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Electrical and optical properties of amorphous carbon layers: limits of the isotropic layer model
Thin Solid Films, 209 (1992) 195 206
195
Electrical and optical properties of amorphous carbon layers: limits of the isotropic layer model M. Vogel, O. Stenzel and W. Griinewald Chemnitz University of Technology, Department of Physics/Electronic Devices, 0-9010 Chemnitz, PSF 964 (FRG)
A. Barna Research Institute for Technical Physics HAS, H-1325 Budapest, P.O. Box 76 (Hungary)
(Received January 9, 1991; revised July 15, 1991; accepted October 10, 1991)
Abstract The electrical and optical properties of amorphous carbon layers deposited by differenttechniquesare presented and compared. The layers investigated may be divided into two groups: low refractive index transparent and insulating samples and, on the contrary, high refractiveindex strongly absorbing and conducting films. Experimental results are presented which indicate that the strongly absorbing and conducting samples exhibit anisotropic properties observedby means of cross-sectionaltransmission electron microscopy,while transparent and insulating samples are electricallyand optically isotropic. An attempt has been made to explain the effectof the ambiguityof electricaland optical properties on the basis of a simple mixing model. The model allows us to reproduce the high refractiveindices of absorbing and conductinglayers as well as the low refractiveindex transparent and insulating films.
1. Introduction The deposition and properties of amorphous carbon films have been the subject of intensive research work for several years. The properties of amorphous hydrogenated carbon (a-C:H) layers are strongly dependent on the film structure and considerable variations have been observed for different deposition techniques and parameters [1, 2]. The purpose of the present paper is to discuss the electrical and optical properties of amorphous carbon films and to reveal their correlation. The layers investigated have been deposited by the following techniques: r.f. sputtering [3]; d.c. plasma decomposition [4]; electron cyclotron resonance (ECR) mirowave plasma deposition [5]; ECR microwave ion beam deposition [5]; electron beam evaporation [6]. Depending on the preparation technique and special preparation parameters, the electrical properties and optical parameters of the layers vary over a wide range. The electrical conductivity reaches values between 10 -11 and 102 (f~cm) -~. The IR refractive indices were between 1.9 and 2.9, corresponding to absorption coefficients between 102 and 105 cm- 1. It will be shown that it is useful to divide the carbon layers investigated into two groups. The first group contains all layers which are electrically insulating and transparent in the IR spectral region (plasma-deposited layers and low refractive index r.f.-sputtered films). The
0040-6090/92/$5.00
second group includes all conducting and strongly absorbing carbon films (high refractive index sputtered carbon layers and evaporated films). Furthermore, it will be demonstrated that the usually applied isotropic layer model is insufficient for discussing the properties of the second group of carbon films.
2. Film preparation In the present study the properties of films deposited by quite different techniques [3-6] are compared and discussed. The main deposition parameters are listed in Table 1. A more detailed description of deposition is beyond the limits of the present paper, but it is the subject of comparative studies [3, 5]. Quartz and silicon were used as substrates. After chemical precleaning, the substrates were in situ physically etched using inert gas ions (except for r.f. sputtering).
3. Measurements 3.1. Mass density and hydrogen content
The mass density of carbon films has been determined by a floating method in a C H 3 O H - C H B r 3 mixture and varies according to the preparation technique and special preparation conditions. Evaporated carbon films have densities in the region of 2.0 g cm 3, while the
© 1992-- Elsevier Sequoia. All rights reserved
196
M. Vogel et al. / Properties q[" amorphous C layers
TABLE 1. Deposition parameters Parameter
Value for the following techniques R.f. sputtering
Residual gas pressure Working gas pressure Working gas Ion current density Bias voltage Target voltage Energy of particles arriving at the substrate Substrate temperature Deposition rate
(Pa) (Pa)
ECR microwave plasma
ECR microwave ion beam
Electron beam evaporation 10 3
2 x 10 3
10 4
10 3
10 3
1
(3 20) x 10 2
(4
(2 8) x I0 .2
Ar or C6H~,
C6H 6 0.15 0.2 0.6 2.4
C6H,, 0.5 1 0.2 1.2
C6H 6 0.1 0.3
10) x 10 2
(mA cm 2) (kV) (kV) (eV)
2.9 1.8 0.1 10
600-2400
200 1200
400 1400
(K) (nm min ~)
320 520 I 10
340 30 50
320 470 120 220
320 470 10 30
UT KIO00 !
D.c. plasma decomposition
I
0.01 0.1 340 720 5 50
TABLE 2. Density and hydrogen content of carbon layers
~ 2000
V
I
I
3000 I
Deposition technique
Mass density (g c m ~)
H content (at.%)
R.f. sputtering D.c. plasma decomposition ECR microwave plasma ECR microwave Ion beam Evaporation
1.6 1.9 1.8 2.1
9- 18 20 30
1.6 2.1
20 40
1.8 2.4
18 20
2.~
glcm 3
1.8 2.0
3
2.0
1.5 I
I 1000 0B
i V
I 20OO
----
Fig. 1. Mass density of amorphous hydrogenated carbon layers depending on the extraction voltage or bias voltage Ue for ion-beamand plasma-deposited layers and depending on the target voltage UT for r.f.-sputtered films: ©, r.f.-sputtering; 0, ECR microwave plasma deposition; I , ECR microwave ion beam deposition; •, d.c. plasma decomposition. otherwise p r o d u c e d films exhibit a significant dependence on the p r e p a r a t i o n p a r a m e t e r s (bias voltage, target voltage) (Fig. 1). T h e h y d r o g e n c o n t e n t o f c a r b o n films on silicon was investigated by m e a n s o f the nuclear r e a c t i o n m e t h o d a n d is listed in T a b l e 2. It should be n o t e d that within a given d e p o s i t i o n technique a n u n a m b i g u o u s correlation between h y d r o g e n c o n t e n t a n d m a s s density m a y
be established. However, in c o m p a r i n g different deposition techniques no clear c o r r e l a t i o n a p p e a r s . W e suppose that the extremely high h y d r o g e n c o n t e n t o f s p u t t e r e d layers is due to the i n c o r p o r a t i o n o f h y d r o g e n c o n t a i n i n g m o l e c u l a r f r a g m e n t s f r o m the residual gas f a v o u r e d b y the very low d e p o s i t i o n rate. It has been established that c h a n g i n g the w o r k i n g gas from a r g o n to C6H 6 did not cause a n y significant increase in the h y d r o g e n c o n t e n t o f r.f.-sputtered layers. 3.2. E l e c t r i c a l p r o p e r t i e s at r o o m t e m p e r a t u r e s
The p l a n a r a n d transverse resistance o f the c a r b o n films (thickness from 0.5 to 3.0 pm) is o b t a i n e d by m e a s u r i n g the current flowing as a result o f the a p p l i e d voltage, using an electrometer. T h e voltage was varied in the range from 0.1 V to 100V, c o r r e s p o n d i n g to electrical fields between 100 a n d 10 000 V cm-~ for b o t h m e a s u r e m e n t s . C a r b o n layers with a p l a n a r resistance lower t h a n 106~~ were investigated by a f o u r - p o i n t m e t h o d . A l u m i n i u m , gold a n d m o l y b d e n u m were used as electrode materials. All films have exhibited o h m i c behaviour. In general, m e a s u r e m e n t s o f p l a n a r resistance were carried out on q u a r t z substrates. In the case o f high
M. Vogel et al. / Properties of amorphous C layers T A B L E 3. Planar and transverse conductivities of amorphous carbon layers deposited by different techniques Preparation technique
Substrate
r.f. sputtering
Si Quartz Quartz
d.c. plasma decomposition ECR microwave plasma ECR microwave ion beam Evaporation
Si Quartz Si Quartz Si Quartz
o"L ((f~ cm) - I)
as ((f~ cm) --i)
10 i 1" 10 7 1 10 ~o 10-2
l0 9 10 4 10 9 10 4 10-~o 10-2
10 l ° - 1 0 4
10 11 lO-m_ 10 - m 10 7
10
I
10 4 i0 7 10 8 10-5
197
100
/~cm)1
6" 10"5
102
"Only the results for three samples are presented.
conducting evaporated and sputtered layers, the use of silicon substrates was also possible. The transverse resistance of the carbon films was determined on silicon as well as on quartz substrates with ground electrodes positioned on the surface of the substrate. Table 3 includes the range of planar (aL for lateral measurements) and transverse (a s for sandwich measurements) conductivities of carbon layers prepared by the described techniques. For an isotropic layer model, a restriction on the determination of one of the conductivities, transverse (as) or planar (aL) with respect to the layer surface, should be possible. However, the evaporated and r.f.-sputtered films exhibit great differences up to six orders of magnitude between as and aL, depending on the preparation conditions. With increasing target voltage, the conductivity generally and the difference between as and aL increase (Fig. 2). Moreover, a certain number of r.f.-sputtered layers deposited onto silicon substrates exhibit azimuthal (with respect to the layer surface) anisotropy of conductivity (Fig. 3). This effect has not been observed for sputtered films deposited onto quartz substrates and for evaporated films. Adkins et al. [7] reported that transverse resistivities of evaporated carbon films were about three orders of magnitude higher than planar resistivities. Hausser [2] showed that this anisotropic behaviour was caused by less strictly controlled conditions of evaporation. Without presputtering of the carbon target, the first few layers are deposited in the presence of air owing to degassing of the target. These initial layers are the cause of Adkins et al.'s observed anisotropy [2]. The observed anisotropic behaviour of our layers cannot be explained by this effect. In general, one may consider that this extraordinary behaviour is either due to a material anistropy or to a gradient in film properties caused by floating deposition conditions. For interpretation, the results of mass density measurements,
I
o GL *
I~ s
10-10
I
!
I 1500
2000
[
2500
V
I
3000
Fig. 2. Planar and transverse conductivities of r.f.-sputtered layers as a function of the target voltage.
90 °
180 °5.10-1
10-1
v "1 161 (~2.cmi1 5.161
0°
Fig. 3. Anisotropy of the in-plane conductivity (with respect to the layer surface).
optical measurements and cross-sectional transmission electron microscopy (XTEM) were used. 3.3. Optical properties of the layers 3.3.1. Middle IR Optical properties of the layers have been investigated by measurements of nearly normal incidence spectral transmittance and reflectance [8] in the wavenumber range from 1200 cm -t to 4000 cm -1. In general, we have tried to discuss the optical properties
M. Vogel et al. f Properties of amorphous C layers
198 .......
dc ptaima d e p o s i t i o n rf s p u t t e r i n g e- beam evaporation microwave plasma deposition
0 0
0
1
0
0 000
A
O0
n
2
lo s
c.m"4 ~
Eo"O E.~O,2eV n -,2,3... 2,9
~
~'~ 10/'
T_
•
I
15
0,o°8
1
~
J
L
I
20
j
01cm3
Fig. 5. IR refractive indices as a function of mass density: ©, sputtering; e , ECR microwave plasma deposition: A d.c. pla: decomposition.
1
,
103
~.
"~'.~, k~ •x
,, II
\
/
~.,,. ~, 1-'1"-,
/
/
E," 0,9 eV
F"" ""'~, \' _. . . . .
.(.
/7
:
n = 2,2...2,3
102 \.
•.
.
.
n " 1,9... 2,3
.
10
IO
~'10 0
1
2000
I
3000
cm"4
I
4000
Fig. 4. Typical IR absorption coefficient behaviour and optical gaps for a-C:H.
in terms of the homogeneous and isotropic layer model [8-10]. In this case, the optical properties may be described by the index of refraction n(v) and absorption coefficient ~(v). Figure 4 shows typical ~(v) dependences for the layers investigated. The refractive index n(v) has been found to be nearly constant over the wavenumber range investigated (weak dispersion), but it varies with film mass density p. This dependence is shown in Fig. 5.
3.3.2. Near-IR and visible Optical properties i n the near-IR-visible region have been investigated from normal incidence transmittance measurements. The optical gaps have been determined from standard Tauc plots and are given in Fig. 4. Some major features should be pointed out here. (1) The d.c. plasma-deposited layers as well as the layers deposited from a microwave plasma exhibit an absorption behaviour typical of a-C:H in the middle IR
and may be called IR transparent. For these samples dramatic change in optical properties could be obser~ when the deposition conditions were changed. Electn beam-evaporated layers are strongly absorbing near to graphite in this connection. The o p t i c a l haviour of r.f.-sputtered layers is extraordinary a seems to represent some kind of "intermediate" tween a-C:H and evaporated carbon. Depending on target voltage applied, the optical properties of r sputtered layers change dramatically: low tar voltages correspond to very weakly absorbing samp] while strongly absorbing films have been found for hJ target voltages. The same may be seen from the opti gaps determined. (2) Extremely high refractive indices have b~ found for some r.f.-sputtered layers. Moreover, r.f.-sputtered layers, the n(p) dependence is ambigu~ (Fig. 5), and the n values may be divided into t' subgroups: n < 2.2 and n > 2.2. Higher refractive dices (n > 2.2) correspond to strongly absorbing lay (~ ~> 3000 cm-'; E 0 < 0.2 eV), while layers with n < '. have displayed lower absorption losses (~ < 3000 cm E 0 > 0.2 eV). The most interesting fact is that this di sion into subgroups correlates with the distinction samples according to electrical properties. Electrica anisotropic samples (high conductivity) have refract indices n > 2.2, while isotropic samples (high resistivi have refractive indices n < 2.2. (3) No evidence has been found for the existence refractive index gradients n(z) (the z axis is direcl normal to the layer surface) for samples deposited or silicon substrates. The T and R spectra recorded cot be analysed in terms of a homogeneous layer model (4) For observing any azimuthal anisotropy, norn incidence transmission spectra (IR) have been record for various directions of the polarization plane of t incidence light. This procedure could be carried c only for samples deposited onto silicon, because qua is non-transparent in the middle IR. For isotro 1 layers, normal incidence transmittance is independ~
M. Vogel et al./ Properties of amorphous C layers
199
of polarization. However, if there is a preferred direction in the material non-parallel to the layer axis z normal incidence transmittance becomes dependent on light polarization. In fact, an effect of polarizationdependent normal incidence transmittance has been found for a certain number of strongly absorbing r.f.sputtered layers. For these layers the "transmittance over polarization" dependence was similar to the picture shown in Fig. 3. This result confirms the possibility of azimuthal anisotropy of sputtered a-C layers. Electrically anisotropic (aS~aL) electron-beam-evaporated films did not exhibit any azimuthal anisotropy. Thus, the preferred direction of these layers should be normal to the substrate surface.
3.4. Cross-sectional transmission electron microscopy investigations The results of electrical and IR-optical investigations suggest that some r.f.-sputtered carbon layers exhibit an azimuthally anisotropic behaviour. In order to emphasize this statement, XTEM investigations have been carried out only for selected r.f.-sputtered samples deposited onto silicon substrates. Sample preparation was implemented in the usual way by mechanical thinning (dimpling, lapping) and a final ion beam etching procedure. Because of the different sputtering rates of carbon and silicon, the angle of incidence of the ion beam was about 85° to the layer axis. Etching was carried out with rotating sample movement. The vertical structure of an optically and electrically isotropic a-C layer on Si(100) is shown in Fig. 6. The Fig. 6. Cross-sectional electron micrograph of an isotropic a-C layer layer is amorphous without evident anisotropy. The on Si(100) viewed in the [011] direction and the diffraction pattern of electron diffraction pattern (selected area diffraction) the carbon layer. displays three diffuse rings. The interface between carbon and silicon is smooth in the given enlargement. The dark region in the carbon layer directly "above" the rings of the carbon film as well as diffraction spots of interface is due to an increase in electron scattering and the single-crystal Si(100) substrate. The superposition may be caused by a phase mixed from carbon and of both diffraction patterns allows the partial determisilicon. The width of this mixed region is approximately nation of the orientation relationship of both lattices. 6 nm. Thus we can establish the following relation between On the contrary, XTEM investigations of an an- the orientation of the cubic lattice (silicon) and the isotropic sample revealed the following results. The hexagonal structure of oriented graphitic areas of the interface between carbon and silicon is rougher than in carbon layer: the previous case, and the width of the mixed region is 8 nm. Moreover, the layer has a columnar structure [001]cn[011]si with a preferred direction inclined to the interface at an This suggests that the c axis of the hexagonal elemenangle of about 80 ° (Fig. 7). Each columnar part is tary cell of carbon is parallel to the [100]-oriented irregularly formed and obviously limited in height. surface of the silicon substrate. The diffraction pattern (Fig. 8) has a sickle-shaped internal diffraction ring suggesting the presence of oriented crystalline areas in the a-C film. The results 4. Discussion are in qualitative agreement with the electrical and IR-optical investigations which indicated graphitic In the previous sections we have presented numerous properties and an anisotropic behaviour of this sample. experimental data about the properties of a-C:H layers This diffraction pattern exhibits the diffuse diffraction deposited by different techniques. Certain properties of
200
M. Vogel et al. / Properties of amorphous C layers
the layers, such as mass density or refractive index, exhibit a significant dependence on the technological deposition parameters. However, other properties, such as d.c. conductivity or near-IR absorptance, which are extremely sensitive to the contamination level (especially nitrogen [11-13]) exhibit a rather involved and partially irreproducible dependence on technological deposition parameters so that a discussion of this correlation is impossible without extremely accurate data about the contamination level of a large number of samples. Such investigations are beyond the limits of the present study. In the subsequent discussion we shall, therefore, restrict our attention to the correlation between different experimental data and layer properties rather than their dependence on deposition parameters.
Fig. 7. Cross-sectional electron micrograph of an anisotropic a-C layer on Si(100) viewed in the [011] direction and the diffraction pattern of silicon and a-C.
Fig. 8. Electron diffraction pattern of an anisotropic r.f.-sputtered layer overlapped by the matrix spots of the silicon lattice.
4.1. Samples with low electrical conductivity In general, samples with low electrical conductivity were transparent in the IR spectral region. Plasma-deposited, microwave ion-beam-deposited and low refractive index r.f.-sputtered layers fall into this group. All these samples exhibit properties very similar to those frequently published about IR-transparent a-C:H [i, 8, 10, 14--18]. In particular, resistivity and optical gap increase with hydrogen content so that layers with about 4 0 a t . % H have optical gaps E0> 1.6eV (microwave plasma-deposited layers), while a decrease in hydrogen content to N H < 20at.% results in optical gaps E 0 < 0.9 eV (r.f.-sputtered layers). No transparent and electrically resistant films exhibited any anisotropic behaviour. The IR absorption picture of these layers is mainly determined by significant vibrational excitations in the network. An adequate description of this absorption (and dispersion) behaviour may be given on the basis of multioscillator models. This treatment is not the subject of this paper, but is published elsewhere [10]. The very broad absorption band around v = 2500-3500 cm -~ in the case of r.f.-sputtered layers (Fig. 4) has to be understood as a superposition of overlapping CH, N H and OH absorption lines probably occurring here as a result of the low deposition rate but very high residual gas pressure in the r.f. sputtering apparatus. Microwave plasma- and d.c. plasma-deposited layers exhibit a rather familiar n(p) dependence. Here a decrease in hydrogen content leads to an increase in mass density and in refractive index. Thus, a hydrogen content of about 40 at.% corresponds to a mass density p~l.6gcm 3 ( n ~ l . 9 ) , while N H ~ 2 0 a t . % corresponds to 2.1 g cm -3 (n ~ 2.3). This may be understood as a result of a replacement of protonated fourfold coordinated carbon atoms (polymeric component) by unprotonated fourfold coordinated carbon atoms (diamond-like component). The extraordinary n(p) behaviour of r.f.-sputtered layers, however, requires a
201
M. Vogel et al. / Properties of amorphous C layers
more detailed discussion and is the subject of Section 4.3.
50
4.2. Samples with high electrical conductivity Electron-beam-evaporated as well as high refractive index r.f.-sputtered layers fall into this group. These films are strongly absorbing in the IR and exhibit an anisotropic behaviour established by measurements of electrical conductivity as well as by optical and XTEM investigations. We suppose that there is a correlation between the jump in refractive indices between transparent and nontransparent samples and the exhibition of anisotropic properties. We believe that both effects are caused by the occurrence of non-localized ~r electron states in the network. Below we will attempt to explain this behaviour on the basis of a simple mixing model. A quite interesting study of partially strongly absorbing (graphitic) amorphous carbon films has been published by Smith [19]. In particular, Smith has succeeded in describing the mass density, refractive index and absorption coefficients (visible and UV region) of carbon films in terms of a mixing model, considering polymeric, diamond-like, graphitic and void components. In more recent work this treatment has been applied to the middle and near-IR spectral region [20]. We will use an equivalent method to give a qualitative explanation of the anisotropy established. Moreover, we shall try to reproduce the optical properties of the r.f.-sputtered layers in terms of a mixing model in a similar way to that in ref. 19.
4.3. The extraordinary behaviour of r.f.-sputtered layers A qualitative explanation of the extraordinary behaviour of r.f.-sputtered layers may be given on the basis of the following simple assumption. The layer is considered to be composed only of polymeric hydrocarbon areas and sp2-hybridized (aromatic) carbon areas. In fact, this simple assumption is sufficient to explain the mass density values obtained as well as the observed hydrogen content. Let us represent the volume fraction of the polymeric part by Vpol, and the volume fraction of the spZ-hybridized fraction by Vc,,. The filling factor p is defined by p : Vpoll(Vpo I ~- Vcar)
1 -p
= Vc.rl(Vpo, +
Vc.r)
For such a model, the density is given by P = PPpol + ( 1 - P)Pcar
For polymeric fractions, Ppol is considered to be 1.0 g cm-3; for sp2-hybridized areas P~ar= 2.2 gcm -3 (density of graphite). The hydrogen concentration is N . =pNH(po,) + ( 1 --p)NR<¢.,)
NH I
I
1.0
1.5
3
glcm 3 2.0
---
(a) case A
4
] caseAandB I case B possible /o ) ] phi~iclike
I
I/aoiso ropio
I 3
~/
I
I /ni~)-d epend ence "(case B)
/o°ol
2
isotropic ni~~ I "Clependence I (case A) I
lj0
I
I 115 9cm "3 2~0
(b) Fig. 9. (a) Hydrogen content predicted by our mixing mode] as a function of mass density including experimental values: ©, r.f. sputtering; 0, ECR microwave plasma deposition; I , ECR microwave ion beam deposition; ~, d.c. plasma decomposition; El, electron beam evaporation. (b) , IR refractive indices predicted by our model as a function of mass density; ©, experimental values for r.f.-sputtered layers.
Here NH(car)=0; NH(pol) has been taken 50%, as it is typical of polymers. Thus N , = p x 50% Figure 9(a) shows the thus predicted Nn(p) dependence together with observed experimental points for several deposition techniques. Densities ( 1.7-1.9 g cm-3) typical of r.f.-sputtered layers correspond to NH values less than 20% in agreement with experimental values [5]. Because of the very different absorption pictures of low refractive index and high refractive index r.f.-sputtered layers, a control of the hydrogen content by means of IR spectroscopy was difficult. However, IR spectra show that no dramatic change in the hydrogen content of these layers occurs. To obtain more accurate information, five
202
M. Vogel et al. / Properties of amorphous C layers
r.f.-sputtered layers have been investigated by means of the nuclear reaction method. Some of the results were identical so that only three points could be presented in Fig. 9(a). The hydrogen content was about 9-11 at.% for high refractive index and 15-18 at.°/,, for low refractive index r.f.-sputtered layers. We suppose that the hydrogen has been incorporated from the residual gas in the deposition chamber favoured by the low deposition rate. Other layers (d.c. plasma, microwave plasma) cannot be discussed by means of this model because the high densities (p--,2.2 g cm 3) disagree with NH values of about 20% (cf Fig. 9(a)) [51. For these layers, a more detailed model (introduction of a "diamond-like" component) should be applied as shown in ref. 19. For r.f.-sputtered layers, our simple model leads to some interesting conclusions. We will now distinguish two special cases: case A in which, single (isolated) aromatic carbon areas are embedded in a polymeric environment; case B, where single polymeric areas are embedded in an (extended) sp2-hybridized carbon environment. This division is not essential for p and N H values because p and NH only depend on the filling factor p. However, macroscopic properties which are sensitive to the degree of the localization of 7z electron states may change dramatically depending on the situation (A or B) realized. In fact, case B corresponds to extended H electron states, which is characteristic of graphite and should result in a more graphitic behaviour of the layer (high IR-absorption, high conductivity, anisotropy). For case A, I-I electron states may be considered as localized in small clusters (in analogy to the a-C models of Robertson and O'Reilly [21]), and a graphitic behaviour is not expected. According to the optical gaps determined for weakly absorbing samples, the size of such clusters should not exceed a few nanometres. It should be mentioned that case A (isolated sp 2 cluster) is close to semiempirical structural models of a-C:H, which are often applied in order to explain transparency and hardness of the layers, although a considerable fraction of threefold coordinated carbon atoms is well known to be present in the layer. Moreover, a random distribution of possible preferred directions of the clusters is sometimes directly postulated in order to obtain an isotropic layer model for a-C:H (cf. ref. 22). The experimental material presented here allows us to establish the hypothesis that this treatment is correct for weakly absorbing, insulating a-C:H but is insufficient for the description of strongly absorbing and conducting layers. Naturally, high absorptance and conduction may be explained in terms of extended threefold coordinated carbon areas. However, the distribution of preferred directions (if there are any) of these extended areas should be more complicated even if they are not isolated. We suppose that in this case
macroscopic anisotropy is possible. We will not attempt to present an adequate structural model for this situation here, but it seems likely that it may be close to the "defected graphite" model [23] proposed recently by Tamor and Wu, which seems suitable as a starting point for three-dimensional anisotropic a-C:H models. In terms of our mixing model, according to filling factors p (and consequently to p), the probability of the appearance of case A or B should vary. Considering the case of high p values ( p - , l), the medium should be composed of small sp2-hybridized areas embedded in a polymeric environment. Thus, the FI electron states are localized in small sp2-hybridized clusters. Following Robertson and O'Reilly [21], this will lead to sufficiently high optical gaps enabling the material to be IR transparent. IR absorption losses are mainly caused by more or less localized network vibrations, which allows us to describe the IR properties in terms of multioscillator models [10]. The single clusters may be anisotropic but, by considering a random distribution of preferred directions for these sp 2 clusters, the medium should be isotropic in a macroscopic sense. In general, one may consider that above some critical filling factor p >Pcrit.I only this isotropic case (case A) is possible. On the contrary, for p ~ 0 the situation is quite different from that mentioned above. Isolated sp 2 areas are not very probable now, and the situation realized is case B. Polymeric areas are now embedded in an sp 2 carbon environment. The extended spZ-hybridized areas allow the ~ electron states to be non-localized, lowering the gap and making the material strongly absorbing even in the IR region. Moreover, a preferred direction of the aromatic network may lead to macroscopic anisotropy. We shall consider that below some critical filling factor p < Pcrit.2 the material should be highly conducting, absorbing and, possibly, anisotropic. The most interesting case is Pcrit,2 < P < Pcrit.I
(1)
In principle, both cases A and B are possible here, which results in a possible ambiguity of macroscopic properties for filling factors p (or mass densities) satisfying eqn. (1). Of course, this is a very qualitative discussion. Quantitative treatment is difficult and demands knowledge of the form and size of the inclusions. However, some simple estimations may be carried out. The following discussion is to show that the experimentally obtained n(p) dependence, corresponding to strongly absorbing (graphitic) r.f.-sputtered layers (n > 2.2), may be explained in terms of our model as a consequence of the realization of case B. On the contrary, case A may be assigned to the typical refraction index behaviour of a-C:H (compare with microwave plasma-deposited and d.c. plasma-deposited layers).
M. Vogel et al. / Properties of amorphous C layers
A crude estimate of critical values Pcrit.l and PcriC2 may be obtained, for a moment considering our material to be built from spherical inclusions of material 1, embedded in a bulk environment of material 2. For such spheres, maximum volume fractions of the inclusions will be 0.74 of the common volume [24]. The simplest possibility is to assign this maximum volume fraction of spherical inclusions to the critical filling factor P~rit.t, which means Pcrit.l=0.74 (Pcrit. I = 1.32 g cm-3). Accordingly, Pcrit.2= 0.26 (Petit.2 = 1.89 g cm-3). In terms of this simple treatment, samples with (p > Pcrit.2 should exhibit a graphitic behaviour, which is in agreement with the experiment. For 0.26 < p < 0.74 (1.89 g cm -3 > p > 1.32 g cm-3), ambiguity of electrical and optical properties is allowed, which is confirmed by the experimental material. Moreover, we may now estimate refractive indices for case B, using typical ~ values for polymers and graphite and connecting them with a suitable mixing model. For polymers, hpot has been considered purely real without dispersion: nvo1= 1.4. For graphite, a complex ~ar has been taken into consideration, and the optical parameters have been taken from polycrystalline graphite [25]. The results obtained correspond to case B, because the use of graphitic optical functions is connected with the presence of extended rc electron states, which is realized only in case B and is possible in our model for mass densities p > Pcrit.l 1.32 g cm -3. Various mixing formulae have been tested to reproduce the experimental n(p) dependence in Fig. 5. The best agreement has been achieved by using the mixing formula found by Yadava and coworkers [26, 27] as a direct consequence of the L o r e n t z - L o r e n z equation: ~--
fi2(v' p) = (1 --p)(rtpol 2 q-- 2)rlcar2(V) q-p[~car2(V) ~- 2]npol 2 ( 1 --p)(r/pol 2 q- 2) + p[hc.r2(v) + 2] (2) In Fig. 9(b) resulting n values for v = 2400 cm -~ are plotted as a function of mass density (upper curve). The corresponding ~ values are not plotted, but are in the range 5000-15 000 cm- ~ for p values of 1.7-1.9 g cm-3 and thus agree with experimental values. The frequency dependences are not presented here: the refractive indices exhibit weak anomalous dispersion and absorption coefficients increase with wavenumber, similar to the experimental curves shown in Fig. 4 (upper curves). Treatment of case A (small isolated sp 2 clusters) is more complicated. The problem is to find a suitable approximation for no,r- Clearly, the IR response of small sp 2 clusters should significantly differ from that of bulk graphite, thus explaining the ambiguity of n(p) values. The lower curve in Fig. 9(b) has been obtained from eqn. (2) with an estimated ncar = 2.6 (purely real F/car : for estimation of near in case A see Appendix A).
203
On comparing calculated and measured n values one problem must be taken into account. The experimental n values have been determined by considering an isotropic layer material. For anisotropic materials, they only correspond to the special direction of the electric field vector realized in the actual measurement. This may explain the very high variance in the experimental n(p) dependence for r.f.-sputtered layers (Fig. 5, upper curve). On the contrary, reliable data on the dielectric tensor of graphite were not available. For that reason, a theoretical estimation of the variance of n values of the carbon layers according to different directions of the electric field vector was impossible. The optical parameters of graphite used for calculation have been taken from polycrystalline graphite and thus represent optical parameters averaged over directions. We may expect that they reflect the trend of the n(p) dependence, but excellent agreement cannot be expected. The above discussion was to show that the presence of anisotropy in r.f.-sputtered a-C:H layers may be explained in terms of a model that considers the layer to be built from large graphitic carbon areas and isolated polymeric components. However, the model does not yield any information about a crystallographic preferred direction in the layer. By means of electron diffraction of an X T E M sample (Fig. 8), it was shown that for anisotropic carbon layers deposited on silicon substrates the c axis of the hexagonal elementary cell of carbon is parallel to the (100) surface of the silicon substrate. This result represents the crystallographic explanation of the azimuthally anisotropic behaviour of the layer. In general, the effect of polarization-dependent normal incidence transmittance requires that the preferred direction should not be normal to the layer surface which is in agreement with the preferred direction found by electron diffraction. The reason for the appearance of azimuthal anisotropy in strongly absorbing r.f.-sputtered layers on [100]-oriented silicon surfaces is not fully understood. We believe that both the low deposition rate and the extremely high deposition temperature give rise to the very different properties in comparison with other layers. Connecting the results of X T E M investigations with our model, we may imagine the highly absorbing r.f.sputtered layers deposited onto silicon to be composed as schematically shown in Fig. 10. The observation direction of the diffraction pattern is the [011] direction normal to that in Fig. 10. The positions of the a and b axes of the hexagonal elementary cell are ambiguous. Comments on the interface region will be given in a later publication. Information on shape, size and arrangement of graphitic and polymeric parts is not available from the experimental material on the basis of the given model.
204
M. Vogel et al. / Properties o f amorphous C ko'ers
graph, t iclike
~ [10015, t
region
interface
region
s u b s t rclte
~
[0111%
Fig. I0. Polymeric areas embedded in a graphitic environment (model for anisotropic r.f.-sputtered layers on silicon).
Figure 10 suggests that the conductivity a s through the film should be higher than the planar conductivity a L. Our experimental data yield the opposite: a s < ae. However, we do not believe that this experimental fact is in disagreement with the model. Because of the finite size of the columnar parts, one cannot simply imagine graphitic planes crossing the whole film so that in fact the transverse conductivity as of the film must be lower than the in-plane conductivity of graphite. Therefore, because of the perhaps very complicated shape of the graphitic parts in the film, our model does not allow us to predict any correlation between a s and aL.
The authors thank Dr. J. Ullmann, Dr. G. Schaarschmidt, B. Mainz, S. Roth, and Dr. G. Schmidt for sample preparation as well as Professor Dr. W. Scharff and Dr. P. Barna for helpful discussions and L. Feige for technical assistance.
5. Conclusion
References
The electrical and optical properties of amorphous carbon layers have been discussed. The layers deposited by d.c. plasma as well as by microwave plasma are isotropic and exhibit high resistivities and an absorption behaviour typical of a-C:H films. Electron-beam-evaporated carbon layers have high conductivities. They are strongly absorbing and anisotropic. R.f.-sputtered layers represent some kind of intermediate between a-C:H films and evaporated films. The extraordinary behaviour of these layers may be explained by means of a simple model. The highly absorbing, conducting and anisotropic layers may be considered to be built
from large graphitic areas and polymeric components. The anisotropy of these layers could also be established by XTEM investigations.
Acknowledgments
1 H. C. Tsai and D. B. Bogy, J. Vac. Sci. Technol. A, 5(1987) 3287. 2 J. J. Hausser, J. Non-Cryst. Solids, 23 (1977) 21. 3 S. Roth, B. Rau, J. Ullmann, G. Schaarschmidt, O. Stenzel, W. Scharff and K. Hammer, in Proc. 7th CIMTEX, Montecatini Terme, June 1990. 4 Chr. Weissmantel, K. Bewilogua, K. Breuer, D. Dietrich, U. Ebersbach, H.-J. Erler, B. Rau and G. Reisse, Thin Solid Films, 96 (1982) 31. 5 W. Scharff, K. Hammer, O. Stenzel, J. Ullmann, M. Vogel, T. Frauenheim, B. Eibisch, S. Roth, S. Schulze and I. Muehling, Thin Solid Films, 171 (1989) 157. 6 J. Ullmann and G. Schmidt, Diamond Relat. Mater., 1 (1992) 321. 7 C. J. Adkins, S. M. Freake and E. M. Hamilton, Philos'. Mag., 7 (1971) 313.
M. Vogel et al. / Properties of amorphous C layers 8 0 . Stenzel, S. Roth and W. Scharff, Th& Solid Films, 190 (1990) 9. 9 O. Stenzel, V. Hopfe and P. Klobes, J. Phys. D, Appl. Phys., 24 (1991) 2088. 10 O. Stenzel, G. Schaarschmidt, F. Wolf, M. Vogel and T. Wallendorf, Thin Solid Films, 203 (1991) 11. 11 J. H. Kaufmann, S. Metin and D. D. Saperstein, Phys. Rev. B, 39 (1990) 13053. 12 T. Nakano, S. Koike and Y. Ohki, J. Phys. D, 23 (1990) 711. 13 R. Kalish, O. Amir, R. Brener, R. A. Spits and T. E. Derry, Appl. Phys. A, 52 (1991) 48. 14 Chr. Weissmantel, in K. J. Klabunde (ed.), Thin FilmsJ?om Free Atoms and Particles, Academic Press, New York, 1985, p. 153. 15 B. Dischler, A. Bubenzer and P. Koidl, Appl. Phys. Lett., 42 (1983) 636. 16 A. Bubenzer, B. Dischler, G. Brand and P. Koidl, J. Appl. Phys., 54 (1983) 4590. 17 L. C. Richard, MRS Symposia Proceedings, Vol. 152, Material Research Society, Pittsburgh, PA, 1982, p. 33. 18 K. Fabisiak, F. Rozploch and J. Wieczorek, J. Phys. D, 21 (1988) 995. 19 F. W. Smith, J. Appl. Phys,, 55 (1984) 764. 20 P. Couderc and Y. Catherine, Thin Solid Films, 146 (1987) 93. 21 J. Robertson and E, P. O'Reilly, Phys. Rev. B, 35 (1987) 2946. 22 D. R. McKenzie, R. C. McPhedran, N. Savvides and D. J. H. Cockayne, Thin Solid Films, 108 (1983) 247. 23 M. A. Tamor and C. H. Wu, J. AppL Phys., 67 (1990) 1007. 24 C. Kittel, Introduction to Solid State Physics, Wiley, New York, 4th edn., 1971. 25 V. I. Gavrilenko, A. M. Grechov, D. V. Korbutyak and V. G. Litovcenko, Opticeskie Svoistva Poluprovodnikov, Naukova Dumka, Kiev, 1987, 197. 26 G. N. Yadava, S. K. Macleod, S. Ogura and E. Pelletier, Thin Solid Films, 17(1973) 243. 27 M. Harris, H. A. Macleod, S. Ogura, E. Pelletier and B. Vidal, T/tin Solid Films, 57 (1979) 173.
Appendix A: Estimation of the dielectric IR response of small aromatic clusters Effective medium approximation studies of amorphous hydrogenated carbon (a-C:H) layers [All generally use the dielectric response of graphitic (evaporated) carbon for describing every sp 2 fraction in the layer. We believe that this treatment is correct for strongly absorbing layers with certainly extended aromatic carbon areas. However, the background for such a treatment in application to IR-transparent carbon layers is not very clear. We believe that in this case the starting point for estimating the dielectric IR response should be aromatic molecules (e.g. liquid benzene) rather than bulk graphite because these molecules provide the advantage that they exhibit localized n-electron states. In this study an attempt was made to find a workable model for the IR response of the clusters, using liquid benzene as a starting point. The result was used for the calculation of n(p) (Fig. 9) by eqn. (2). The density and IR refractive index of liquid benzene are p = 0.874 g cm 3 and n ~ 1.45 [A2], and the gap is 6 eV. A
205
simple estimation of the refractive index of small clusters of aromatic rings with a density of 2.2 g c m -3 is possible using the L o r e n t z - L o r e n z equation: n2--1
1
n2 + 2
3eo
N~
where N is the concentration of molecules and X the molecular polarizability. This estimation gives near = 2.7 for p = 2.2 g cm -3. However, the problem in this simple treatment is that the decrease in optical gap due to clustering cannot be considered. In fact, aromatic clusters are treated here as compressed benzene. We have, therefore, tried to find another estimation of n .... taking the decrease in the optical gap due to clustering into account. The K r a m e r s - K r o n i g relation is the starting point: n 2(00) _ 1
2 f 00'e"(00') = n J 0 0 ,2 - 002 d00' 0
where e" is the imaginary part of the dielectric function. If absorption (e" ~ 0) is restricted to a spectral region ((D I ,¢..O2) , and co is beyond this range (00 < 001,002), this equation may be rewritten: oJ2
n2(00) - 1
2 f 00'#'(co') 2 00oe"(~o0) = ~ J 00,2 0 0 ~__ dco' ~ -n 00o--00-~, (co2 - col ) ~o 1 (D O ¢Od
0002 -- (0 2
This equation is identical with Wemple's dispersion relation [A3]. coo is between ~oI and 002 and represents some kind of a resonance frequency of a one-oscillator model. This resonance frequency decreases with increasing size (and mass density) of aromatic clusters. For estimation, we will identify 000 with the gap E o so that for benzene 000 corresponds to a photon energy of 6 eV, while for aromatic clusters 000 corresponds to photon energies of 1.0-1.5 eV. In application to the IR, co2 ,~ 0002, and thus /7 2 IR,benzene ~
l -t- (Od'benzene (D0,benzene
n~a r = 1 + 00d,clusterr (DO,cluster
If cod is identical for all clusters including the single benzene ring we obtain finally: H c2a r =
1 - ~ - ( g / b2 . . . . . .
-- l)(J)0.b ...... (D0.cluster
= 1 + 1.1 co0,ben.... (D0,cluster
Typically, coo,b...... /00Ox~uster= 4 - 6 , leading to n~,~ = 2.4-2.8. Obviously, the results of both estimation
206
M. Vogel et al. / Properties of amorphous C layers
procedures are in surprisingly good agreement. In our mixing model, an near value of 2.6 has been applied. We suppose that this approximation is an alternative to the application of bulk graphite dielectric functions to IRtransparent a-C(:H).
References A1 P. Couderc and Y. Catherine, Thin Solid Films, 146 (1987) 93. A2 T. G. Goplen, D. G. Canieron and R. N. Jones, Appl. Spectrose 34 (1980) 657. A3 S. H. Wemple, Phys. Rev. B, 7 (1973) 3767.
195
Electrical and optical properties of amorphous carbon layers: limits of the isotropic layer model M. Vogel, O. Stenzel and W. Griinewald Chemnitz University of Technology, Department of Physics/Electronic Devices, 0-9010 Chemnitz, PSF 964 (FRG)
A. Barna Research Institute for Technical Physics HAS, H-1325 Budapest, P.O. Box 76 (Hungary)
(Received January 9, 1991; revised July 15, 1991; accepted October 10, 1991)
Abstract The electrical and optical properties of amorphous carbon layers deposited by differenttechniquesare presented and compared. The layers investigated may be divided into two groups: low refractive index transparent and insulating samples and, on the contrary, high refractiveindex strongly absorbing and conducting films. Experimental results are presented which indicate that the strongly absorbing and conducting samples exhibit anisotropic properties observedby means of cross-sectionaltransmission electron microscopy,while transparent and insulating samples are electricallyand optically isotropic. An attempt has been made to explain the effectof the ambiguityof electricaland optical properties on the basis of a simple mixing model. The model allows us to reproduce the high refractiveindices of absorbing and conductinglayers as well as the low refractiveindex transparent and insulating films.
1. Introduction The deposition and properties of amorphous carbon films have been the subject of intensive research work for several years. The properties of amorphous hydrogenated carbon (a-C:H) layers are strongly dependent on the film structure and considerable variations have been observed for different deposition techniques and parameters [1, 2]. The purpose of the present paper is to discuss the electrical and optical properties of amorphous carbon films and to reveal their correlation. The layers investigated have been deposited by the following techniques: r.f. sputtering [3]; d.c. plasma decomposition [4]; electron cyclotron resonance (ECR) mirowave plasma deposition [5]; ECR microwave ion beam deposition [5]; electron beam evaporation [6]. Depending on the preparation technique and special preparation parameters, the electrical properties and optical parameters of the layers vary over a wide range. The electrical conductivity reaches values between 10 -11 and 102 (f~cm) -~. The IR refractive indices were between 1.9 and 2.9, corresponding to absorption coefficients between 102 and 105 cm- 1. It will be shown that it is useful to divide the carbon layers investigated into two groups. The first group contains all layers which are electrically insulating and transparent in the IR spectral region (plasma-deposited layers and low refractive index r.f.-sputtered films). The
0040-6090/92/$5.00
second group includes all conducting and strongly absorbing carbon films (high refractive index sputtered carbon layers and evaporated films). Furthermore, it will be demonstrated that the usually applied isotropic layer model is insufficient for discussing the properties of the second group of carbon films.
2. Film preparation In the present study the properties of films deposited by quite different techniques [3-6] are compared and discussed. The main deposition parameters are listed in Table 1. A more detailed description of deposition is beyond the limits of the present paper, but it is the subject of comparative studies [3, 5]. Quartz and silicon were used as substrates. After chemical precleaning, the substrates were in situ physically etched using inert gas ions (except for r.f. sputtering).
3. Measurements 3.1. Mass density and hydrogen content
The mass density of carbon films has been determined by a floating method in a C H 3 O H - C H B r 3 mixture and varies according to the preparation technique and special preparation conditions. Evaporated carbon films have densities in the region of 2.0 g cm 3, while the
© 1992-- Elsevier Sequoia. All rights reserved
196
M. Vogel et al. / Properties q[" amorphous C layers
TABLE 1. Deposition parameters Parameter
Value for the following techniques R.f. sputtering
Residual gas pressure Working gas pressure Working gas Ion current density Bias voltage Target voltage Energy of particles arriving at the substrate Substrate temperature Deposition rate
(Pa) (Pa)
ECR microwave plasma
ECR microwave ion beam
Electron beam evaporation 10 3
2 x 10 3
10 4
10 3
10 3
1
(3 20) x 10 2
(4
(2 8) x I0 .2
Ar or C6H~,
C6H 6 0.15 0.2 0.6 2.4
C6H,, 0.5 1 0.2 1.2
C6H 6 0.1 0.3
10) x 10 2
(mA cm 2) (kV) (kV) (eV)
2.9 1.8 0.1 10
600-2400
200 1200
400 1400
(K) (nm min ~)
320 520 I 10
340 30 50
320 470 120 220
320 470 10 30
UT KIO00 !
D.c. plasma decomposition
I
0.01 0.1 340 720 5 50
TABLE 2. Density and hydrogen content of carbon layers
~ 2000
V
I
I
3000 I
Deposition technique
Mass density (g c m ~)
H content (at.%)
R.f. sputtering D.c. plasma decomposition ECR microwave plasma ECR microwave Ion beam Evaporation
1.6 1.9 1.8 2.1
9- 18 20 30
1.6 2.1
20 40
1.8 2.4
18 20
2.~
glcm 3
1.8 2.0
3
2.0
1.5 I
I 1000 0B
i V
I 20OO
----
Fig. 1. Mass density of amorphous hydrogenated carbon layers depending on the extraction voltage or bias voltage Ue for ion-beamand plasma-deposited layers and depending on the target voltage UT for r.f.-sputtered films: ©, r.f.-sputtering; 0, ECR microwave plasma deposition; I , ECR microwave ion beam deposition; •, d.c. plasma decomposition. otherwise p r o d u c e d films exhibit a significant dependence on the p r e p a r a t i o n p a r a m e t e r s (bias voltage, target voltage) (Fig. 1). T h e h y d r o g e n c o n t e n t o f c a r b o n films on silicon was investigated by m e a n s o f the nuclear r e a c t i o n m e t h o d a n d is listed in T a b l e 2. It should be n o t e d that within a given d e p o s i t i o n technique a n u n a m b i g u o u s correlation between h y d r o g e n c o n t e n t a n d m a s s density m a y
be established. However, in c o m p a r i n g different deposition techniques no clear c o r r e l a t i o n a p p e a r s . W e suppose that the extremely high h y d r o g e n c o n t e n t o f s p u t t e r e d layers is due to the i n c o r p o r a t i o n o f h y d r o g e n c o n t a i n i n g m o l e c u l a r f r a g m e n t s f r o m the residual gas f a v o u r e d b y the very low d e p o s i t i o n rate. It has been established that c h a n g i n g the w o r k i n g gas from a r g o n to C6H 6 did not cause a n y significant increase in the h y d r o g e n c o n t e n t o f r.f.-sputtered layers. 3.2. E l e c t r i c a l p r o p e r t i e s at r o o m t e m p e r a t u r e s
The p l a n a r a n d transverse resistance o f the c a r b o n films (thickness from 0.5 to 3.0 pm) is o b t a i n e d by m e a s u r i n g the current flowing as a result o f the a p p l i e d voltage, using an electrometer. T h e voltage was varied in the range from 0.1 V to 100V, c o r r e s p o n d i n g to electrical fields between 100 a n d 10 000 V cm-~ for b o t h m e a s u r e m e n t s . C a r b o n layers with a p l a n a r resistance lower t h a n 106~~ were investigated by a f o u r - p o i n t m e t h o d . A l u m i n i u m , gold a n d m o l y b d e n u m were used as electrode materials. All films have exhibited o h m i c behaviour. In general, m e a s u r e m e n t s o f p l a n a r resistance were carried out on q u a r t z substrates. In the case o f high
M. Vogel et al. / Properties of amorphous C layers T A B L E 3. Planar and transverse conductivities of amorphous carbon layers deposited by different techniques Preparation technique
Substrate
r.f. sputtering
Si Quartz Quartz
d.c. plasma decomposition ECR microwave plasma ECR microwave ion beam Evaporation
Si Quartz Si Quartz Si Quartz
o"L ((f~ cm) - I)
as ((f~ cm) --i)
10 i 1" 10 7 1 10 ~o 10-2
l0 9 10 4 10 9 10 4 10-~o 10-2
10 l ° - 1 0 4
10 11 lO-m_ 10 - m 10 7
10
I
10 4 i0 7 10 8 10-5
197
100
/~cm)1
6" 10"5
102
"Only the results for three samples are presented.
conducting evaporated and sputtered layers, the use of silicon substrates was also possible. The transverse resistance of the carbon films was determined on silicon as well as on quartz substrates with ground electrodes positioned on the surface of the substrate. Table 3 includes the range of planar (aL for lateral measurements) and transverse (a s for sandwich measurements) conductivities of carbon layers prepared by the described techniques. For an isotropic layer model, a restriction on the determination of one of the conductivities, transverse (as) or planar (aL) with respect to the layer surface, should be possible. However, the evaporated and r.f.-sputtered films exhibit great differences up to six orders of magnitude between as and aL, depending on the preparation conditions. With increasing target voltage, the conductivity generally and the difference between as and aL increase (Fig. 2). Moreover, a certain number of r.f.-sputtered layers deposited onto silicon substrates exhibit azimuthal (with respect to the layer surface) anisotropy of conductivity (Fig. 3). This effect has not been observed for sputtered films deposited onto quartz substrates and for evaporated films. Adkins et al. [7] reported that transverse resistivities of evaporated carbon films were about three orders of magnitude higher than planar resistivities. Hausser [2] showed that this anisotropic behaviour was caused by less strictly controlled conditions of evaporation. Without presputtering of the carbon target, the first few layers are deposited in the presence of air owing to degassing of the target. These initial layers are the cause of Adkins et al.'s observed anisotropy [2]. The observed anisotropic behaviour of our layers cannot be explained by this effect. In general, one may consider that this extraordinary behaviour is either due to a material anistropy or to a gradient in film properties caused by floating deposition conditions. For interpretation, the results of mass density measurements,
I
o GL *
I~ s
10-10
I
!
I 1500
2000
[
2500
V
I
3000
Fig. 2. Planar and transverse conductivities of r.f.-sputtered layers as a function of the target voltage.
90 °
180 °5.10-1
10-1
v "1 161 (~2.cmi1 5.161
0°
Fig. 3. Anisotropy of the in-plane conductivity (with respect to the layer surface).
optical measurements and cross-sectional transmission electron microscopy (XTEM) were used. 3.3. Optical properties of the layers 3.3.1. Middle IR Optical properties of the layers have been investigated by measurements of nearly normal incidence spectral transmittance and reflectance [8] in the wavenumber range from 1200 cm -t to 4000 cm -1. In general, we have tried to discuss the optical properties
M. Vogel et al. f Properties of amorphous C layers
198 .......
dc ptaima d e p o s i t i o n rf s p u t t e r i n g e- beam evaporation microwave plasma deposition
0 0
0
1
0
0 000
A
O0
n
2
lo s
c.m"4 ~
Eo"O E.~O,2eV n -,2,3... 2,9
~
~'~ 10/'
T_
•
I
15
0,o°8
1
~
J
L
I
20
j
01cm3
Fig. 5. IR refractive indices as a function of mass density: ©, sputtering; e , ECR microwave plasma deposition: A d.c. pla: decomposition.
1
,
103
~.
"~'.~, k~ •x
,, II
\
/
~.,,. ~, 1-'1"-,
/
/
E," 0,9 eV
F"" ""'~, \' _. . . . .
.(.
/7
:
n = 2,2...2,3
102 \.
•.
.
.
n " 1,9... 2,3
.
10
IO
~'10 0
1
2000
I
3000
cm"4
I
4000
Fig. 4. Typical IR absorption coefficient behaviour and optical gaps for a-C:H.
in terms of the homogeneous and isotropic layer model [8-10]. In this case, the optical properties may be described by the index of refraction n(v) and absorption coefficient ~(v). Figure 4 shows typical ~(v) dependences for the layers investigated. The refractive index n(v) has been found to be nearly constant over the wavenumber range investigated (weak dispersion), but it varies with film mass density p. This dependence is shown in Fig. 5.
3.3.2. Near-IR and visible Optical properties i n the near-IR-visible region have been investigated from normal incidence transmittance measurements. The optical gaps have been determined from standard Tauc plots and are given in Fig. 4. Some major features should be pointed out here. (1) The d.c. plasma-deposited layers as well as the layers deposited from a microwave plasma exhibit an absorption behaviour typical of a-C:H in the middle IR
and may be called IR transparent. For these samples dramatic change in optical properties could be obser~ when the deposition conditions were changed. Electn beam-evaporated layers are strongly absorbing near to graphite in this connection. The o p t i c a l haviour of r.f.-sputtered layers is extraordinary a seems to represent some kind of "intermediate" tween a-C:H and evaporated carbon. Depending on target voltage applied, the optical properties of r sputtered layers change dramatically: low tar voltages correspond to very weakly absorbing samp] while strongly absorbing films have been found for hJ target voltages. The same may be seen from the opti gaps determined. (2) Extremely high refractive indices have b~ found for some r.f.-sputtered layers. Moreover, r.f.-sputtered layers, the n(p) dependence is ambigu~ (Fig. 5), and the n values may be divided into t' subgroups: n < 2.2 and n > 2.2. Higher refractive dices (n > 2.2) correspond to strongly absorbing lay (~ ~> 3000 cm-'; E 0 < 0.2 eV), while layers with n < '. have displayed lower absorption losses (~ < 3000 cm E 0 > 0.2 eV). The most interesting fact is that this di sion into subgroups correlates with the distinction samples according to electrical properties. Electrica anisotropic samples (high conductivity) have refract indices n > 2.2, while isotropic samples (high resistivi have refractive indices n < 2.2. (3) No evidence has been found for the existence refractive index gradients n(z) (the z axis is direcl normal to the layer surface) for samples deposited or silicon substrates. The T and R spectra recorded cot be analysed in terms of a homogeneous layer model (4) For observing any azimuthal anisotropy, norn incidence transmission spectra (IR) have been record for various directions of the polarization plane of t incidence light. This procedure could be carried c only for samples deposited onto silicon, because qua is non-transparent in the middle IR. For isotro 1 layers, normal incidence transmittance is independ~
M. Vogel et al./ Properties of amorphous C layers
199
of polarization. However, if there is a preferred direction in the material non-parallel to the layer axis z normal incidence transmittance becomes dependent on light polarization. In fact, an effect of polarizationdependent normal incidence transmittance has been found for a certain number of strongly absorbing r.f.sputtered layers. For these layers the "transmittance over polarization" dependence was similar to the picture shown in Fig. 3. This result confirms the possibility of azimuthal anisotropy of sputtered a-C layers. Electrically anisotropic (aS~aL) electron-beam-evaporated films did not exhibit any azimuthal anisotropy. Thus, the preferred direction of these layers should be normal to the substrate surface.
3.4. Cross-sectional transmission electron microscopy investigations The results of electrical and IR-optical investigations suggest that some r.f.-sputtered carbon layers exhibit an azimuthally anisotropic behaviour. In order to emphasize this statement, XTEM investigations have been carried out only for selected r.f.-sputtered samples deposited onto silicon substrates. Sample preparation was implemented in the usual way by mechanical thinning (dimpling, lapping) and a final ion beam etching procedure. Because of the different sputtering rates of carbon and silicon, the angle of incidence of the ion beam was about 85° to the layer axis. Etching was carried out with rotating sample movement. The vertical structure of an optically and electrically isotropic a-C layer on Si(100) is shown in Fig. 6. The Fig. 6. Cross-sectional electron micrograph of an isotropic a-C layer layer is amorphous without evident anisotropy. The on Si(100) viewed in the [011] direction and the diffraction pattern of electron diffraction pattern (selected area diffraction) the carbon layer. displays three diffuse rings. The interface between carbon and silicon is smooth in the given enlargement. The dark region in the carbon layer directly "above" the rings of the carbon film as well as diffraction spots of interface is due to an increase in electron scattering and the single-crystal Si(100) substrate. The superposition may be caused by a phase mixed from carbon and of both diffraction patterns allows the partial determisilicon. The width of this mixed region is approximately nation of the orientation relationship of both lattices. 6 nm. Thus we can establish the following relation between On the contrary, XTEM investigations of an an- the orientation of the cubic lattice (silicon) and the isotropic sample revealed the following results. The hexagonal structure of oriented graphitic areas of the interface between carbon and silicon is rougher than in carbon layer: the previous case, and the width of the mixed region is 8 nm. Moreover, the layer has a columnar structure [001]cn[011]si with a preferred direction inclined to the interface at an This suggests that the c axis of the hexagonal elemenangle of about 80 ° (Fig. 7). Each columnar part is tary cell of carbon is parallel to the [100]-oriented irregularly formed and obviously limited in height. surface of the silicon substrate. The diffraction pattern (Fig. 8) has a sickle-shaped internal diffraction ring suggesting the presence of oriented crystalline areas in the a-C film. The results 4. Discussion are in qualitative agreement with the electrical and IR-optical investigations which indicated graphitic In the previous sections we have presented numerous properties and an anisotropic behaviour of this sample. experimental data about the properties of a-C:H layers This diffraction pattern exhibits the diffuse diffraction deposited by different techniques. Certain properties of
200
M. Vogel et al. / Properties of amorphous C layers
the layers, such as mass density or refractive index, exhibit a significant dependence on the technological deposition parameters. However, other properties, such as d.c. conductivity or near-IR absorptance, which are extremely sensitive to the contamination level (especially nitrogen [11-13]) exhibit a rather involved and partially irreproducible dependence on technological deposition parameters so that a discussion of this correlation is impossible without extremely accurate data about the contamination level of a large number of samples. Such investigations are beyond the limits of the present study. In the subsequent discussion we shall, therefore, restrict our attention to the correlation between different experimental data and layer properties rather than their dependence on deposition parameters.
Fig. 7. Cross-sectional electron micrograph of an anisotropic a-C layer on Si(100) viewed in the [011] direction and the diffraction pattern of silicon and a-C.
Fig. 8. Electron diffraction pattern of an anisotropic r.f.-sputtered layer overlapped by the matrix spots of the silicon lattice.
4.1. Samples with low electrical conductivity In general, samples with low electrical conductivity were transparent in the IR spectral region. Plasma-deposited, microwave ion-beam-deposited and low refractive index r.f.-sputtered layers fall into this group. All these samples exhibit properties very similar to those frequently published about IR-transparent a-C:H [i, 8, 10, 14--18]. In particular, resistivity and optical gap increase with hydrogen content so that layers with about 4 0 a t . % H have optical gaps E0> 1.6eV (microwave plasma-deposited layers), while a decrease in hydrogen content to N H < 20at.% results in optical gaps E 0 < 0.9 eV (r.f.-sputtered layers). No transparent and electrically resistant films exhibited any anisotropic behaviour. The IR absorption picture of these layers is mainly determined by significant vibrational excitations in the network. An adequate description of this absorption (and dispersion) behaviour may be given on the basis of multioscillator models. This treatment is not the subject of this paper, but is published elsewhere [10]. The very broad absorption band around v = 2500-3500 cm -~ in the case of r.f.-sputtered layers (Fig. 4) has to be understood as a superposition of overlapping CH, N H and OH absorption lines probably occurring here as a result of the low deposition rate but very high residual gas pressure in the r.f. sputtering apparatus. Microwave plasma- and d.c. plasma-deposited layers exhibit a rather familiar n(p) dependence. Here a decrease in hydrogen content leads to an increase in mass density and in refractive index. Thus, a hydrogen content of about 40 at.% corresponds to a mass density p~l.6gcm 3 ( n ~ l . 9 ) , while N H ~ 2 0 a t . % corresponds to 2.1 g cm -3 (n ~ 2.3). This may be understood as a result of a replacement of protonated fourfold coordinated carbon atoms (polymeric component) by unprotonated fourfold coordinated carbon atoms (diamond-like component). The extraordinary n(p) behaviour of r.f.-sputtered layers, however, requires a
201
M. Vogel et al. / Properties of amorphous C layers
more detailed discussion and is the subject of Section 4.3.
50
4.2. Samples with high electrical conductivity Electron-beam-evaporated as well as high refractive index r.f.-sputtered layers fall into this group. These films are strongly absorbing in the IR and exhibit an anisotropic behaviour established by measurements of electrical conductivity as well as by optical and XTEM investigations. We suppose that there is a correlation between the jump in refractive indices between transparent and nontransparent samples and the exhibition of anisotropic properties. We believe that both effects are caused by the occurrence of non-localized ~r electron states in the network. Below we will attempt to explain this behaviour on the basis of a simple mixing model. A quite interesting study of partially strongly absorbing (graphitic) amorphous carbon films has been published by Smith [19]. In particular, Smith has succeeded in describing the mass density, refractive index and absorption coefficients (visible and UV region) of carbon films in terms of a mixing model, considering polymeric, diamond-like, graphitic and void components. In more recent work this treatment has been applied to the middle and near-IR spectral region [20]. We will use an equivalent method to give a qualitative explanation of the anisotropy established. Moreover, we shall try to reproduce the optical properties of the r.f.-sputtered layers in terms of a mixing model in a similar way to that in ref. 19.
4.3. The extraordinary behaviour of r.f.-sputtered layers A qualitative explanation of the extraordinary behaviour of r.f.-sputtered layers may be given on the basis of the following simple assumption. The layer is considered to be composed only of polymeric hydrocarbon areas and sp2-hybridized (aromatic) carbon areas. In fact, this simple assumption is sufficient to explain the mass density values obtained as well as the observed hydrogen content. Let us represent the volume fraction of the polymeric part by Vpol, and the volume fraction of the spZ-hybridized fraction by Vc,,. The filling factor p is defined by p : Vpoll(Vpo I ~- Vcar)
1 -p
= Vc.rl(Vpo, +
Vc.r)
For such a model, the density is given by P = PPpol + ( 1 - P)Pcar
For polymeric fractions, Ppol is considered to be 1.0 g cm-3; for sp2-hybridized areas P~ar= 2.2 gcm -3 (density of graphite). The hydrogen concentration is N . =pNH(po,) + ( 1 --p)NR<¢.,)
NH I
I
1.0
1.5
3
glcm 3 2.0
---
(a) case A
4
] caseAandB I case B possible /o ) ] phi~iclike
I
I/aoiso ropio
I 3
~/
I
I /ni~)-d epend ence "(case B)
/o°ol
2
isotropic ni~~ I "Clependence I (case A) I
lj0
I
I 115 9cm "3 2~0
(b) Fig. 9. (a) Hydrogen content predicted by our mixing mode] as a function of mass density including experimental values: ©, r.f. sputtering; 0, ECR microwave plasma deposition; I , ECR microwave ion beam deposition; ~, d.c. plasma decomposition; El, electron beam evaporation. (b) , IR refractive indices predicted by our model as a function of mass density; ©, experimental values for r.f.-sputtered layers.
Here NH(car)=0; NH(pol) has been taken 50%, as it is typical of polymers. Thus N , = p x 50% Figure 9(a) shows the thus predicted Nn(p) dependence together with observed experimental points for several deposition techniques. Densities ( 1.7-1.9 g cm-3) typical of r.f.-sputtered layers correspond to NH values less than 20% in agreement with experimental values [5]. Because of the very different absorption pictures of low refractive index and high refractive index r.f.-sputtered layers, a control of the hydrogen content by means of IR spectroscopy was difficult. However, IR spectra show that no dramatic change in the hydrogen content of these layers occurs. To obtain more accurate information, five
202
M. Vogel et al. / Properties of amorphous C layers
r.f.-sputtered layers have been investigated by means of the nuclear reaction method. Some of the results were identical so that only three points could be presented in Fig. 9(a). The hydrogen content was about 9-11 at.% for high refractive index and 15-18 at.°/,, for low refractive index r.f.-sputtered layers. We suppose that the hydrogen has been incorporated from the residual gas in the deposition chamber favoured by the low deposition rate. Other layers (d.c. plasma, microwave plasma) cannot be discussed by means of this model because the high densities (p--,2.2 g cm 3) disagree with NH values of about 20% (cf Fig. 9(a)) [51. For these layers, a more detailed model (introduction of a "diamond-like" component) should be applied as shown in ref. 19. For r.f.-sputtered layers, our simple model leads to some interesting conclusions. We will now distinguish two special cases: case A in which, single (isolated) aromatic carbon areas are embedded in a polymeric environment; case B, where single polymeric areas are embedded in an (extended) sp2-hybridized carbon environment. This division is not essential for p and N H values because p and NH only depend on the filling factor p. However, macroscopic properties which are sensitive to the degree of the localization of 7z electron states may change dramatically depending on the situation (A or B) realized. In fact, case B corresponds to extended H electron states, which is characteristic of graphite and should result in a more graphitic behaviour of the layer (high IR-absorption, high conductivity, anisotropy). For case A, I-I electron states may be considered as localized in small clusters (in analogy to the a-C models of Robertson and O'Reilly [21]), and a graphitic behaviour is not expected. According to the optical gaps determined for weakly absorbing samples, the size of such clusters should not exceed a few nanometres. It should be mentioned that case A (isolated sp 2 cluster) is close to semiempirical structural models of a-C:H, which are often applied in order to explain transparency and hardness of the layers, although a considerable fraction of threefold coordinated carbon atoms is well known to be present in the layer. Moreover, a random distribution of possible preferred directions of the clusters is sometimes directly postulated in order to obtain an isotropic layer model for a-C:H (cf. ref. 22). The experimental material presented here allows us to establish the hypothesis that this treatment is correct for weakly absorbing, insulating a-C:H but is insufficient for the description of strongly absorbing and conducting layers. Naturally, high absorptance and conduction may be explained in terms of extended threefold coordinated carbon areas. However, the distribution of preferred directions (if there are any) of these extended areas should be more complicated even if they are not isolated. We suppose that in this case
macroscopic anisotropy is possible. We will not attempt to present an adequate structural model for this situation here, but it seems likely that it may be close to the "defected graphite" model [23] proposed recently by Tamor and Wu, which seems suitable as a starting point for three-dimensional anisotropic a-C:H models. In terms of our mixing model, according to filling factors p (and consequently to p), the probability of the appearance of case A or B should vary. Considering the case of high p values ( p - , l), the medium should be composed of small sp2-hybridized areas embedded in a polymeric environment. Thus, the FI electron states are localized in small sp2-hybridized clusters. Following Robertson and O'Reilly [21], this will lead to sufficiently high optical gaps enabling the material to be IR transparent. IR absorption losses are mainly caused by more or less localized network vibrations, which allows us to describe the IR properties in terms of multioscillator models [10]. The single clusters may be anisotropic but, by considering a random distribution of preferred directions for these sp 2 clusters, the medium should be isotropic in a macroscopic sense. In general, one may consider that above some critical filling factor p >Pcrit.I only this isotropic case (case A) is possible. On the contrary, for p ~ 0 the situation is quite different from that mentioned above. Isolated sp 2 areas are not very probable now, and the situation realized is case B. Polymeric areas are now embedded in an sp 2 carbon environment. The extended spZ-hybridized areas allow the ~ electron states to be non-localized, lowering the gap and making the material strongly absorbing even in the IR region. Moreover, a preferred direction of the aromatic network may lead to macroscopic anisotropy. We shall consider that below some critical filling factor p < Pcrit.2 the material should be highly conducting, absorbing and, possibly, anisotropic. The most interesting case is Pcrit,2 < P < Pcrit.I
(1)
In principle, both cases A and B are possible here, which results in a possible ambiguity of macroscopic properties for filling factors p (or mass densities) satisfying eqn. (1). Of course, this is a very qualitative discussion. Quantitative treatment is difficult and demands knowledge of the form and size of the inclusions. However, some simple estimations may be carried out. The following discussion is to show that the experimentally obtained n(p) dependence, corresponding to strongly absorbing (graphitic) r.f.-sputtered layers (n > 2.2), may be explained in terms of our model as a consequence of the realization of case B. On the contrary, case A may be assigned to the typical refraction index behaviour of a-C:H (compare with microwave plasma-deposited and d.c. plasma-deposited layers).
M. Vogel et al. / Properties of amorphous C layers
A crude estimate of critical values Pcrit.l and PcriC2 may be obtained, for a moment considering our material to be built from spherical inclusions of material 1, embedded in a bulk environment of material 2. For such spheres, maximum volume fractions of the inclusions will be 0.74 of the common volume [24]. The simplest possibility is to assign this maximum volume fraction of spherical inclusions to the critical filling factor P~rit.t, which means Pcrit.l=0.74 (Pcrit. I = 1.32 g cm-3). Accordingly, Pcrit.2= 0.26 (Petit.2 = 1.89 g cm-3). In terms of this simple treatment, samples with (p > Pcrit.2 should exhibit a graphitic behaviour, which is in agreement with the experiment. For 0.26 < p < 0.74 (1.89 g cm -3 > p > 1.32 g cm-3), ambiguity of electrical and optical properties is allowed, which is confirmed by the experimental material. Moreover, we may now estimate refractive indices for case B, using typical ~ values for polymers and graphite and connecting them with a suitable mixing model. For polymers, hpot has been considered purely real without dispersion: nvo1= 1.4. For graphite, a complex ~ar has been taken into consideration, and the optical parameters have been taken from polycrystalline graphite [25]. The results obtained correspond to case B, because the use of graphitic optical functions is connected with the presence of extended rc electron states, which is realized only in case B and is possible in our model for mass densities p > Pcrit.l 1.32 g cm -3. Various mixing formulae have been tested to reproduce the experimental n(p) dependence in Fig. 5. The best agreement has been achieved by using the mixing formula found by Yadava and coworkers [26, 27] as a direct consequence of the L o r e n t z - L o r e n z equation: ~--
fi2(v' p) = (1 --p)(rtpol 2 q-- 2)rlcar2(V) q-p[~car2(V) ~- 2]npol 2 ( 1 --p)(r/pol 2 q- 2) + p[hc.r2(v) + 2] (2) In Fig. 9(b) resulting n values for v = 2400 cm -~ are plotted as a function of mass density (upper curve). The corresponding ~ values are not plotted, but are in the range 5000-15 000 cm- ~ for p values of 1.7-1.9 g cm-3 and thus agree with experimental values. The frequency dependences are not presented here: the refractive indices exhibit weak anomalous dispersion and absorption coefficients increase with wavenumber, similar to the experimental curves shown in Fig. 4 (upper curves). Treatment of case A (small isolated sp 2 clusters) is more complicated. The problem is to find a suitable approximation for no,r- Clearly, the IR response of small sp 2 clusters should significantly differ from that of bulk graphite, thus explaining the ambiguity of n(p) values. The lower curve in Fig. 9(b) has been obtained from eqn. (2) with an estimated ncar = 2.6 (purely real F/car : for estimation of near in case A see Appendix A).
203
On comparing calculated and measured n values one problem must be taken into account. The experimental n values have been determined by considering an isotropic layer material. For anisotropic materials, they only correspond to the special direction of the electric field vector realized in the actual measurement. This may explain the very high variance in the experimental n(p) dependence for r.f.-sputtered layers (Fig. 5, upper curve). On the contrary, reliable data on the dielectric tensor of graphite were not available. For that reason, a theoretical estimation of the variance of n values of the carbon layers according to different directions of the electric field vector was impossible. The optical parameters of graphite used for calculation have been taken from polycrystalline graphite and thus represent optical parameters averaged over directions. We may expect that they reflect the trend of the n(p) dependence, but excellent agreement cannot be expected. The above discussion was to show that the presence of anisotropy in r.f.-sputtered a-C:H layers may be explained in terms of a model that considers the layer to be built from large graphitic carbon areas and isolated polymeric components. However, the model does not yield any information about a crystallographic preferred direction in the layer. By means of electron diffraction of an X T E M sample (Fig. 8), it was shown that for anisotropic carbon layers deposited on silicon substrates the c axis of the hexagonal elementary cell of carbon is parallel to the (100) surface of the silicon substrate. This result represents the crystallographic explanation of the azimuthally anisotropic behaviour of the layer. In general, the effect of polarization-dependent normal incidence transmittance requires that the preferred direction should not be normal to the layer surface which is in agreement with the preferred direction found by electron diffraction. The reason for the appearance of azimuthal anisotropy in strongly absorbing r.f.-sputtered layers on [100]-oriented silicon surfaces is not fully understood. We believe that both the low deposition rate and the extremely high deposition temperature give rise to the very different properties in comparison with other layers. Connecting the results of X T E M investigations with our model, we may imagine the highly absorbing r.f.sputtered layers deposited onto silicon to be composed as schematically shown in Fig. 10. The observation direction of the diffraction pattern is the [011] direction normal to that in Fig. 10. The positions of the a and b axes of the hexagonal elementary cell are ambiguous. Comments on the interface region will be given in a later publication. Information on shape, size and arrangement of graphitic and polymeric parts is not available from the experimental material on the basis of the given model.
204
M. Vogel et al. / Properties o f amorphous C ko'ers
graph, t iclike
~ [10015, t
region
interface
region
s u b s t rclte
~
[0111%
Fig. I0. Polymeric areas embedded in a graphitic environment (model for anisotropic r.f.-sputtered layers on silicon).
Figure 10 suggests that the conductivity a s through the film should be higher than the planar conductivity a L. Our experimental data yield the opposite: a s < ae. However, we do not believe that this experimental fact is in disagreement with the model. Because of the finite size of the columnar parts, one cannot simply imagine graphitic planes crossing the whole film so that in fact the transverse conductivity as of the film must be lower than the in-plane conductivity of graphite. Therefore, because of the perhaps very complicated shape of the graphitic parts in the film, our model does not allow us to predict any correlation between a s and aL.
The authors thank Dr. J. Ullmann, Dr. G. Schaarschmidt, B. Mainz, S. Roth, and Dr. G. Schmidt for sample preparation as well as Professor Dr. W. Scharff and Dr. P. Barna for helpful discussions and L. Feige for technical assistance.
5. Conclusion
References
The electrical and optical properties of amorphous carbon layers have been discussed. The layers deposited by d.c. plasma as well as by microwave plasma are isotropic and exhibit high resistivities and an absorption behaviour typical of a-C:H films. Electron-beam-evaporated carbon layers have high conductivities. They are strongly absorbing and anisotropic. R.f.-sputtered layers represent some kind of intermediate between a-C:H films and evaporated films. The extraordinary behaviour of these layers may be explained by means of a simple model. The highly absorbing, conducting and anisotropic layers may be considered to be built
from large graphitic areas and polymeric components. The anisotropy of these layers could also be established by XTEM investigations.
Acknowledgments
1 H. C. Tsai and D. B. Bogy, J. Vac. Sci. Technol. A, 5(1987) 3287. 2 J. J. Hausser, J. Non-Cryst. Solids, 23 (1977) 21. 3 S. Roth, B. Rau, J. Ullmann, G. Schaarschmidt, O. Stenzel, W. Scharff and K. Hammer, in Proc. 7th CIMTEX, Montecatini Terme, June 1990. 4 Chr. Weissmantel, K. Bewilogua, K. Breuer, D. Dietrich, U. Ebersbach, H.-J. Erler, B. Rau and G. Reisse, Thin Solid Films, 96 (1982) 31. 5 W. Scharff, K. Hammer, O. Stenzel, J. Ullmann, M. Vogel, T. Frauenheim, B. Eibisch, S. Roth, S. Schulze and I. Muehling, Thin Solid Films, 171 (1989) 157. 6 J. Ullmann and G. Schmidt, Diamond Relat. Mater., 1 (1992) 321. 7 C. J. Adkins, S. M. Freake and E. M. Hamilton, Philos'. Mag., 7 (1971) 313.
M. Vogel et al. / Properties of amorphous C layers 8 0 . Stenzel, S. Roth and W. Scharff, Th& Solid Films, 190 (1990) 9. 9 O. Stenzel, V. Hopfe and P. Klobes, J. Phys. D, Appl. Phys., 24 (1991) 2088. 10 O. Stenzel, G. Schaarschmidt, F. Wolf, M. Vogel and T. Wallendorf, Thin Solid Films, 203 (1991) 11. 11 J. H. Kaufmann, S. Metin and D. D. Saperstein, Phys. Rev. B, 39 (1990) 13053. 12 T. Nakano, S. Koike and Y. Ohki, J. Phys. D, 23 (1990) 711. 13 R. Kalish, O. Amir, R. Brener, R. A. Spits and T. E. Derry, Appl. Phys. A, 52 (1991) 48. 14 Chr. Weissmantel, in K. J. Klabunde (ed.), Thin FilmsJ?om Free Atoms and Particles, Academic Press, New York, 1985, p. 153. 15 B. Dischler, A. Bubenzer and P. Koidl, Appl. Phys. Lett., 42 (1983) 636. 16 A. Bubenzer, B. Dischler, G. Brand and P. Koidl, J. Appl. Phys., 54 (1983) 4590. 17 L. C. Richard, MRS Symposia Proceedings, Vol. 152, Material Research Society, Pittsburgh, PA, 1982, p. 33. 18 K. Fabisiak, F. Rozploch and J. Wieczorek, J. Phys. D, 21 (1988) 995. 19 F. W. Smith, J. Appl. Phys,, 55 (1984) 764. 20 P. Couderc and Y. Catherine, Thin Solid Films, 146 (1987) 93. 21 J. Robertson and E, P. O'Reilly, Phys. Rev. B, 35 (1987) 2946. 22 D. R. McKenzie, R. C. McPhedran, N. Savvides and D. J. H. Cockayne, Thin Solid Films, 108 (1983) 247. 23 M. A. Tamor and C. H. Wu, J. AppL Phys., 67 (1990) 1007. 24 C. Kittel, Introduction to Solid State Physics, Wiley, New York, 4th edn., 1971. 25 V. I. Gavrilenko, A. M. Grechov, D. V. Korbutyak and V. G. Litovcenko, Opticeskie Svoistva Poluprovodnikov, Naukova Dumka, Kiev, 1987, 197. 26 G. N. Yadava, S. K. Macleod, S. Ogura and E. Pelletier, Thin Solid Films, 17(1973) 243. 27 M. Harris, H. A. Macleod, S. Ogura, E. Pelletier and B. Vidal, T/tin Solid Films, 57 (1979) 173.
Appendix A: Estimation of the dielectric IR response of small aromatic clusters Effective medium approximation studies of amorphous hydrogenated carbon (a-C:H) layers [All generally use the dielectric response of graphitic (evaporated) carbon for describing every sp 2 fraction in the layer. We believe that this treatment is correct for strongly absorbing layers with certainly extended aromatic carbon areas. However, the background for such a treatment in application to IR-transparent carbon layers is not very clear. We believe that in this case the starting point for estimating the dielectric IR response should be aromatic molecules (e.g. liquid benzene) rather than bulk graphite because these molecules provide the advantage that they exhibit localized n-electron states. In this study an attempt was made to find a workable model for the IR response of the clusters, using liquid benzene as a starting point. The result was used for the calculation of n(p) (Fig. 9) by eqn. (2). The density and IR refractive index of liquid benzene are p = 0.874 g cm 3 and n ~ 1.45 [A2], and the gap is 6 eV. A
205
simple estimation of the refractive index of small clusters of aromatic rings with a density of 2.2 g c m -3 is possible using the L o r e n t z - L o r e n z equation: n2--1
1
n2 + 2
3eo
N~
where N is the concentration of molecules and X the molecular polarizability. This estimation gives near = 2.7 for p = 2.2 g cm -3. However, the problem in this simple treatment is that the decrease in optical gap due to clustering cannot be considered. In fact, aromatic clusters are treated here as compressed benzene. We have, therefore, tried to find another estimation of n .... taking the decrease in the optical gap due to clustering into account. The K r a m e r s - K r o n i g relation is the starting point: n 2(00) _ 1
2 f 00'e"(00') = n J 0 0 ,2 - 002 d00' 0
where e" is the imaginary part of the dielectric function. If absorption (e" ~ 0) is restricted to a spectral region ((D I ,¢..O2) , and co is beyond this range (00 < 001,002), this equation may be rewritten: oJ2
n2(00) - 1
2 f 00'#'(co') 2 00oe"(~o0) = ~ J 00,2 0 0 ~__ dco' ~ -n 00o--00-~, (co2 - col ) ~o 1 (D O ¢Od
0002 -- (0 2
This equation is identical with Wemple's dispersion relation [A3]. coo is between ~oI and 002 and represents some kind of a resonance frequency of a one-oscillator model. This resonance frequency decreases with increasing size (and mass density) of aromatic clusters. For estimation, we will identify 000 with the gap E o so that for benzene 000 corresponds to a photon energy of 6 eV, while for aromatic clusters 000 corresponds to photon energies of 1.0-1.5 eV. In application to the IR, co2 ,~ 0002, and thus /7 2 IR,benzene ~
l -t- (Od'benzene (D0,benzene
n~a r = 1 + 00d,clusterr (DO,cluster
If cod is identical for all clusters including the single benzene ring we obtain finally: H c2a r =
1 - ~ - ( g / b2 . . . . . .
-- l)(J)0.b ...... (D0.cluster
= 1 + 1.1 co0,ben.... (D0,cluster
Typically, coo,b...... /00Ox~uster= 4 - 6 , leading to n~,~ = 2.4-2.8. Obviously, the results of both estimation
206
M. Vogel et al. / Properties of amorphous C layers
procedures are in surprisingly good agreement. In our mixing model, an near value of 2.6 has been applied. We suppose that this approximation is an alternative to the application of bulk graphite dielectric functions to IRtransparent a-C(:H).
References A1 P. Couderc and Y. Catherine, Thin Solid Films, 146 (1987) 93. A2 T. G. Goplen, D. G. Canieron and R. N. Jones, Appl. Spectrose 34 (1980) 657. A3 S. H. Wemple, Phys. Rev. B, 7 (1973) 3767.