphitic bonding in a growing film (33,39).: The verification of the highly sp ~ character of MSIB a-C has been crucial to the field of hard carbons, as it shows that a purely sp 3 bonded random network can exist, even when chemistry allows other coordinations to co-exist. The structure of MSIB a-C has been studied by EELS, electron diffraction and neutron diffraction (39-41,77,90,91). A macroscopic density of 2.85 gm.cm -3 was found by floatation (90), while the valence plasmon energy of 32 eV in low energy EELS indicates a microscopic density of 3.1, approaching that of diamond (39). Its high energy EELS spectrum in Fig. 14 shows only a small peak at 285 eV from n* states, consistent with about 85% sp a bonding (77). The S(k) of MSIB a-C measured by neutron diffraction (41) is shown in Fig. 15, and the R D F is shown in Fig. 16. The k,,~ was limited to 8A-' because of the small sample size. The first neighbour distance of 1.53A and a bond angle of 11 I* indicates a s p 3 content of 90_5%, consistent with other estimates. The absolute values of the peak areas are less reliable indicators of coordinations in this material, due to the large scattering by a small amount (-~9%) of unbonded hydrogen. This hydrogen appears to be present as H~ molecules at voids, rather than as C-H bonds, as the latter interpretation would give a poorer fit to the RDF. The first and second coordination numbers are related by n2 = n l ( n , -
!)
[73
for a network without 4-membered rings (as here). Their ratio in MSIB a-C suggests a lower sp '~ fraction of below 80%. However, this value depends on the assignment of atoms around 3.0A to second or third neighbor peaks, which needs further study. A comparison of the R D F with that of a-Ge, normalized to the same bond length (Fig. 18), shows that the first neighbor peak is wider that in a-Ge, which is consistent with the mixed coordination (40). On the other hand, the second neighbor peak is narrower than in a-Ge, due to the greater relative stiffness of bond bending forces in diamond than in Ge. Note that the
8 6
A
- - MSIB a-C
4 A
2
G(r)
"" a-Ge
0 -2 -4 0.5
Fig. 18. JPSSC 21:4-C
1
1.5 2 2.5 r (Reduced Units)
3
3.5
R D F of MSIB a-C and a-Ge normalised to the same bond length (40).
J. Robemon
224
R D F displays a flat region between the second and third peaks which is characteristic of all tetrahedrally bonded networks and is caused by the uniform distribution of dihedral angles and third neighbor distances. We can therefore concluded that an essentially fully sp3 bonded form of a-C, analogous to a-Si, does exist, despite the greater bond bending stiffness of C. Some workers have doubted this was possible. 3.4 Structural Modelling of a-C There are numerous ways of modelling the structure of a-C. Some analyses of a-C have consisted of blending functions of S(k) of graphite and diamond in order to estimate the fractions of sp 2 and sp 3 bonding (98,87). The:structure of amorphous solids is also often studied using random network models (99). These can be built by hand or on a computer by, for instance, making topological rearrangements of crystalline lattices. A continuous randon network (CRN) has no broken (dangling) bonds and its average bond lengths and bond angles are set to the chemical determined values. The networks can be further refined by relaxing their structure under a valence force field (VFF) in which the distortions of bond length (Ar) and bond angle (A0) give an elastic energy of AE ffi I
I k°rlA0 2 2 + -~I kj,rlA# 2 2 krAr 2 + "T
E83
The VFF of sp 3 sites consists of a bond stretching force kr and a bond bending force ko. The VFF of graphite and sp ~ sites must also include a four-body out-0f-plane force k, which opposes the puckering of the layers (100). The values of force constants are found by fitting data such as the IR and Raman modes, elastic constants, and the phonon dispersion curves found by neutron scattering. They are kr= 270Nm -~, ke--25Nm-' for sp3 sites and k , = 363Nm-' , k0--- 36Nm -I k~ = 134Nm-' for graphite. In simple systems like a-Si, the values of Kr and Ke give a small bond length distortion and a A0"~I0 ° . Beeman and others (101,102) have hand-built C R N models of a-C, containing varying fractions of sp2 and sp 3 sites. Their characteristics are summarised in Table 7, and their RDFs are shown in Fig. 19(a). The C1120 model consists of four warped layers of sp 2 sites. The C340 model contains 9.1% sp 3 sites, and the C356 model contains 51.4%sp 3 sites. The C519 model contains only sp 3 sites and is the Polk (99) model of a-Ge rescaled to the C sp3 bond length. The bond lengths are set to those appropriate for the hybridization. The density of the models increases with the sp ~ fraction. The sp" bonded models have a low density because of their large interlayer space. All models contain a sizeable fraction of odd-membered rings. The author believes that these models contain a much higher fraction • of odd-membered rings of sp3 sites than is probably realistic, in that they do not take into account the lower stability of odd-membered rings of sp ~ sites, as discussed in section 4.2. Beeman et al (101) compared the RDFs of the models to the P,DF of evaporated a-C of Kakinoki et al (88) and Boiko et al (89). He concluded that the C340 model with 9% sp 3 sites ftted the experimental structure most closely. The interference functions of all four Beeman models are shown in Fig. 19(b). All four models
225
Diamond-LikeCarbons Table 7.
Structural characteristics o f the Beeman random network models (104) %sp 3
rl, ,~
nt
r2, A
n2
density, gm.cm -3
6
2. I I
C I 120
0
1.42
3
2.44
C340
9.1
1.42
3.28
2.43
2.69
C356
51.4
1.51
3.53
2.5,5
3.21
C519
100
1.55
4
2.52
(a)
,~,
I
I
I'll
~
I
I
I
12 I
I
3.39
I~J
J
I
II
I
,
I
_ ,__ •.4,,,..;,OvoU;orate d (KQkinoki) ....... glassy (Mildner) C 1120 .._.,~--" ; |00% sp2... ~.,...__....~
4O 2O
o 40 C340 20 8
0 40
r~
c3
6
o
49°1o ~ / ' ~ " . . .
i:5 2 O
'e o
n'-
0
40
C519 0 % sP2
20
.. _.....-" -'""
/-,,,,,,..._~..~.._. ./.;)'~.. ~ _ ~ . . - - . ? e.e
i
0
I
I
I
[~
• ° °.%. o
I ~ / I , I t 2
I r"; 3
R (~)
oot °
i , , Ill, 4
I
5
J. R o b e m o n
'J "1
(b)
I
I
i A'l
I
I
I
I .... I
I
'1
C340
A
91% sp2
A
4o
o m
C356 4 9 % sp2
2 o ~
.0 0 t_
v, V
C519 0 % sp 2
0
Fig. 19.
2
4
6
8 k (~,-11
t0
t2
14
16
(a) Radial distribution functions and (b) structure factors of the random network models of Beeman et al (101).
produce a peak around 3A-' and a main pe~tk around 5.5A-' The C! 120 and to a lesser extent the C340 model possess a pre-peak around 1.8A-L Such a pre-peak is charcteristie of layered structures and is the analogous of the (002) peak of graphite. It is interesting that this survives the introduction of some sp 3 sites in the C340 model, in which the more obvious layering charcter is lost. A noticeable feature is the similarity of the peak positions of all four models, despite the change from 3-fold to 4-fold bonding. This emphasises that structural differences produce quite subtle changes in the S(k).
Diamond-Like Carbons r
,
.
~
|
~
1
~ .~,
t ....
~..
~l '~
-
1
,,fT
i v
A
~
.
I
'
i
.
;
.
i
.
~
C~}
[! i~|
"
/i
~-
;'
I ! It
2
i
:!
"
Exp {D} I
/t \ ,,'?
...
I
',,
~
i
iiii
F" 8 ~"
IL
'
Cb)
-
I
II 4
, I I
-
1_
I
/ Il
i i
"""
/" /!
2
0
,dr
8
~ll
,
--
-
I
r.,..o.
!
-
..............
i
"",
m
co~
!
I
/ ~,
6 4
i
//','l/-
Beeman
C340
2
F,,,
0
,..I,,,
, I..........
I
2 r
Fig. 20.
, ,ll
li,,
0 ,,,
o
,
!,,
3
.....
t , ,
4
(A)
Comparison of the radial distribution function of sputtered a-C (Li and Lannin (92)) (solid line) with the simulations of Galli et al (103) and Tersoff (105) and the C340 random network model of Beeman (101) (dashed lines).
228
J. Robe~'umn
Li and I.annin (92) have compared the R D F of sputtered a-C with those of the simulations of Galli (103,104) and of Tersoff(105), and of the C340 Beeman model (Fig. 20). They found that both the Galli and Beeman models reproduced the significant bond length disorder found experimentally. They found that the models of Tersoff and Galli placed the second neighbor peak too distant, thereby overestimating the bond angle. The Beeman model was found to reproduce well the shape and position of the second peak, and in addition the relatively fiat region between the second and third peaks due to topological disorder. 3.5 EXAFS
Extended X-ray Absorption Fine Structure (EXAFS) are the small oscillations in absorption intensity occuring above the X-ray absorption edge. They are caused by an interference between the outgoing wave of the photoelectron and the back-reflections from the surrounding atoms, which causes variations in the absorption cross-section for the photon. The EXAFS intensity is given by 0t ----- ~,i0ti sin(kr i 4- r/) exp( -2o~k 2) exp(-2ri/2e(k))
[9]
Here k is the wavevector of the photoelectron, n is the distance from the excited atom and the i-th atom, al is the width of the n distribution, ,t, is the electron mean free path and ,/ is the phase shift. The effect of 2 is to damp out the effects of neighbors more distant than about 5 A. In disordered solids, the effects of second and higher order neighbors tend to be damped out by their larger static broadening ai. EXAFS is often the method of choice for determining local structure, because of its chemical selectivity and its sensitivity to bond lengths, ttowever, their are two problems with EXAFS in a-C(:H); the low atomic number causes problems in setting the phase shift and secondly EXAFS is unable to detect hydrogen. There have been numerous measurements of the EXAFS on a-C, by Batson and Craven (106), Denley et al (107), and Fink et al (78). Fink (78) compared the EXAFS of diamond, graphite, evaporated a-C and PD a-C:H (Fig. 21). The EXAFS of diamond and graphite extended to about 100 eV above the absorption edge. In contrast, the EXAFS of evaporated a-C are highly damped, decaying within 40 eV of the edge. This is due to the variation in bond length aj = 0.1 - 0.2A. Lannin (92) found a similar variation in bond length in sputtered a-C. This variation does not arise from hybrdization disorder, as both forms of a-C are over 95% sp 2 bonded. Oddly, Fink (78) found that the EXAFS of PD a-C:H were less damped that a-C, as a-C:}t has more coordination disorder. Comelli et al (108) observed a relatively undamped EXAFS for an a-C sample. This sample was created by Ar ion bombardment o f P I ) a-C:H. Its EXAFS were found to decay at a similar rate to those of graphite and to have about 2/3 of their intensity. They corresponded to a coordination number of about 2 and a bond length of 1.44A. It is difficult to accept such a low value of coordination for a-C, which conflicts with all other data on this system, but it is difficult to find the source of the problem. 3.6 Structure of a-C:H
The determination of the structure of a-C:H is more difficult than that of a-C because the hydrogen cannot be treated as a minor constituent, The minimum requirement of a structural determination is a value for the hydrogen content and the carbon coordination number. One
Diamond-Like Carbons
,
i'i
,
,'
I
I
'
i
229
J
,
I
I
J
i
graphite
a-C:H
"~- Jl./ \
~ - ~ ' ~
W
TQ:
r,,
a-C:H
2oc
-o_c
'~;o'
'"
'~'o'
' ' '~'oo'
'
Energy (eV) Fig. 21.
Extended X-ray absorption fine structure of graphite, annealled PD a-C:H, PD a-C:H, evaporated a-C and diamond, after Fink et al (78).
230
J. Robettson
should emphasise that there is no unique structure of a-C:H, it depends very strongly on deposition conditions. The hydrogen content can be determined by nuclear reaction analysis (NRA), elastic recoil detection (ERD), spin counting in proton NMR, thermal evolution and combustion analysis. Thermal evolution is the simplest method, and is most commonly used in a-Si:H. Care should be taken in a-C:H because some hydrogen can evolve as hydrocarbons, particularly from highly hydrogenated forms of a-C:H. The relative merits of the various techniques of determining sp3 fraction were summarised in Table 4. N M R (68-75) and XANES (78) are particularly valuable for a-C:H. Extensive NMR, IR and hydrogen evolution studies of PD a-C:H have been carried out as a function of preparation conditions and are summarised later. McKenzie et al (109) studied the structure of a-C:H by electron diffraction. The difficulty in applying electron or X-ray diffraction to a-C:H is that they do not detect hydrogen, so they give only the partial C-C coordination not the total C coordination. It is therefore unclear whether coordinations below 4 arise from C-H bonds or sp2 bonding. This is a non-trivial issue for H contents of 30-60%. Neutron diffraction detects hydrogen strongly. The S(k) of a-C:ll deposited from acetylene has been measured by Newport et al (i 10) to k,,,~ = 50A -~ . The sample had a hydrogen content of 32% and a density of 1.51 gm.cm -3. The low k region of S(k) is shown in Fig. 15 and the associated R D F is shown in Fig. 16. The total R D F of a-C:H is the sum of the three partial RDFs, weighted by the relevant elemental scattering lengths. The total R D F is dominanted by the C-C and C-H terms in a-C:tl, with the C-It peaks being negative going because of the negative scattering length o f H I. The first peak of the R D F at 0.8 A is due to H-H bonds. This is due to either Its molecules at voids or H-H clustering of CH, groups. 1t2 molecules have been detected by neutron scattering from their rotational spectrum. The second (negative) peak at 1.05A is due to C-H bonds. The third peak is found to be a split peak at 1.39 and 1.52A, which can be ascribed to sp 2 and sp 3 sites respectively. A s p 3 fraction of 80% was estimated from the relative sizes of these components, equivalent to a mean C coordination of 3.8. The area under this peak-pair is 2.5 atoms, equivalent to a total C coordination of 3.0 atoms for 3 2 0 H content, but much smaller than that deduced from the sp3 fraction. 3.7 Real Space Studies.
Hard carbons can Show various degrees of longer range order. There appears to be two forms of this, inhomogeneities and sp ~ site clustering. It was noted in section 1 that ion beam deposition could produce hard carbon which was a mixture of amorphous C and microcrystalline diamond inclusions. The inclusions typically have a 100A grain size and can be detected by real space imaging processes such as transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM)and scanning tunneling microscopy (STM). On the other hand, many deposition methods such as sputtering and plasma depostion produce films which are fully amorphous and show no crystailinity at the 10-100A scale, as evidenced by TEM (90,91,111,112). There is a degree of medium range order in these films which shows up as the zero k peak in S(k), which can arise from residual layering or Sl~ clustering described shortly. In particular, Li and Lannin (92) noted that evaporated C may contain graphitic fragments originating from the evaporation source.
Diamond-Like C~bons
,
,
•¢
,,
¢
,
';
,;
4
'¢', t
231
4. ~i
t<,
#
, ~,,11
(aJ ,i,l
(b:
(cJ
f/.zm Fig. 22.
Scanning tunnelling microscope images of (a) evaporated C, (b) ion beam deposited C and (c) laser plasma deposited C, after Collins (35).
232
Fig. 23.
J. Robertson
Transmission electron micrograph of laser plasma C sample of Collins et al (35), after J. C. Pivin (CSNSM, Orsay) with thanks.
Collins et al (35) have compared carbon produced by evaporation, ion beams (IB) and laser plasma (LP) deposition by TEM and STM. STM images such as those in Fig. 22 were interpreted as showing that evaporated carbon consisted of a s p 2 matrix, as expected, IB carbon consisted of a series of diamond-like grains lying as ribbons in a s p 2 bonded matrix, and LP carbon consisted on a dense three-dimensional mesh of diamond-like grains. The diamond-like grains are further seen in the TEM picutre of LP carbon shown in Fig. 23. This material in clearly not amorphous. Medium range ordering is expected in PD a-C:H, but on a much smaller 4-10A scale. Electronic structure calculations in section 4.2 suggest that the sp 2 and sp a sites in this material tend to segregate into sp~-bonded graphitic clusters embedded in a sp a bonded matrix. The clusters are typically 4-10A wide and theory suggests that they should be compact rather than elongated. Raman spectra descibed in section 3.8 provide strong indirect evidence for their existance. It is possible that graphitic clusters have been directly observed in sputtered a-C by STM by Marchon et al (I 13), Fig. 24. This image o f a 28x12A area shows some 6-fold and 5-fold rings of atoms; the 6-fold rings may correspond to graphitic bonding. Nevertheless, care is needed
Diamond-Like Carbons
233
(a)
(b)
Fig. 24.
(c)
Scanning tunnelling microscope image of (a) 28x12A area of sputtered a-C, with close-ups of (b) left- and (c) right-hand parts of the image below, showing possible 6- and 5-fold rings of atoms, after Marchon et ai (113).
in using STM in graphitic systems because the weak interlayer bonding may not support a layer against the STM probe tip. Fig. 25 shows topographical images of a flake of MSIB a-C taken by energy filtered scanning transmission electron microscopy (STEM) by Juan et al (112). Each image is taken for electrons which have lost the indicated energy passing through the specimen. The images therefore represent real space electron energy loss (EELS) images of the local bonding. The losses in this case occur by the excitation of valence plasmons (see section 4.7), The 7r electrons of sp 2 sites produce losses at 5-7 eV and their cr+~t electrons produce losses at 20-24 eV, The electrons of sp 3 sites produce losses at 30-33 eV. While a specimen of a-C can have a
234
J. Robertsou
> ¢,q t~
N
e~
0
p..
i 0
O~
t'q
O0
t,q p,.
t~ r~
i~i!~i~i~i!~~ii~il!!~!~ ~i~i~~~ ~' i~~~ ,~!~~
t,.., 0
.E r~ t_.
> t'q 04
,q.
> o
cq
,,
rn
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IE r"
o
r~
2,35
Diamond-Like Carbons
diamond
graphite
5 e
~
01
glassy
._=
g E a-C:H,
¢r
25C
t_
0
sput, 25 C
ol L_
o
~
LL
evap, 25 C , S----
0
I
500
I
,
i
1000
1500
,
%.
2000
Wavenumber (cm-1) Fig. 26.
First order Raman spectra of diamond, highly oriented pyrolytic graphite (hopg), microcrystalline graphite, glassy C, PD a-C:H, sputtered a-C and evaporated a-C, after Shroder et al (! 14), Nemanich and Solin (116) and Wagner et al (130).
236
J. Robertson
macroscopic loss from 20 to 33 eV, depending on its sp 3 content, one might expect that the loss locally would be either that of sp 2 or sp 3 bonding. This behaviour is indeed seen in the figure, bright regions at 6 eV are bright at 22 eV but dark at 32 eV. However, there are strong losses at 28 eV, perhaps indicating the presence of mixed bonding. This technique has great potential in hard carbons, with perhaps the highest ultimate resolution of 5 A. Losses due to C is excitations at 285-290 eV can also be used to distinquish between sp ~ and sp 3 sites. 3.8 Infrared and Raman S p e c t r a
The infrared (IR) and Raman activity of crystals is restricted by symmetry and k conservation to a series of sharp lines. In diamond, there is one Raman active mode at 1332cm -~ and no IR active modes (114). In graphite (100), four atoms per unit cell, there are two IR active modes, the main E~u longitudinal optic mode at 1585cm-' and the out-of-plane A2u mode at 868cm -t. There are two Raman active modes both of E2s symmetry, the main 'G' mode at 1580cm -~ and the rigid layer mode at 50 cm -t. A 'D ~mode around 1350 cm -j is also found in microcrystalline and disordered graphites but not in highly crystalline graphite (I 15,116), as seen in Fig. 26.
t/.I Fig. 27.
1
Mechanism of infra-red activity in a random covalent network (I 17).
~s
Diamond-Like Carbons
237
The k conservation rule no longer holds in amorphous solids because of the loss of periodicity, and all vibrational modes can have IR or Raman activity. The most common IR activity arises from the vibration of ions in ionic crystals like NaCI. IR activity can also occur in a network of purely covalent bonds if there is no center of inversion symmetry. The simplest example of this is trigonal Se. The most simple, localized mechanism of IR activity in a covalent network is the creation of an induced dipole by charge flow from extended bonds to contracted bonds, as proposed by Albert et al (117), Fig. 27. The resulting IR spectrum resembles the phonon DOS, but with greater contributions from the higher lying modes of LO character. The phonon spectra of a covalent network can be calculated using the valence force field {8}. Fig. 28 shows the resulting phonon DOS for diamond, graphite and the four Beeman models (I01). These phonon DOS do not show sharp van Hove singularities because the equation of motion method used there causes a smoothing. The graphite spectrum shows a large peak at o9 = 1 3 5 0 - 1 5 5 0 c m -~ due to bond stretching modes, two lower peaks around 300 and 600 cm -~ due to modes of bond bending character, and a large peak around oJ = 0 due to rigid layer translational modes (118-123). The diamond spectrum shows a large peak at 1100-1300 cm -~ due to bond stretching modes and again two lower peaks at 600 and 900 cm -t (118). In general, the random networks show a gradual evolution of features and peak shifting with changing sp 3 content. In particular, the band maximum falls with increasing sp3 content, from about 1600 cm -~ in graphite and the Cl120 model to about 1350 cm -~ in diamond and the C519 model. Fig. 28 compares these DOS with the IR absorption of evaporated a-C found by Knoll and Geiger (124). Raman spectroscopy is a popular tool for characterising both the crystalline quality of diamond films and the nature of a-C(:H) films (114,125,126,9). Fig. 26 compares the Raman spectra of a diamond thin film, highly crystalline graphite (HOPG), microcrystalline graphite and some amorphous carbons (114,116,9). The Raman spectrum of a good diamond film consists of a single sharp line at 1332 cm --j with no background. Highly crystalline graphite has a single Raman peak at 1580 cm -~ known as the G peak. This is a zone center mode of E2s symmetry, whose eigenvector is shown in Fig. 29. An additional feature occurs in microcrystaUine and disordered graphites known as the D peak and centered on 1350 cm-L This mode is inactive for an infinite layer and is activated by the absence of k conservation. It is a common feature of disordered carbons. Tuinstra and Koenig (115) associated the D peak with the A~, mode at the K point of the Brillouin zone, whose eigenvector is also shown in Fig. 29. The intensity of the D mode relative to the G mode is found to vary with the crystallite size as (I 15) I(D)/I(G) = k/I.~
{10-I
While the Raman activity of the D mode can be found to cancel about each atom for an infinite layer, there is no cancellation at the perimeter sites of a crystallite, leading to the proportionality given in [10]. More generally, Nemanich and Solin (116) attributed the D mode to the large DOS around the K point, which arise from the nearby fiat bands, as seen in the calculated phonon dispersion curves of Lespade et al (123) in Fig. 30. The Raman spectra ofa-C and a-C:lI should in principle give considerable information on their local bonding. The loss of k conservation allows each mode to become Raman active to some degree. The Raman spectrum of a highly disordered solid will resemble the phonon DOS but weighted by a matrix element which tends to vary as o92 at low phonon frequency, o9. The Raman spectra of the various amorphous carbons have similarities to microcrystaUine graphite
J. Robertson
238
I
>,, e
I
l
~
I
l
l
l
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i
;
]
~
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i
j
Infra-red oborption
m
C c-
Roman
scottering
rheor.y
~)
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Cl120
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'4--
C 340
0 >, .4..# II) c-
f
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C 519
0
500 Wove
Fig. 28.
I
1000 number
I
1500
w
I
t
~1
2000
(cm -1)
Calculated phonon DOS of diamond, graphite and Beeman random networks for a nearst neighbor valence force field (104), compared to experimental IR absorption spectrum of evaporated a-C of Knoll and Geiger (124) and the Raman spectrum of sputtered a-C.
(Fig. 26). This is because the Raman cross-section of graphite is 30-60 times that of diamond, so the siC bonded regions tend to dominate the spectrum (127,128).
Diamond-Like Carbons
239
AIg disorder mode
E2g Roman mode at r
Fig. 29.
Eigenvectors o f t h e E2t zone center G mode and the A~ disorder (D) Raman mode.
I-
I
t
M
K Wavevector
160C
J200
400
0
Fig. 30.
r'
r DOS
Phonon dispersion curves and DOS for single layer of graphite, after l.espade et al (123).
We now consider the experimental situation in more detail (128-138). Fig. 31(a) shows the Raman spectrum of plasma-deposited hard a-C:lI, as a function of excitation frequency, v (129). Fig. 31(b) shows the spectrum of a-C:H annealed at 600°C, which is now essentially sp ~ a-C. JP$SC 21:4-D
J, Robomon
240
o-C "H as deposited
o-C:H
G
hVL= J2.188V
>.
2.sTe
~
IJJ I-Z_
i I,
vii
2.57eV
z
G
600°I: onneol//~
hVL=2.18 eV ,,
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3:5/.
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/..82 e y ~
~v~"
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I00--012~00-1400 1600 1800 RAMAN SHIFT(cm "11 Fig. 31
I
1000 1200 1400 1600 1800 RAHAN SHtFT(cm "1)
Raman spectra of(a) PD a-C:H and (b) a-C:H annealed at 600°C, vs. excitation frequency, after Wagner et al (I 30). t~
m
m
!m
j-
NO
m
IOO = 1 ~ ......... --tii00 I1~ 1(100 st40
---t4O0
.
tim
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0 It00
iN0
(c=-I)
S00
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loo
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190 tOO 0 li~0
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Roam= ¢b,ift (=m-I)
Fig. 31
It00
t000
141100
13~0
I~mO
1000
Ram,m sh/ft (¢ma)
(c) Raman Spectra of sputtered a-C for different RF sputtering powers, after Cho et al (27).
Dimnond-Like Carbons
1600
(a)
241
Graphite
-2"
1580 A
G" 1560
I
A'
•g
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•
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459 nm 515 nm 628nm
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1500
I
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0
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•
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s
4.0
m
o6L
2.0 A
e~
~
500
1000
S
@
o
0.0
0
1500
2000
Bias Voltage (V)
Fig. 32.
Variation of (a) the ratio of D and G mode intensities I(D)/I(G) and (b) the G mode frequency with excitation frequency and bias voltage for PD a-C:H, after Tamor et al (130).
The spectrum of as-deposited a-C:fl at hv = 2.18 eV is seen to consist of a broad peak centered on 1520 cm -m and a shoulder around 1300cm -~, perhaps related to the G and D modes of
242
J. Robertson
graphite. On annealing, the upper peak sharpens into a well defined G peak, and the D peak develops around 1350 cm -I. This behaviour is consistent with a transformation of a-C:H into graphitic a-C by annealling. Fig 32(c) shows the Raman spectrum of sputtered a-C as a function of sputtering power. Each spectrum has been decolvolved into two peaks, a D and a G peak. Note that the D peak has a much greater area than the G peak in some samples. Note also that the D peak is much wider than the D peak in microcrystalline graphite (Fig. 26), so that this spectra is not simply attributable to microcrystalline graphite inclusions. The intensity of the D peak in a-C and a-C:H varies with deposition conditions. It is tempting to assume that the D and G peaks arise from graphitic clusters and so deduce a value of Lo from [10]. Tamor et al (134) studied the variation of I(D)/I(G) for PD a-C:H as a function of bias voltage Vb, as seen in Fig. 32(a). They found that I(D)/I(G) increases with Vb, which would imply that Lo decreased with increasing bias. ttowever, the optical gap also depends on the size of graphitic clusters, varying as Eg = k/L~
as shown in section 4.3. As the gap decreases strongly with increasing bias, we would expect L, to increase with bias, the opposite way. Tamor (134) therefore suggested that eqn [10] fails at low values of I.~ and that I(D)/I(G) varies instead, as shown in Fig. 33, reaching a maximum around L, = 12A. This seems reasonable; I(D) cannot increase without bound at low Lo, as it is bounded above by the DOS in the region of the K point. I(D) is then likely to decrease again in very disordered cases with L, < 12A, as the DOS around K becomes broadened and spreads into modes with lower matrix element.
4
3
1
0
I
0
I
I
I
10
20 L
Fig. 33.
(A)
Proposed variation of I(D)/I(G) vs Sl~ crystallite size I~
30
Diamond-Like Carbons
243
I
glassy C 1600
'mme~e~e
~
graphite (hopg)
a-C:H ~
"\
sputtered a-C
1500
).oo iiim
J:
"\ "\
¢
E
~
"\
sputtered a-C
"\ '\
'\ 1300
"\
"\
glassy C
"\
"\
"\ "\ \
\ \ \
1200 200
Fig. 34.
I 300
J J 400 500 Wavelength, nm
a-C:H
600
tO0
Raman peak shift vs. excitation wavelength, for graphite, glassy C, sputtered a-C (136) and PD a-C:H (130).
The spectra show pronounced changes as a function of excitation frequency. Inspection of Fig. 31 also shows that the G peak shifts upwards with v in the as-deposited film while the D peak moves upwards in the annealed film but the G peak does not (129,130). These movements are
J. Robextmn
244
a common feature of graphitic carbons. Fig. 34 shows the movements of the G and D modes of HOPG, glassy C, sputtered C and a-C:H plotted as a function of excitation wavelength (130,137). The G mode in HOPG does not shift. The G mode in glassy C also does not shift, nor does it in the annealed a-C iti Fig: 31(b). The G mode moves only in the very disordered carbons, a-C and a-C:H, and the movement saturates once a) reaches 1600 cm -t. On the other hand the D mode moves in all forms of carbon. A further factor is that the rate of G peak shift varies with bias voltage for PD a-C:H, as evident in the data of Tamor et al (134), as seen in Fig. 32(b). The parameter controlling the shift rate could be either L, or the sp 3 content. Two types of behaviour are evident in Fig. 34, one in which the G peak remains fixed and one in which it shifts. The distinction between the two behaviours correlates best with whether L, is greater or less than 12A, the critical size in Fig. 33. The G peak shifts only for the more disordered carbons with L, < 12A. The alternative explanation is that the shift arises from a finite sp3 content (132). However, the sp3 in unhydrogenatedsputtered a-C is quite low, about 5%, yet its rate of shift is nearly as great as that o f P D a-C:H. In addition to peak movements, the I(D)/I(G) ratio also varies with excitation frequency v. The spectra in Fig. 31 show that I(D)/I(G) increases at low v. Yoshikawa et al (136) found that the i
I
i
4
o-C:H 3
"
,
o
1600 cm "1
A
1520
o
t
/
cm "1
~ , ,
a 1300 cm"1
~ . .
," " "
== o
1
A
" ~....,O/O'-
o
o .<,:~_._ ...a._ ._a. _,
.....
I
,
1.9
~
,
,
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,
2.3 PHOTON
Fig. 35.
....
.--'o""""
"
~-
,
I
I
~
2.7 ENERGY
,
I
3.1
I
i
~
I
,
3.5
{eV)
Relative Raman intensities of the D and G modes, after Ramsteiner et al (129).
Diamond-LikeCarbons
245
variation is similar for a-C and glassy C and approximately linear with excitation wavelength. Wagner et al (129-131) studied these changes further by obtaining the absolute variations in Raman intensity of the G and D features in a-C:H as a function of v. Sitting at fixed phonon frequencies, rather than moving with the peaks, they nevertheless found that the intensity ofthe G peak increased strongly with v while the D peak stayed relatively constant (Fig. 35). Wagner et al (129-131,9) noted that the intensity changes of the G and D peaks arose from the Resonant Raman effect. The Raman cross-section L2 arises from the changes in bond polarizability X = ~ - 1 with atomic displacement. ~ results from electronic transitions across the optical gap, so that f~ will vary as ~X 2 n - k(=~=v )
[11]
If the excitation frequency v is below the gap in the transparent region, fl is independent of v. Moving v towards a band edge causes a resonant increase in f 2 , giving the resonant Raman effect. A relatively simple example of this effect is the resonant behaviour of the 1332 cm -~ mode in diamond, found by Wagner et al (131), Wagner et al (129-13 !,9) also interpreted the shifts of the G and D peaks in terms of resonant effects. A more complex two-phase model is now necessary, as the different lmhaviour of the G and D peak intensity in Fig. 28 cannot be expained within a single phase. Phase 1 was assumed to give peaks at 1300 and 1500 cm -t and was attributed to the sp 3 network. Phase 2 was assumed to give a peak at 1600 cm -~ and was attributed to spa clusters. The peak shifts then result from the different dependence of the f2 of each phase on v. This explanation may be partly wrong. The shifting of the G and D peaks is a common feature of disorderd spa carbons, as seen in Fig. 31. In view of the greater Raman cross-section of bonds it seems more likely that essentially all the features of the Raman spectra of a-C:H arise from its spa sites. In the author's opinion, there no satisfactory theory of the Raman effect in amorphous carbons at present. Raman scattering can be modelled as the change in bond polarizability due to atomic displacement. The bond polarizabilities of graphite and diamond are often treated as equal. This would give the same L2 for graphite anddiamond and is wrong. Clearly, an extra contribution to f~ must be included from the ~r bonds, which would be larger due to their smaller gap. Alben (117) noted that there are three basic mechanisms to give changes in bond polarizability in a random network. Mechanism (I) associated with bond stretching is of most interest here as this affects the high frequency part of the spectrum. This gives a Raman tensor of the form
1 where I is the atom index, A is a bond at 1, r is the borid vector and C is the bond compression. Beeman et al (101) used this expression to calculate the Raman spectra of their random network models. However, this form does not allow for the higher bond polarizability of graphite. AI-
246
J. Robertson
though n bonding can be long range, its polarizability is likely to be short range. should be possible to modify 1!2] in the form 0C'
- 1 = Y~a{rAr& - .-~ T}Ca{];I;
c2 2 I,iCl,J
Hence, it
Cn3]
(E, - (E i - Ej)) 2 }
where the sum is over the i electronic valence states and j conduction states of energy E, and E), whose eigenvector component on site 1 is c,.i, etc. This expression would give a resonant Raman effect which varies with the local band gap at each bond. i
q)
CH
/%
a)
STRETCH
|
oc BEND (ROCK OR WAG) i
CH 2
b)
CH 3
SYMMETRIC ASYMMETRIC STRETCH
ROCK
WAG
SYMMETRIC DEGENERATE STRETCH
SCISSORS BEND
TWIST
SYMMETRIC DEGENERATE DEFORMATION
x
c) Fig. 36.
ROCK, WAG
TWIST
Description and symmetries of the C-H I R vibration modes of CH. groups (146).
Diamond-Like Carbons
247
The Raman spectrum has also been used to deduce the sp a fraction. Richter et al (132) noted that the upper limit o f the p h o n o n DOS is lower in diamond than in graphite, and that it moves to lower frequency in the Beeman (101) random networks as the sp ~ content increase (Fig. 26). A fair approximation would therefore be to take the sp "~fraction as proportional to the redshift of the G peak. There are a number o f problems with this approach. The band limit o f a homogeneous random network undoubtedly does shift downwards with sp 3 content. However, if the network is inhomogeneous for Raman as the Wagner 2-phase model implies, and if the Raman cross-section o f sp 2 sites is 30-60 times larger, the Raman scattering o f sp ~ clusters will always dominate the aggregate spectrum. Also, as the G peak appears to shift by similar a m o u n t in sputtered a-C with 5% sp .~ sites or in PD a-C :H with 30-50 sp 3 sites, the sp 3 content is not so obviously the major factor. The author thus concludes that the first necessity is to provide an adequate theoretical model of the peak shifts in sp ~ bonded C, as a function of disorder. 3.9 C-H Vibrational Modes
The C-H vibrational modes produce a series o f infrared (IR) absorption peaks which can provide very detailed information on the local C-H bonding (140-145). It is possible to assign each peak to a different carbon configuration - sp 3, olefinic sp 2, aromatic sp 2 or sp t - and the number o f hydrogen neighbors. The local symmetries and names of the vibrational modes of CH, CH2 and CH3 groups are given in Fig. 36 (these do not depend on the C hybridization). The naming o f the modes is taken from work on a-Si:H (64,146). One may approximate that only the H moves in these modes, due to the large difference in C and tl masses. Each configuration gives rise to one C-H stretching mode per H atom, at around 3000 cm -~, plus two further deformation modes per atom below 1500 cm -~. All modes are IR active, except the A2 twisting modes (146). Dischler (140) assigned each absorption peak, as listed in Table 8, on the basis o f existing assignments in hydrocarbon molecules and from their shifts under deuterium substitution. The assignments for the C-II stretching modes are generally agreed, but the recent neutron scattering data o f t t o n e y b o n e et al suggest different assignments o f some off the deformation modes. Firstly, noting the ordering and spacings of the Si-H modes o f SiH~ groups in a-Si:H (146), scissors at 880 c m -1, wag at 850cm -1, twist at 820cm -I and rock at 630cm -I, we reassign the modes of sp 3 CH2 groups as scissors at 1470cm -t, wagging at 1330cm -t, twist at 1300cm -~ and r o c k i n g at 1030cm-L Secondly, the twisting As mode is IR inactive (146), and cannot be the H I 8 mode at 1180 cm -~. Thirdly, as the Sill bending mode has a similar frequency to the B~ rocking mode of Sill2 (630cm-~), we assign the H I 8 peak at 1180cm -~ instead to sp 3 CH bending. These changes are summarised in the last column of Table 8. The new assignments agree broadly with those of H o n e y b o n e et al (145), but agree less well with those o f T i b b i t t et al 044). They still leave peak HI5 unassigned. Dischler (140) and many others (60,61) have used the peak intensities o f the C-H stretching bands to deduce both the sp 3/sp ~ ratio and the H content of a-C:H films, as a function of bias voltage, source gas, gas pressure and thermal annealling. The IR method has been very popular because o f its wide availability and ease of use. However, it clearly needs a uniform distribution of l-! over the sp 3 and sp ~ sites to give reliable concentrations o f these sites. N M R suggests that this is untrue as tl bonds preferentially to sp 3 sites. The method therefore tends to neglect sp 2 sites, particularly those within clusters.
248
J. Robertson
Table 8.
line 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
C-H infra-red vibrational mode assignments in a-C :H. Modes 1-10 are C-H stretch, lines 11-27 are C-H deformation. s = stretch, ss = symmetric stretch, as--antisymmetric stretch, sd-- symmetric deformation, dd-- degenerate deformation. wavenumber, cm -t hard a-C:tt soft a-C:tt 3300 3300 3045 3060 3025 3000 3000 2970 2945 2920 2920 2920 2875 2850 2850
1440 1435 1370 1290 1170
1030 910 840 755
700
1490 1450 1450 1445 1325 1280 1180 1110 1075 1030 910 840 755 700 700 700
Dischler assignment configuration symmetry spl CH A s arom sp2 Ctt A s olef sp2Ctt2 B~ as olef sp2 CH A s sp3 CIt3 E ds olef sp2 CH2 A~ ss sp3 Ctt2 B~ as sp3 CH At s sp3 CtI3 At ss sp3 CI-I2 At ss sp3 CH3 sp2 CH2 sp3 CIt2 arom sp2 CH sp3 CH sp3 Ct-I3 olef sp2 CH sp3 CH2 olef sp2CH2 sp3 CIt3 sp3 Ctt2 olef sp2 Ctt~ olef sp2 CH arom sp2 CH spl CH olef sp2Cl-12 sp2 Ctt2 olef
E dd As scissors At scissors A bend E bend At sd A bend A, twist B2wag E dd B2 wag A2 twist B bend B bend E bend B, rock B~ rock
New assignment config
unassigned sp3 CH2 B~ wag sp3 CH
E bend
sp3 C1t2 B, rock
C-C Infra, Red vibrational mode assignments for a-C:H, after Dischler (141). line 1 2 3 4 5 6 7 8 9 10
wavenumber, cm-' 2180 1620-1600 1580 1515 1300-1270 1245 1160 970 885-855 840
assignment olef arom mixed mixed mixed olef arom
spl sp2 sp2 sp2/sp3 sp2/sp3 sp2/sp3 sp3 sp2 sp3 sp2
Tamer et al (147,148) in particular noted these problems. They found that a-C:H deposited from benzene at low bias voltage had an increasing fraction of 'pendant benzene' groups, sidechain phenyl groups which were undissociated by the plasma and which do not contribute to the band gap or rigidity of the main network, but serve only to change its density. It could even
Diamond-Like Carbons
249
be suggested that the hydrogens of the pendant phenyls would dominate the IR spectra, and overshadow any Sl~-H sites in the main network. In this way the IR method might be of little use for finding the sp ~ content of the extended network. 4 ELECTRONIC STRUCTURE 4.1 Coordination This section considers the bonding configurations likely to be found in amorphous carbons and their electronic structures. Let us first consider the coordination number. Typical group IV elements like Si and Ge are most stable in the 4-fold coordinated diamond structure than in the 3-fold coordinated graphite structure or the more highly coordinated metallic structures like simple cubic or//-Sn. Si and Ge transform to the higher coordination structures under pressure or on melting. Carbon is different (149-151). It is most stable in the 3-fold coordinated graphite structure. This difference in stability of graphite and diamond is actually very small at NTP, 0.03 eV. C~0 is estimated to be a further 0.4 eV less stable (167). Higher coordination structures are not favoured for carbon at high pressures because they have atomic volumes which are no smaller than that of diamond. Additionally, experiments and simulations suggest that liquid carbon has a lower coordination than the solid, nearer 2. Carbon is atypical because it is a first row element. It has no p core electrons. Its 2p electrons feel the full core potential, while its 2s electrons feel a pseudopotential in which the short range part is screened out. This causes carbon's 2p orbitals to be relatively more tightly bound than
15 t0
T >
A
(D e-
uJ
t5
5 0
£voc
£F
-5
-10 -15 -2C
-25 K Fig. 37.
A
F
~
LL
A
F
A
X
T.
F
Tight binding band structure of (a) single layer of graphite and (b) diamond (7).
250
J. Robertson
its 2s orbitals, compared to the 3s and 3p orbitals in Si. This effect stabilizes carbon's sp2 bonds compared to its sp' bonds. It also reduces the stability of higher coordinations, dependent on p-like bonding. 4.2 Huckel Calculations The key to understanding the electronic structure of all amorphous carbons is to realise that this is controlled by the rt states of the sp~ sites (7,152,153) as these lie closest to the Fermi level EF. This is seen in Figs. 37 and 38, which show the density of states (DOS) and band structures of diamond and a single layer of graphite. The sp3 hybridisation of diamond leads to a wide band gap between the valence band of occupied bonding (o) states and a conduction band of empty antibonding (o*) states. In graphite the o and o* states lie at similar positions to this and the n states form a band which lies across the or-o* gap, with a minimum in the DOS at EF.
A standard approximation is to decouple the o and n states and to treat them separately. This is possible because the orbitals lie perpendicular to each other for planar Sl~ sites (Fig. 1) and because their states tend to lie in different energy ranges (Fig. 4), which minimizes their coupling. The o and n states behave very differently. The o states are the 2-center bonds which form the back-bone of the network. Their bonding is very localized and their bonding energy can be expressed as the sum of the energies of each bond, as for instance in bond orbital approximation of Harrison. Their energetics can also be expressed as a short range valence force field (cf [8]). This causes the a electrons to control the Short-Range Order ( S R O ) o f the network, iv its bond lengths and bond angles, but it leaves the longer range order undefined. The n states are more complex in that they can form both localized 2-center bonds as in ethylene and multicenter or resonant bonds as in benzene or graphite. Their bonding energy is longer range and non-local. It cannot in general be subdivided into the contributions from individual bonds. In this way n electrons may introduce Medium Range Order (MRO) into the structure. A key feature of the n states is that they form a half-filled band. Creating a gap in their spectrum at Er will lower the energy of the occupied states and stabilize the resulting structure. These effects can be analyzed using the Huckel model. This is a simplified tight-binding Hamiltonian which retains only the n orbitals and their nearest neighbor interaction, B = V(pTt). The absence of n states on sp3 sites blocks the n interaction passing through that site. The Huckel model therefore maps the original network of C and H sites into a series of separate n-bonded clusters. Finding the stable structure is reduced to maximizing the total n binding energy per site Etot of each cluster. The possible configurations of these clusters are of course similar to those of the analogous organic molecules (154). We have investigated the binding energy and band gap of a wide range of possible structures. Some of their normalized n binding energies Etot/fl are given in Table 9 and their electronic spectra are given in Fig. 39. This leads to the following observations; (a) Clusters tend to planar. This aligns the 7t orbitals on adjacent sites parallel and maximizes their interaction. (b) There should be an even number of sites in each cluster. Otherwise a half-filled state exists near E = 0 with low binding energy which reduces Etot. as N --) co.
Diamond-LikeCarbons
graphite
251
~
I/} (1} 4.a
0
.l.a {/}
o .ca (/} e-
o l
(D
(:3
-25 -20 -15 -10 -5 0 Energy (eV) Fig. 38.
5
t0
5
Tight-binding density or states of graphite, diamond, and the Beeman random network models of a-C (152). Their sp 3 fractions are given.
252
J. Robertmn
Table 9. Total n binding energies per site of various C configurations.
('~")n
G
# I
•
group
gtot/~
ethylene
1
polyacetylene
1.273
~ benzene
1.333
~napthalene
1.368
azulene
1.336
quinoid
1.240
polyacene
1.403
graphite
1.616
(c) The simplest configuration is the ethylenic double bond C = C which has E~o,/fl = 1. E,oJP of a row of double bonds as in alternant polyacetylene is also 1 in this model, so such olefinic chains are not particularly favoured. (d) E,o, is dramatically increased by combining three C = C bonds into a planar 6-fold (benzene) 1 ring by -~fl per site. Such rings are called aromatic. (e) Etot is further increased by fusing benzene rings into aromatic layers. In this way aromatic clusters are built up. Thus graphitic clusters are favoured over acenic clusters. (f) Compact clusters are favoured over row (acenic) clusters because of their fewer edge sites. (g) Quinoid groups are not favoured. They have a low band gap and a low E~. They would tend to dissociate into separate aromatic and olefinic groups if allowed. (h) 5,7 and 8-fold rings are unfavoured as these give states at or close to E--0. 4-fold rings are unfavoured because they have too much bond angle distortion. The behaviour of oddmembered ring combinations is more complex (! 55,156).
Diamond-Like Carbons
253
(i) A quadrupole of two 5-fold and two 7-fold rings can be created in a perfect graphite layer by rotating two sites by 90 ° and rejoining the bonds (Fig 39 e). This configuration gives quite a high density of states near E = 0 and so is unfavoured. However, an adjacent pair of 5-fold and 7-fold rings as in azulene has states well away from E = 0. Its F~otis only slightly lower than that of naphthalene (Table 9) and it can be considered to be an excited state of the basic structure. The configuration was also found in simulation of Galli et al (106).
ethylene N-fold rings N=5
II
II
I
N=6
.=7 I II . =8 III
II
I II
II
II
fused rings
~ c~
I II III II Ii II
:5
2
I
~111 II I IIIII I! I
0
-1
-2
-3
Energy (/~) Fig. 39.
Electron states and spectra of carbon bonding configurations (152).
254
J. Robertson
A value of /~ = 1.35 eV
[14]
has been found by fitting the bond energies of C = C, benzene and graphite, Such comparisons also show that the Huckel model overestimates aromatic stabilisation - E,ot/B~ 1.19 for benzene rather than the theoretical value of 1.33 given in Table 9, and 1.37 for graphite rather than 1.616. Summarising, rt bonding strongly favours aromatic rings over olefinic chains and also favours the the clustering of separate rings into graphitic sheets. Hence we expect aromatic ring clusters to be the dominant species of sp 2 sites. The o binding energy is independent of the degree of clustering, llence, for a given fraction of sp 2 and sp3 sites, rt bonding favours the formation of the sp2 sites forming sizeable graphitic clusters rather than being spread homogeneously through the sample.
Table 10. 2-phase model of amorphous carbons.
sp2 phase
sp s phase
evap. a-C
sheets
sheet rims
a-C:H
small clusters
sp3 or polymeric matrix
control
electronic properties
mechanical properties
We are therefore led to a 2-phase model of amorphous carbons, Table 10. The first phase is the n bonded clusters. These determine the optical properties. This phase is embedded in a second phase. This second phase can exist as a rim of sp3 sites around the clusters when sp 3 sites are few, as in sputtered a-C. In a-C:H the second phase is the major sp3-bonded phase, which can be either a highly cross-linked as in hard a-C:H, or a more polymeric hydrogenated phase as in softer a-C:H. This phase largely determines the mechanical propeties as shown later. 4.3 Band Gap
The band gap (LUMO-HOMO gap, lowest unoccupied molecular orbital to highest occupied molecular orbital) in all amorphous carbons is controlled by the n states because these states lie closest to E~ as shown in Fig. 4. The familiar amorphous semiconductors like a-Si are o bonded. Their band gap is given by the o-o* gap and this depends mainly on short range order (SRO), such as the coordination number, the bond length and the bond angles. These are conserved in the amorphous phase, so the band gap tends to be unchanged. The band gap of n-bonded systems is very different. It depends mainly on the medium range order (MRO), the degree of clustering (7). This is seen clearly in the Huckel model (152). The band gap of both ethylene and benzene is calculated to be
Eg = 2# The gap of olefinic chains can be found from their eigenvalues
[15]
Diamond-Like Carbons
10 "~////////// a - C : H
-
i
0.11
1
-
o--C~
I
10
0.01
-
I
I0(
go
EL
-1.0 >
•
(!;
uJ 0.1-
M-g
0.1 0.01 1
10
100
Number of rings (M) Fig. 40.
Calculated band gap vs. number of rings, for planar clusters of fused 6-fold rings of sp 2 sites (152). Inset shows likely ring orders for a-C and a-C:[t. ~n
t = 2p c o s ( ~ ) ,
n = I..N
[16]
This gives 2p,~
Eg -~
N
[17]
for N large and even. Fig. 40 shows the gap or compact (upper line) and acenic (lower line) aromatic clusters as a function of M the number of rings. The gap of compact clusters, the most stable sort, declines slowly and irregularly with M, according to the approximate relation
P
Eg ~ 2 MI/-----T JPSSC 21:4-E
[18]
I. Robertmn
256 or
[19]
Eg --6/M ~/2 eV where p--- -2.9eV. It can also be expressed as Eg "-, 7.7/La eV
[20]
where L,(A) is the cluster diameter or in-plane correlation length. The gap of acenic clusters falls off more rapidly, as roughly 60 eV Eg --- (M + 2.16) 2
[21]
The band gap is measured experimentally optically. In the absence of a sharp band edges in an amorphous semiconductor, the optical gap is defined empirically as either as the Eo4 gap, the energy at which the optical absorption coefficient a = 104cm-I, or the Tauc gap given by fitting a to the Tauc formula
[22]
(aE) 1/2 = B ( E " F~r)
s s
J"
..,,"~//"
J
5 10
sputtered a-C
MSIB a-C
Eo ~o4
I
PDa-C:H//~~/
.~, lo 3
/
10 2
/ /
/.-.,.
10
0
1
2
3
4
5
Energy, eV Fig. 41.
Experimental optical absorption spectra of a hard PD a-C:I] (158), a sputtered a-C (157), MSIB a-C (40), and a-Si:H (64).
Diamond-Lii
Carbons
257
for a = 104- lO%~rn-~.The Taut approximation found to be obeyed with fair accuracy by a wide This and other approximations are discussed by Cody range of amorphous semiconductors. (213). The absorption edges of sputtered a-C (157) and a hard PD a-CA-1 (158) are shown in Fig. 41 and can be interpreted within the above model. The edges are quite broad compared to that of a-Si:H which would indicate that a range of cluster sizes are present, each with its local band gap. The observed gap will correspond to that of the largest significant spJ cluster, rather than the average cluster size. For sputtered a-C with E,= 0.5 eV this is M = 140 for a large cluster and perhaps M = 35 for a typical cluster, coresponding to an in-plane correlation length of L. = 9A . For the hard a-C:H, a typical gap of 1.2 eV give M = 25 for the large clusters and perhaps M = 6 for average clusters, or L, = 3.8A. For a soft a-C:H, a gap of 2.5 eV gives M = 5 and perhaps M = 2 for a typical cluster size.
Table 11, A binding energies per site
E,Llt/P
WP
1.407
0.445
1.400
0.520
1.399
0.568
1.352
0.422
1.385
0.295
1.367
0.523
1.352
0.456
1.345
q.31a
1.326
0.097
258
J. Robertson
The relatively small size of the band gap in a-C and much a-C :H is one ofthe reasons why the aromatic cluster model was first proposed for these materials. Bredas and Street (153) indpeendently also reached the same conclusion using more sophisticated calculations. One should note that the E0, gap probably has a firmer theoretical foundation than the Tauc gap, because it is related to a definite density of states. While the E~ gap and Tauc gap are reasonably close in a-Si:H, E04 is 1.25-1.4 greater than the Tauc gap in a-C:tt because of its broad absorption edge. Other arrangements of rings within the clusters give band gaps lying between these limits. Table 11 shows the values of Eto, and band gap for various configurations with M = 5. Interestingly, the unsymmetric configurations tend to have energies and gaps similar to the compact clusters rather than the acenic clusters which have low gaps. Similar results are found for other M values. Thus, the compact clusters are actually fairly typical of unsymmetric clusters. Table 11 also gives Etot and band gap of aromatic clusters with quinoid spurs. The quinoid spurs are seen to strongly reduce the band gap. The band edge states are localized on the quinoid bonds. It is possible that the broad optical absorption edges in Fig .38 arise not from a wide distribution of M values, but a narrower range of M values plus a variety ofquinoid spurs. This might be particularly true of the broad edges which occur after thermal annealling, where the quinoid bonds arise from hydrogen elimination.
4.4 6 - n Mixing n interactions tend to keep n states on adjacent sites parallel and sp 2 clusters planar. This jus-
graphite
------
u) 0r~
puckered graphite
-20
Fig. 42.
S
-10
0 Energy (ev)
10
Calculated TB DOS for a planar and puckered graphite layer. Full line - total DOS, dashed line - s-like DOS.
Diamond-LikeCarbons
a
ii
J
259
/ \
b
(a) Staggered biphenyl molecule (b) Cross-linked sp 2 layers.
titles the convenience o f treating a and n states separately and necessary for the Huckel model. However, any warping or cross connection o f sp 2 layers may create a - n mixing. Their effects can be studied in terms of two limiting cases. The first case is the distortion o f a graphite layer by puckering. The new DOS is shown in Fig. 42. The puckering causes a hybridisation o f s states into the pn states, so the n states become sp lone pairs. This produces a finite s state density around Ev. It gives a second order reduction in the band gap of sp 2 clusters. The second case concerns when the n states on adjacent sites are orthogonal. A simple example o f this is staggered biphenyl, consisting o f two benzene rings with orthogonally oriented planes, Fig. 43(a). This distortion essentially decouples the n systems on each benzene ring. It causes a slight spn mixing and a slight narrowing of the gap. Hardness data (27) discussed in section 8 suggest that the largely sp ~ networks o f sputtered a-C are considerably cross-linked. The present model of n bonding emphasises the planarity o f the n clusters, and needs to be modified to allow cross-linking by sp ~ sites. Cross linking between n bonded planes by sp ~ sites can be analysed by considering the n states in different planes separately. In the network shown in Fig. 42(b), the n,. states o f the extended network form one n system and the n~ states o f sites 1 and 2 form a separate n system associated with a single C = C bond. Their energetics are again roughly separable. There is clearly some distortion o f either the o network or the rt network when sp ~ sites cross-link.
J. RobinSon
260
The presence of s,pn mixing can be seen in the spectral band structure of ion-beam deposited a-C. The retention of a band structure or momentum energy relationship may seem odd in disordered solid in which momentum k is not a good quantum number. However, the disorder in k, Ak, is only large in specfic parts ofthe band structure, such as near EF. The band structure of a-Si has been calculated by Hickey (159). It is found to be essentially parabolic (in an extended zone) and crosses EF at the 'zone boundary', as expected for a semiconductor. The band structure o f I B a-C has been measured by energy loss by Gao et al (160), Fig. 44. Two bands are found, as in graphite, a parabolic band due to a states a n d a higher band attributed to r~ states. The n band is curved in graphite, but is found to be fiat in a-C, for as yet unknown reasons (160-162). (Note that the energy resolution is only 8 eV). The spectral intensity of the fiat band does not fall to zero at k = 0, as it should by symmetry for a n band, indicating a s-like admixture in this band, which is attributed to warping. 4.5 Electronic Structure Simulations
The most sophisiticated simulation to date is that of Galli et al (103,104) who used first principles atomic pseudopotentials, the local density approximation for the electronic screening and
Spectral intensity (Arb. units)
EF
Momentum (~-I) I .o ,rM 2.0
:).o /
i
T
/
I
I
l /
20
3.0 I
l
J I
!
~QFwHM
Fig. 44.
Experimental spectral b a n d structure of ion-beam deposited a-C, measured by electron energy loss (I 81).
Diamond-Like Carbons
261
the Car-Parrinello molecular dynamics algorithm to treat both the electronic and nuclear degrees of freedom at the same time. A small sample of 54 atoms was placed in a periodic fcc lattice with a density set at 2 gm.cm-3 and was given a particular quenching sequence. It was found to consist of 85% sp 3 sites and 15% sp3 sites, with an RDF given in Fig. 20. The sp2 sites were found to be clustered into highly warped largely graphitic layers, which also contained some of the adjacent 5- and 7-fold ring configurations mentioned above. The sp3 sites were also found to be slightly clustered. Fig. 45 shows their calculated density of states. It shows the .w
(7"
(:7"
A
7r
71-~"
I/}
c
S
.6
A
F
•
L_
0
f,r)
o C3 LIJ
/UV
,
~EF ' I
,] ,T TI,T I,
-2o Fig. 45.
-~o o Energy (eV)
~o
Caculated DOS ofa-C from the simulation ofGalli et al (106)
262
J. Robertson
expected features with a small band gap of 0.5 eV lying between the n and the n* states. Their results generally support the model developed above from quantum chemical arguments. In practice, their sample size is too small to study MRO effects properly and their effect on the band gap. Indeed, the band gap in the simulation may arise purely from the model's periodicity. Tersoff (105) investigated the structure of a-C and liquid C. He used an elaborate valence force field which allowed coordination changes in addition to the usual bond length and bond angle changes. Its force constants were fitted to the calculated total energies of C in the graphite, diamond and cubic structure. With a larger cell of 216 atoms, he found a-C to consist of about 91% sp2 sites, with an RDF given in Fig. 20. These were arranged in a more recognisable graphitic structure. The Tersoff method uses only short range valence potentials and excludes the electronic states. It presumably derives a graphitic structure on the basis of the imposed density and the constraints on the possible bond angles. The density of states of a-C(:H) has also been calculated by the tight-binding method by Robertson and O'Reilly (152). It used a sp3s* basis and mainly nearest neighbor interactions. The interactions for C-C bonds were found by fitting the band structures of graphite and diamond (163-165). The parameters are given in Table 12, E(s) etc are the orbital energies and V(ss) ere are the bond parameters. It was found possible to use a single set of parameters for both C-C and C = C bonds, despite their slightly different bond lengths. V(p,n) is the interaction between n states which are treated separately to n interactions between o states. The interactions for C-H bonds were found by fitting the molecular orbital levels of methane. A number of other tight-binding parameterisations of the C-C bond are available. All use a sp 3 basis and nearest neighbor interactions. The early parameters of Chadi (166) are only suitable for the valence band. The parameters of Drchal and Malek (102) use separate interactions for C-C and C = C bonds, but the large difference in their orbital energies for sp3 and sp2 sites will cause trouble. The recent parameters of Tomanek and Schluter (167) are reasonably close to those in Table 12, given that they omitted the s* state.
"Fable 12. Tight-binding parameters, in eV. V(ss)
V(sp)
V(ppo)
V(pn)
V(p,n) V(ps*)
C-C
4.55
5.2
5.45
1.6
2.9
II-C
7.5
8.9
Bond
E(s)
E(p)
E(s*)
C
-5.3.5
0.
14.0
H
-2.3 4.5
Fig. 38 shows the calculated DOS of diamond, graphite and the Beeman (I01) random network models. The valence band of diamond consists of s-like states at -22 to -10 eV and a peak of po states centered on -7 eV. The conduction band consists of a* states above 2 eV. The C519 network with only sp 3 sites, the Polk network, has a DOS which resembles that of diamond. Its gap is slightly lower than that of diamond due to the effects of bond angle distortions. The states of graphite have a similar disposition, with the n states lying across the a-a* gap, as atrowed. The other three networks each have sp2 sites. These introduce n states. Unfortunately, the networks contain many odd-membered rings and these give rise to peaks at E =0, rather than giving an semiconductor.
Diamond-Like Carbons
1
i
I
I
263
I
i
I
a
b
= C - H in graphite
J
ID
C
- ~ C - H in graphite
0
0 °
~
m ¢-
(CH) n layer
(CH2) n chain
-25
Fig. 46.
-,; Energy(eV)
A'
I
5
1 t0
t
Calculated local II DOS for various C-tl bonding configurations (152)
Fig, 46 shows the states calculated for various C-It bond configurations in a random network. Each configuration gives rise to states only well away from the gap. Thus C-H bonds are electrically passive. 4.6 Photoemission
Photoemission spectroscopy gives the valence band DOS weighted by the appropriate cross section (168-173). The spectra are dominated by carbon states because the cross section of H ls states is lower than that of C 2s and 2p states at all photon energies of interest. Varying the
J. R ob e r ~ n
264
i i ii
.,
i.,
UPS
diamond
~l
-25 - 2 0
ii • i ii
-t5
-t0
-5
0
Energy (eV) Fig, 47.
Photoemission spectra of diamond, graphite, a-C (annealed a-C:H) and PD a-C:H, for 120 eV photons, after Wesner et al (169)
photon energy varies the relative cross section of the C 2s and 2p states. The ultraviolet photoemission spectra (UPS) with 20 or 40 eV photons are dominated by the C 2p states, while the X-ray photoemission spectra (XPS) with 1486 eV photons are dominated by the C 2s states, and photoemission spectra at around 100 eV using a synchroton source gives a similar weighting to 2s and 2p states. Fig. 47 shows the 120 eV photoemission spectrum of Wesner et al (169) for diamond, graphite, a-C and a-C:H. Their a-C:H sample was plasma deposited below 100° C while their 'a-C' sample consists of the a-C:H sample annealed to 5000C. The spectra can becompared with the
265
Ditmoad-Like C='oo,,=
calculated valence band DOS in Fig. 38. The upper peak in the photoemission DOS at 0-12 eV is due to p states and the lower peak at 12-22 eV due to s states. The upper peak contains both ~ and ~ states. The ~ states are apparent as a shoulder at 2 eV in the graphite spectrum and as a weak shoulder in the a-C spectrum, but no shoulder is visible in the a-C:H spectrum. Fig. 48 shows the UPS spectra of a-C:H as a function of annealling temperature T,. The ~z states are more visible in the more recent UPS spectra of Ugolini and Oelhafen (171) of a-C:H
ups hv = 40.8 eV
a-C:H
T=25°C U'3 rI -a
Z
T=350°C n" <:
u
O3
T=400°C
Z ILl I-Z m
T=500oC
T=600oC
16
Fig. 48.
12 8 4 BINDING ENERGY (eV, EF-0)
EF=0
Photoemission spectra of a-C:lt and as a function of annealling, after Ugolini and Oelhafen (171), with by-- 20 eV
266
J. Robertson
as a function of annealling temperature. They form a shoulder at 4 eV in the as-deposited sample and an increasing peak in the annealed samples. This spectrum confirms that the valence band edge of a-C:H is n-like. Fig. 49 shows the UPS spectrum of a-C:H samples prepared by ion beam deposition for various source gases as a function of ion beam energy (172,173). The contribution due to n states is again seen as a highlighted shoulder at -4 eV in the spectra of methane-derived films, Fig. 49(a), and as a peak in the other spectra. The shape of the s peak gives information on the topolgy of the network, for both n and a bonded networks. The s peak of a network containing only 6-fold rings consists of two peaks as seen in the calculated DOS of graphite and diamond in Fig. 38. However, introducing isolated 5- and 7-fold rings, as in the C519 model in Fig. 38(e), washes out the dip between the peaks. Thus it is interesting that the s-band shows two peaks for a-C and only one peak for a-C:H. The a-C result is consistent with its dominant n bonding which strongly favours 6-fold rings. On the other hand, a single peak is found for a-C:tt because its sp 3 bonding allows oddmembered rings. The photoemission cross-section of H states is too low for the local DOS at a H site to be visible in the experimental spectra. Nevertheless, the a-C:it spectra may contain features related
i
i
i
i
i
1
i
i
i
i
BenzeflelAu IBD
UPS hv = ~1 ~RV
I
I
n~
16
12
B
4
BINDING ENERGY (eV)
Fig. 49.
0
16
12
8
4
BINDING ENERGY (eV)
0
16
12
8
4
0
BINDING ENERGY (eV~
Photoemission of a-C:lt prepared by ion beam deposition for (a) methane, (b) benzene (c) styrene precursor, versus ion beam energy, after Oelhafen et al (172,173).
Diamond-LikeCarbons
o
267
=CH 2
e l
in ¢:
-CH 3
-25
-20
-15
-10
-5
0
5
t0
t5
~"nercjy (eV) Fig. 50.
Calculated local C DOS for C-H bonding configurations.
to H bonding. The calculated DOS at a s p 3 C site varies strongly with the number of H neighbors (Fig. 50). The s peak is seen to move deeper to larger binding energies, and to become sharper with increasing number of It neighbors. A similar movement is seen in the photoemission spectrum of a-C:lI in Fig. 46, the two s peaks of a-C not only merge into one,
268
I. Robemon
the upper peak also tends t o v a n i s h . Similar effects are found to occur in the spectra of a-SiC:H. Hydrogenation is seen to make the C DOS sharper in Fig. 50. This effect allows photoemission spectra to differentiate between soft a-C:H and hard a-C:H (172,173). The spectra of hard a-C:[t show broad peaks due to band states, as expected for a highly cross-linked solid, while the spectra of soft a-C:H show much sharper peaks with more molecular character. This effect can be seen in the spectra in Fig 49, where the degree of cross-linking increases with ion energy. This is discussed in more detail in section 5.1. 4.7 Optical Spectra
The optical spectra can provide valuable data on' the local structure of amorphous carbons. The complex dielectric function is given in terms of its real and imaginary parts as m el+~2
[233
e I := n 2 _ k 2
[24]
e2 -- 2nk
[25]
k = a/4n2
[26]
Experimentally, ~t and Ea are given by
and
where n is the refractive index and
where a is the optical absorption coefficient, tt and e., are related by the Kramers-Kronig relationship
et(E) = 1 +
-E- '-' - 7E" dE'
[27]
e2 is given by e2(E)----- {(21te2)2/NA}px2(E)J(E)
[28]
where Nt, is the atomic density, and J(E) is the joint valence and conduction band density of states J(E) =
Nv(E')Nc(E + E')dE'
[29]
0
R(E) is the position matrix dipole element and is related to the momentum matrix element by P(E) = [mE/~]R(E)
[30]
The Tauc approximation to the optical gap assumes the band edge DOS to have a parabolic (free electron) form and P(E) to be energy independent. It has been Found to be valid emprically for a wide range of amorphous semiconductors.
81/,
Diamond-Like Carbons
269
6--
2
IL 0
~
0
Fig. 51.
= zo c ~
10
20 eV
30
40
Wide band optical spectra o f diamond, graphite, PD a-C :H and annealled after Fink et al (174)
a-C:H,
The excitations o f a and n electrons show up as two largely ~ p a r a t e contributions in the optical spectra o f carbons (174). This is because a--+ n * and n - + o* transitions are weak for planar sp 2 sites, so that a and = states are also effectively decoupled in the optical spectra. Fig. 51 shows the optical spectra e, o f diamond, graphite for E ± c , a PD a-C :H and an a-C:H annealed at 540°C, the latter curve representing sp 2 a-C (174-177). Each curve consists o f two peaks, a peak at 4-5 eV due to n -+ =* transitions and a peak around 13 eV due to a -+ ~* transitions. Graphite also has a singularity at E = 0 eV as expected for a metal. This suggests that it is possible to estimate the number o f electrons N . . which contribute to each
270
J. Robertson
peak from El to E2 by the sum rule
[3U
• = rcEp/ fo,~Ee2(E)dE 22 with
E~m Ndf = (
[32]
4zee2~2NA )
to give m Netf = ( 2n2NAe2~ 2 )f~aE~'.e.2(E ~' )dE.'
[33]
where N^ is the number of C atoms per unit volume, m is the electron mass and e is the electronic charge. The prefactor takes the value 0.766 for N^ in m ~ and E in eV. N,~ of graphite was found to reach a plateau of one electron per atom by 9 eV and a second plateau of---4 electrons by 30 eV. For diamond, Ne, was found to be very low for E < 8 eV and to plateau at four electrons by 40 eV. It therefore seems possible to assume that all transitions for 0-8 eV i
I
I
I
|
i
|
I
graphite, E.L.C a-C
2
Nff
0
a-C:H
i
~
0
10
20
30
I 40
50
Energy, e V Fig. 52.
Effective number of electrons contributing to the optical spectrum, N,u, for graphite, PD a-C:lt and a-C (180)
Diamond-Like Carbons
271
are due to n electrons and all transitions above 8 eV are due to ~r electrons. In this manner Fink
et al (174) estimated the sp 3 fraction of evaporated a-C and a range of PD a-C:tt samples. The advantage of this N,, method is that it is unaffected by clustering or the presence of hydrogen. However, there are number of possible sources of error in this method. Firstly, Gao et al (160), Sonnenschein et al (178) and Daniels et al (179) have drawn attention to an error in the numerical determination of N~, of graphite by Taft and Phillip (177) resulting in N,~ being reduced by a factor 2/n. Fig. 52 shows the N,, for graphite for E_Lc (corrected), a-C and a sample o f a - C : H (180). N,, no longer reaches 1 at 8 eV nor 4 at 40 eV. Thus, the n and tr + n oscillator strengths are no longer exhausted by the expected energies. This is even more apparent in the E//c spectrum of graphite shown in Daniels et al (179). Thus the fundamental basis of the 8 eV cutoff is removed. A second problem is that the n and o transitions are poorly separated at 8 eV. A separation requires that as ~ 0 in the dip around 8 eV for Ne, to plateau around 8 eV. It is clear from the optical spectra in Fig. 51 and elesewhere that this dip is much weaker in a-C(:H) than in graphite itself. This results in a poor separation and indeed N~, only has an inflexion around 8 eV rather than a plateau in Fig, 52. The cause of this lack of separation are two-fold. The total ~ + ~t* bandwidth is 17 eV, so it is unlikely that the rt oscillator strength would always be exhausted by 8 eV. Also, while diamond has not started to absorb significantly by 8 eV, the loss of k selection in a-C(:It) can allow transitions to occur from a states at lower energies, immediately above the minimum gap. These seem to be the primary factors but the poor separation could also arise from a poor decoupling of ¢r and zt excitations due to the warping of sp~ layers, as suggested by Gao. Nevertheless, we note that the ratio N(o + rt)/N(rt) = Neff(0 - 40eV)/Nerf(0 - 8eV)
[342
is approximately 4 for a-C in Fig. 52, as expected for sp ~ bonding. It is therefore possible to deduce sp ~ contents by this method on an empirical if not fundamental basis. A third source of error in this method is that the density may not be known accurately. This can be circumvented by using ratios, as in eqn [34]. Recently, Tagliaferro et al (181) refined the method of deducing sp 2 fractions and Ne, from optical spectra. They decomposed the e.2 spectrum into two guassians, for n - n * and t r - t r * transitions respectively, which can overlap if necessary. N,, then can be calculated analytically by the sum rule. The method can even be used when optical spectra are only available up to 8 eV. In this case, e, is calculated from e2 by the Kramers-Kronig relation, N(n) is found from the first peak in ~ and then ~., is used to find N(a + n). Finally, the sp ~ fraction is found from the ratio N(~t) to N(n +a), again avoiding the need to know the density explicitly. This formalises the method used by Savvides (24,25) to find sp 2 fractions in sputtered a-C.
4.8 Electron Energy Loss Spectra The electron energy loss function is defined as 1 -lm(-~-) =
£'2 ("e2+ i 2.2)
[35]
where "Im' is the imaginary part of. The loss function can be calculated from the optical spectra or measured directly. The valence loss functions of a-C(:l I) have been oRen measured and are aPSE 21:4-F
272
J. Robertson
4
2 graphite 0 a-C 0 a-C:H E
T. = 650 C
I--I
0
0 -
0 0
~ I A-r-"-
10
diamond I
I
20
I-
30
I
I
40
Energy (ev) Fig. 53.
Electron energy loss spectra of diamond, graphite, evaporated a-C and PD a-C:tt (176,178,78)
frequently used for characterization. Fig. 53 compares the EELS of diamond, graphite, evaporated a-C, sputtered a-C and some PD a-C:H (182,183, 78). The loss function can show both one-elelctron features (band-to-band transitions) and many electron features (plasma oscillations). Plasma oscillations produce a peak in the loss function if the particular plasmon energy occurs where F., is small. Thus, the loss function of carbon consists in general of two peaks, a lower one due to the n plasma oscillations and an upper peak due to all the valence electrons, a + n. ~ is given by
Diamond-Like Carbons
273
4tte2~-2NaNeff I/2 m )
Ep = (
[36]
where N~ is the number of participating electrons per C atom (1 or 4). This equation results. from the sum rule {31} above, with El = 0 and E2 is a cutoff below the core orbital excitation energies. Table 13 compares E, values given by eqn [36] and those found experimentally. The comparison is good for the # + rr plasmon in graphite and diamond. However, the ~t plasmon of graphite lies well below its expected position. This is because its expected energy, 12.5 eV, coincides with the main tr ~ a* band to band transitions, where ra is high (177). This effect Table 13. Plasmon energies in Carbon, in eV. tr A- 7r
7t
Exp Graphite
7.2
Theory
Exp
Theory
Ref
12.5
25.2
25. !
177
30-32
31
175
Diamond a-C.
6
24.9
78
a-C:H
7
20.8-24
78
a-C:H, 1", = 600°C
6
21
78
21
177
glassy C
6° I 50
2:
Methane
4O Benzene
(g
3O
[
.-.._
20
10
I
0
Fig. 54.
I
i
200
i
I
I
I
400 600 Bias voltage (V)
I
I
800
I
J
1000
Hydrogen content vs. bias voltage for PD a-C:H, deposited from methane (75), acetylene (62) and benzene (9)
274
J. Robertmn
40
30 20
0
200
4~
Imll
6~ i im
8~
B
1~0 i
0.8
~sp
2~ •
C3
= 0 0.6
8 m
C3,h 0.4
0
I
polymeric
• C4,h
0.2
o'[ 0
diamond-like 200
400
C4 600
800
1000
Bias voltage, V Fig. 55.
(a) sp s fraction vs. bias voltage for PD a-C:H deposited from methane at 3 Pa, as measured by NMR, from Tamor et al (75) (b) Carbon bonding vs. bias voltage for PD a-C:H deposited from methane, from Tamor et al (75)
Diamond-Like Carbons
275
lowers F~ to its observed position. Consequently, F~ of the a + n is very useful for obtaining the density of a-C(:H). The n plasmon can be used to indicate the presence of sp= sites but it cannot usefully give the n electron density. 5 PROPERTIES OF a-C AND a-C(:H) 5.1 a-C'H
The properties of a-C:H depend primarily on the mean ion energy, E,. In the case of PD a-C:H they depend on the negative substrate bias voltage Vb. Fig. 54 shows the variation of H content for films deposited from methane and benzene at a gas pressure of 3 Pa and at room temperature. The H content was derived from N M R data for the methane films of Tamor et al (75) and by NRA for the benzene films of Koidl et al (9). The H content is seen to decline rapidly with increasing bias. The variation is seen to be similar in each type of film despite the different measurement techniques. Interestingly, a much lower hydrogen content is found for a-C:H deposited from acetylene. The H content again decreases with increasing bias, but at a uniformly lower level. These films were deposited at a gas pressure of 2.6 Pa and measured by ERD by Zou et al (61).
2.2 Acetylene
2.0
1.8
1.6/ 1.4 1.2
Benzene
,
,
, 200
Fig. 56.
I 400
z
, , , 600 800 Bias voltage (V)
,
, 1000
~
, 1200
Density vs. bias voltage for PD a-C:tt, deposited from acetylene, after Zou et al (61), from methane after Tamor et al (75,185), and deposited from benzene, after Koidl et al (9).
276
J. Robertson
Fig. 55 (a) shows the variation of sp a fraction for films deposited from methane, as measured by N M R by Tamor et al (75). The sp a fraction is seen to decline steadily with increasing bias. A similar dependence was found for a-C:H by Jarman et al (71) and Yamamoto et al (73) using NMR. A similar bias dependence is also expected for benzene-derived films, although they have not yet been studied by N M R or XANES, to the author's knowledge. A rather different bias dependence was found by the IR method (60,61,141), with a rather high sp ~ fraction being found at low V~. This emphasises the unreliability of the method and the data are not included in the figure. These variations lead to three regimes of properties (9). At low bias, the bonding is dominated by = CH2 groups and the properties are rather polymeric, giving 'soft' a-C:H. At intermediate bias, the decline in H content gives the films their most "diamond-like' character. This regime of'hard' a-C:H extends from about 100 V to 1 kV for methane films and 200 V to 1.2 kV for benzene films. Finally, sp 2 bonding predominates at the highest bias, where the structure is highly disordered graphitic. These variations are summarised in Fig. 55(b). The mass density of methane-derived a-C:H has been measured by Couderc and Catherine (184), Zou et al (60) and Wang et al (81) with broadly similar results. Fig. 56 shows the variation of mass density with bias, for both the methane-derived films of Tamor (185) and the benzene-derived films of Koidl et al (9). Both were determined by weight gain. The density is seen to increase continuously with bias for the benzene-derived films but to pass through a peak for the methane-derived films. The density of a-C:H deposited from acetylene tends to vary in a similar fashion to methane films with a peak at 200-400V, but to reach much higher values. These densities were measured by RBS by Zou et al (61). These RBS data for acetylene films show more scatter than those found by other methods, but a comparison of RBS and other data
2.3 2.2 Met
2.1 2.o
~1.9 1.8 1.7
Fig. 57.
I
I
200
I
I
I
I
400 600 Bias voltage (V)
I
I
800
I
1000
Refactive index vs. bias voltage for PD a-C:H deposited from methane after Serra et al (186) and benzene after Koidl et al (9).
Diamond-LikeCarbons
277
for methane-derived films shows the RBS data to be moderately reliable, except that they miss the reduction in density at low bias. Fig. 57 shows the variation of refractive index n with bias for methane-derived a-C:H from Serra et al (186) and for benzene-derived a-C:H deposited from Koidl et al (9). The refractive index is seen to vary similarly to the density, passing through a peak for the methane-derived films and increasing progressively for benzene-derived films. The optical gap is found to vary in a very similar fashion for a-C:H derived from both methane (134,185) and benzene (9), as seen in Fig. 58. The gap declines rapidly with bias, from 2.5-3.5 eV for Vb= 0 to 1.0 eV at V~= I kV. [lard a-C:H has E+ < 1.6 eV. Koidl et al (9,56) proposed the useful rule that the properties of hard and graphitic a-C:H were independent of source gas, while those of soft a-C:tl depended on source gas. The foundation of this rule is their observation that the source gas is essentially completely decomposed in the plasma at higher bias voltages, but not at low bias (59,187). Thus, Koidl (9) noted that the H content, sp 3 content as determined by IR, optical gap and refractive index were each very similar for hard a-C:H deposited from methane, benzene, n-hexane and cyclo-hexane at Vb=400 V. In contrast, there are strong differences in film structures of soft a-C:tt, as is seen readily in their
2.8' 2.6 l l t
2.4
\
2.2 ~ Benzene ~---. 2.0
~
~
N
1.8 1.6
~Methane
1.4
1.2
1.0
0.8
Fig. 58.
0
I
I
200
i
I
400
I
I
I
i
600 800 Bias voltage (V)
i
i
1000
t
i
1200
Optical (Tauc) gap vs. bias voltage for PD a-C :H deposited from methane after Tamor et al (134,185) and benzene, after Koidl et al (9).
278
J. Robertson
a) Benzene 600
VB
400
500V
200
'T
a
E
b)
fJ
I.Z LIJ (.3 14. 14.. 14.1 0 (.3
i
',,~;
Benzene
400
n-Hexane .......
m
/
~: t
m
Z
C) I-n n, (:3 Ul
300, 200
i
CD <
100 0 1200
I
i
i
i
I
c)
%
Benzene
•
n - H e x a n e ....... VB,, 1 0 0 V
800
' ,' j, e I e e # #
'
'I
, ',, t t S t t | S
!
/,00 0
|
i
3300
Fig. 59.
i
i
3100 2900 WAVENUMBERS (cm "1)
C-H stretch I R spectra of PD a-C:H deposited from benzene and n-hexane, at various bias voltages, aRer Koidl et al (9).
Diamond-LikeCarbons
279
IR spectra. For instance, Fig. 59 shows that the C-It stretch absorption is similar for films deposited from n-hexane and benzene at a bias of 400V, while there are substantial differences at a bias of 100V. Similar effects were noted between films deposited from methane and benzene by Tamor et al (147), particluarly the presence ofphenyl side-chain groups in low films. More detailed comparisons in Figs. 54-58 above show that electronic properties such as the optical gap follow this rule very well, but that the density, refractive index and hardness do not, remaining quite different at high bias. The cause of this failure is not understood. The difference between the molecular bonding of soft a-C :H and the network bonding of hard a-C:H is perhaps most apparent in the photoemission spectra (172,173) shown in Fig. 49, of a-C:H deposited by ion beam from various source gases. These spectra use a photon energy of 21.2 eV and emphasise the C 2p states. They have a broad peak due to a states and a knee or peak around -4 eV on its leading edge due to r~ states. The network of hard a-C:lt deposited at higher ion energies gives rise to broad spectra, while the molecular bonding of soft a-C:H deposited at lower ion energies produces much sharper spectra. The rr state peak allow this transition to be studied more precisely, and it is found to occur at 300___20 eV for a-C :H deposited from benzene and at 165-t-20 eV in a-C :H deposited from methane. The photoemission spectra therefore support Koidl's general model of soft and hard a-C:H, but note that the threshold ion energy (or bias voltage in PD) does depend on the source gas. This dependence on source gas is further emphasised by the spectra for styrene precursor. Now even the spectra for 1 kV have not lost all their molecular character, indicating that such energies are unable to fully decompose large, aromatic molecules. Indeed, the photoemission spectra of soft a-C:tt prepared from styrene are similar to that of the monomer (173). This emphasises that PD soft a-C:H is very similar to plasma-polymerized hydrocarbon (65). The n electron fraction and sp~ fraction can also be estimated from the UPS spectra, as shown shaded in Fig. 49. The sp2 fraction is found to increase with ion energy for a-C:H deposited from methane, as found by NMR (Fig. 55). The sp2 fraction varies less in a-C:H deposited from benzene. This is significant and suggests that there are many sp~ sites in this soft a-C:lt, presumably at pendant phenyl groups. The ability to vary the optical gap and refractive index of PD a-C:H makes them particularly suitable for protective optical coatings. The films can be prepared at a bias voltage which allows their refractive index to be matched to the substrate. In fact, the dependence on bias and gas pressure P is quite complex. Bubenzer et al (13) found that the gap varies as Vb with only a weak pressure dependence, while the refractive index varies as V,P-~ and the density varies as VbP -1/~. The harder a-C:H films only have low absorption in the far IR, rather than the optical, as seen for a typical film in Fig. 41. The C-H vibrational bands create absorption in the near IR. This absorption can be reduced by using fluorinated a-C:H (a-C:It,F) deposited from fluorinated benzenes, as shown by Sah et al (188). 5.2 Role of Hydrogen
We may summarise that the role of hydrogen is primarily to saturate n bonds, converting sp 2 sites into sp 3 sites. This occurs because the reaction =C=C=
+ tt 2 ~
=CII-(7tt=
[37]
J. Robertson
280 '
t5
I
.
'
I
'
I
'
I
._._._._..,.
I
'
I
',
,,°,
o. ,.s°
I
Io-C:HI
tO
_u. 0.5
'
"x ! ,
I
,
,
,
I
,
I
,•
I
ee
W
le •
•Q
2:1.0
,?.
'~,.. i
o.s
i (b)
Z
0
"~
(c)
'°i o~ 20 I,d O,.
>.
0 0
100
200
300
t,00
500 600
ANNEAL TEHP. (oC) Fig. 60.
Effect of thermal annealling on the sp 2 fraction, I[ content and optical gap for PD a-C:II, aRer Dischler (141)
281
Diamond-Like Carbons
is exothermic. The cluster model suggests that the effect of hydrogen on the band gap is indirect; the reduction in sp~ fraction will tend to reduce the size of the sp 2 clusters and thereby increase the gap. The dependence o f t l content, sp2 content and gap o f P D a-C :H on bias voltage and anneailing temperature generally supports this idea. In rare cases little correlation between Et content and gap is found (74). The addition reaction {37} can be reversed at higher temperatures, by thermal annealing or high temperature deposition. The thermal annealing process is likely to have many similarities to the pyrolysis of hydrocarbons. Pyrolyis occurs in three stages (189); carbonisation with the loss of volatile species, polymerisation with the conversion of olefinic groups into aromatic groups and the graphitisation of aromatic groups into graphitic layers. The first stage of thermal annealing involves largely hydrogen elimination. The simplest reaction is elimination from adjacent sites, the reverse or reaction [37], to form olefinic groups, =CII.CH=
~
=C=C=
+ H2
[38]
The second stage is the conversion of olefinic groups into aromatic rings. We now consider these changes in more detail. The deposition or annealling or a-C:H above about 300°C causes a decline in hydrogen content, and increase in sp~ fraction and a closing of the optical gap. Fig. 60 shows these changes with annealling for a hard a-C:H film deposited at a bias of 1 kV, after Dischler (141). The hydrogen content and sp2 fraction were estimated from the C-H stretching modes around 3000cm-', so the latter is a guide only. The sp~ fraction is seen to reach almost 100% by 600°C, where the gap has closed. The data suggest that lq begins to evolve at 300°C while the sp2 fraction begins to increase at 400°C. Smith (190) observed similar variations of optical gap and hydrogen content. The closing of the optical gap is accompanied by a broadening or the absorption edge (190-192, 142), as discussed in more detail in section 6.2. The C-H modes also show a conversion or olefinic CH groups to aromatic CH groups as temperature is raised, due to polymerisation. ]'he corresponding increases in sp ~ cluster sizes have been observed in the Raman spectra (129,138,139), as noted earlier. In contrast to this, Grill et al (193) studied the behaviour of the 1600 cm -1 IR C = C bond stretching mode and found that the sp~ fraction begins to increase before the onset orhydrogen loss. Grill (193) also noted a reduction in residual stress at higher deposition temperatures. The thermal stability of a-C:H is limited by the loss of hydrogen and the consequent bonding changes (140,194,195). Consider first the simpler case ofa-Si:H. Hydrogen evolves from a-Si:H at two temperatures, roughly 300°C and 550°C (196,197). The low temperature evolution is attributed to weakly bound hydrogen from polymeric or void surface sites. Its evolution rate is limited by the recombination or pairs of H atoms at the internal surface, and the H2 molecule subsequently reaches the film surface by permeation along micropores. The high temperature evolution is due to strongly bound hydrogen from the bulk film. Its evolution rate is limited by the diffusion of atomic tl across the bulk film. These differences were verified by varying film thicknesses and studying isotopic mixing from a-Si:ll/a-Si:D film sandwiches. The peak evolution temperature varies with film thickness for diffusion limited evolution, but not for recombination limited evolution. A sandwich structure evolves 1t5, HD and D2 in the ratio 1:2:1 for diffusion of H in the atomic form, as a complete mixing or the isotopes occurs. In contrast, there is little evolution of tID molecules where evolution occurs by molecular permeation as either H2 or D2 molecules are formed locally.
282
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~
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~H2
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300V
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Fig. 61.
400
600
8OO 200 400 Temperature, °C
600
800
i
1000
Thermal evolution spectra of PD a-C:H deposited from methane, after Xiang et al (194), and benzene, after Wild and Koidl (193).
The H evolution from a-C:tI differs in a number of ways. Fig. 61 shows typical evolution spectra for PD a-C:it deposited from methane (195) and benzene (194). The evolution spectra depend primarily on bias voltage and to a lesser extent on precursor gas. Soft a-C:H evolves H over a broad temperature range beginning at 300C, while hard a-C:H evolves H at 600-700* There is little isotopic mixing in evolution from a-C:H/a-(" :D sandwiches (Fig. 62), indicating that evolution occurs by the permeation of It2 rather than atomic H (194,198). Also, the absence of a temperature shift indicates that evolution is limited by H recombination rather than diffusion (194). The recombination rate is found to have an activation energy of 2.7 eV, in benzene-derived films (194). A similar evolution mechanism is found in a-C:H films produced by the proton irradiation of graphite (199-201) These results show that a-C:H has a relatively open network, allowing the relatively easy permeation of H2. This contrasts with the denser networks of a-Si:H which favour transport as atomic H. The network of soft a-C:H is particularly open, being suffiently permeable for evolution from pendant groups as hydrocarbons rather than as I-I2. This is particularly true of benzene-derived films. The technical interest in the density and hydrogen evolution spectra of a-C:H is the indication they give of the network coordination, and thereby of the film's hardness. Hydrogen evolution spectra indicate the hydrogen transport mechanism; an atomic transport mechanism implies a dense network, while a molecular transport mechanism implies an open network. Consider a-Si:H as an example again. The most stable configuration of H in a-Si:H is the Si-H bond. It can also exist at the less stable interstitial sites, such as the bond centered interstitial (202). H diffuses between bonds via these interstitial sites (202,203). A dense network stabilises the interstitial sites, thereby lowering the activation energy of diffusion for atomic H, and favouring atomic H diffusion. On the other hand, molecular H2 is slightly less stable than a Si-H bond.
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283
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H evolution spectra from a-C:H/a-C:D sandwich structures after Wild and Koidl (193)
It is immobile in a-Si:H except where it can permeate along micropores associated with voids or (Sill2), groups. Hence, a dense network favours the diffusion of hydrogen as atomic H as seen in the high temperature evolution peak, while an open network favours the permeation of hydrogen as molecular H2, as in the low temperature evolution peak of poorer a-Si:H. A-C:H is expected to behave similarly. The fact that H always transports as Ha shows that the network of all a-C:It prepared to date is still too open. Particle bombardment appears to have a similar effect on a-C:lt as temperature, causing a loss of hydrogen and a reduction in the optical gap. Fig. 63 shows the variation of H content and gap for a-C:H versus ion dose for bombardment with 50 keV C + ions, from Prawer and Kalish (204,205). The reductions in H content and gap are seen to track each other with dose, suggesting that the primary effect of bombardment is to drive off hydrogen, which causes an increase in the sp 2 content and a reduction in the band gap. 5.3 a-C
The properties of sputtered a-C have been studied less intensively than those of PD a-C:H. The
284
J. Robertson I
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I 1015
I 10 16'
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Variation of tl content, optical gap, and spin density of a-C :tt with dose for 50 keV C ~ ion bombardment, after Prawer et al (204).
dependence of properties of deposition conditions have been studied principally by Cho et al (27), Savvides (24) and Cuomo et al (28). The optical absorption spectrum of a sputtered a-C of Hauser is shown in Fig. 41. Its gap is 0.5 eV. Optical gaps in the range 0.4-0.7 eV have been found by Savvides (24) and Cho (27). The gap increases with decreasing RF power. In Cho's work, the sp3 fraction was deduced by the less reliable Raman peak shift method, but was supported by XANES spectra, and was also found to increase with decreasing RF power (27). The density also increased with decreasing RF power. Rossnagel et al (26) found the gaps and densities to vary inversely with gas pressure. These variations can be attributed to the ion fraction being highest at low gas pressures and RF powers. Cuomo et al (28) sputtered a-C onto a series of increasing well heat-sunk substrates. They estimated the density from low energy EELS and the sp.~ fraction from XANES (high energy EELS). They observed that the sp 3 content increased strongly with the thermal conductivity of the substrate material. The sp"~content was found to vary almost linearly with density (Fig. 64). A peak sp3 content of about 50% was reached. This result is significant in terms of the deposition mechanism because it indicates that high sp3 contents can be produced even by low energy ions. However, the deposition rate was low, 8A/min.
Diamond-Like Carbons
APPARENT DENSITY (g/cm"3) 2.4 2.8 3.2 3.6 4.0
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The atomic structure or MSIB a-C has been discussed in detail earlier. Fig. 41 shows its optical absorption spectrum from McKenzie et al (39). The spectrum has a strong tail down to I..5 eV, which can only be due to n states at sp~ sites. Fig. 65 shows the absorption replotted in Tauc form as (~E) '2 vs. E. The spectrum does not fit this form well, so that gaps from 1.3 eV to 3.5 eV can be found by extrapolating different parts or the curve. The E~ gap is 3.5 eV, consistent with predominantly sp 3 bonding. The electrical gap appears to be similar. Itowever, the absorption only falls very gradually within the gap. This absorption must be attributed to n states. Lower optical gaps of 0..5-i.5 eV were quoted by Ishikawa (47). The dependence of properties or MSIB a-C on ion energy can be studied by applying a bias voltage to the ion gun. McKenzie et al (39) found that its density passed through a peak at ion energies or order 30 eV, as shown in Fig. 66. They also found that the films were under large compressive strains, which were deduced from substrate curvature. They found the density and strain variations to be strongly correlated (39,40). Koskinen (44) and lshikawa et al (47) also
J. Robertson
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Dependence of density on ion beam energy for MSIB a-C, from McKenzieet al (39) and lshikawa et al (47).
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Variation of optical gap with density, for a-C and a-C:H, based on Tamor 047). Data for MSIB a-C from McKenzie (39) and lshikawa (47).
found that the density and other properties passed through a peak with ion energy, although at a much higher energy of 1.50-300 eV. Fig. 66. The reason for this difference to McKenzie's (39) results is not known, lshikawa used C- ions. Tamor (147) noted a clear difference in the behaviour of a-( 2 and a-(" :11 if their optical gaps are plotted against density, Fig. 67. The correlations of atomic densi.ty and hydrogen fraction JPSSC 21:4-G
288
J. Robertson
o f Angus (I) are also relevant, Fig. 3. "File gap o f both a-C and a-C:ll increases with sp s content. I lowever, in a-C increasing the sp a fraction gives a direct increase in both atom and mass density, whereas in a-(':ll increasing the hydrogen fraction increases the sp s fraction, increases the atom density but decreases the mass density, because o f the greater polymeric component. 6 LOCALIZED STATES
6.1 Origins of Localized States The electronic states o f an amorphous semiconductor can be classified as either extended states and localized states. Extended states lie within the bands and conduct electricity at 0°K. The extended states are separated from the localized states by mobility edges, which are analogous to the band edges o f a crystalline semiconductor (Fig. 68). The region o f low DOS between the mobility edges defines a mobility gap which acts like the band gap of a crystalline semiconductor (206). It is convenient to further classify localized states as either band tail states or deep states. Tail states lie adjacent to the mobility edges. Deep states are more localized, lie nearer midgap and are generally associated with specific 'defect' configurations whose bonding differs from that o f bulk sites. The chemistry of amorphous carbon suggests that its defect configurations will be more complicated than those of a-Si (152). The principal defect of a-Si is the dangling bond, a trivalent
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TAILS
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Fig. 68.
ENERGY
Schematic picture of electron states near the band gap region o f an amorphous semiconductor, showing localized and extended states, tail and defect states.
Diamond-Like Carbons
289
Si site, formed by breaking a a bond. A defect in a-C can be formed by breaking a a or a n bond. Naturally as n bonding is weaker, we expect n defects to predominate because o f their lower creation energy. A defect will therefore be any configuration o f n states which gives a state near midgap (152). For a more quantitative understanding o f the origins of localized states, we use the I-Iuckel model o f n states. We recall that all states around the gap arise from n states. We set the p orbital energy E , = 0. Within this model, the n electron spectrum tends to be symmetric about E = 0. The tail states are the states o f large clusters. Any cluster with an odd number o f re states automatically gives a state near E = 0 which is half-filled - is a paramagnetic defect level. The simplest olefinic defect is a row o f three n sites and the simplest aromatic defect is cluster o f three fused rings. It is possible to define a defect creation energy Ed for rt defect clusters as (152) Ed = N(EN - EN)
[39]
Here N is the number o f sites, eN is the total n energy per site o f the defect cluster and EN is the n energy o f the equivalent non-defect cluster with a similar number of sites. Fig. 69 shows that Ed decrease rapidly for the olefinic chain defects but only slowly for aromatic clusters. Fig. 69 illustrates two differences between o and n defects. Firstly, Ed is not single valued for n defects.
compact grophitic
0.5
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100
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Calculated defect creation energies for ~ bonded clusters as a function o f cluster size (I,52)
290
J. Robert,son
Secondly, Ed is much smaller for n defects. The maximum Ea of aromatic defects is about 0.4 eV from Fig. 69, while the Ed of a defects is about half of t h e C-C bond energy or 1.8 eV for a-C. The relatively low creation energies of n defects will give rise to high defect densities on a-C(:H). In a mixed o, n bonded system like a-C, a dangling bond must be defined as an isolated trivalent site (152). Its creation energy is expected to be about 1.8 eV, as noted earlier. It is expected to adopt a planar configuration, by analogy to the methyl radical CH~, and so the unpaired electron will occupy a n orbital. Thus the dangling bond in a-C will have n character, and not sp 3 character as in a-Si. The discussion of electronic structure suggests that tail states in a-C are associated with n states of the larger clusters. Thus tail and defect states have basically the same character in a-C(:H).
6.2 Localization
The optical absorption edge of an amorphous semiconductor such as those shown in Fig. 41 has three regions. The region above about ~ = 104 cm -I corresponds to band to band transitions between extended states (206-209). Below this lies the Urbach tail in which the absorption falls rapidly and often in an exponential manner, due to transitions between localized tail states and band states. The exponential dependence arises from exponential density of states distributions, and the slope represents the slope of the broader of the tails. Finally, there is often an addition step in absorption at the base of the tail, due to absorption by midgap defect states. The empirical definitions of optical gap in an amorphous semiconductor such as the Tauc or Eo, gaps correspond to placing "optical band edges' at a certain density of states near the band
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Effect of n bonded clusters on local band gaps, mobility edges and optical band gaps in a-C:H (208)
Diamond-LikeCarbons
291
edges. In o bonded amorphous semiconductors where the potential fluctuations are short range and only moderate in size, the mobility edges also tend to lie at certain density of states, at roughly 1/3 of the corresponding free-electron value (206). Thus, it is possible to define the optical band gap Eo,, to equal the mobility gap E, so that the optical band edges lie at roughly the same energy as the mobility edges. Jackson et al (209) recently thoroughly investigated the sizes of E, and the various optical gaps for a-Si :H. The presence of sp ~ bonded clusters produces large fluctuations in the local band edges (210). These have a profound effect on the localization of states around the gap, particularly in a-C:H which has a similar concentration of sp 2 and sp 3 sites. A schematic band diagram of a-C:H is shown in Fig. 70(a). The n states lie symmetrically about midgap. Their local band gaps vary inversely with cluster size. The gap of the o phase is over 6 eV. It acts as a tunnel barrier between each n cluster and tends to localize n states within each cluster. The 'optical' band edges, depending just on the density of states N(E), will depend primarily on the cluster size distribution. In contrast, the mobility edges also depend strongly on the width of the sp3 barriers. Widening the barriers forces the mobility edges further into the bands, well beyond the optical band edges. Thus, E~ will exceed Eop, in the n states ofa-C:H, Fig. 70(b), in contrast to the case of a-Si:H (210). The potential fluctuations due to clusters also have a strong effect on the optical transitions. There are two types of fluctuations, those in which the band edges move either symmetrically or antisymmetrically about midgap (207,21 i), Fig. 71. The symmetrical fluctuations arise from elastic or deformation potentials such as strained bonds while the antisymmetric fluctuations arise from electrostatic effects such as trapped charges. Fluctuations in amorphous semiconductors are frequently assumed to be of the antisymmetric type, being due to charged defects or ionized dopants. There are four possible types of optical transitions between extended (E) and localized (L) states; extended to extended (EE), LE and EL, and LL. Antisymmetric fluctuations tend to localize the initial and final states of an LL transition in different parts of the sample (Fig 71b)
/ symmetric
Fig. 71.
antisymmetric
Symmetric and antisymmetric band edge fluctuations.
292
J. Robertson
so that LL transitions have only a small matrix element. On the other hand, because of phase randomness, EL and LE transitions tend to have a similar matrix element to EE transitions (208). Thus, EE, EL and LE transitions are allowed but LL transitions are essentially forbiddened for the case of antisymmetric fluctuations, and so they tend to be treated as forbidden in most amorphous semiconductors. This situation is reversed in a-C :It where the clusters create strong symmetric fluctuations, Fig 71(a). LL transitions can now occur between the initial and final states localized in the same cluster. These transitions have a large matrix element and are now strongly allowed. Indeed, the cluster model suggests that optical absorption in a-C:H is due to LL transitions up to well above E04. The consequences of symmetric fluctuations has rarely been studied so the size of the fluctuations in a-C:H makes this an interesting system in this respect. It is interesting that despite the different origins and length scales of the disorder that a-Si:H and a-C:H should each have rather similar optical absorption edges, each displaying a Tauc region and an exponential (Urbach) tail (Fig. 41). Abe and Tozoyawa (211) investigated formally the effect of disorder on the absorption edge. They used a virtual crystal with Guassian site disorder for both the valence and conduction bands, and allowed the disorder to be correlated (symmetric fluctuations), anticorrelated or uncorrelated between the bands. They calculated the optical absorption spectrum in the coherent potential approximation (CPA) within the one-electron approximation. They found that 0t varied in a Tauc-like and Urbachlike manner over different ranges, for both symmetric and antisymmetric fluctuations. Thus, Tauc-like and Urbach behaviour is a fairly widespread behaviour to find in an absorption edge. They also proved that I.L transitions are forbidden for antisymmetric fluctuations but are allowed for symmetric fluctuations, as deduced above. The Urbach slope E, is a measure of the disorder potential. It is given by the sum of the thermal and effective structural disorder (211-213), E0 ~ - O{D(_?_) + l +2X
}
[4o]
where ® is the Debye temperature, D is the Debye function, and X is the mean square value of the structural disorder. Abe and Toyozawa (211) found that the Tauc and Urbach regions each came to a 'focus' about the zero disorder band gap energy. The Urbach focus is a typical feature of the absorption edge ofa-Si:H (212). Cody et al (212,213) studied the variation of Urbaeh slope F~ as a function of measurement temperature and thermal annealling. They found that F~ varied with Tauc gap ET as ET = Bro - CE 0
[41]
whether the changes were due to measurement temperature or to structural disorder (hydrogen loss during annealing). This confirms the equivalence of structural and thermal disorder in the definition of E0 {40}. ET0 would correspond to the zero disordered gap in this model. Datta et al (191) found that the optical edge ofa-C :H also displayed an Urbach focus, They also found a linear variation of E0 with Er, as shown in Fig. 72 Their data was restricted to changes due to the annealing in a wide band gap variety of a-C:H. It is interesting that their Urbach focus was found to be 5.6 eV, close to 2fl, the gap of a single benzene ring and perhaps
Diamond-LikeCarbons
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tu a_
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f
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0
Fig. 72.
I
0
1
Vb I
1 2 OPTICAL GAP, eV
3
Dependence of Urbach tail slope E0 on optical gap E~ for a-C:H, as a function of annealling temperature T, for films deposited at low bias (191), and as a function of bias voltage Vb for films deposited at nominally 25°C (158).
the gap of a zero disordered rt band. value.
ttowever, they also found Er0 = 3.5 eV, a much lower
It is possible that a wider range of behaviours may occur in a-C :H. The gap of a-C:It can be varied between 0.5 and 3.0 eV by changing the bias voltage during plasma deposition (9). In this case, using data from Dischler (158), Fig. 72 also shows that E0 tends to vary linearly with E~ as a function of bias, in a very different manner to the thermally-induced changes. This may indicate that two types of disorder occur in a-C:H, with the gross changes in cluster size and band gap caused by bias voltage being analogous to alloying rather than to changing structural disorder.
6.3 Electrical Conductivity The existance of a range of defect centers means that the electronic density of states in the
294
J. Robertson
mobility gap ofa-C(:H) consists of a featureless spectrum, as in Fig. 68. The Fermi level EF lies near midgap in a-C and undoped a-C:H. There are three conduction mechanisms in a-C(:H); hopping between states near EF, thermal activation to a higher density of localized states near a mobility edge, and thermal activation and conduction in extended states above a mobility edge (206). The mechanisms of conductivity a can be distinguished from their temperature dependence which can be expressed in the general form = o 0 exp( - (Tn/T) n)
o
[42]
A regime with n-- 1 indicates thermally activated conduction in states kT, away from EF, where k is Boltzmann's constant. Conduction is in extended states if the prefactor a0 > i0 s ~-~cm-' and in localized states if 00 < 103~-'cm-L If n < 1, this suggests that conduction occurs by
' 10-4
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I
I
~
I
2.5 3.0 IO001T ( K-I)
i
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Temperature dependence of the conductivity of a-C:H, deposited at various temperatures, after Meyerson and Smith (216).
Diamond-Like Carbons
295
variable range hopping in localzied states near Er. n = I/4 is the classic power law for variable range hopping, while n > 1/4 can indicate either a rapidly changing DOS near EF. For n = 1/4,
T4-
16a 3 kN(Er0
[43]
where ~-~ is the decay length o f the localized state (206). For thin films, the hopping distance can exceed the film thickness d, and give a n = I/3 regime, with
T3 -
8a 2 kdN(EF )
[44]
It is conventional to estimate N(EF) from [43] using a-~ = lOAngstroms if only an n = 1/4 regime exists. However, i r a transition from n = 1/4 to n = I/3 can be found with decreasing d, both and N(EF) can be found, tlauser (157) used this method for sputtered a-C to find -1
c~
= 12A
and N(Ev) = 10 is e V - l c m -3 consistent with a defect density of---10r"cm-3 over a mobility gap o f 0.8 eV. Shimakawa (214) noted that the conductivity o f a-C also fitted the relation o = o0(T,/T)" with n = ! 5-17, consistent with a multi-phonon mechanism. A-C:H conducts mainly by hopping in localized states (215-218,142). Fig. 73 shows the conductivity o f PD a-C:H of various deposition temperatures (216). The conductivity does not follow a single power law. It has a simple activated form at high temperatures with n = 1, and the low value o f a0 indicates that conduction occurs by hopping in a band tail. At lower temperatures, conductivity is by hopping near EF, which is confirmed by the low value of the thermopower. The decay length of the defect states in a-C:I| is expected to be much shorter in a-C:H than in a-C because o f the effects o f clustering (Fig. 70). The sp 3 regions are a strong tunnel barrier and cause cc-I < 3A , much lower than is used in a-Si or a-C. This lower value gives an acceptable values of N(E~-) when used with {43} for the low temperature regime (210).
6.4 Doping The Fermi level of an amorphous semiconductor tends to lie near midgap in a low density o f states, giving a low conductivity. E~ o f c-Si can be moved towards a band edge by substitutionally doping with an element of group III or V. Spear and LeComber (219) found that PD a-Si:H could be substitutionally doped by boron and phosphorus by adding diborane or phosphine to the gas stream entering the plasma reactor. Meyerson and Smith (218) discovered that a-C:H could be doped in a similar manner by B~H~ or PH3. Fig. 74 shows typical changes in the electrical conductivity for 1% diborane, phosphine and nitrogen gas doping ratios for a-C:H deposited at 250C from Jones and Stewart (217). Fig. 75 shows typical changes in the activation energy o f conduction at room temperature and compares them with the anal-
296
J. Robertson
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Conductivity ofundoped and doped a-C:H, after Jones and Stewart (217)
ogous changes found for a-Si:H by Spear and LeComber (219). It is clear that a substantial change in conductivity has occured, increasing the room temperature conductivity art from l0 -t2 ~-tcm-I to 10-7 ~--Icm -l for a gas phase doping ratio of 10%. However, it is also clear from Fig. 75 that the doping efficiency is lower than in a-Si:H. A greater doping ratio is needed to produce a large reduction in the activation energy and the conductivity can only be reduced to 10-7 f~-' rather than 10-2 £'-~-Icm-t as in a-Si :H. Meyerson and Smith (218) confirmed that the conductivity changes corresponded to substitutional doping by observing the necessary changes in the sign of the carrier, via the thermopower. There are a number of interesting features of substitutional doping in a-C:H and a-Si:H. Firstly, an element from group V dopes crystalline Si because it is forced to enter a 4-fold coordinated site but only uses four of its valence electrons to form bonds to the neighboring silicons, leaving a free electron (Fig. 76). This free electron lies in a donor level close to the conduction band in
Diamond-Like Carbons
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I 1
Variation of activation energy of conduction vs. doping ratio for a-C:H (218) and a-Si:H (219).
c-Si which forces EF tO lie there. The absence of periodicity in a-Si means that a group III or V element need no longer enter a 4-fold site, but can instead enter a chemically prefered 3-fold coordinated site in which all the valence states will be filled, so there will be no free carriers. The five phosphorus electrons lie in three bonding states and an s-like lone pair (220), Fig 76. Doping occurs in a-Si:H because a small fraction of dopant atoms enter 4-fold sites, from where they donate carriers. It turns out that these sites have only slightly higher energy than the 3-fold sites, and the doping fraction is found to obey the law of mass action and MaxwellBoltzmann statistics (64). The second factor reducing the efficiency of doping in a-Si is the density of gap states. Doping can only shift EF above midgap by filling up the gap states through which it shifts (Fig. 77). E~ will only shift far if the dopant density exceeds the density of gap states. The passivation of most gap states by hydrogen was therefore an important requirement for the observation of doping in a-Si:H. The gap state DOS is higher in a-C:H (section 6.5) and this is probably the major factor which reduces its doping efficiency. It is interesting that it is possible to dope a-C:H despite its high content of3-fold C sites. There is no forcing of atoms into 3-fold sites, This is further support for the idea that the type of
298
J. Robert.son
:::::::::::::::::::::::::::
-o-,-o-¢°-.-o
:::::.'::~__:."~:~:~:~:~:i :::::.-::::::':'~::::::::::::
S
•
:::::::::::::::::::::::::::::::
'
!:~:!:~:~::.:~'!.':':~: O
:!:!:~:.":~:::-':":::-'::'::ii~N
p
......
EF
....:,..:.:.:.::.::i:i:i:i:i~:i
o S
Fig. 76.
iiiiiii::iiiiiiiiiiiii/ili!::ii t l
~:!:~:i:!:!....-........!~:i~:
Bonding and electronic configurations at a 4-fold coordinated P site in Si and a 3-fold-coordinated P site in Si. Subscripts denote coordinations.
bonding in a-C is determined by relative site energies and a degree of equilibrium, rather than by strong thermal quenching. It is also possible to dope a-C:H n-type with nitrogen (217). This contrasts with diamond where N forms a deep distorted substitutional level 1.4 eV below Ec. It is possible that 4-fold N sites can dope a-C:tt because their donor level is now above E~ due to the smaller gap of a-C :H. The doping efficiency of N in a-C:l I is low, and there are suggestions that a true substitutional mechanism is not involved (217). It is noted that higher N contents promote sp 2 coordination of carbon (221), so that a-C, xNx alloys become primarily 3-fold coordinated at both sites at high x, and no ordered composition is found at CsN,. Clearly, increased sp~ C bonding will narrow the gap at low x and also increase the conductivity, which could be confused with doping.
Diamond-Like Carbons
299
\
t0 22
."A'
~02o
0
10 t8
It}
I::1 03
t020L
"f/
/
\
\
~
EF /
I| /
N'N~ ~donors
I 0 t 8 ~
-6 -4 -2 0 2 4 6 Energy(eV) Fig. 77.
Density o f states near the Fermi level in (a) undoped a-C:tl, (b) n-type a-C:H
6.5 Defect Densities The defect density in a a bonded amorphous solid tends to indicate its degree o f disorder. This in turn depends on the lack of equilibrium during the deposition process and the degree o f any subsequent annealling, lligh defect densities arise from low deposition temperatures, rapid deposition rates or strong ion bombardment. Low defect densities can reflect a gentler growth process or some annealling o f damage. Defect densities of order 10~ cm 4 are typical o f evaporated or sputtered a-Si, and these can be reduced to 10 '9 cm -3 by thermal annealling. Much lower densities such as 10 '6 cm -3 can be achieved in PD a-Si:H, due to passivation o f dangling bonds by hydrogen (64). This line o f argument must be used with care for amorphous carbons where the defects are probably multi-site entities. If the electron correlation energy. (U) is positive, defects are
300
J. Robertson
~,Eo1020
1018 c
\
lo16 0
Fig. 78.
I 500 Bias voltage, V
! 1000
i 200 250 Deposition
i 300
I 350
Temperature, °C
(a) Spin density N, vs. bias voltage for PD a-C:It (224,228,134). Dashed line is the defect density from the weak bond dangling bnod conversion model, eqn {48}. (b) Spin density N, vs. deposition temperature for PD a-C:H deposited at low bias voltage (226).
normally in their paramagnetic (singly occupied) state. Defect densities can then be measured directly by electron spin resonance (ESR). Orzeszko et al (222) found a spin density of about 10~Scm-3 in evaporated a-C which was relatively independent of annealling temperature. A similar value was deduce for sputtered a-C from conductivity data by Hauser (157), as discussed above. Wada et al (128) found 2.1019cm -3 spins in sputtered a-C. A much larger density of 2.102°cm-3 was found in the sputtered a-C of Pan et ai (76), deposited at 77K. The defect densities in a-C:H can be much higher than in PD a-Si:H, tligh values of spin density have been found in reactively sputtered a-C and a-C:H (223) Spin densities ranging from 10'~ to 102' cm --3 have been measured in PD a-C:H, depending on deposition conditions (224-229,134). The data of Reyes-Mena et al (224), Tamor et al (134), Fabisiak et al (228) and Watanabe et al (226) suggest that the spin density N, passes through a maximum as a function of bias voltage for PD a-C:H, as shown in Fig. 78(a). The defect density is low in soft a-C:tt prepared at low bias, presumably because possible defect states are passivated by hydrogen. In a-C:H prepared at ihgh bias, the defect density again becomes low perhaps because of the effects of delocalization in the increasingly graphitic material. Thermal annealling generally increases the density of gap states in a-C:H. This occurs because of the loss of hydrogen, the increase in sp 2 fraction, the narrowing of the band gap and the broadening of the band tails, noted in section 5.2. The spin density of a-C:H of large band gap deposited at low bias is seen to increase with thermal anneaUing above 300C (224-226), and then to decline above 600C, as shown in Fig. 78(b). Note that a different behaviour is found in a-Si:H, because of the absence of sp 2 sites. There thermal annealing up to 300C decreases defect densities and only higher temperature anneals cause an increase in defect density. Singly occupied defect levels can be characterised by electron spin resonance.
Miller and
Diamond-Like Carbons
301
McKenzie (225) and Watanabe and Okumura (227), resolved two different spin signals in a-C:H, a narrow line at g--- 2.003 and a wider line at g= 2.011. Ehrhardt et al (229) resolved a number of lines in their a-C:H, which they attributed to n bonded clusters of different size (230). They found that small defect clusters predominated for films deposited at low ion energy and larger clusters at higher ion energy, in agreement with our cluster model. Structural defects can give rise to electronic states deep within the band gap. In a-Si, dangling bonds give rise to localized defect states near midgap. Transitions from these states to extended conduction band states cause a subgap optical absorption which is seen as an excess absorption above the Urbach tail (231). The excess absorption is found to be proportional to the dangling bond density as measured by electron spin resonance. In amorphous carbons, rc defects are the predominant defects because of their lower creation energies (152). In the graphitic cluster model, any cluster which gives a state at midgap, including all clusters with an odd number of sites, can be defined as a defect configuration. Fig. 79 compares the optical absorption spectra
106
I
I
I
I
l
105
104 "7
a-C:H
103 a-Si:H
/
102
//defects/ 10
I
0
I
1.0
I
2.0 Energy (eV)
Fig. 79.
Optical absorption spectrum ofa-C:H compared to a-Si:H (158,224).
3.0
J. Robertson
302
of a-Si:H with about 10's cm-~ defects (231) to that of a-C:H with a similar spin density (158). No excess absorption is apparent above the a-C:H tail before the C-H stretch band intervenes at 0.4 eV. The absence of defect absorption in a-C:H, first noticed by DasGupta et al (223) in samples of a higher spin density, suggests that the defect excitations have shifted to higher energy. This is also evidence for the cluster model. As defects are relatively rare, on average, band edge states tend to lie on non-defect clusters. Transitions from a defect level to these states on other clusters have low matrix elements and the main transitions from a defect level are to higher levels in the same cluster. Thus, transitions from midgap defect levels will tend to lie well above l/2Eopt and so they will not create subgap absorption.
i
I
~
I
'
I
'
Td(C) @mmm
200.~.~
\
t-
@ m
U ¢-
2
U C/} r-
E
300
1.2
1.6
2.0
Energy(eV) Fig. 80.
Typical luminescence spectra ofa-C:H of various gaps (226)
Diamond-Like Carbons
303
6.6 Luminescence
Optical excitation creates an electron hole pair. These carriers can recombine non-radiatively with the release of heat (phonons) or radiatively with the release of light (luminescence). The process is geminate if the original electron-hole pair recombines and non-geminate if electron and hole recombine after mixing. The various processes occuring in luminescence and recombination have been discussed in detail by Street (64). Non-radiative recombination is favoured by the presence of high defect densities so luminescence has only been found to date in a-C:H (226,232-239). The luminescence spectra depend mainly on the band gap, the defect density, the excitation energy and the temperature. Fig. 80 shows the luminescence spectra of a-C:H samples of different band gaps (233). It is interesting that the peak of the luminescence spectra in the sample of lower gap occurs above its Tauc gap (but still below its E~ gap). The variation of peak luminescence is plotted versus Tauc gap in Fig. 81 for a-C:H from various workers (226,233,238). The luminescence peak is seen to increase only slowly with gap. The luminescence efficiency is high in a-C:H, particularly in samples with a wide gap. Indeed, luminescence can sometimes obscure Raman spectra measurements. The luminescence efficiency is also relatively independent of temperature (234,236), whereas it declines strongly with temperature in a-Si:H (64). Many of these features of luminescence are evidence in favour of the cluster model. We noted earlier that the optical absorption edge originates from states which are strongly localized within
3
!
I
I
I
'
I
I
2-
i
O IJ.I
1
"0
i
0
Fig. 81. dPSgC 2 1 : 4 - X
I
1
,
i
i
2 OPTICAL GAP, eV
I
3
Variation of peak luminesence energy vs. optical gap for a-C :H (226,233,238).
4
304
J. Robertson
1.0
..I ~D % m
m
E L_
0
Z
0 1.6
2.0
2.4
2.8
Photon Energy (eV) Fig. 82.
Luminesence spectra vs. excitation energy for wide gap a-C:H (238). (E,,= 3.5 eV).
clusters. Optical excitation in the region of the edge will create electron hole pairs localized in the same cluster. They will be trapped in the cluster by the surrounding tunnel barrier and so will tend to recombine radiatively. This will produce a luminescence which is relatively independent of temperature and electric fields, as observed (235-238). A temperature dependence generally arises when the electron and hole can hop apart by thermal activation, find some defect center and recombine non-radiatively, as occurs in a-Si:H (64). Fig. 82 shows the luminmescence spectra of a wide gap a-C :I4 (E04= 3,5 eV) as a function of the excitation energy (238). Generally, luminescence is not expected above the excitation energy Eex, shown arrowed in each spectrum. However, closer inspection shows that their is a finite emission above Ee~ in each spectrum. Volkov et al (238) attribute this to a further thermal excitation of the electron or hole while it is trapped in the cluster. They found this so-called Anti-Stokes luminescence to be strong evidence of the presence of clusters, although further details of the mechanism must still be worked out.
6.7 Defect Equilibria The role of hydrogen in a-Si:H is often said to be that of reducing defect densities by passivating dangling bonds, converting them to Si-ll bonds (64). In fact there is a great excess of H in a-Si:H (197). However, even the best a-Si:H still has a defect density ofover 101Scm-3. It is now
Diamond-Like Carbons
305
realised that the defect density in a-Si:H is largely controlled by metastable equilibrium process, which are mediated by the local motion of atomic hydrogen (240-242). In more detail, many workers have noted that an interconversion between weak bonds and dangling bonds can occur. -Si-Si----
~
-Si
+
=Si
[45]
The barrier to interconversion can be lowered by the motion of atomic hydrogen. Although the most stable location of hydrogen is at a Si-H bond, it is also relatively mobile. It moves via interstitial sites such as the bond center site, as also occurs in crystalline Si (202,203). A hydrogen at a weak bond center site is actually more stable than at a normal Si-Si bond (241). This is because the H induces an opening of a weak Si-Si bond towards the configuration of a dangling bond and a Si-tI bond. ---Si-H-Si=-
~
=Si-H
+ .Si-
[46]
In this way, it is possible for the majority of Si-Si bonds to be rigid and to define a random network, while a minority of weak bonds may interconvert with dangling bonds, via the mediation of hydrogen. The hydrogen evolution spectra of a-Si:H verify that atomic H is the dominant transport mode of H in a-Si:Iq (197). It is suggested that the weak bonds form the tail states in a-Si:H, particularly the valence tail, the wider of the two tails (243). Thus, the density of weak bonds with energy E can be written as
N(E) = N Oexp(-E/E0)
[47]
where E0 is the slope of the valence band tail, which equals the slope of the Urbach tail for the case when it is the broader tail. No is the density of states at the top of the tail. The bond strength is proportional to the bonding-antibonding splitting, so the weakest bonds lie at the base of the tail. Stutzmann (244) proposed that all states lying closer to midgap than A are so weak that they would spontaneously convert into d.angling bonds according to reaction [45], thereby releasing an energy A. Treating reaction [45] as an equilibrium and applying the law of mass action, we find that the density of dangling bonds is given by N s = N0E 0 exp( - (Eg/2 - A)/E0)
[48]
A is treated as an adjustable parameter. This weak bond dangling bond conversion model is found to describe the defect density in undoped a-Si:H under a wide range of conditions (244), and also in Si-rich a-SiN~ and a-SiC~ alloys (245-247). This model might be expected to apply to the n defects of a-C:tt, after re-identifying tail states as 'weak clusters' and defect states as defect clusters, llowever, the defect density in a-C:H does not follow eqn [48]. The gap and the Urbach slope decline with increasing bias, so N, should increase monotonically with bias, rather than pass through a maximum as it does in Fig. 78(a). This failure suggests that either the interconversion of tail states and defects is hindered or that their energetics do not follow the equations. Interconversion might be hindered as the reaction now involves multisite clusters rather than single a bonds. However, in principle a tail cluster can become a defect cluster just by changing the number of its sites by one, eg. by the hydrogenation of one of its sp ~ sites or dehydrogenation of an adjacent sp 3 site. The energetics of the model are sound, as they are based on quite general quantum chemical principles, that deeper tail states are more weakly bound and that defect states have even lower stability. The
306
J. Robertson
problem may lie in the multivaluedness of defect and tail state energies (Fig 69), which does not arise for the simpler case of a bond defects, and which would require a more complex analysis than eqns {47,48}. 7 DEPOSITION MECHANISMS 7.1 Plasma Deposition, Case of a-Si
:H It is likely that a range of deposition mechanisms are involved in the production of hard a-C(:H) films in view of the range of processes used. The processes involve aspects of radiation effects, ion-beam modification of materials, and plasma chemistry. We will consider the deposition mechanism of PD a-C:tt, ion-beam a-C and sputtered a-C in detail.: We shall first consider PD a-C:H by using PD a-Si:H as a guide, as this system is now reasonably well understood. It was noted earlier in Table 3 that the process parameters for the deposition of high quality a-Si:H from a silane plasma (low RF power, moderate silane pressure, no ion bombardment, moderate substrate temperature) differ considerably from those used to obtain hard a-C:H from a hydrocarbon plasma (high RF power, lower gas pressure, high ion bombardment, low substrate temperature). In general terms, Tsai et al (248) noted that high quality a-Si:H was deposited under conditions described as chemical vapour deposition (CVD) in which there was conformal surface coverage of slots and steps, rather than under physical vapour deposition (PVD) conditions in which only surfaces in direct line of sight of the source
multipole,
ECR
- - - - > DC or RF discharges
Ar or He d i l u t i o n , d - - - pure S i l l 4 100
. . . . . . . . . . . . . . . . .
•
~_SiH
2
,
. . . . . . . .
H
,
, .
.... + ~ ~iN 3 ~
. . . . . .
.:
1
I
~ "
SJH n m
! , I
= 4
c
1
S| H +
I
~
n m •
0"4
"Fig. 83.
,
•
.=,,i
,
•
•
,
,
==,1
ii " ~ ,
1 0 .3 1 0 "= silane pressure
,
,
.
..=.11
|,
,
•
1 0 "1 (Torr)
Ion to Radical flux ratio in a low power silane plasma (250)
•
,
=.=
10°
Diamond-Like Carbons
307
are covered. CVD conditions arise when the main growth species has multiple surface reflections or high surface mobility, and is relatively weakly bound, In the plasma, electron collisions cause the dissociation of silane molecules (249-256). dominant channels just above the ionisation threshold of silane produce the radicals
The
Sill4 --* SiH~'+ H
1,49]
Sitt4 ~ S i l l 2 + 2 H
1,50]
However, the lowest enthalpy channel Sill 4 ~ S i l l 2 + H a"
[51]
is forbidden because it is a non-vertical transition (250). At lower gas pressures, ions are dominant
1-52]
Sill 4 ~ Sill3 + + 1-1 + eThe ion to radical flux ratio is shown as a function of silane pressure (250) in Fig 83.
The interaction of an incident species with a surface can be defined in terms of r, the reflection coefficient, B the surface reaction probability, s the fraction permanently absorbed (the sticking coefficient) and y the fraction which reacts to form a volatile product (253), Fig. 84. // = l - r
= s+~
1-53]
Incident flux nation (7)
Surface Diffusion
('
Deposition (s) Fig. 84.
Reactions of impinging ions with a surface (253)
308
J. Robertson
with 0 >/~ > 1. The CVD regime corresponds to low values o f p as this allows multiple surface reflections. High quality a-Si:H is formed when Sill3 is the main growth species (250,256). The coefficients for a-Si:H are defined by the fact that the growing surface of a-Si:H is almost fully hydrogenated. Sill and Sills radicals have two or more dangling bonds and can easily insert into a Si-H surface bond, resulting in a low surface mobility,/~-~1, and a low quality (rough, porous) film. In contrast, Sill3 does not insert into a Si-tt bond. It can only physisorb onto Si-H surface bonds as a 3-center bond = Si - H + SiH~ --, - Si.tI.SiH 3
[54]
and diffuse along the surface until it chemisorbs onto a dangling bond = S i + Sill 3 ~
=Si-Silt 3
[55]
or until it recombines to form silane by 1t abstraction -Si-H
+ SiI-I3 -
- - - S i + Sill 4
[56]
This gives a low value of p-0.26 and of s"~0.08 (249). (Atomic H can also cause H abstraction, but atomic H concentrations are relatively low in plasmas for a-Si:H or hard a-C:H growth.) The growth of a-Si:H therefore requires two Sill3 radicals, one to create the dangling bond by H abstraction (257) and the second to chemisorb into the growing film. Note that a closed shell molecule such as silane only physisorbs weakly onto a hydrogenated surface with s~10 -4, while all incident ions with moderate energy will bury themselves and have p = s = 1. In the subsurface region, the highly hydrogenated surface layers must be converted into a-Si:H by hydrogen elimination (249,258). The hydrogen content of a-Si:tt falls with increasing temperature with an apparent activation energy of 0.05-0.1 eV. Hydrogen dilution of a silane plasma tends to produce microcrystalline Si (/~c-Si). The tt atoms are believed to luther hydrogenate the surface and induce a higher surface mobility in Sill3 radicals so that they search out only the most stable sites - those leading to epitaxial growth (255,256). Atomic H is also a key factor in the growth of uc diamond from hydrocarbon plasmas (1-3). This suggests that atomic tt has a number of effects in diamond growth. 7.2 Plasma Deposition of a-C:H
We now consider the growth of a-C:H from methane plasmas. The behaviour of methane and methane/H2 plasmas has been closely studied from the point of view of CVD diamond growth (259,260), but less so for the conditions which give rise to a-C:H growth (261-264). Two additional features must be considered compared to silane plasmas. Firstly, there are many more potential growth species due to carbon's multiple hybridisation. Also, the large bias voltages allow neutrals - radicals and undissociated molecules - to acquire energy by collisional exchange in the plasma, which will increase their sticking coefficients (63). The dominant dissociation channels for a methane plasma produce radicals like CH3 and CH2, ions like CI-t3+ and Ctts ~, and molecules like C~H~ (259-263). The growing surface of a-C:H is also highly hydrogenated. The sticking and p coefficients of the species can be estimated in terms of their unsatisfied valences using silane plasma species as a guide (Table 14). Note that
Diamond-Like Carbons
309
Table 14. Estimated surface reaction probabilties p and sticking coefficients s for PD a-C:H growth species.
Ctt3
0.1
0.3
CI-t~
1
1
CH]
1
I
C[t~
I
1
C~H~
I
1
unsaturated molecules like acetylene can insert directly into C-H bonds. Apart from methane itself, acetylene, CH3 and CH~ are believed to be the main species of interest in the methane plasmas, so this would suggest that these are also the main growth species. Methane molecules are unlikely to contribute much to growth, unless they have acquired kinetic energy, as they have a low sticking coefficient. Indeed, Vandentop et al (265,266) found by mass spectrometry that methyl radicals were the dominant growth species of a-C:H. The general relevance of the weak sticking model to PD a-C :H growth is the observation that the growth rate declines as the temperature increases (50,267). This is ascribed to the thermal activation of either y or of the tI abstraction reaction (253). Strong sticking is likely to give a constant deposition rate. Interestingly, the growth rate of a-Si:tt (in the low power regime though) is temperature independent (253). Ions are likely to become more important growth species in lower pressure plasmas (250). However, Zhang and Catherine (268) found little change in the degree of ionisation at lower pressures. Note that the ion/neutral flux ratio used to compare different sources should exclude closed shell species like methane or Ar, unless they are energetic, as these closed shell molecules have minimal interaction with the surface. We noted earlier that the role of hydrogen in a-C:H was to promote sp3 bonding, but that too high a H content produces many = CIt2 groups and a poorly cross-linked network. The role of ion bombardment in PD a-C:H is to dehydrogenate the subsurface zone and produce this cross-linked network. In a-Si:tl dehydrogenation occurs by H elimination between Si sites on neighboring chains, =Si-H
+ H-Si-=
~
----Si-Si= + I-I2
-5kcals
[57]
This reaction is exothermic (154) so that the equilibrium concentration of Si-It bonds at say 500 °C would be only 10-2. It is only necessary to thermally activate H elimination in a-Si'H to promote this reaction. In contrast, the reaction =(7-tt
+ It-C=
~
-=C-C=+[12
12kcal
[58]
is endothermic, so the equilibrium concentration of C-H bonds in a-C:H would be high. A second H elimination channel exists in a-C:H, in which II atoms leave adjacent sites and produce sp2 sites rather than network cross-linking, =CH-CIt=
~
=C=C=
+ II 2
29kcals
[59]
310
J. Robertson
Although this reaction is endothermic, it has a low activation energy. It is therefore undesireable to use heat to eliminate H from a-C:H to produce a highly cross-linked network. On the other hand ion bombardment will dehydrogenate a-C:H by the preferentially sputtering of hydrogen (268-271). This occurs becuase H is lighter and more weakly bound than C. The radiation studies of Kalish et al (204,205) suggest that the primary effect of ionbombardment on a-C:H is dehydrogenation. This may account for why some studies find that the mean energy deposition rate rather than the mean ion voltage can sometimes control the properties of a-C:H (264,265,272) 7.3 Ion-Solid Interactions We now consider ion-matter interactions in more detail. The stopping power (energy loss per
,~
I02
I Q .J W~
WO
i0 -z
13. (I')
f
102 -I 1,1 >I,Z i,i
=E hi
e,
"
I
I0
Fig. 85.
I02
ENERGY(eV)
103
I04
Sputter yield, displacement yield, and range for C ~ ions in a-C, vs. ion energy (272).
Diamond-LikeCarbons
311
unit path length) equals the product of the atomic cross section and the atomic density of the target (204). The stopping power for a medium energy ion ( < 10 keV) is primarily nuclear, due to interactions with the nuclei rather than the electrons in the target. The overall interaction can be characterised by the ion range, the displacement yield (the number of permanent vacancy-interstitial pairs of the target created per incident ion) and the sputter yield (the number of target atoms emitted from the target surface per incident ion). These parameters can be calculated for an incident C + ion for a-C by the TRIM code, as a function of ion energy (272), as shown in Fig. 85. TRIM assumes an isotropic target of density (set to 2 gm.cm-3) and a displacement threshold of 25 eV, as discussed later. We see that 100 V C + ions have a range of about 7A in a-C, while 1 kV ions have a range of about 30A. As nuclear stopping power dominates at the low ion energies of interest, < 10 kV, the much lower mass of hydrogen means that incident H ~ ions have much less effect than C* ions of similar energy. Also, the lower mass of It and its lower displacement threshold (about the C-It bond strength 4 eV) means that H atoms are much more easily displaced or sputtered than C atoms in a-C:H. This accounts for the preferential sputtering of II by impinging ions. Impingement of muiticenter ions of moderate energy results in their complete dissociation at the surface, with the energy partitioned in proportion to their mass. Acetylene and benzene plasmas are frequently used for a-C :H deposition. The key differences to methane are the different C/t I ratio in the source gases and the great stability of the benzene molecule. Acetylene itself is likely to be a main growth species in its plasmas, with the ions C2I{ + and Ctt ~ being the important ions. Interestingly, the properties of a-C:H deposited from acetylene are relatively similar to those from methane (60,61), suggesting some similarities in their plasmas. In contrast, a-C:H films deposited from benzene are very different overall from those depositied from methane or acetylene, as seen in Figs. 54,56. Wagner et ai (187) studied growth species in benzene plasmas by optical emission spectroscopy. They noted that the CH radical was the dominant species in benzene and methane plasmas for bias voltages of 400 V and above. ttowever, optical emission spectra are misleading in this respect as CIt is a very emissive species while many others do not emit. I.arger radicals and ions may still be dominant growth species at the film surface. This leads to a preponderance of undissociated phenyl groups in films deposited at low bias voltages (147). For higher bias, these species dissociate on striking the surface, with the energy partitioned between each daugther species (272). Thus a C ion will have only 1/6 of the energy of an incident phenyl ion. If this full dissociation occurs mainly at the film surface rather than in the plasma itself, this may explain why the maximum density and hardness of such a-C:H occurs at much higher biases than for a-C:H derived from methane or acetylene. The photoemission spectra of IB a-C:H for a stryene precursor (173) give further strong evidence of the difficulty of dissociating some molecules by impact even at moderate ion energies, Fig. 59. 7.4 Ion Beam Deposition
Different deposition mechanisms must be responsible for the promotion of sp s bonding in unhydrogenated a-C films. Four mechanisms have been proposed for this case, preferential sputtering (11), thermal spike (30), preferential displacement (48,13,272,273) and ion-peening mechanisms (39,40,274). Spencer et al (11) suggested that the sp2 sites had a higher sputtering yield than sp s sites, and this would eventually lead to an increased sp s content. Lifshitz et al
312
J. Robertson
lO
Gra .0
0.1
0.01
I 10
Fig. 86.
I
I 100
I
I
Energy,
eV
I 1000
I
Displacement yield vs. C ~ ion energy for sp 2 and sp 3 sites when the have displacement thresholds of 25 eV and 80 eV respectively (272,13).
(48,273) noted that the sputtering yield of any carbon site is very low, because of its high cohesive energy, so that this mechanism is unlikely. Weissmantei (30) proosed the thermal spike mechanism, that a phase change to sp 3 bonding occured in the pressure front ahead of an incident ion. Lifshitz (48), Moller (273) and others have noted that the ion energies of relevance are quite low, with a relatively low displacement yield, so that the concept of thermal spike is not really relevant. Thermal spikes apply to ion energies above 100 kV where incident ions cause great ion displacement and energy transfer, l.ifshitz et al (48,272) instead proposed that sp3 bonding was promoted by the preferential displacement of sp~ sites. I.ifshitz (48) noted that the quoted displacement yield of sp2 sites in graphite (25-30 eV) was much lower than that for sp3 sites in diamond (275,276). The difference might arise from the lower density and more free space in graphite or sp~ bonded carbon and would therefore carry over into the amorphous phase. The difference causes the displacement yield to be 20 times greater for sp 2 sites than sp3 sites for 100 eV C* ions and about 3 times higher for 1000 eV ions (48), Fig. 86. If, after displacement, the ions settle back into sp3 and sp 2 sites with similar probability, sp 3 sites would tend to be dominant, particularly for ion deposition in the range 100-200 eV which is observed
Diamond-LikeCarbons
313
to be the range which gives the highest density for MSIB a-C according to Ishikawa (47) and Hirovinen et al (45), Fig 65. However, recent analysis (277) suggests that the displacement threshold of diamond is much lower than 80 eV, and closer to the 30 eV value of graphite (the threshold for graphite is well defined from nuclear reactor physics). There would then be little difference in the displacement rates for sp2 and sp 3 sites. McKenzie (39,40) proposed that sp 3 bonding was promoted by an ion peening mechanism. In this, impinging ions cause a build up of compressive stress in the film which moves its conditions into the thermodynamic stability region of diamond, which is only 0.04 eV higher at NTP. This mechanism was supported by the observation that the s ~ content of his MSIB a-C films correlated with this internal stress (40). This mechanism is the ion-peening mechanism proposed by Thornton (278) and analysed in more detail by Windischmann (279,280). Ion peening results from the momentum from the incident ions displacing target atoms which tend to become quenched in position. Windischmann (279,280) noted that the peening effects correlated with the momentum rather than the energy of the incident ion. The ideas are often used in the field of ion-beam modification of materials where it is noted that ion bombardment improves the compaction of deposited films (281). The density and compaction of such films improves when the internal stress is found to change from tensile to compressive (280). Kaukonen and Nieminen (274) have recent carried out a molecular dynamics simulation of this process. They observed the displacemnt and quenching-in of atoms in the interstital positions. They noted that the quenching process set an upper limit to the ion energy and was favoured by a high local thermal conductivity. They observed that the optimum ion energy for promoting sp 3 bonding was about 50 eV, closer to that found experimentally by McKenzie et al (40), as seen in Fig. 66. The work of Cuomo et al (28) is not really consistent with the ion-peening model. They observed that a high fraction of sp 3 sites could be produced for mean ion energies of order 7 eV, provided that the deposition occured onto a substrate of high thermal conductivity. Although the ion energies in this case were low, the ion flux ratio was still very high in this case. There is no adequate theory to the author's knowledge for such low ion energies. 8 MECHANICAL PROPERTIES 8.1 Survey The mechanical properties of diamond-like carbon, its elastic modulus, hardness, friction and wear, are of great interest for its use as a coating. Table 15 compares the mechanical properties of various forms of a-C with those of diamond, graphite, Si and polythene. The strength and rigidity of diamond arises from its strong, directional o bonds. The very high bulk modulus derives largely from its short bond length, because the bulk modulus B of covalent solids tend to vary with bond length R as (282) B = Bo R-'~s
[60]
The sp 3 bonds of diamond are also exceptionally resistant to angular distortions; a reasonable measure of this is the ratio of shear to bulk modulus, S/B, which is twice as high in diamond
314
J. Robertson
Table 15. Mechanical properties. Comparsion of Youngs modulus E, Bulk modulus K, Shear modulus G, Poissons ratio v, Hardness II and Yield stressY. E, GPa
K, GPa
G, GPa
v
H, GPa
Y, GParef.
Diamond
1050
442
478
0.104
103
59
16,289-291
PD a-C:tI, 100 V
145
52
24
0.4
16
9.7
296,297
PD a-C:H 1 kV
55
23
31
0.2
6.3
3.1
296,297
sputtered a-C
140
15
MSIB a-C
20-110
27 12-65
38,44
graphite,//a
686
290
glassy C, GC10
29
12.5
0.15
3.0
1.0
293,294
glassy C, GC20
32
13.5
0.17
2.2
0.73
293,294
polythene
,~0. I
Si
130
a-Si:H
100
0.01 97.8
50.9
292
0.278
10.4
5.0
290
0.32
10.0
4.9
298
as in other diamond-structure crystals like Si and Ge, as seen in Table 15. 8.2 Con~raint Model
The mechanical properties of amorphous carbons clearly depend on the strength of their component bonds. Their mechanical properties are inferior to those of diamond because of their finite sp 2 and H content (Table 1). It is possible to give a firmer theoretical model of these properties, starting with elasticity, the most tractable. The elasticity of amorphous carbons can be related the elasticity of the individual bonds and the connectivity or coordination of the network using the constraint counting model of Phillips (283) and Thorpe (284,285). The energetics of a covalent network can be represented by a valence force field of first neighbour bond stretching and bond bending forces as in eqn {8}. When the mean coordination r is low, there are many ways in which the network can be deformed at zero energy cost, ie. leaving bond lengths and bond angles unchanged. The number of these deformations or zero-frequency vibration modes of a network of N atoms is given by the number of degrees of freedom (3N) minus the number of constraints N~o. The number of constraints varies with the coordination, r. There is one constraint associated with each bond (shared between two atoms) and 2r-3 constraints with the angles of each r-coordinated atom, giving a total of (285,286) Neon(r) = T5 r - 3
1,6U
per site, except for monovalent atoms like hydrogen for which Neon (I) = 1/2
162]
The fraction of zero-frequency modes is then given by f = I - (N~o/3N). Writing f = ~gf,x,, we obtain f = Y~r>l Xr(2- --~r)5 = 2 ---~r 5-
1,,63]
Diamond-LikeCarbons
315
where x, is the concentration of r-fold sites and ~ = ~.Xrr is the mean coordination. Eqn [63] shows that a critical coordination or percolation threshold rp exists rp = 2.4
[64]
below which the network can be deformed a zero energy cost and is called underconstrained or 'floppy'. Above rp the network is called overconstrained or 'rigid'. Its modulus then varies as ( - 0 '.s or
E = Eo(
_f
)
i.s
r-2.4
= Eo( 7o-- :a )
~,s
[65]
where Eo is the modulus of the fully coordinated network, r0 = 4 in our case. Angus and Jansen (287) noted that condition [64] for r~ can still be used for a network containing hydrogen if r now represents only the C-C coordination, the skeletal coordination, found by treating each C-H bond as a broken bond contributing no rigidity. This requiries substituting r ~ r - x~.dx, in [61] and x, - x,/(l - x,) in [63] where xt., is the concentration of hydrogen bonded to r-fold sites, to give
5 [(2---E, 5 r)xr + --ff-x,,,]/[I
f =
- x,]
[66]
Indeed, all pendant groups like - C t h contribute no network rigidity. The constraint model must also be modified to take into account n bonding (13,288). A n bond between two sp 2 sites as in ethylene adds torsional rigidity to that bond. It therefore adds a 1/2 constraint per atom, increasing N~o, from 4.5 to 5 for a s p 2 site. Thus a sp ~ C atom is more constrained than a trivalent P atom. The constraint counting model must clearly be modified to treat graphitic bonding (288). Graphite is a slippery solid with no rigidity between its layers, despite it having a coordination of 3, well above the critical minimum value of r, = 2.4. The model fails for graphite because of its anisotropic bonding. It is strongly bonded in two dimensions but has only weak van der Waals bonding between the layers. In terms of constraints, graphite uses all of its constraints in maintaining rigid layers and none in its interlayer bonding. A graphite layer of N' atoms can be treated as an internally rigid disk with 3N'-3 constraints, 3 for each site minus 3 for its translational degrees of freedom. Such an internally rigid graphite layer or graphitic cluster embedded in a network at N " perimeter sites acts like a N"-fold coordinated site. This adds a further (5N"/2 -3) constraints, to give Neon(3 ) = [(JN' - 3 ) + ( @ N" - 3)]
[67]
and
f3
= 1-T
1
Ne°n =
2 N'
5N" 6N'
[68]
N " is typically much less than N'. For a circular cluster N " ~ T t x / - ~ 2 , and typically N" "-'2.5~N7- for a compact cluster, giving 2.1
[693
316
J. Robertmn
This shows that clustering has the effect of raising rp for sp~ sites and making graphite itself borderline floppy. As clusters tend to be large, we take N'--, oo and fa -~ 0
[70-1
giving finally (288) --f~"
x,t -
-
(1 m
Xl ~ f4 =
4
5
.J
U
[71]
("~-X4---ZX1,4)/(I--XI)
where xt.4 is the fraction of hydrogen bonded to 4-fold sites. We thus reach the important conclusion that both graphitic and polymeric bonding tend to reduce rigidity. The lack of rigidity from graphitic bonding can be confirmed by considering the Youngs modulus of glassy carbon (Table 15). Its modulus is seen to be only about 1/20 of that ofthe in-plane modulus of graphite (293). This is consistent with a modulus derived only from the inter-plane cross links, occurring every L,-~20 rings apart, the observed value (9). 8.3 Ela~ic Moduli - Comparison with Experiment
In the 2-phase model, the network of a-C:H consists of sp2 clusters which control the band gap
0.2
O1 C
= 0.1
0 >-
"O
I
O
Z
0 0
Fig. 87.
500 BIAS VOLTAGE, V
1000
Comparison of experimental (298) and calculated normalised Youngs modulus of a-C:H.
Diamond-Like Carbons
317
embedded in the sp 3 phase whose C-C coordination controls the rigidity (288). Fig. 87 shows the Youngs modulus of PD a-C:H deposited from methane by Jiang et al (296,297) compared with that calculated from eqns [65,71] using the coordination data of Tamor (75) for similar films and with E0 taken from diamond. The agreement is seen to be good, considering the approximations made and the remaning uncertainties in the coordination data. The model shows that E is small at low bias because of the predominance of polymeric groups and declines again at high bias because of the increasing sp ~ content. This decline cannot be reproduced unless the sp2 sites form clusters which contribute little rigidity. The effective C-C coordination may be estimated for these films from equation [65], to give r=2.83 for the 100V film and r=2.63 for the I kV film, Table 15. Clearly, these networks have coordinations well below the ideal limit of 4 but well above rp. Angus and Jansen (287) argued that the H content and sp2 content of a-C:H are optimized during deposition to give ?-,,2.4, as this is the coordination at which the energy gain from increased bond density might balance the increase in network strain energy. The above derivation suggests that the coordination of the network must exceed 2.4 otherwise it would have no rigidity (or hardness). Happily, for the sake of forming hard carbons, it does. Nevertheless, the low Youngs modulus of a-C:H compared to that of diamond serves to emphasise that the C-C coordination of PD a-C:lt is still relatively low. The Youngs modulus of magnetron sputtered a-C has been found to be I15-141 GPa (27), Table 15, as high as that of hard PD a-C:H. This material has at most 5% sp3 sites and little hydrogen. Its rigidity must originate largely from its sp2 sites. An isotropically bonded 3-fold coordinated network with 1.42A bond length would have a modulus of 30% ofthat of diamond, 300 GPa, from eqn [65]. The observed maximum modulus is 45% of this. It is likely that the rigidity of the sp 2 network arises from a significant interlayer cross-linking, giving it a limited form of isotropic bonding. Indeed, E does vary with the Raman D intensity and hence with L, (27). A periodic model with cross-linking and a high modulus is the H-6 structure of Tamor and Hess (299). In contrast, it appears that the sp 2 clusters give little rigidity in a-C :tt because they are well separated and cannot crosslink. 8.4 Hardness
Hardness is the key parameter of diamond-like carbons of technological relevance. It is measured by indentation and is the pressure over the permanently indented area at a given applied load. ttardness is a measure of the yield stress, Y, It is related to Y by an equation of the form H/Y = 0.07 + 0.6 In(E/Y)
[72]
for an isotropic solid. This equation is based on an analysis of tile stress field around the indenter tip. The constants in [72] were found by fitting data for a range of materials - metals, polymers and glasses - which cover a wide range of Y/E ratios (300,301). (The measurements for polymers are most relevant for diamond and a-C in that polymers also have a low Y/E ratios). It can be rearranged to give rl/Y -~ - 0 . 0 4 + 0.77 ln(E/tl)
[73]
l i l y ~ 1.8
[74]
or
318
J. Robet'tson
for materials with low Y/E ratios like diamond and a-C :H (note that this is much lower than the typical factor of 3 used for metals). The yield stress of a metal is controlled by dislocation flow, which gives relatively low values of Y/E. In contrast, dislocation motion is much more difficult in covalent materials like diamond, and yield tends to occur by cleavage, giving a high value of Y/E. The existence of dislocations in amorphous solids is contentious. In any case, they are likely to be pinned by the topological and bond length disorder. Hence yield is also expected to occur by cleavage in a-C(:H). The cleavage stress is the stress needed to separate two adjacent planes of atoms of the solid. This in turn can be related to the Youngs modulus by the Orowan approximation of replacing the interplanar force by a sine function and equating E to the initial slope, to give (290) Y-~E/n
[75]
Combining with eqn [74] gives It-~E/6. The values for diamond in Table 13 show that H/E ~ O.I
[76]
is a better approximation (288). Hardness measurements on a-C and a-C:H films must ensure that the indent depth does not exceed 10% of the film thickness and must allow for elastic recovery. The limit on indent depth is necessary because the substrate often has a lower hardness than the film. On the other hand
3
I
I
I
es °
z E
2 / el
Loading ojO
f10
O ..-I
.,I
:""
0 0
Fig. 88.
'
jLD S
S°
/
/--j
Unloading
--r"/,
..sO
hf
/ /
hp 50 100 Displacement [nml
150
Load vs. depth curve for and indentation measurement, illustrating the elastic recovery (298)
Diamond-LikeCarbons
319
if the penetration is too small, some error arises because of deformation of the indenter tip. The problem of elastic recovery is shown in Fig. 88. Hardness is the average pressure under the indenter, given by the applied load divided by the projected area of contact. In conventional microhardness tests, the indent area is measured by imaging after removing the load. However, if there is significant elastic recovery, the area is underestimated and the hardness overestimated (297). The extreme example is rubber which apparently has high hardness because indents in it recover totally. Many early hardness measurements on a-C(:H) suffered from this error, giving values up to 60 GPa for a-C:H. The true hardness is found by estimating the area in the loaded condition from the load vs. indent depth curve, Fig. 88. A tangent is drawn to the unloading curve at maximum load and extrapolated to zero load. Its slope is proportional to the Youngs modulus and it subtends the elastic depth on the displacement axis. The remainder is the plastic depth, h~, needed for hardness. Elastic recovery is significant when Y/E is not small, such as in covalent solids. Corrected hardness values are typically 30% of uncorrected values. Hardness values for diamond, PD a-C:H, sputtered a-C and MSIB a-C are given in "Fable 15. In each case, H is found to scale with Youngs modulus according to eqn [76]. This scaling holds despite the bonding changes occurring in the a-C:H and despite the changes in Poissons ratio. The validity of eqn [76] in a-C(:tt) allows the previous model of E to be extended to cover hardness. The hardness of MS1B a-C has been found to reach values similar to that of diamond (38). As diamond is the hardest solid, this is perhaps the simplest demonstration of the high sp 3 content of MSIB a-C. The hardness of MSIB a-C has also been studied as a function of ion energy. It is found to peak at a similar energy as its density (44).
I
|
I
I
15
Benzene
m a. ~10 oe-
Z
5
Methane~
O,
0
Fig. 89. JPSSC
21:4-I
200
400
600 800 Bias voltage (V)
1000
1200
Hardness vs. bias for PD a-C:H deposited from methane (298) and benzene (9,30)
320
J. R o b e r t s o n
Fig. 89 shows in more detail the variation of hardness with bias for both the methane films of Jiang et al (297,298) and the benzene films of Koidl et al (9). H is very low at V~= 0 V for soft a-C :H. It then increases and passes through a maximum at around 200 V for the methane films whereas it increases continuously for the benzene films. The data of Weissmantel (30) suggest that H declines again above I-1.5 kV, as shown schematically by a dashed line in Fig. 89. The hardness of a-C:H deposited from acetylene has been measured with a nanoindenter as a function of gas pressure, and by microindenter as a function of bias voltage (61). The measurements as a function of gas pressure suggest that the microindenter overestimates hardness by a constant factor. Thus, Fig. 90 shows the approximate corrected hardness values ofa-C:tt deposited from acetylene as a function of bias. The hardness is seen to vary in a similar fashion to that of methane-derived films (297), but with a substantially higher peak value. Interestingly, the hardness variations for each type of a-C:H are very similar to those of the density. Fig. 91 shows that the hardness increases further as the source gas pressure is reduced (although this reduces deposition rates). These hardness data suggest that acetylene may be the most useful precursor gas for PD a-C:H, combining reasonable deposition rates (Fig. 10) and the highest hardness. Collins et al (35,99,302) have produced hard carbon films by laser-plasma deposition. These films appear to be microscopically inhomogeneous, with apparently highly sp3 bonded possibly diamond grains embedded in a more sp~ bonded matrix of a-C. Fig. 23 showed a TEM micrograph of this material. Its mean hardness has been measured by a nano-indenter to be
30
20
A
o. r3 f~
(g
-r
10-
00
Fig. 90.
a
I
200
,
i
I
i
i
400 600 Bias voltage (V)
I
i
800
i
1000
Approximate micro-hardness vs. bias for PD a-C:H deposited from acetylene (61).
Diamond-LikeCarbons
321
\
30 0
•
~20
• \0
- -
\o
L-0
10
Vb--300 v
0 10-3
Fig. 91.
1 I 10-z 10-1 Pressure of CzHz [rnbor]
\ \
100
Hardness vs. gas pressure, for PD a-C:H deposited from acetylene (61)
30-40GPa, which is particularly high. The indent size is much larger than the grain size, so the hardness respresents an average. Collins (302) noted that the lower modulus of this carbon than diamond could be advantageous, as it lessens the transmission of mechanical shocl~s through such a coating to a weaker substrate. It is also possible that microscopic inhomogeity may raise the stress intensity factor Klc = ~ , by dispersing fractures into microscopic cracks. This could be useful as Kjc of diamond is not so high, its fracture energy y being close to the ideal surface energy value.
8.5 Friction The friction properties of PD a-C:tl deposited from ethylene has been measured by Enke and others (303-307). The coefficient of friction was found to increase strongly with atmospheric humidity, from a low value of 0.05 at 12% relative humidity to 0.30 at 100% humidity. There are basically three regimes of friction on ceramics (308,309). At low loads, friction occurs by the adhesion mechanism, contact is elastic and leaves no permanent groove. At moderate loads, a permanent groove is left by "ploughing" and plastic deformation of the surface. At high loads, a gross cracking and deformation of the surface occurs. Diamond itself has a low friction, due to a combination of its high elastic modulus and its low adhesion (16). This keeps contacts on diamond in the adhesive regime and also minimises their effects (308). The low adhesion arises
322
J. Robertson
from the passivation of its surface with stable C-H bonds. Hard a-C and a-C:H are expected to have generally similar frictional behaviour to diamond, but higher absolute friction coefficients, because they have low adhesion, passivated surfaces but lower elastic moduli. The low friction of a-C:H in dry conditions is consistent with this behaviour, but it is difficult to account for the humidity dependence. Grill et al (193) also observed a friction coefficient of order 0.3. 8.6 Wear
Wear of surfaces can arise from several mechanisms such as adhesion, abrasion and tribochemical (308,309). Adhesive wear occurs by adhesive contact at the asperities where stress magnification causes a local cold-welding of the two surfaces, i f the interface bond is weak, it shears and no wear occurs. If the interface bond is strong, there is shear within the weaker material, transferring material to the tougher surface. The wear rate in volume per unit track length V/L is given by V L
kW 3Y
kW H
177]
where W is the load, Y is the yield stress of the weak surface and H is its hardness (H = 3Y). Abrasive wear occurs at contacts between materials of dissimilar hardness. It occurs by ploughing, by microcracking or local plastic deformation of the softer surface. The wear rate is given the extent of the indented groove, V I-'7 =
Wcot(0) nI-I
1,'78]
where 0 is the indent's pyramidal angle. Thus, adhesive and abrasive wear rates of a surface vary inversely with its hardness. Tribochemical wear is the main form of wear in diamond in air (16). It occurs at high rubbing speeds from a gradual rise in friction coefficient leading to local heating which converts the diamond to graphite which then oxidises to CO2. A number of wear tests have been carried out on amorphous carbons. Abrasive wear has been observed in a-C:H (3 I0) while abrasive and tribochemical wear have been observed in sputtered a-C (311). The abrasive wear rate of a surface varies inversely with its hardness, according to eqn 1,-78]. The abrasive wear rate of a-C:tt was found to increase by a factor of nearly 10~ as the hardness (22) fell as the hydrogen content varied from 0 to 60%, which is consistent with expectations. Marchon et al (311) observed abrasive and tribochemical wear in sputtered a-C. They found that the abrasive wear rate varied inversely with the Raman I(D)/I(G) ratio. This dependence is unexpected as hardness has not been previously correlated with this ratio. Marchon et al (31 I) found the tribochemical wear rate fell for films of lower Raman G mode frequency. Hirvonen et al (45) observed that the wear of MSIB a-C occured by a combination abrasion and cracking. The abrasive wear rate was a factor of 230-290 lower than that of SiC and A1203, and a factor 60 lower than that of WC-Co composite, with only diamond itself being lower. g.7 Internal Stress
A major problem with a-C(:H) films is that they usually possess substantial intrinsic stress. This limits the adhesion of thicker films and their potential applications (308,312). Fig. 92 shows the
Diamond-Like Carbons
323
interface. Evidence of strong bonding was found at Si/C and metal/C interfaces by Raman (317) and photoemission (318-320) respectively.: Adhesive failure of thin films occurs when the internal stress o exceeds a critical value. A film of thickness h delaminates when the mechanical energy density exceeds the energy needed to create two new surfaces (321), o2h 2E
< 2y
[79]
where ~ is the surface/interracial energy. It is preferable to rewrite this in terms of strain t as this is continuous across the interface and to factor out the large variations in Youngs modulus of the films. Eqn 1-79] becomes h <
4yE 2
[80]
for adhesion, where the numerical factor 4 is approximate (321). This sets an upper limit on film thickness. The interracial energy of a-C(:H) films equals the energy needed to break the bonds across a given plane. Its maximum value is that of diamond (16), 5.7 J/m s. Adhesion is measured empirically by the scratch test, in which a stylus in drawn across a surface under continuously increasing normal force, until the film begins to peel off at a critical load W~. The limiting interracial stress c/~ is the sum of the internal stress c/, and the applied stress (322), C/c ----- C/internal +
kl'c
[81]
so the critical load gives an indication of c/c. Metal-containing a-C:H (Me-C:II) films were introduced to improve the adhesion properties of a-C:H (308,323). 9 Conclusions
The hard forms ofa-C and a-C:it can be prepared with significant sp .~contents and much higher atomic densities than other forms of non-crystalline carbon.: The hard carbons can be produced by a range of deposition processes such as ion-beam deposition, plasma deposition, sputtering, laser plasma deposition, cascade arc, and mass selected ion beam deposition. A common factor is the ion bombardment of the growing film. Hard a-C(:H) films tend to have mixed sp ~, sp 3 bonding. Quantum chemical arguments suggest that the sp 2 and sp3 sites will segregate into sp2 aromatic clusters embedded in a s p 3 bonded matrix. The electronic properties depend on tile n states of the sp 2 clusters. The optical gap varies as 6/M 1/~with the cluster size M. The mechanical properties depend on the cross-linking of the sp3 phase in a-C:H, and additional on the warping and cross-linking of the sp2 layers in a-C. Experimental results such as optical absorption, Raman spectra and luminesence spectra support the two-phase model of a-C:H. The sp 3 content of a-C(:H) is best measured by NMR or X-ray near edge spectra. The C-H configurations can be found from infra-red absorption. The Raman spectra reflect mainly the sp~ sites and give information on the degree of clustering. A good theory of Raman is still required.
324
J. Robertson
Hard a-C prepared by RF sputtering has about 95% sp 2 sites, a gap of 0.5-0.7 eV and a true hardness of up to 15 GPa. This hardness indicates a considerable cross-linking of the sp 2 layers. Magnetron sputtering can raise the sp 3 content and optical gap. The most popular preparation method of a-C:H is by RF self-bias plasma-deposition. The properties of PD a-C:H depend primarily on the self-bias voltage. The H content and sp 3 fraction falls steadily with bias, to give three structural regimes. Soft, polymeric films are formed at low bias. Hard, transparent 'diamond-like' films are formed at intermediate bias (100-1000 V depending on source gas) with a highly cross-linked network. Less hard, more graphitic films are formed at high bias. Many properties of hard a-C:tt are independent of source gas, but hardness, density and deposition rate do depend on source g a s . Acetylene seems to give the hardest, highest density a-C:H films, of the commonly available source gases, reaching hardnesses of 30 GPa. A remarkable form of a-C can be prepared by mas selected ion beam deposition, with "~90% sp 3 sites and a low H content. It appears to consist of flakes of sp 3 carbon surrounded by a thin 10A surface layer of sp 2 sites. Its hardness is 30-110 GPa. Laser plasmas can produce a microscopically inhomogeneous form of hard carbon, apparently consisting of small diamond(-like) nodules embedded in a s p 2 matrix. Its hardness is 30-50 GPa. The deposition mechanism needs further study. In PD a-C:tt the major growth species are neutral radicals and ion bombardment is used to dehydrogenate the film and raise netwrok cross-linking. In a-C ion-bombardment is found to promote sp 3 bonding, probably via an ionpeening mechanism, but other mechansims are also active. [lard a-C(:H) has many present applications as a hard, transparent inert coating material. Its low deposition temperature allows it to be applied to a wide range of substrate materials. It is presently used for magnetic disc coatings, protective coatings on optical windows and on orthopaedic implants. The problems of a-C(:tl) coatings concern its high internal stress, lack of adhesion and poor temperature stability.
Acknowledgements The author is very grateful for discussions and information from M. A. Tamor, D. McKenzie, P. Gaskell, G. Gilkes, R. Newport, B. Dischler, J. Fink, J. Perrin, C. B. Collins and J. Prins.
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