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Structure of amorphous hydrogenated carbon: experiment and computer simulation
Diamond
tmd Related
Materiuls.
3 (1994) 245-253
245
Structure of amorphous hydrogenated carbon: experiment and computer simulation M. Weiler, R. Kleber, S. Sattel, K. Jung and H. Ehrhardt Fachhereic,h Phq’sik der UnioersitSit
G. Jungnickel,
Kaiserslautern,
S. Deutschmann,
W-6750 Kaiserslautern
U. Stephan,
Fachhereic h Physik der Technischen
UnitiersitBt
(Received
in revised form July 6, 1993)
March 30. 1993: accepted
Chemnitz,
(Germany]
P. Blaudeck
O-9010 Chemnitz
and Th. Frauenheim
(Germany)
Abstract The microstructure of amorphous hydrogenated carbon films has been studied by electron diffraction measurements and comparison of the results with simulated diffraction data which have been modelled by molecular dynamics (MD) calculations. The films have been produced partly by a plasma-enhanced chemical vapour deposition process and partly by a plasma beam deposition method. The MD simulation is based on an annealing process cooling down a liquid phase ensemble of 64 carbon and a corresponding number of hydrogen atoms using a density functional approach to account for the interatomic forces.
1. Introduction
In spite of the increasing interest in amorphous hydrogenated carbon films with physical properties adaptable to special technical applications, the microstructures of these materials are still not well understood. Therefore a comparison of a variety of experimental data with corresponding theoretical simulations of structures is necessary in order to find correlations between microstructural details and macroscopic properties. This study intends to contribute to this general goal. It is well known that the macroscopic film properties are strongly related to the ratio of sp2 to sp3 bonding of the carbon atoms and to the hydrogen concentration in the material [l]. These quantities in turn depend largely on the ion energies and on the particle flux composition. Many phenomenological correlations between the mechanical and optical film properties and the flux quantities have been found, but it is essentially not yet clear how the particle flux controls the sp2/sp3 ratio. Recently McKenzie et al. [2] found that amorphous carbon (a-C) films deposited from a pure C+ ion beam have maximum density and sp3 content for ion energies between 30 and 50 eV. Robertson [3, 41 postulated an energy-dependent balance between sp* and sp3 sites, because collisions of the C+ ions create vacancies and interstitials. If a C atom is forced into a position with close distances to neighbouring C atoms in the second or third layer below the surface, such a process is called subplantation [S]. Such an atom tends to
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hybridize within an sp3 configuration. Consequently, the concentration [6] of the sp3 C-C bonds increases with increasing film density. In the present paper the preparational conditions are chosen in such a way that the plasma parameters determine the energy and the relative proportion of ions and neutrals in the particle flux to the substrate. The parameters have been varied over a rather wide range, but excluded have been those experimental conditions under which loose polymeric films are formed. These materials are of minor technical relevance and cannot be described appropriately by the theory applied in this investigation. After the description of the deposition processes the measurements are presented with special emphasis on electron diffraction data, which are well suited to investigate the short-range order of the network. The last two sections deal with the theoretical methods and with a comparison of experimental and theoretical data.
2. Film deposition Amorphous hydrogenated carbon (a-C : H) films may vary from loose, polymer-like to dense, strongly interconnected diamond-like networks. To cover a wide range of film properties, two different experimental arrangements have been used. Employing an r.f. discharge apparatus for plasma-assisted chemical vapour deposition (CVD) can yield polymer-like films but also
246
M. Weiler et al. / Structure of a-C:H
diamond-like carbon. The result depends mostly on the energies of the ions when deposited on the substrate, but also on the total flux composition and therefore on the precursor or working gas. The use of a plasma beam source (PBS) offers the preparation of samples with high density, corresponding to high sp 3 C C bonding concentrations. The plasma CVD reactor has been described in detail earlier [7]. The r.f. discharge is operated at 13.56 MHz with a power of 100 W, coupled to the plasma partly inductively and partly capacitively. C2H2 was used as working gas. It has been shown earlier [8, 9] that the film properties are mainly determined by the ion energy and by the ratio (Di~/(De, where (Die is the ion flux of carbon-containing particles to the substrate and (De is the total flux of carbon atoms contributing to the film growth. The ion flux consisted mainly (more than 50%) of C2H + (x=0,1,2) ions. The average ion energy E varied between 30 and 250 eV; the ratio (Di~/(Dovaried between 5% and 30% depending on the pressure in the discharge. With low (DiJ(Dc ratios and low ion energies polymer-like a-C:H films are deposited. To prepare films with densities higher than 2 g cm-3, a plasma beam source has been used. The configuration of electrodes and magnetic field is chosen similar to an apparatus described by Oechsner et al. [10]. The r.f. plasma is operated at 13.56 MHz with C 2 H 2 as working gas and is confined magnetically (200 G). The plasma beam consists mainly of C2H+ ions with well-defined ion energies. The ions are extracted through a grid of high transmission by the r.f. self-bias between plasma and grid. The ion energy can be varied between 250 and 580 eV. The ion energy has been measured by a retarding field after having separated the electrons from the plasma beam. The energy resolution A E / E was about 10%. For all ion energies the ratio (Di~/(De is about 90% if one assumes that the sticking coefficients for the C-containing ions are close to unity. During the experiments the ion current density (0.3 mAcm -2) and the pressure (1 x 10-3 mbar) in the plasma reactor are kept constant.
3. Film charaeterization The properties of the four a-C:H films studied are given in Table 1, where the notations of the samples indicate the preparation method as either CVD or PBS. The macroscopic a-C : H film properties density (floating method), hardness (Knoop microindenter) and internal stress (bending beam method) have been measured. Electron energy loss spectroscopy (EELS), electron spin resonance (ESR),. IR spectroscopy and electron diffraction experiments have been used to characterize the microscopic structures of the films. Additionally, the
optical gap and the hydrogen content (15N method) of the layers were determined. Only the CVD samples could be analysed with respect to sp 3 concentrations using a 13C nuclear magnetic resonance (NMR) measurement, because only for these samples could sufficient material (about 400 mg) be produced. Details on the various experiments have been published by Kleber et al. [11]. The ratio of sp 3 to sp 2 bonds in the PBS films was estimated by EELS using the integral of the counts in the ls ~ n* peak and comparing that with graphite [12]. Sample CVD1 was deposited at E=170eV and (Dic/(Dc = 13%, resulting in a rather dense a-C: H network. The mechanical properties hardness HK = 20 GPa, density p=2.0 g cm -3 and internal stress a=2.4 GPa show that the network is quite strongly interconnected. The rather tow hydrogen content of 32.5 at.% is due to the high energy of the impinging ions causing hydrogen atoms of the adsorption layer and the hydrocarbon ions to be dissociated and hydrogen released. Therefore the number of C-H bonds is low and the formation of sp 2 (C-C) bonds is supported. For the experimental conditions applied for CVD1 an sp 2 fraction of 61% is obtained. The rather small optical gap of 1.3 eV indicates the arrangement of these sp2-bonded atoms in the form of sp 2 clusters [13]. The n--.rc* transition between 4 and 7 eV in the EEL spectrum shows a broad peak at about 5.6 eV, suggesting several sp 2 cluster sizes. Sample CVD2 deposited at E = 250 eV and (Dic/(De= 29% with p = 2 . 2 g c m -3 possesses a somewhat more densified a-C:H network. The hydrogen content is reduced to 28 at.%, which gives rise to a different bonding of the network with a reduced number of sp 3 CH bonds. This is confirmed by IR analysis of the samples in the range 2800-3100cm -1. It is observed that the IR intensity ratio of sp 3 CH1, 2 to sp2CH1,2 lines decreases with increasing ion energy. The EEL spectrum of CVD2 shows that the sp 2 cluster size distribution is still enlarged in comparison with CVD1, because no sharp peak in the r ~ r t * transition is observed. From the position of the broad structure in the EEL spectrum it can be assumed that the average sp 2 cluster size is larger than in CVD1. The enhancement of the sp 2 cluster sizes is also confirmed by the decrease in the optical gap to 1.1 eV. An sp 2 fraction of 75% was determined by Auger spectroscopy in combination with factor analysis 1-14]. With c o n s t a n t spa C-C fraction, further decreasing sp 3 CH concentration and increasing sp 2 cluster sizes the mechanical properties of this network are altered to a higher hardness (HK=40 GPa) and a larger internal stress (~ = 4.4 GPa). The films prepared by the plasma beam source method are deposited with a much higher ion contribution in the particle flux ((Dic/(D¢= 90%), resulting in even denser a-C:H networks. Sample PBS1 (E=260 eV) has a den-
247
M. Weiler et al. / Structure of a-C:H
TABLE 1. Compilation of the experimental results for the four samples studied. Samples CVDI and CVD2 were prepared using a plasmaenhanced CVD method. Samples PBS1 and PBS2 were produced by a plasma beam source Sample
CVD 1 CVD2 PBS 1 PBS2
~bic/~b~ (%)
Mean energy (eV)
Density (g cm 3)
Knoop hardness (GPa)
Stress (GPa)
13 29 80 80
170 250 260 300
2.0 2.2 2.7 2.4
20 30-40 42 33
2.4 4.4 6.0 5.0
H
Sp-'
content (at.%)
content lat.%)
32.5 28.0 25.0 24.0
61 75 45 70
sity of 2.7 g cm 3, which cannot be reached by the CVD process. The optical gap of 1.38 eV and the ESR linewidth indicate that the sp 2 cluster size is similar to that of CVD2. The low spin density of 2 x 10 t9 cm 3 (in spite of the low hydrogen content of 25 at.%) indicates a low concentration of dangling bonds and nonsaturated rt states. The rather small optical gap is an indication of the existence of large sp 2 cluster sizes, but it is not possible to draw the conclusion that the sp 2 content is large, because it is known that already a very small concentration of these clusters leads to a strong absorption [13]. This network possesses a much higher sp 3 C C fraction than the CVD2 film. The density of 2.7 g cm - 3, exceeding significantly the density of graphite (p = 2.2 g cm -3), indicates an sp 3 C - C fraction of about 30% (Paiam = 3.5 g cm 3), whereas in the CVD films the sp 3 C C component is only about 10%. The large density of sp a C C sites causes a rather large internal stress ( a = 6 GPa). Similar results have been obtained with vacuum-arc-deposited a-C films [15]. Sample PBS2 deposited at 300 eV ion energy shows already some signs of graphitization. The density is reduced to 2.4 g cm -3, the optical gap is decreased to 1.26 eV and the hardness and stress values are reduced, implying that the sp 3 C - C sites are transformed by irradiation damage during the film growth into s p 2 sites. As we know from VRIMsimulations, at higher ion energies the formation of vacancies exceeds the formation of interstitials.
4. Electron diffraction measurements
One of the aims of the present investigation was to characterize the films according to their short-range structure. Therefore electron-scattering measurements have been performed. The electron-scattering intensity l(s) with the momentum transfer s = (2g/2) sin(O) and the scattering angle O was measured with a JEM 100CX electron microscope in the range 0.5 ~
Spins (102ocm 3)
Bandwidth (mT)
Optical gap (eV)
Plasmon energy (eV)
1.6 4.3 0.20 0.16
0.210
1.30 l.l 1.38 1.26
24.4 25.6 28.0 26.6
0.288 0.285
typical for the films studied here, a multiple-scattering correction has to be applied. By using a transformation described by Misell and Burge [16] and a subsequent Fourier transformation, the single-scattering contribution IVy(s) is related to the total intensity I v by
II-
1
v ln(1 + I% v)
The average number of interactions, v, can be obtained from transmission electron microscopy (TEM) mass thickness measurements. The inelastic scattering part has been determined by a fit proposed by Palinkas and Radnai [17]. The reduced scattering intensity d(s)= S[IXl(S)-(f2)]/(f) 2 with the atomic density distribution J'and the reduced atomic density distribution
2r a(r) = ~ d ( s ) exp(-~2s 2) sin(sr)ds can then be calculated, where (J') is the average over the f concentration. Because the atomic charge distribution in carbon bulk material deviates from that of free carbon atoms, the bulk charge density for a single carbon atom was derived from localized atomic valence orbitallocal density approximation (LCAO LDA) calculations. From this charge distribution an improved atomic scattering factorJc for carbon was obtained [18]. The influence of the electron scattering from hydrogen is very small. For the described analysis the atomic scattering factor fH for hydrogen was determined by the Warren Krutter Morningstar approximation assuming fH =Jc/6. To reduce cancellation effects in G(r) caused by the discontinuity of d(s) at the maximal experimentally reached momentum transfer, d(s) was multiplied by an exponential damping factor exp(-~2s 2) (~ =0.1 A) before performing the Fourier transformation. This correction leads to a peak broadening in G(r). For this reason it is better to use d(s) for comparison with theoretical models, although this function allows no simple conclusions on the microstructure. For each measurement the electron beam position is manually adjusted to zero scattering angle. Thus the momentum transfer axis s is very well established and the next-neighbour distances taken from G(r) are exact within 1 % - 2 % .
248
M. Weiler et al. / Structure of a-C.'H
5. Structure modelling Theoretical structure simulations developed during the last decade have been established as a powerful tool to understand the microscopic structure and its influence on the physical properties of hydrogenated amorphous semiconductor materials. However, there are only a few attempts related to a-C and a-C:H. Apart from qualitative arguments in the discussion of structural and physical properties of a-C:H [13], there are many open questions regarding the nucleation and structure formation processes during film growth, primarily the hydrogen influence on clustering and medium-range order, which control the macroscopic physical properties of the material. Performing molecular dynamic (MD) simulations of hydrogenated amorphous carbon on the basis of quantum mechanically derived interatomic forces is an attempt to tackle these problems. This goal is achieved by applying an approximate well-tested ab initio scheme using a minimal basis set [19, 20] of the localized atomic valence orbitals of all atoms in the atomic network. In contrast with classical potential concepts [21], this ab initio type of approximation allows the inclusion of hydrogen and overcomes the difficulty of nontransferability from bulk material to finite clusters and surfaces. Compared with fully self-consistent field (SCF) ab initio calculations [22], this method reduces the computational efforts by at least two orders of magnitude and avoids problems in the construction of a pseudopotential for hydrogen. On this basis, systematic dynamic annealing simulations of rather large amorphous supercell clusters (up to about 100 atoms) become possible even on computer workstations. The approximate ab initio calculation of the MD interatomic forces is based on the density functional theory (DFT) within the LDA using an LCAO basis [19, 22]. Applying MD-simulated annealing (SA) conditions like those employed by Blaudeck et al. [19] for stability studies on a-C and a-C:H modifications [23], the following process steps are carried out: (1) equilibration of a (hard sphere gas) starting configuration with maximal interatomic distances at 8000 K for 10-13s choosing an atomic time step width of about 10716 s; (2) cooling down of the structure by simulated annealing at a cooling rate of 10x5 K s-1; (3) equilibration of the structure for 10-13 S at room temperature. We have performed a study of hydrogenated amorphous carbon for various microscopic densities and several hydrogen concentrations using periodically arranged supercells containing a constant number of 64 carbon atoms. The approximation has been tested by reproducing all relevant results from more accurate
(SCF) calculations with respect to structure statistics (bond lengths and angles) and differences in the binding energies of well-known stable and of metastable hydrocarbon structures, including clusters, molecules, surfaces and bulk crystalline as well as amorphous materials [20]. As a result of the simulation, we obtain final minimal energy a-C:H configurations at chosen input conditions (density, H concentration), starting from which theoretical data may be derived for comparison with experimental results. The final structures are analysed using the coordinates by searching nearest neighbours in spheres of radius 1.8 A centred on each given atom. The hybridization status is then determined by the number of nearest neighbours. For comparison with experiment an atom with fourfold coordination is said to be an sp3-1ike atom, whereas atoms with lower coordination number are detected as sp 2 like. From this information bond length, bond angle, dihedral angle and ring statistics are obtained. Although of one-dimensional character, the reduced radial distribution function, derived from a histogram of pair distances of atoms [24], and its Fourier transform, the so-called interference function, are useful for comparison with scattering data on thin carbon films to check the short- and intermediate-range order of a given model. The reduced radial distribution function G(r) is broadened by multiplying the interference function by an exponential function in order to agree with experiment. This convolution has been applied in all cases where it is necessary to reduce cancellation effects of the Fourier transformation of the interference function d(s).
6. Results and discussion Recognizing the fact that in calculating the radial distribution function (RDF) from the interference function d(s) some information is lost owing to the precautions in suppression of the cancellation effects, the agreement with the interference function is more relevant than the agreement with the RDF. However, it makes sense also to compare the experimentally determined RDF with the corresponding curve of the simulation, because a relationship in coordinate space can be interpreted much more easily than a correlation in momentum space. Before starting the comparison for the individual a-C:H films, some general aspects of the d(s) and G(r) functions relevant for structural information will be described. The information obtained in this study is essentially limited to the short-range order of the film structures. In the experiment the distance range providing clear evidence is limited, because the long-distance correlations are coupled to low momentum transfers and small scattering angles. In this region the signal is disturbed
M. Weiler et al.
by the inelastic scattering processes and by the strong elastic scattering background. Although both effects are taken into account, the data become less reliable if the scattering angle gets smaller than about 0.1 °, corresponding to a momentum transfer s = 4 A 1. In the simulation the scope of relevant distances is limited, because only a supercell arrangement including a constant number of 64 carbon atoms plus hydrogen atoms is taken into consideration. Therefore in practice only the correlations over a distance of 2R1 can be described by the theory. This limit corresponds to a momentum transfer s = 3 A 1. Qualitative information about the hybridization state of the a-C : H structure can be obtained from the behaviour of the significant double peak in d(s) in the region from 8 to 11 A 1. For amorphous diamond, i.e. high sp 3 concentrations, the left-hand peak is about two times larger than that on the right side. The opposite behaviour is observed for graphite-like layers. Owing to this fact, the s p 3 c o n t e n t is indicated by the intensity ratio of the two peaks. Because of the different bond lengths of sp 3 and sp2-hybridized C atoms, the sp 3 content has some influence on the double-peak position, shifting it to lower momentum transfer values for increasing sp 3 concentrations. Bond lengths, bond angles and coordination numbers correspond directly to well-defined characteristics in the radial distribution function. The average distances to the first neighbours, R~, and to the second neighbours, R2, are identical with the positions of the corresponding peaks. The ratio of R1 and R 2 allows the determination of the average bond angle. In a first approximation the fraction sp3/sp 2 can be calculated from the bond length of the next-neighbour atoms. R~ increases with increasing sp 3 hybridization in the range between the limits of 1.42 A (graphite) and 1.54 A (diamond). The concentration of fourfold atoms is also monitored by the coordination number, determined by the area of the first peak of the G(r) function. In the range below 0.7 A a straight line of the reduced RDF is expected, because in this region the intensity should be proportional to the distance. Such a behaviour of the curve indicates that the elastic scattering background is approximately taken into account. Generally the experimental radial distribution functions show a broader and more intense first peak and a more narrow second peak than their theoretical counterparts. Because of the larger area of the first peak, the experimental coordination number is always higher than the theoretical coordination number. The agreement between theoretical and experimental peak widths depends on the potential used for the simulation. For the present investigation, in the potential the bond length variation was reduced compared with the bond angle variation. Owing to the fact that the position R2 of the
Structure qf'a-C.'H
249
second-neighbour distance in the simulation is influenced by peak tails of higher order neighbours, a small artificial shift of R 2 ( A R 2 < 5 % ) to larger values occurs. As a direct consequence, the bond angle determined from the ratio of R1 and R 2 is slightly, higher than the bond angle obtained from the theoretical simulation. The results from the electron diffraction experiments for samples CVDI, CVD2, PBS1 and PBS2 and the corresponding data of the theoretically simulated structures are represented in Table 2. The experimental and theoretical interference functions and the radial distribution functions for each thin film are shown in Figs. 1 4. The electron diffraction data of sample CVD1 agree best with those of the simulated structure with p = 2.2gcm 3 and xH=33at.%. Figure l(a) shows the reduced scattering intensity function d(s) and Fig. l(b) the reduced radial distribution function G(r) of sample CVD1 (full curves) and the simulated curves (broken curves). The short-range order is well reproduced by the theory with respect to R1 (Rt~he°r= 1.47/k, R~xp= 1.47 A) and hydrogen content (x}~e°r=33.3 at.%, ,,exp_ 32.5at.%). The differences in coordination number (nthe°r=2.84, nexP=2.9) and bond angle (Othe°r= 114.0", O exp 118.0 '~) can be traced back to the general insufficiencies of the comparison of experimental and theoretical data already described above. The sp 3 fraction calculated for sample CVDI (see Table 2) is only 28%, which is much lower than the experimental value (39%). This difference can be explained by a significant component of polymer-like chains in sample CVD1. This generates difficulty in comparing homogeneous theoretical structures with to some extent inhomogeneous experimental a-C : H layers. The difference between the theoretical and experimental mass densities of CVD1 shows that a-C:H networks with densities below 2.0 g cm -3 generally include an increasing amount of polymer-like components which cannot be described appropriately by this molecular dynamic simulation method using such small supercells. The interference function d(s) and the RDF G(r) of sample CVD2 are shown in Fig. 2. The interference function d(s) (Fig. 2(a)) agrees best with the simulated curve calculated with 20at.% hydrogen content and 2.0 g cm 3 density. The theoretical model (see Table 2) reproduces very well the first-neighbour distance (Rt~he°r= 1.47 A, ''loexp----1"46 A), the second-neighbour distance (R~he°r=2.53 /k, R~xp=2.51 A) and the bond angle value (Othe°r= 116.6 °, O~xP= 118.5°). Consequently the coordination number (n'he°~=2.91, neXp=3.3) must also be in good agreement. This means that the shortrange order of sample CVD2 is well described by the theoretical model. In addition, the mass density obtained by theory and experiment is identical and the sp 3 fraction agrees well with the experimental value (sp3th~°~= 22 at.%, sp 3~xp= 25 at.%) too. Only the total hydrogen -~'H
=
--
250
M. Weiler et al. / Structure of a-C.'H
TABLE 2. Comparison of various characteristicstructure data of the a-C : H films with the correspondingdata of the theoretical simulation CVD1
Density (g cm - a) H content (at.%) R 1 (A) R2 (A) O (deg) Coordination number Sp a content (%)
CVD2
PBS1
PBS2
Exp.
Theor.
Exp.
Theor.
Exp.
Theor.
Exp.
Theor.
2.0 32.5 1.47 2.52 118.0 2.9 39
2.2 33.3 1.47 2.47 114.0 2.84 28
2.2 28.0 1.46 2.51 118.5 3.0 25
2.2 20.0 1.47 2.53 116.6 2.91 22
2.7 25.0 1.49 2.53 116.2 3.8 55
2.7 20.0 1.48 2.52 114.8 3.1 34.4
2.4 24.0 1.47 2.52 118.0 3.5 30
2.2 20.0 1.47 2.53 116.6 2.91 22
r
5
T
"r
CVD 1
CVD 1
Pth = 2.2 g/cm 3 x H = 33 %
~l 4
Pth = 2.2 g/crn 3
xH = 33 % 3
3
2 t-
2
o
1 O3 "10
0
-2
-1
"3
V
-4 -2 -6
-3
0 (a)
2
4
6
8
10
12
14
16
18
s [A- I
0
(b)
1
2
3
r[~,]
Fig. I. (a) Reduced interferencefunction d(s) as a function of the momentum transfer s of sample CVD1 and (b) corresponding reduced radial distribution function G(r). The broken curves represent the experimental results. The full curves show the simulated results of the theoretically modelled a-C : H networks. content of CVD2 of 28 at.% is somewhat higher than that of the model (20 at.%). The high experimental value could possibly be explained by free hydrogen molecules trapped in the network or even within voids. The shape of the interference function d(s) of sample PBS1 shown in Fig. 3(a) agrees very well with that of the simulated carbon structure with p = 2.7 g c m -3 and 20 at.% hydrogen content. With the exception of the coordination number exhibiting the usual overestimation by the evaluation procedure, all experimental data given in Table 2 also agree very well with the theoretical data (see Table 2). The sp 3 content is higher than in CVD2 and PBS2 as is predicted from the theoretical modelling. The experimental value in the table represents a mean value. At different positions the experiment provided somewhat different results. The uncertainty is assumed to be about +10%. The theoretical value is just at the lower bound of this confidence interval.
The interference function d(s) (Fig. 4(a)) of sample PBS2 is very similar to that of sample CVD2. Therefore the electron diffraction data of PBS2 (Fig. 4(b)) are compared with the same theoretically simulated structure as sample CVD2. The theoretical model agrees quite well with the experimental data of sample PBS2, especially with respect to the bond length of the firstneighbour distance (Rtlhe°r= 1.47 A, R ] xp= 1.47 A), the second-neighbour distance (Rhhc°r=2.53 A, R~xP=2.52 A) and the mean bond angle value (Othc°r=ll6.6 °, OeXP=ll8.0°). Again the experimentally determined coordination number n = 3.5 deviates from the theoretical value n=2.91. Obviously the short-range order of PBS2 is similar to that of CVD2. Therefore sample PBS2 has an sp a content of the same order as CVD2. Comparing samples CVD2 and PBS2 leads to the strange situation that the two samples have a very similar electron diffraction spectrum (Figs. 2 and 4,
M, Weiler et al. / Structure of a-C.'H 7
251
'~
"l
r
T
1 ' ~
6 6
II
I
4
1
v
-
Pth = 2.2 g/cm 3
4
xH=20%
'
CVD 2
5
5
m
x H = 20 %
3
I ¢.-a
3
=5
2
¢-
. I
. I
4
o
1 v
-o
~ 0
-2 ,E /
-a
-1
-4
-2
-5 -6
-3
2
0
4
6
8
(a)
lo
12
1,~
16
8
1
(b)
s [,~~]
2
3
r[~]
Fig. 2. Same as Fig. I but for sample CVD2.
I
6 7 Pth = 2.7 g/cm 3
I
PBS 1
5
t
Pth = 2.7 g/cm 3
4
°
~
FI
4
1
J
x H = 20 %
I
3
A
2 . i
t-
~
a
-~-
2
~
1
~2
0
"G"
-1
....j...
v
(.9 0 ,
-3
I I I] v
'
J
"
'\x....~ I
-4
kJ
-5
-Z -
2
~a~
-2
4
iVl
-6
s"a
~o
s
~2
~4
16
~a
[~"1
I
0
(b)
I
1
I
I
2
i
I
3
I
4
r[~]
Fig. 3. Same as Fig, 1 but for sample PBS1.
Table2) but also have some properties (see Table 1) which are significantly different. Of course, the electron diffraction pattern is only a characterization method of the positions of C atoms in the network. Additional microstructural information can be obtained by EELS. Spectra for CVD2 and PBS2 are shown in Fig. 5. In the CVD2 spectrum a rather strong r¢--*~* transition is clearly visible at about 5.5 eV energy loss, whereas such a peak is missing in. the spectrum of the PBS2 sample. To ensure correct results, EELS measurements have
been performed before and after the additional diffraction measurements in order to exclude the possibility that the material has been modified by irradiation effects. The original results have been fully confirmed, i.e. no irradiation damage was detected. Thus the coincidence in the diffraction data of the two samples (CVD2 and PBS2), despite the different mechanical properties of the films, leads to the following conclusion. In the case of the less dense carbon film (CVD2) there must be a twophase structure. Most of the carbon atoms are contained
252
M. Weiler et al.
Structure o f a - C . H
.
[
Pth =
~
[_
2.2
.
.
.
;.s; t
.
Pth= 2.2 g/cm31
g/cm 3 4
/',
i"!
II
w
o~
,A
2
e-
a
~
o
A
~~'
/-
=
1
~d
0
t~
1
XH = 2 0 °/°
3
J
i,....d
~W
L~
-2
VJ
-3
-1
-4 -5
-2
-6
-3 2
4
6
(a)
8
10
12
14
I
(b)
S D~-1]
I
1
0
18
16
I
I
2 r[~]
I
I
I
3
Fig. 4. Same as Fig. 1 but for sample PBS2.
1.6
,
,
,
,
1.4
,
I pasz
//'~.,
c:23
,Bs,
cv, l .,,A-h cvo2 ~. \
1.0
.~. o.8 ._e" r- 0.6 c
. N
0.4 0.2 o
0
5
10
15
20
25
30
35
40
45
50
energy loss [oV]
Fig. 5. Electron energy loss spectra of the samples.
in a rather dense structure similar to the structure of PBS2. These hard clusters are embedded in a loose polymer-like phase with low density. If one assumes that the spatial extension of a plasmon, i.e. the size of the wavefunction of the excited electron, is larger than the cluster size, then the plasmon energy depends on the mean density of the material including the polymer-like component. The mechanical properties, however, are mainly determined by the polymer-like matrix. Furthermore, there could be some void structure in
sample CVD2 explaining the higher hydrogen content of CVD2 of 28 at.% ( P B S 2 : x n = 2 4 at.%). This interpretation allows us to draw a rough conclusion on the size of these hard clusters. They should be l a r g e e n o u g h so that nearly all atoms have strongly connected neighbours. This means that the fraction of surface atoms has to be small in comparison with that of bulk atoms. However, the clusters must be so small that the plasmon size is distinctly larger than the cluster size. Cluster sizes of a few hundred atoms could fulfil
M. Weiler et al. / Structure of a-C.H
both conditions. The percentage of carbon atoms outside the clusters must probably be considerably smaller than 20%. The low density material connecting the clusters is formed by chain-like polymerized hydrocarbons showing a high affinity for hydrogen bonding. The occurrence of these seemingly contradictory results in the case of these two samples leads to the following conclusion. The comparison of experimental and theoretical diffraction data only allows us to compare the short-range order of the network. If the material is not homogeneous, the results may thus be misleading, especially for the correlation of microstructure and film properties. The macroscopic properties of inhomogeneous a-C' H films depend strongly on the medium-range order effects. Therefore additional measurements should be performed to ascertain the homogeneity of the film.
Acknowledgments We thank U. Falke for performing the EELS measurements and Dr. Amaratunga and Dr. Veeresamy for additional measurements and helpful discussions. The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
References 1 J. C. Angus, P. Koidl and S. Domitz, in J. Mort (ed.), Plasma Deposited Thin Films, CRC Press, Boca Raton, FL, 1986, p. 89. 2 D. R. McKenzie, D. A. Muller and B. A. Pailthorpe, Phys. Rev. Lett., 67 (1991) 1286.
253
3 J. Robertson, Sur£ Coat. Technol., 50 (1992) 185. 4 J. Robertson, in R. E. Clausing (ed.), Diamond and Diamond-like Carbon Films, Plenum, New York, 1991, p. 37. 5 Y. Lifshitz, S. R. Kasi and I. W. Rabalais, Phys. Rev. B, 41 (1990) 10468. 6 H. P. Kaukonen and R. M. Nieminen, Ph)s. Rev. Lett. B, 68 (1992) 620. 7 W. Dworschak, R. Kleber, A. Fuchs, B. Scheppat, G. Keller, K. Jung and H. Ehrhardt, Thin Solid Films, 189 (1990) 257. 8 M. Weiler, R. Kleber, K. Jung and H. Ehrhardt, Diamond Relat. Mater., 1 (1992) I21. 9 R. Kleber, M. Weiler, A. Krfiger, S. Sattel, G. Kunz, K. Jung and H. Ehrhardt, Diamond Relat. Mater., 2 (1993) 246. 10 H. Oechsner, K. J. FfiBer, J. Waldorf and A. Fuchs, Proe. /st Int. Conf. on Plasma SurJace Engineering, Garmisch-Partenkirchen, 1988, Vol. II, DGM, Oberursel, 1989, p. 1017. 11 R. Kleber, W. Dworschak, J. Gerber, A. Krfiger, K. Jung, H. Ehrhardt, S. Schulze, J. Mfihling, S. Deutschmann, W. Scharff, F. Engelke and H. Metz, Mater. Sci. Eng. A, 140 (1991) 775. 12 S. D. Berger, D. R. McKenzie and P. J. Martin, Philos. Mag. Lett., 57 (1988) 6. 13 J. Robertson and E. P. O'Reilly, Phys. Rev. B, 35 (1987) 2946. 14 T. Piitz, A. Fuchs and H. Ehrhardt, SurJl Sci., 265 (1992) 219. 15 D. R. McKenzie, D. A. Muller, E. Kravtchinskaia, D. Segal, D. J. H. Cockayne, G. Amaratunga and R. Silva, Thin Solid Films, 206 (1991) 198. 16 D. L. Misell and R. E. Burge, J. Phys. C: Solid State Phys., 2 (1969) 61. 17 G. Palinkas and T. Radnai, Acta Crystallogr. A, 32 (1976) 666. 18 S. Deutschmann, in preparation. 19 P. Blaudeck, Th. Frauenheim, D. Porezag, G. Seifert and E. Fromm, J. Phys.: Condens. Matter, 4 (1992) 6389. 20 Th. Frauenheim and P. Blaudeck, Appl. Surf Sci., 60-61 (1992) 281. 21 J. Tersoff, Phys. Rev. Lett., 61 (1988) 2879. 22 G. Galli, R. M. Martin, R. Car and M. Parinello, Phys. Rev. B, 42 (1990) 7470. 23 P. Blaudeck, Th. Frauenheim, G. Jungnickel and U. Stephan, Solid State Commun., 85 (1993) 997. 24 C. N. J. Wagner, J. Non-Cryst. Solids. 31 (19781 1.
tmd Related
Materiuls.
3 (1994) 245-253
245
Structure of amorphous hydrogenated carbon: experiment and computer simulation M. Weiler, R. Kleber, S. Sattel, K. Jung and H. Ehrhardt Fachhereic,h Phq’sik der UnioersitSit
G. Jungnickel,
Kaiserslautern,
S. Deutschmann,
W-6750 Kaiserslautern
U. Stephan,
Fachhereic h Physik der Technischen
UnitiersitBt
(Received
in revised form July 6, 1993)
March 30. 1993: accepted
Chemnitz,
(Germany]
P. Blaudeck
O-9010 Chemnitz
and Th. Frauenheim
(Germany)
Abstract The microstructure of amorphous hydrogenated carbon films has been studied by electron diffraction measurements and comparison of the results with simulated diffraction data which have been modelled by molecular dynamics (MD) calculations. The films have been produced partly by a plasma-enhanced chemical vapour deposition process and partly by a plasma beam deposition method. The MD simulation is based on an annealing process cooling down a liquid phase ensemble of 64 carbon and a corresponding number of hydrogen atoms using a density functional approach to account for the interatomic forces.
1. Introduction
In spite of the increasing interest in amorphous hydrogenated carbon films with physical properties adaptable to special technical applications, the microstructures of these materials are still not well understood. Therefore a comparison of a variety of experimental data with corresponding theoretical simulations of structures is necessary in order to find correlations between microstructural details and macroscopic properties. This study intends to contribute to this general goal. It is well known that the macroscopic film properties are strongly related to the ratio of sp2 to sp3 bonding of the carbon atoms and to the hydrogen concentration in the material [l]. These quantities in turn depend largely on the ion energies and on the particle flux composition. Many phenomenological correlations between the mechanical and optical film properties and the flux quantities have been found, but it is essentially not yet clear how the particle flux controls the sp2/sp3 ratio. Recently McKenzie et al. [2] found that amorphous carbon (a-C) films deposited from a pure C+ ion beam have maximum density and sp3 content for ion energies between 30 and 50 eV. Robertson [3, 41 postulated an energy-dependent balance between sp* and sp3 sites, because collisions of the C+ ions create vacancies and interstitials. If a C atom is forced into a position with close distances to neighbouring C atoms in the second or third layer below the surface, such a process is called subplantation [S]. Such an atom tends to
0925-9635 SSDl
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I? 1994 -
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Elsevier Sequoia.
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hybridize within an sp3 configuration. Consequently, the concentration [6] of the sp3 C-C bonds increases with increasing film density. In the present paper the preparational conditions are chosen in such a way that the plasma parameters determine the energy and the relative proportion of ions and neutrals in the particle flux to the substrate. The parameters have been varied over a rather wide range, but excluded have been those experimental conditions under which loose polymeric films are formed. These materials are of minor technical relevance and cannot be described appropriately by the theory applied in this investigation. After the description of the deposition processes the measurements are presented with special emphasis on electron diffraction data, which are well suited to investigate the short-range order of the network. The last two sections deal with the theoretical methods and with a comparison of experimental and theoretical data.
2. Film deposition Amorphous hydrogenated carbon (a-C : H) films may vary from loose, polymer-like to dense, strongly interconnected diamond-like networks. To cover a wide range of film properties, two different experimental arrangements have been used. Employing an r.f. discharge apparatus for plasma-assisted chemical vapour deposition (CVD) can yield polymer-like films but also
246
M. Weiler et al. / Structure of a-C:H
diamond-like carbon. The result depends mostly on the energies of the ions when deposited on the substrate, but also on the total flux composition and therefore on the precursor or working gas. The use of a plasma beam source (PBS) offers the preparation of samples with high density, corresponding to high sp 3 C C bonding concentrations. The plasma CVD reactor has been described in detail earlier [7]. The r.f. discharge is operated at 13.56 MHz with a power of 100 W, coupled to the plasma partly inductively and partly capacitively. C2H2 was used as working gas. It has been shown earlier [8, 9] that the film properties are mainly determined by the ion energy and by the ratio (Di~/(De, where (Die is the ion flux of carbon-containing particles to the substrate and (De is the total flux of carbon atoms contributing to the film growth. The ion flux consisted mainly (more than 50%) of C2H + (x=0,1,2) ions. The average ion energy E varied between 30 and 250 eV; the ratio (Di~/(Dovaried between 5% and 30% depending on the pressure in the discharge. With low (DiJ(Dc ratios and low ion energies polymer-like a-C:H films are deposited. To prepare films with densities higher than 2 g cm-3, a plasma beam source has been used. The configuration of electrodes and magnetic field is chosen similar to an apparatus described by Oechsner et al. [10]. The r.f. plasma is operated at 13.56 MHz with C 2 H 2 as working gas and is confined magnetically (200 G). The plasma beam consists mainly of C2H+ ions with well-defined ion energies. The ions are extracted through a grid of high transmission by the r.f. self-bias between plasma and grid. The ion energy can be varied between 250 and 580 eV. The ion energy has been measured by a retarding field after having separated the electrons from the plasma beam. The energy resolution A E / E was about 10%. For all ion energies the ratio (Di~/(De is about 90% if one assumes that the sticking coefficients for the C-containing ions are close to unity. During the experiments the ion current density (0.3 mAcm -2) and the pressure (1 x 10-3 mbar) in the plasma reactor are kept constant.
3. Film charaeterization The properties of the four a-C:H films studied are given in Table 1, where the notations of the samples indicate the preparation method as either CVD or PBS. The macroscopic a-C : H film properties density (floating method), hardness (Knoop microindenter) and internal stress (bending beam method) have been measured. Electron energy loss spectroscopy (EELS), electron spin resonance (ESR),. IR spectroscopy and electron diffraction experiments have been used to characterize the microscopic structures of the films. Additionally, the
optical gap and the hydrogen content (15N method) of the layers were determined. Only the CVD samples could be analysed with respect to sp 3 concentrations using a 13C nuclear magnetic resonance (NMR) measurement, because only for these samples could sufficient material (about 400 mg) be produced. Details on the various experiments have been published by Kleber et al. [11]. The ratio of sp 3 to sp 2 bonds in the PBS films was estimated by EELS using the integral of the counts in the ls ~ n* peak and comparing that with graphite [12]. Sample CVD1 was deposited at E=170eV and (Dic/(Dc = 13%, resulting in a rather dense a-C: H network. The mechanical properties hardness HK = 20 GPa, density p=2.0 g cm -3 and internal stress a=2.4 GPa show that the network is quite strongly interconnected. The rather tow hydrogen content of 32.5 at.% is due to the high energy of the impinging ions causing hydrogen atoms of the adsorption layer and the hydrocarbon ions to be dissociated and hydrogen released. Therefore the number of C-H bonds is low and the formation of sp 2 (C-C) bonds is supported. For the experimental conditions applied for CVD1 an sp 2 fraction of 61% is obtained. The rather small optical gap of 1.3 eV indicates the arrangement of these sp2-bonded atoms in the form of sp 2 clusters [13]. The n--.rc* transition between 4 and 7 eV in the EEL spectrum shows a broad peak at about 5.6 eV, suggesting several sp 2 cluster sizes. Sample CVD2 deposited at E = 250 eV and (Dic/(De= 29% with p = 2 . 2 g c m -3 possesses a somewhat more densified a-C:H network. The hydrogen content is reduced to 28 at.%, which gives rise to a different bonding of the network with a reduced number of sp 3 CH bonds. This is confirmed by IR analysis of the samples in the range 2800-3100cm -1. It is observed that the IR intensity ratio of sp 3 CH1, 2 to sp2CH1,2 lines decreases with increasing ion energy. The EEL spectrum of CVD2 shows that the sp 2 cluster size distribution is still enlarged in comparison with CVD1, because no sharp peak in the r ~ r t * transition is observed. From the position of the broad structure in the EEL spectrum it can be assumed that the average sp 2 cluster size is larger than in CVD1. The enhancement of the sp 2 cluster sizes is also confirmed by the decrease in the optical gap to 1.1 eV. An sp 2 fraction of 75% was determined by Auger spectroscopy in combination with factor analysis 1-14]. With c o n s t a n t spa C-C fraction, further decreasing sp 3 CH concentration and increasing sp 2 cluster sizes the mechanical properties of this network are altered to a higher hardness (HK=40 GPa) and a larger internal stress (~ = 4.4 GPa). The films prepared by the plasma beam source method are deposited with a much higher ion contribution in the particle flux ((Dic/(D¢= 90%), resulting in even denser a-C:H networks. Sample PBS1 (E=260 eV) has a den-
247
M. Weiler et al. / Structure of a-C:H
TABLE 1. Compilation of the experimental results for the four samples studied. Samples CVDI and CVD2 were prepared using a plasmaenhanced CVD method. Samples PBS1 and PBS2 were produced by a plasma beam source Sample
CVD 1 CVD2 PBS 1 PBS2
~bic/~b~ (%)
Mean energy (eV)
Density (g cm 3)
Knoop hardness (GPa)
Stress (GPa)
13 29 80 80
170 250 260 300
2.0 2.2 2.7 2.4
20 30-40 42 33
2.4 4.4 6.0 5.0
H
Sp-'
content (at.%)
content lat.%)
32.5 28.0 25.0 24.0
61 75 45 70
sity of 2.7 g cm 3, which cannot be reached by the CVD process. The optical gap of 1.38 eV and the ESR linewidth indicate that the sp 2 cluster size is similar to that of CVD2. The low spin density of 2 x 10 t9 cm 3 (in spite of the low hydrogen content of 25 at.%) indicates a low concentration of dangling bonds and nonsaturated rt states. The rather small optical gap is an indication of the existence of large sp 2 cluster sizes, but it is not possible to draw the conclusion that the sp 2 content is large, because it is known that already a very small concentration of these clusters leads to a strong absorption [13]. This network possesses a much higher sp 3 C C fraction than the CVD2 film. The density of 2.7 g cm - 3, exceeding significantly the density of graphite (p = 2.2 g cm -3), indicates an sp 3 C - C fraction of about 30% (Paiam = 3.5 g cm 3), whereas in the CVD films the sp 3 C C component is only about 10%. The large density of sp a C C sites causes a rather large internal stress ( a = 6 GPa). Similar results have been obtained with vacuum-arc-deposited a-C films [15]. Sample PBS2 deposited at 300 eV ion energy shows already some signs of graphitization. The density is reduced to 2.4 g cm -3, the optical gap is decreased to 1.26 eV and the hardness and stress values are reduced, implying that the sp 3 C - C sites are transformed by irradiation damage during the film growth into s p 2 sites. As we know from VRIMsimulations, at higher ion energies the formation of vacancies exceeds the formation of interstitials.
4. Electron diffraction measurements
One of the aims of the present investigation was to characterize the films according to their short-range structure. Therefore electron-scattering measurements have been performed. The electron-scattering intensity l(s) with the momentum transfer s = (2g/2) sin(O) and the scattering angle O was measured with a JEM 100CX electron microscope in the range 0.5 ~
Spins (102ocm 3)
Bandwidth (mT)
Optical gap (eV)
Plasmon energy (eV)
1.6 4.3 0.20 0.16
0.210
1.30 l.l 1.38 1.26
24.4 25.6 28.0 26.6
0.288 0.285
typical for the films studied here, a multiple-scattering correction has to be applied. By using a transformation described by Misell and Burge [16] and a subsequent Fourier transformation, the single-scattering contribution IVy(s) is related to the total intensity I v by
II-
1
v ln(1 + I% v)
The average number of interactions, v, can be obtained from transmission electron microscopy (TEM) mass thickness measurements. The inelastic scattering part has been determined by a fit proposed by Palinkas and Radnai [17]. The reduced scattering intensity d(s)= S[IXl(S)-(f2)]/(f) 2 with the atomic density distribution J'and the reduced atomic density distribution
2r a(r) = ~ d ( s ) exp(-~2s 2) sin(sr)ds can then be calculated, where (J') is the average over the f concentration. Because the atomic charge distribution in carbon bulk material deviates from that of free carbon atoms, the bulk charge density for a single carbon atom was derived from localized atomic valence orbitallocal density approximation (LCAO LDA) calculations. From this charge distribution an improved atomic scattering factorJc for carbon was obtained [18]. The influence of the electron scattering from hydrogen is very small. For the described analysis the atomic scattering factor fH for hydrogen was determined by the Warren Krutter Morningstar approximation assuming fH =Jc/6. To reduce cancellation effects in G(r) caused by the discontinuity of d(s) at the maximal experimentally reached momentum transfer, d(s) was multiplied by an exponential damping factor exp(-~2s 2) (~ =0.1 A) before performing the Fourier transformation. This correction leads to a peak broadening in G(r). For this reason it is better to use d(s) for comparison with theoretical models, although this function allows no simple conclusions on the microstructure. For each measurement the electron beam position is manually adjusted to zero scattering angle. Thus the momentum transfer axis s is very well established and the next-neighbour distances taken from G(r) are exact within 1 % - 2 % .
248
M. Weiler et al. / Structure of a-C.'H
5. Structure modelling Theoretical structure simulations developed during the last decade have been established as a powerful tool to understand the microscopic structure and its influence on the physical properties of hydrogenated amorphous semiconductor materials. However, there are only a few attempts related to a-C and a-C:H. Apart from qualitative arguments in the discussion of structural and physical properties of a-C:H [13], there are many open questions regarding the nucleation and structure formation processes during film growth, primarily the hydrogen influence on clustering and medium-range order, which control the macroscopic physical properties of the material. Performing molecular dynamic (MD) simulations of hydrogenated amorphous carbon on the basis of quantum mechanically derived interatomic forces is an attempt to tackle these problems. This goal is achieved by applying an approximate well-tested ab initio scheme using a minimal basis set [19, 20] of the localized atomic valence orbitals of all atoms in the atomic network. In contrast with classical potential concepts [21], this ab initio type of approximation allows the inclusion of hydrogen and overcomes the difficulty of nontransferability from bulk material to finite clusters and surfaces. Compared with fully self-consistent field (SCF) ab initio calculations [22], this method reduces the computational efforts by at least two orders of magnitude and avoids problems in the construction of a pseudopotential for hydrogen. On this basis, systematic dynamic annealing simulations of rather large amorphous supercell clusters (up to about 100 atoms) become possible even on computer workstations. The approximate ab initio calculation of the MD interatomic forces is based on the density functional theory (DFT) within the LDA using an LCAO basis [19, 22]. Applying MD-simulated annealing (SA) conditions like those employed by Blaudeck et al. [19] for stability studies on a-C and a-C:H modifications [23], the following process steps are carried out: (1) equilibration of a (hard sphere gas) starting configuration with maximal interatomic distances at 8000 K for 10-13s choosing an atomic time step width of about 10716 s; (2) cooling down of the structure by simulated annealing at a cooling rate of 10x5 K s-1; (3) equilibration of the structure for 10-13 S at room temperature. We have performed a study of hydrogenated amorphous carbon for various microscopic densities and several hydrogen concentrations using periodically arranged supercells containing a constant number of 64 carbon atoms. The approximation has been tested by reproducing all relevant results from more accurate
(SCF) calculations with respect to structure statistics (bond lengths and angles) and differences in the binding energies of well-known stable and of metastable hydrocarbon structures, including clusters, molecules, surfaces and bulk crystalline as well as amorphous materials [20]. As a result of the simulation, we obtain final minimal energy a-C:H configurations at chosen input conditions (density, H concentration), starting from which theoretical data may be derived for comparison with experimental results. The final structures are analysed using the coordinates by searching nearest neighbours in spheres of radius 1.8 A centred on each given atom. The hybridization status is then determined by the number of nearest neighbours. For comparison with experiment an atom with fourfold coordination is said to be an sp3-1ike atom, whereas atoms with lower coordination number are detected as sp 2 like. From this information bond length, bond angle, dihedral angle and ring statistics are obtained. Although of one-dimensional character, the reduced radial distribution function, derived from a histogram of pair distances of atoms [24], and its Fourier transform, the so-called interference function, are useful for comparison with scattering data on thin carbon films to check the short- and intermediate-range order of a given model. The reduced radial distribution function G(r) is broadened by multiplying the interference function by an exponential function in order to agree with experiment. This convolution has been applied in all cases where it is necessary to reduce cancellation effects of the Fourier transformation of the interference function d(s).
6. Results and discussion Recognizing the fact that in calculating the radial distribution function (RDF) from the interference function d(s) some information is lost owing to the precautions in suppression of the cancellation effects, the agreement with the interference function is more relevant than the agreement with the RDF. However, it makes sense also to compare the experimentally determined RDF with the corresponding curve of the simulation, because a relationship in coordinate space can be interpreted much more easily than a correlation in momentum space. Before starting the comparison for the individual a-C:H films, some general aspects of the d(s) and G(r) functions relevant for structural information will be described. The information obtained in this study is essentially limited to the short-range order of the film structures. In the experiment the distance range providing clear evidence is limited, because the long-distance correlations are coupled to low momentum transfers and small scattering angles. In this region the signal is disturbed
M. Weiler et al.
by the inelastic scattering processes and by the strong elastic scattering background. Although both effects are taken into account, the data become less reliable if the scattering angle gets smaller than about 0.1 °, corresponding to a momentum transfer s = 4 A 1. In the simulation the scope of relevant distances is limited, because only a supercell arrangement including a constant number of 64 carbon atoms plus hydrogen atoms is taken into consideration. Therefore in practice only the correlations over a distance of 2R1 can be described by the theory. This limit corresponds to a momentum transfer s = 3 A 1. Qualitative information about the hybridization state of the a-C : H structure can be obtained from the behaviour of the significant double peak in d(s) in the region from 8 to 11 A 1. For amorphous diamond, i.e. high sp 3 concentrations, the left-hand peak is about two times larger than that on the right side. The opposite behaviour is observed for graphite-like layers. Owing to this fact, the s p 3 c o n t e n t is indicated by the intensity ratio of the two peaks. Because of the different bond lengths of sp 3 and sp2-hybridized C atoms, the sp 3 content has some influence on the double-peak position, shifting it to lower momentum transfer values for increasing sp 3 concentrations. Bond lengths, bond angles and coordination numbers correspond directly to well-defined characteristics in the radial distribution function. The average distances to the first neighbours, R~, and to the second neighbours, R2, are identical with the positions of the corresponding peaks. The ratio of R1 and R 2 allows the determination of the average bond angle. In a first approximation the fraction sp3/sp 2 can be calculated from the bond length of the next-neighbour atoms. R~ increases with increasing sp 3 hybridization in the range between the limits of 1.42 A (graphite) and 1.54 A (diamond). The concentration of fourfold atoms is also monitored by the coordination number, determined by the area of the first peak of the G(r) function. In the range below 0.7 A a straight line of the reduced RDF is expected, because in this region the intensity should be proportional to the distance. Such a behaviour of the curve indicates that the elastic scattering background is approximately taken into account. Generally the experimental radial distribution functions show a broader and more intense first peak and a more narrow second peak than their theoretical counterparts. Because of the larger area of the first peak, the experimental coordination number is always higher than the theoretical coordination number. The agreement between theoretical and experimental peak widths depends on the potential used for the simulation. For the present investigation, in the potential the bond length variation was reduced compared with the bond angle variation. Owing to the fact that the position R2 of the
Structure qf'a-C.'H
249
second-neighbour distance in the simulation is influenced by peak tails of higher order neighbours, a small artificial shift of R 2 ( A R 2 < 5 % ) to larger values occurs. As a direct consequence, the bond angle determined from the ratio of R1 and R 2 is slightly, higher than the bond angle obtained from the theoretical simulation. The results from the electron diffraction experiments for samples CVDI, CVD2, PBS1 and PBS2 and the corresponding data of the theoretically simulated structures are represented in Table 2. The experimental and theoretical interference functions and the radial distribution functions for each thin film are shown in Figs. 1 4. The electron diffraction data of sample CVD1 agree best with those of the simulated structure with p = 2.2gcm 3 and xH=33at.%. Figure l(a) shows the reduced scattering intensity function d(s) and Fig. l(b) the reduced radial distribution function G(r) of sample CVD1 (full curves) and the simulated curves (broken curves). The short-range order is well reproduced by the theory with respect to R1 (Rt~he°r= 1.47/k, R~xp= 1.47 A) and hydrogen content (x}~e°r=33.3 at.%, ,,exp_ 32.5at.%). The differences in coordination number (nthe°r=2.84, nexP=2.9) and bond angle (Othe°r= 114.0", O exp 118.0 '~) can be traced back to the general insufficiencies of the comparison of experimental and theoretical data already described above. The sp 3 fraction calculated for sample CVDI (see Table 2) is only 28%, which is much lower than the experimental value (39%). This difference can be explained by a significant component of polymer-like chains in sample CVD1. This generates difficulty in comparing homogeneous theoretical structures with to some extent inhomogeneous experimental a-C : H layers. The difference between the theoretical and experimental mass densities of CVD1 shows that a-C:H networks with densities below 2.0 g cm -3 generally include an increasing amount of polymer-like components which cannot be described appropriately by this molecular dynamic simulation method using such small supercells. The interference function d(s) and the RDF G(r) of sample CVD2 are shown in Fig. 2. The interference function d(s) (Fig. 2(a)) agrees best with the simulated curve calculated with 20at.% hydrogen content and 2.0 g cm 3 density. The theoretical model (see Table 2) reproduces very well the first-neighbour distance (Rt~he°r= 1.47 A, ''loexp----1"46 A), the second-neighbour distance (R~he°r=2.53 /k, R~xp=2.51 A) and the bond angle value (Othe°r= 116.6 °, O~xP= 118.5°). Consequently the coordination number (n'he°~=2.91, neXp=3.3) must also be in good agreement. This means that the shortrange order of sample CVD2 is well described by the theoretical model. In addition, the mass density obtained by theory and experiment is identical and the sp 3 fraction agrees well with the experimental value (sp3th~°~= 22 at.%, sp 3~xp= 25 at.%) too. Only the total hydrogen -~'H
=
--
250
M. Weiler et al. / Structure of a-C.'H
TABLE 2. Comparison of various characteristicstructure data of the a-C : H films with the correspondingdata of the theoretical simulation CVD1
Density (g cm - a) H content (at.%) R 1 (A) R2 (A) O (deg) Coordination number Sp a content (%)
CVD2
PBS1
PBS2
Exp.
Theor.
Exp.
Theor.
Exp.
Theor.
Exp.
Theor.
2.0 32.5 1.47 2.52 118.0 2.9 39
2.2 33.3 1.47 2.47 114.0 2.84 28
2.2 28.0 1.46 2.51 118.5 3.0 25
2.2 20.0 1.47 2.53 116.6 2.91 22
2.7 25.0 1.49 2.53 116.2 3.8 55
2.7 20.0 1.48 2.52 114.8 3.1 34.4
2.4 24.0 1.47 2.52 118.0 3.5 30
2.2 20.0 1.47 2.53 116.6 2.91 22
r
5
T
"r
CVD 1
CVD 1
Pth = 2.2 g/cm 3 x H = 33 %
~l 4
Pth = 2.2 g/crn 3
xH = 33 % 3
3
2 t-
2
o
1 O3 "10
0
-2
-1
"3
V
-4 -2 -6
-3
0 (a)
2
4
6
8
10
12
14
16
18
s [A- I
0
(b)
1
2
3
r[~,]
Fig. I. (a) Reduced interferencefunction d(s) as a function of the momentum transfer s of sample CVD1 and (b) corresponding reduced radial distribution function G(r). The broken curves represent the experimental results. The full curves show the simulated results of the theoretically modelled a-C : H networks. content of CVD2 of 28 at.% is somewhat higher than that of the model (20 at.%). The high experimental value could possibly be explained by free hydrogen molecules trapped in the network or even within voids. The shape of the interference function d(s) of sample PBS1 shown in Fig. 3(a) agrees very well with that of the simulated carbon structure with p = 2.7 g c m -3 and 20 at.% hydrogen content. With the exception of the coordination number exhibiting the usual overestimation by the evaluation procedure, all experimental data given in Table 2 also agree very well with the theoretical data (see Table 2). The sp 3 content is higher than in CVD2 and PBS2 as is predicted from the theoretical modelling. The experimental value in the table represents a mean value. At different positions the experiment provided somewhat different results. The uncertainty is assumed to be about +10%. The theoretical value is just at the lower bound of this confidence interval.
The interference function d(s) (Fig. 4(a)) of sample PBS2 is very similar to that of sample CVD2. Therefore the electron diffraction data of PBS2 (Fig. 4(b)) are compared with the same theoretically simulated structure as sample CVD2. The theoretical model agrees quite well with the experimental data of sample PBS2, especially with respect to the bond length of the firstneighbour distance (Rtlhe°r= 1.47 A, R ] xp= 1.47 A), the second-neighbour distance (Rhhc°r=2.53 A, R~xP=2.52 A) and the mean bond angle value (Othc°r=ll6.6 °, OeXP=ll8.0°). Again the experimentally determined coordination number n = 3.5 deviates from the theoretical value n=2.91. Obviously the short-range order of PBS2 is similar to that of CVD2. Therefore sample PBS2 has an sp a content of the same order as CVD2. Comparing samples CVD2 and PBS2 leads to the strange situation that the two samples have a very similar electron diffraction spectrum (Figs. 2 and 4,
M, Weiler et al. / Structure of a-C.'H 7
251
'~
"l
r
T
1 ' ~
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I
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1
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-
Pth = 2.2 g/cm 3
4
xH=20%
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. I
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8
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Fig. 2. Same as Fig. I but for sample CVD2.
I
6 7 Pth = 2.7 g/cm 3
I
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4
°
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I
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Fig. 3. Same as Fig, 1 but for sample PBS1.
Table2) but also have some properties (see Table 1) which are significantly different. Of course, the electron diffraction pattern is only a characterization method of the positions of C atoms in the network. Additional microstructural information can be obtained by EELS. Spectra for CVD2 and PBS2 are shown in Fig. 5. In the CVD2 spectrum a rather strong r¢--*~* transition is clearly visible at about 5.5 eV energy loss, whereas such a peak is missing in. the spectrum of the PBS2 sample. To ensure correct results, EELS measurements have
been performed before and after the additional diffraction measurements in order to exclude the possibility that the material has been modified by irradiation effects. The original results have been fully confirmed, i.e. no irradiation damage was detected. Thus the coincidence in the diffraction data of the two samples (CVD2 and PBS2), despite the different mechanical properties of the films, leads to the following conclusion. In the case of the less dense carbon film (CVD2) there must be a twophase structure. Most of the carbon atoms are contained
252
M. Weiler et al.
Structure o f a - C . H
.
[
Pth =
~
[_
2.2
.
.
.
;.s; t
.
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g/cm 3 4
/',
i"!
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w
o~
,A
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a
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-3 2
4
6
(a)
8
10
12
14
I
(b)
S D~-1]
I
1
0
18
16
I
I
2 r[~]
I
I
I
3
Fig. 4. Same as Fig. 1 but for sample PBS2.
1.6
,
,
,
,
1.4
,
I pasz
//'~.,
c:23
,Bs,
cv, l .,,A-h cvo2 ~. \
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.~. o.8 ._e" r- 0.6 c
. N
0.4 0.2 o
0
5
10
15
20
25
30
35
40
45
50
energy loss [oV]
Fig. 5. Electron energy loss spectra of the samples.
in a rather dense structure similar to the structure of PBS2. These hard clusters are embedded in a loose polymer-like phase with low density. If one assumes that the spatial extension of a plasmon, i.e. the size of the wavefunction of the excited electron, is larger than the cluster size, then the plasmon energy depends on the mean density of the material including the polymer-like component. The mechanical properties, however, are mainly determined by the polymer-like matrix. Furthermore, there could be some void structure in
sample CVD2 explaining the higher hydrogen content of CVD2 of 28 at.% ( P B S 2 : x n = 2 4 at.%). This interpretation allows us to draw a rough conclusion on the size of these hard clusters. They should be l a r g e e n o u g h so that nearly all atoms have strongly connected neighbours. This means that the fraction of surface atoms has to be small in comparison with that of bulk atoms. However, the clusters must be so small that the plasmon size is distinctly larger than the cluster size. Cluster sizes of a few hundred atoms could fulfil
M. Weiler et al. / Structure of a-C.H
both conditions. The percentage of carbon atoms outside the clusters must probably be considerably smaller than 20%. The low density material connecting the clusters is formed by chain-like polymerized hydrocarbons showing a high affinity for hydrogen bonding. The occurrence of these seemingly contradictory results in the case of these two samples leads to the following conclusion. The comparison of experimental and theoretical diffraction data only allows us to compare the short-range order of the network. If the material is not homogeneous, the results may thus be misleading, especially for the correlation of microstructure and film properties. The macroscopic properties of inhomogeneous a-C' H films depend strongly on the medium-range order effects. Therefore additional measurements should be performed to ascertain the homogeneity of the film.
Acknowledgments We thank U. Falke for performing the EELS measurements and Dr. Amaratunga and Dr. Veeresamy for additional measurements and helpful discussions. The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
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253
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