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Correlation of residual stress with optical absorption edge in diamond-like carbon films
Diamond and Related Materials 12 (2003) 1576–1583
Correlation of residual stress with optical absorption edge in diamond-like carbon films Sushil Kumar*, P.N. Dixit, O.S. Panwar, R. Bhattacharyya Thin Film Technology Group, National Physical Laboratory, Dr K.S. Krishnan Road, New Delhi 110 012, India Received 13 September 2002; received in revised form 6 June 2003; accepted 20 June 2003
Abstract A correlation has been observed between the residual stress and the optical absorption edge of diamond-like carbon films and on the basis of this correlation, an empirical relation has been established between the Urbach energy (E0 ) and the residual stress (S) in the films given by E0 sE00 qmS, where E00 s140 meV and ms37 meVyGPa. The residual stress and the optical absorption edges of diamond-like carbon films, grown by different techniques, are then discussed in terms of amount of disorder in the network. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Diamond-like carbon; Stress; Optical absorption edge; Disorder
1. Introduction In the crystalline semiconductors, the width of the exponential absorption tail is a measure of the temperature induced disorder, due to the thermal occupancy of phonon states in the crystal. In amorphous semiconductors there is an additional non-thermal component to the disorder, i.e. structural disorder due to the nature of random network, which is exhibited by the existence of an Urbach edge w1,2x. Cody et al. w3x have expressed similar views and they determined the relative magnitude of the thermal and structural disorder in hydrogenated amorphous silicon (a-Si:H) films from the measured optical absorption edge as a function of temperature of a-Si:H films studied. They found that both the width of the exponential edge and the optical bandgap are controlled by the amount of disorder (structural and thermal) in the network. An interesting correlation has also been observed by Stutzmann w4x between the residual stress (S) in a-Si:H films and the creation of metastable dangling bonds. Datta et al. w5x studied optical absorption edge and disorder effects in a-C:H films as a function of heat treatment. In an important publication, Maity et al. w6x have proposed a model to *Corresponding author. Tel.: q91-1125742610; fax: q911125726938. E-mail address: [email protected] (S. Kumar).
evaluate the stress and hardness in the polycrystalline thin films from the broadening of the absorption band tail. All these studies present strong evidences that, perhaps, a close relation exists among the stress, the disorder and the optical absorption edge of amorphousy polycrystalline thin films. This is not limited to a particular type of material and is rather universal in nature. We, however, restrict, in the present study, our discussion to diamond-like carbon (DLC) films. Diamond-like carbon (DLC) films (this includes tetrahedral amorphous carbon i.e. ta-C also) generally exhibit large values of S (1–10 GPa) w7,8x. Such high values of S can significantly alter the mechanical, electrical and optical properties of these thin films. A correlation has been observed to exist between S and E0, which is generally considered a measure of disorder in the material, which we wish to present in this article. 2. Formulation of stress and optical absorption edge with disorder Stresses, present in these materials, arise from various causes and depending upon those causes they can be classified into: thermal, intrinsic and extrinsic stress w9x. Thus, the total stress (Stotal) in a film can be expressed as a sum of all the types of stresses,
0925-9635/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-9635(03)00245-0
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
StotalsStqSiqSe
(1)
where St is the thermal stress, Si is the intrinsic stress and Se is the extrinsic stress. Analogous to the above formulation, as the residual stress is found to be a measure of disorder in the film, the total disorder NDtotalM can also be expressed as a sum of all the types of disorder which can be written as, NDtotalMsNDtMqNDiMqNDeM
(2)
where the disorder NDtM arises due to the thermal stresses, the disorder NDiM is attributed to the intrinsic stresses and the disorder NDeM relates to the extrinsic stress. The disorder NDtM, has its origin within the difference between the mean coefficients of thermal expansion of the substrate and the film. This is manifested when there exists a difference in the measurement temperature (Tm) compared with the deposition temperature (Td) of the a-C:H films. The disorder, NDiM is determined by the nature of both the film and the substrate and this is fundamentally related to the process of deposition of the film. In other words, growth parameters of the film, such as temperature, pressure, concentration of reactant, impurity incorporation, etc., significantly influence the state of the stress. In general, Si is generated by the atoms or ions, which are not found to be in their lowest energy configuration in the deposited film. The disorder NDeM is caused by the structural changes, which also produce dimensional changes. Most of these films are also subjected to an increase in the density due to the structural evolution, such as the crystallization of the amorphous phase or its densification, which leads to the film shrinkage and the resultant stresses in the films. In addition, ambient interactions in the film such as hydration or dehydration can also result in dimensional changes, which also result in creating additional stresses in the film. Since there is less possibility of structural changes taking place in DLC film studied here, which are grown at room temperature, extrinsic disorder NDeM term will be a negligible quantity in Eq. (2). Thus, we are left with the part of disorder, which arises, only from the Si and St type of stresses. Thus, Eq. (2) can be rewritten, in our case as: NDtotalMsNDiMqNDtM
(3)
When Td and Tm are the same then it seems that there will be no St in the film. Thus, the thermal part in the disorder, due to St can be taken to be negligible. This way, we can evaluate NDiM in the DLC films in terms of Si, and thus Eq. (3) reduces to NDtotalMsNDiM
(4)
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We will now attempt to see how optical absorption and stress are related to the disorder in the DLC films. It is believed that in hydrogenated amorphous materials like a-Si:H, a-Ge:H the network is distorted, mainly due to the deviation in the bond angle, which is responsible for the occurrence of the tail states w10x. However, in aC:H system the situation is more complicated because besides sp3 bonding sp2 or even sp1 hybdrization may also occur and this makes a-C:H network more distorted w11x. Compressive stress (S) arises when atoms or ions with energies of several eV bombard the growing film by a process of atomic penning w12x. The energetic ions cause atoms to be incorporated into spaces in the growing films, which are smaller than the usual atomic volume, and this leads to an expansion of the film outwards from the substrate. In the plane of the film, however, the film is not free to expand and the entrapped atoms distort the network. This distortion may be referred to as ‘disorder’ and that lead to a situation of very large values of S in these DLC films. Also, band tailing in the optical absorption spectra of DLC films (characterized by E0) is a measure of disorder. This disorder may be a sum of structural disorder due to the random network and temperature induced thermal disorder, due to the thermal occupancy of phonon states. These two contribute to the localized states in these films. The presence of such localized states are again referred to as ‘disorder’ in a-C:H films. Thus, in the present investigation the word ‘disorder’ is related to both S and E0. This way the additional bonds that need to be accommodated in an overconstrained network cause compressive stress, owing to the increased bond stretching and bond bending, which may be reflected in the band tailing in the observed optical absorption spectra of these DLC films. Thus, Eq. (4) can be expressed as: NDtotalMsNDiMsNDBAMqNDBLM
(5)
where NDBAM is the disorder due to the bond angle distortion and NDBLM is the disorder due to the bond length distortion. a-C:H system can be visualized as a ensemble of tetrahedral sp3 bonding, leading to a diamond-like network and trigonal sp2 bonding, leading to a graphite-like network w13,14x. Of course, some sp1 hybridized hydrocarbon polymer structure may also be present, which we are neglecting here. Thus, Eq. (5) can be rewritten as: NDtotalMsNDiMsNDBAMDiamondqNDBAMGraphite qNDBLMDiamondqNDBLMGraphite
(6)
where NDBAMDiamond and NDBAMGraphite are the disorders that arise due to the bond angle distortion of diamondlike component and graphite-like component, respectively, and similarly NDBLMDiamond and NDBLMGraphite are the
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disorder due to the bond length distortion of diamondlike component and graphite-like component, respectively, of the a-C:H films. The presence of two bonding types i.e. sp3 and sp2 structure in a-C:H films are found to be somewhat segregated and clustered w15x. The sp3 sites possess only s bonds whereas sp2 sites possess both s and p bonds. Thus, the structure of DLC film is very complex and it becomes difficult to classify its structure in terms of bond angle and bond length as it exists in other amorphous materials like a-Si:H, where only one type i.e. sp3 bonding is predominant. It is estimated that the fluctuations of bond lengths and bond angles are within "1% and "10%, respectively, in amorphous semiconductors w16x. Since the optical absorption in DLC films is primarily due to the p states of carbon, the observed changes in the E0 value may be due to the changes in just the behavior of the p states. However, the increase of stress in DLC films generally correlates with the increase in the sp3 ysp2 bonding ratio. Hence, the number of sp2 bonds decreases with stress. Therefore, the increase in E0 values with increasing stress may be due to an increase in the disorder involving just the sp2 bonds as the number of sp2 bonds decreases, i.e. the smaller number of sp2 bonds at higher residual stress levels may be more disordered. Further, the disorder involving the sp3 bonds could actually be decreasing or remaining unchanged, as the number of sp3 bonds increases with higher stress level. Because the bandgap for the carbon atoms in sp3 states is actually larger than those in sp2 states, the study of E0 parameter may not be indicative of the sp3 bonding disorder. Therefore, the E0 parameter may be related to the disorder of only a subset of the bonds in the material (i.e. p bonds) and it is not directly indicative of the overall disorder of the entire material. In the present investigation we have used the models and concepts of a-Si:H up to a certain extent for the discussion in a-C:H films. The most significant difference between a-C:H network and a-Si:H network is the inability of silicon to form sp2 bonds. Carbon may form both s and p bonding, whereas, silicon can form only s bonding. Therefore, careful attention is needed to apply the models of a-Si:H to a-C:H. In spite of the differences between them, many of the basic properties of a-C:H, such as the nature of amorphous state, imperfect tetrahedral bonding and the relaxation of structure by hydrogen, etc. are found to be similar to those of aSi:H w17x. Therefore, to an extent one may borrow some of the concepts from a-Si:H to interpret the experimental results relating to a-C:H. 3. Experimental In order to attempt an experimental verification of the above formulation, we have grown three different types
of DLC films using C2H2 gas on well cleaned Corning 7059 glass substrates and polished silicon wafers in an asymmetric rf PECVD reactor. We have chosen two frequencies (namely 13.56 and 100 MHz) as also pulsing of 13.56 MHz discharge (modulation). Other details about the deposition of the films and the reactor have already been reported elsewhere w18–21x. As a matter of fact choosing a number of techniques for growing DLC films has enabled us to have films of widely different stress values. We have measured the absorption coefficient (a) at different photon energies (hn) using a photothermal deflection spectroscopy (PDS) set-up w22x and the S values using a semiconductor laser based scanning technique w23x. The values of E0 were estimated from the plot of optical absorption coefficient (a) vs. photon energy (hn). This plot for most of the DLC films studied here and grown by various techniques is presented in Fig. 1a–c. The a data for the DLC films were also obtained from reflection and transmission (R and T) measurement. The a values evaluated by both PDS and R and T method above 1.7 eV energy closely matches. The values of optical band gap (Eg) of these DLC films were determined from the intercept of 6ahn vs. hn curve to the xaxis. 4. Results and discussion Fig. 2 shows E0 vs. S plot for DLC films grown by different techniques. It is also evident from the figure that E0 values are smaller for pulse plasma grown DLC films than RF grown DLC films, whereas for VHF grown DLC films, it lies between the values of RF grown DLC films and pulse plasma grown DLC films. These values of E0 were found to be in the range of 149–165 meV, 186–264 meV and 252–311 meV for DLC films grown using pulse, VHF and RF plasma techniques, respectively. Broad band tails are usually found in a-C:H, and the values of E0 are frequently over 500 meV w24x; but somewhat narrower tails (E0f150– 300 meV) have also been seen in a-C:H by Dischler et al. w25x and Schutte et al. w26x. The values of E0 in a highly tetrahedral hydrogenated amorphous carbon (taC:H) are found to be ;350 meV w27x. Thus, the values of E0 evaluated for DLC films grown by RF, VHF and Pulse plasma techniques in the present study, are found to be comparable to the values of E0 (150–500 meV) for DLC films reported in the literature w24–27x. Again, change in E0 values is found to be consistent with the variation of S values in these DLC films. Pulse plasma grown DLC films recorded smaller value of E0 than the cw discharge grown DLC films. This could mean pulsed discharge grown DLC films are less disordered than cw discharge grown DLC films. This is found to be consistent with the low values of S observed for the pulse plasma grown DLC films. It is also evident
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
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Fig. 1. (a) Variation of optical absorption coefficient (a) vs. photon energy (hn) for DLC films grown by rf technique; (b) Variation of optical absorption coefficient (a) vs. photon energy (hn) for DLC films grown by VHF pulse technique; and (c) Variation of optical absorption coefficient (a) vs. photon energy (hn) for DLC films grown by pulse technique.
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Fig. 2. Variation of Urbach energy (E0) vs. residual stress (S) for DLC films grown by various techniques.
from this figure that with the increase of S values, the values of E0 also increase, for all types of DLC films studied. Since E0 is a measure of disorder in the material and an increase in E0 values implies an increase of the disorder in the material. One can thus conclude that the S and the disorder of the material may be interrelated. From the analysis of the result of Fig. 2, a quantitative relationship between the values of E0 and S, was deduced as follows: E0sE00qmS
(7)
where, m is a constant which is the slope of the straight line drawn between E0 vs. S curve, E00 is a constant which represents the minimum E0 value in this type of material and is the intercept of the straight line of the E0 vs. S curve which corresponds to the zero S value. The values of E00 and m are found to be 140 meV and 37 GPaymeV, respectively. From these observations, it becomes clear that in the network of a-C:H reduction of E0 value less than 140 meV may not be possible. It is seen that a-C:H (DLC) films are highly disordered as compared to a-Si:H films. The values of E0 for c-Si and a-Si:H have been reported as 8.6 meV and 40 meV, respectively w28x. Further, the change in the observed values of E0 are found to be consistent with the change in the optical properties of DLC films of varying S values, i.e. with the increase of E0, the values of Eg decrease as shown in Fig. 3. However, there appears to be some small inconsistency in this behavior, which can, perhaps be attributed to the change of the technique for growing these films. In a study by O’Leary, it has been mentioned that Eg is found to be insensitive to the amount of
disorder w29x. In contrast, a quantitative relation between the values of Eg and E0 in a-Si:H films has been reported by Cody et al. w30x, which has also been confirmed by us w31x. It is found that the values of E0 decrease with the increase of Eg. Such quantitative relationship has earlier been reported by other groups w3,5,32x for a-Si:H, a-C:H and a-SiC:H systems. It is important to mention here that the value of Eg in all form of amorphous carbon is decided by p states. Since p states are weakly bound in a-C:H, they lie closer to the Fermi level compared to the s states. Consequently, the filled p states form the valence band and the empty p* states form the conduction band and thereby the size of Eg is determined. Whereas in a-Si:H system, Eg is decided entirely by the s states.
Fig. 3. Variation of Urbach energy (E0 ) vs. optical bandgap (Eg) for DLC films grown by various techniques.
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
It is reasonable to assume that S values for the films deposited at room temperature will mostly be governed by the structural disorder in the films, whereas the S values for the films deposited at higher temperatures, disorder may have two components i.e. structural and thermal disorder. In the case of rf self bias deposited DLC films, structural and thermal disorder are always present, even if there is no deliberate heating of the substrates, since substrates are anyway heated by ionic bombardment. Yamada et al. w33x, in a study of DLC films grown using rf self bias technique, found that as a result of the ion impact, Ts is found to increase and, thus it becomes difficult to maintain Td. Keeping this point in mind, Yamada et al. w33x have grown DLC films using a pulse plasma discharge technique. Earlier studies of DLC films grown by pulse plasma growth technique reported by us w20x, which shows that Ts does not raise due to the ionic bombardment, as during OFF time of the pulse, substrate gets cooled. Thus, in pulse plasma grown DLC films, at room temperature, only the structural disorder is expected to dominate. In the present study, we have estimated the rise of Ts for the rf self bias deposited DLC films from Fig. 4. It is to be noted that the energy of the bombarding ions on the substrate increases with the increase of applied power, which causes the enhancement of Ts. Fig. 4 indicates a rise in Ts from 30 to 80 8C kept at the cathode, with the change of self bias voltage from 0 to 400 V for the discharge, sustained using C2H2 gas. By estimating the values of Td from Fig. 4, at different self bias voltages and comparing it with the values of E0 corresponding to the DLC films grown at different self bias voltages from Table 1, one obtains the values of
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Table 1 Properties of DLC films grown using C2 H2 gas by RF (13.56 MHz), VHF (100 MHz) and pulse plasma techniques at constant pressure (25 mTorr) and flow rate (3.2 sccm) Sample No. Power density Self bias (Wycm2) voltage (V)
Residual E0 Eg Stress, S (meV) (eV) (GPa)
RF (13.56 MHz) CRF-7 0.10 CRF-8R 0.20 CRF-9R 0.30 DCRF-1 0.42
y98 y150 y250 y300
3.60 3.80 4.40 4.60
252 259 298 311
1.75 1.40 1.25 1.15
VHF (100 MHz) CHF-2 0.10 CHF-1 0.20 CHF-3 0.30 DCHF-5 0.10 DCHF-1 0.10 DCHF-3 0.10
y7.43 y19.95 y39.67 y(10q0) y(10q230) y(10q390)
1.70 1.75 1.99 1.70 2.20 2.90
196 202 242 204 244 264
1.55 1.45 1.40 1.60 1.55 1.60
Pulse CP-1 CP-2 CP-4 CP-3
– – – –
0.13 0.28 0.31 0.37
– 149 163 165
1.60 1.48 1.35 1.00
0.42 1.00 1.50 2.00
E0 at different temperatures. E0 values thus evaluated at different temperatures are shown in Fig. 5. It is evident from Fig. 5 that E0 increases with the increase of the Td. It is revealed from Fig. 5 that the minimum values of E0s140 meV is obtained for a temperature corresponding to 0 8C, which is found to be the same as that deduced from Eq. (7). This corresponds to the situation of absolutely no residual stress. From this result it is evident that the value of E0f140 meV evaluated,
Fig. 4. Variation of the substrate temperature vs. the self-bias voltage for the rf self bias deposited DLC films.
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
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Fig. 5. Variation of Urbach energy (E0) vs. the substrate temperature for the rf self bias deposited DLC films.
corresponds to the structural disorder only in the a-C:H family of materials. Thus, it becomes quite evident that there is a one-to-one correlation between the residual stress (S) and the disorder present in these films. From the present studies, it appears that in order to minimize the value of E0 in a-C:H films, deposition parameter should be chosen in such a way so that one can get minimum values of S. But we have seen in the present investigation that even pulse plasma grown DLC films with S values ranging from 0.1 to 0.4 GPa, show significantly higher values of E0, in the range of 140– 165 meV, compared to the lowest value of E0f40–50 meV obtained in a-Si:H films. Typical opto-electronic grade a-Si:H films grown using glow discharge technique, show S values in the range of 0.1–0.8 GPa with E0f50 meV w34x. These higher values of E0 obtained for a-C:H films may be due to the complex bonding arrangements of carbon than silicon, on account of its ability to form sp1, sp2 and sp3 hybridization. Further, carbon structure has more phonon assisted vibrations compared to silicon structure w35x that may also contribute to some part of the disorder in a-C:H films. Thus, from all that has been said so far it appears that a-C:H film with minimum value of E0f140 meV may be considered in quality as equivalent to a-Si:H films with E0f40 meV w28,36x. This minimum value of E0 observed in the a-Si:H and a-C:H may be the lower limit of the best quality material produced to date. E0s 8 meV has been observed to be the lower limit in case of c-Si w28x. 5. Conclusions The residual stress (S) and the Urbach energy (E0) of diamond-like carbon films have been discussed in
terms of disorder in the carbon network. A correlation has been observed to exist between the residual stress (S) and Urbach energy (E0) in these films. From the observed correlation, it is further inferred that the Urbach energy (E0) in DLC (a-C:H) films less than 140 meV may not be possible. Acknowledgments Authors are grateful to the Director, National Physical laboratory, New Delhi for his kind permission to publish this article and acknowledge with thanks Dr D. Sarangi and Dr C. Mukherjee, our past colleagues, for many valuable discussions. Authors also wish to acknowledge Department of Science and Technology, Govertment of India for providing financial assistance. References w1x J. Tauc, Mater. Res. Bull. 5 (1970) 721. w2x H. Oheda, Jpn. J. Appl. Phys. 18 (1979) 1973. w3x G.D. Cody, T. Tiedje, B. Abeles, B. Brooks, Y. Goldstein, Phys. Rev. Lett. 47 (1981) 1480. w4x M. Stutzmann, Appl. Phys. Lett. 47 (1985) 21. w5x T. Datta, J.A. Woollam, W. Notohamiprodjo, Phys. Rev. B 40 (1989) 5956. w6x A.B. Maity, M. Basu, S. Chaudhuri, A.K. Pal, J. Phys D:Appl. Phys. 28 (1995) 2547. w7x K. Enke, Thin Solid Films 80 (1981) 227. w8x C. Weissmantal, C. Schurer, F. Frohlich, P. Grau, H. Lehmann, Thin Solid Films 61 (1979) L5. w9x S.B. Desu, Phys. Stat. Sol. (a) 141 (1994) 119. w10x P. Hess, Thin Solid Films 241 (1994) 318. w11x J. Robertson, J. Non-Cryst. Solids 137–138 (1991) 825. w12x F.M. d’Heurle, J.M.E. Harper, Thin Solid Films 171 (1989) 81.
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583 w13x D.G. McCulloch, D.R. Mckenzie, C.M. Goringe, Phys. Rev. B 61 (2000) 2349. w14x A.C. Ferrari, A. Libassi, B.K. Tanner, V. Stolojan, Y. Yuan, L.M. Brown, et al., Phys. Rev. B 62 (2000) 11089. w15x J. Robertson, Adv. Phys. 35 (1986) 317. w16x K. Morigaki, Physics of Amorphous Semiconductors, World Scientific-Imperial College Press, London, 1999. w17x D. Dasgupta, C. De’Martino, F. Demichelis, A. Tagliaferro, J. Non-Cryst. Solids 164–166 (1993) 1147. w18x P.N. Dixit, S.P. Verma, O.S. Panwar, T. Seth, D. Gupta, R. Bhattacharyya, Infrared Phys. Technol. 35 (1994) 617. w19x S. Kumar, P.N. Dixit, D. Sarangi, R. Bhattacharyya, Appl. Phys. Lett. 69 (1996) 49. w20x S. Kumar, P.N. Dixit, D. Sarangi, R. Bhattacharyya, J. Appl. Phys. 85 (1999) 3866. w21x S. Kumar, D. Sarangi, P.N. Dixit, O.S. Panwar, R. Bhattacharyya, Thin Solid Films 346 (1999) 130. w22x W.B. Jackson, N.M. Amer, Phys. Rev. B 25 (1982) 5559. w23x A.K. Sinha, H.J. Levinstein, T.E. Smith, J. Appl. Phys. 49 (1978) 2423. w24x D. Das Gupta, F. Demichelis, C.F. Pirri, A. Tagliaferro, Phys. Rev. B 43 (1991) 2131.
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w25x B. Dischler, A. Bubenzer, P. Koidl, Appl. Phys. Lett. 42 (1983) 2131. w26x S. Schutte, S. Will, H. Mell, W. Fuhs, Diamond Relat. Mater. 2 (1993) 1360. w27x M. Weiler, S. Sattel, T. Giessen, K. Jung, H. Ehrhardt, V.S. Veerasamy, et al., Phys. Rev. B 53 (1996) 1594. w28x G.D. Cody, J. Non-Cryst. Solids 141 (1992) 3. w29x S.K. O’Leary, Appl. Phys. Lett. 72 (1998) 1332. w30x G.D. Cody, B. Abeles, B. Brooks, P. Persan, C.R. Wronski, J. Non-Cryst. Solids 59–60 (1983) 325. w31x O.S. Panwar, C. Mukherjee, R. Bhattacharyya, Sol. Energy Mater. Sol. Cells 57 (1999) 373. w32x F. Zhang, H. Xue, Z. Song, Y. Guo, G. Chen, Phys. Rev. B 46 (1992) 4590. w33x H. Yamada, O. Tsuji, P. Wood, Thin Solid Films 270 (1995) 220. w34x K.S. Stevens, N.M. Johnson, Mat. Res. Soc. Symp. Proc. 219 (1991) 715. w35x M.N. Yoder, in: R.E. Clausing, et al. (Eds.), I, Diamond and Diamond-like Films and Coatings, 266, Plenum, New York, 1991, p. 4. w36x T. Tiedje, J.M. Cebulka, Phys. Rev. B 28 (1983) 7075.
Correlation of residual stress with optical absorption edge in diamond-like carbon films Sushil Kumar*, P.N. Dixit, O.S. Panwar, R. Bhattacharyya Thin Film Technology Group, National Physical Laboratory, Dr K.S. Krishnan Road, New Delhi 110 012, India Received 13 September 2002; received in revised form 6 June 2003; accepted 20 June 2003
Abstract A correlation has been observed between the residual stress and the optical absorption edge of diamond-like carbon films and on the basis of this correlation, an empirical relation has been established between the Urbach energy (E0 ) and the residual stress (S) in the films given by E0 sE00 qmS, where E00 s140 meV and ms37 meVyGPa. The residual stress and the optical absorption edges of diamond-like carbon films, grown by different techniques, are then discussed in terms of amount of disorder in the network. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Diamond-like carbon; Stress; Optical absorption edge; Disorder
1. Introduction In the crystalline semiconductors, the width of the exponential absorption tail is a measure of the temperature induced disorder, due to the thermal occupancy of phonon states in the crystal. In amorphous semiconductors there is an additional non-thermal component to the disorder, i.e. structural disorder due to the nature of random network, which is exhibited by the existence of an Urbach edge w1,2x. Cody et al. w3x have expressed similar views and they determined the relative magnitude of the thermal and structural disorder in hydrogenated amorphous silicon (a-Si:H) films from the measured optical absorption edge as a function of temperature of a-Si:H films studied. They found that both the width of the exponential edge and the optical bandgap are controlled by the amount of disorder (structural and thermal) in the network. An interesting correlation has also been observed by Stutzmann w4x between the residual stress (S) in a-Si:H films and the creation of metastable dangling bonds. Datta et al. w5x studied optical absorption edge and disorder effects in a-C:H films as a function of heat treatment. In an important publication, Maity et al. w6x have proposed a model to *Corresponding author. Tel.: q91-1125742610; fax: q911125726938. E-mail address: [email protected] (S. Kumar).
evaluate the stress and hardness in the polycrystalline thin films from the broadening of the absorption band tail. All these studies present strong evidences that, perhaps, a close relation exists among the stress, the disorder and the optical absorption edge of amorphousy polycrystalline thin films. This is not limited to a particular type of material and is rather universal in nature. We, however, restrict, in the present study, our discussion to diamond-like carbon (DLC) films. Diamond-like carbon (DLC) films (this includes tetrahedral amorphous carbon i.e. ta-C also) generally exhibit large values of S (1–10 GPa) w7,8x. Such high values of S can significantly alter the mechanical, electrical and optical properties of these thin films. A correlation has been observed to exist between S and E0, which is generally considered a measure of disorder in the material, which we wish to present in this article. 2. Formulation of stress and optical absorption edge with disorder Stresses, present in these materials, arise from various causes and depending upon those causes they can be classified into: thermal, intrinsic and extrinsic stress w9x. Thus, the total stress (Stotal) in a film can be expressed as a sum of all the types of stresses,
0925-9635/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0925-9635(03)00245-0
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
StotalsStqSiqSe
(1)
where St is the thermal stress, Si is the intrinsic stress and Se is the extrinsic stress. Analogous to the above formulation, as the residual stress is found to be a measure of disorder in the film, the total disorder NDtotalM can also be expressed as a sum of all the types of disorder which can be written as, NDtotalMsNDtMqNDiMqNDeM
(2)
where the disorder NDtM arises due to the thermal stresses, the disorder NDiM is attributed to the intrinsic stresses and the disorder NDeM relates to the extrinsic stress. The disorder NDtM, has its origin within the difference between the mean coefficients of thermal expansion of the substrate and the film. This is manifested when there exists a difference in the measurement temperature (Tm) compared with the deposition temperature (Td) of the a-C:H films. The disorder, NDiM is determined by the nature of both the film and the substrate and this is fundamentally related to the process of deposition of the film. In other words, growth parameters of the film, such as temperature, pressure, concentration of reactant, impurity incorporation, etc., significantly influence the state of the stress. In general, Si is generated by the atoms or ions, which are not found to be in their lowest energy configuration in the deposited film. The disorder NDeM is caused by the structural changes, which also produce dimensional changes. Most of these films are also subjected to an increase in the density due to the structural evolution, such as the crystallization of the amorphous phase or its densification, which leads to the film shrinkage and the resultant stresses in the films. In addition, ambient interactions in the film such as hydration or dehydration can also result in dimensional changes, which also result in creating additional stresses in the film. Since there is less possibility of structural changes taking place in DLC film studied here, which are grown at room temperature, extrinsic disorder NDeM term will be a negligible quantity in Eq. (2). Thus, we are left with the part of disorder, which arises, only from the Si and St type of stresses. Thus, Eq. (2) can be rewritten, in our case as: NDtotalMsNDiMqNDtM
(3)
When Td and Tm are the same then it seems that there will be no St in the film. Thus, the thermal part in the disorder, due to St can be taken to be negligible. This way, we can evaluate NDiM in the DLC films in terms of Si, and thus Eq. (3) reduces to NDtotalMsNDiM
(4)
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We will now attempt to see how optical absorption and stress are related to the disorder in the DLC films. It is believed that in hydrogenated amorphous materials like a-Si:H, a-Ge:H the network is distorted, mainly due to the deviation in the bond angle, which is responsible for the occurrence of the tail states w10x. However, in aC:H system the situation is more complicated because besides sp3 bonding sp2 or even sp1 hybdrization may also occur and this makes a-C:H network more distorted w11x. Compressive stress (S) arises when atoms or ions with energies of several eV bombard the growing film by a process of atomic penning w12x. The energetic ions cause atoms to be incorporated into spaces in the growing films, which are smaller than the usual atomic volume, and this leads to an expansion of the film outwards from the substrate. In the plane of the film, however, the film is not free to expand and the entrapped atoms distort the network. This distortion may be referred to as ‘disorder’ and that lead to a situation of very large values of S in these DLC films. Also, band tailing in the optical absorption spectra of DLC films (characterized by E0) is a measure of disorder. This disorder may be a sum of structural disorder due to the random network and temperature induced thermal disorder, due to the thermal occupancy of phonon states. These two contribute to the localized states in these films. The presence of such localized states are again referred to as ‘disorder’ in a-C:H films. Thus, in the present investigation the word ‘disorder’ is related to both S and E0. This way the additional bonds that need to be accommodated in an overconstrained network cause compressive stress, owing to the increased bond stretching and bond bending, which may be reflected in the band tailing in the observed optical absorption spectra of these DLC films. Thus, Eq. (4) can be expressed as: NDtotalMsNDiMsNDBAMqNDBLM
(5)
where NDBAM is the disorder due to the bond angle distortion and NDBLM is the disorder due to the bond length distortion. a-C:H system can be visualized as a ensemble of tetrahedral sp3 bonding, leading to a diamond-like network and trigonal sp2 bonding, leading to a graphite-like network w13,14x. Of course, some sp1 hybridized hydrocarbon polymer structure may also be present, which we are neglecting here. Thus, Eq. (5) can be rewritten as: NDtotalMsNDiMsNDBAMDiamondqNDBAMGraphite qNDBLMDiamondqNDBLMGraphite
(6)
where NDBAMDiamond and NDBAMGraphite are the disorders that arise due to the bond angle distortion of diamondlike component and graphite-like component, respectively, and similarly NDBLMDiamond and NDBLMGraphite are the
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disorder due to the bond length distortion of diamondlike component and graphite-like component, respectively, of the a-C:H films. The presence of two bonding types i.e. sp3 and sp2 structure in a-C:H films are found to be somewhat segregated and clustered w15x. The sp3 sites possess only s bonds whereas sp2 sites possess both s and p bonds. Thus, the structure of DLC film is very complex and it becomes difficult to classify its structure in terms of bond angle and bond length as it exists in other amorphous materials like a-Si:H, where only one type i.e. sp3 bonding is predominant. It is estimated that the fluctuations of bond lengths and bond angles are within "1% and "10%, respectively, in amorphous semiconductors w16x. Since the optical absorption in DLC films is primarily due to the p states of carbon, the observed changes in the E0 value may be due to the changes in just the behavior of the p states. However, the increase of stress in DLC films generally correlates with the increase in the sp3 ysp2 bonding ratio. Hence, the number of sp2 bonds decreases with stress. Therefore, the increase in E0 values with increasing stress may be due to an increase in the disorder involving just the sp2 bonds as the number of sp2 bonds decreases, i.e. the smaller number of sp2 bonds at higher residual stress levels may be more disordered. Further, the disorder involving the sp3 bonds could actually be decreasing or remaining unchanged, as the number of sp3 bonds increases with higher stress level. Because the bandgap for the carbon atoms in sp3 states is actually larger than those in sp2 states, the study of E0 parameter may not be indicative of the sp3 bonding disorder. Therefore, the E0 parameter may be related to the disorder of only a subset of the bonds in the material (i.e. p bonds) and it is not directly indicative of the overall disorder of the entire material. In the present investigation we have used the models and concepts of a-Si:H up to a certain extent for the discussion in a-C:H films. The most significant difference between a-C:H network and a-Si:H network is the inability of silicon to form sp2 bonds. Carbon may form both s and p bonding, whereas, silicon can form only s bonding. Therefore, careful attention is needed to apply the models of a-Si:H to a-C:H. In spite of the differences between them, many of the basic properties of a-C:H, such as the nature of amorphous state, imperfect tetrahedral bonding and the relaxation of structure by hydrogen, etc. are found to be similar to those of aSi:H w17x. Therefore, to an extent one may borrow some of the concepts from a-Si:H to interpret the experimental results relating to a-C:H. 3. Experimental In order to attempt an experimental verification of the above formulation, we have grown three different types
of DLC films using C2H2 gas on well cleaned Corning 7059 glass substrates and polished silicon wafers in an asymmetric rf PECVD reactor. We have chosen two frequencies (namely 13.56 and 100 MHz) as also pulsing of 13.56 MHz discharge (modulation). Other details about the deposition of the films and the reactor have already been reported elsewhere w18–21x. As a matter of fact choosing a number of techniques for growing DLC films has enabled us to have films of widely different stress values. We have measured the absorption coefficient (a) at different photon energies (hn) using a photothermal deflection spectroscopy (PDS) set-up w22x and the S values using a semiconductor laser based scanning technique w23x. The values of E0 were estimated from the plot of optical absorption coefficient (a) vs. photon energy (hn). This plot for most of the DLC films studied here and grown by various techniques is presented in Fig. 1a–c. The a data for the DLC films were also obtained from reflection and transmission (R and T) measurement. The a values evaluated by both PDS and R and T method above 1.7 eV energy closely matches. The values of optical band gap (Eg) of these DLC films were determined from the intercept of 6ahn vs. hn curve to the xaxis. 4. Results and discussion Fig. 2 shows E0 vs. S plot for DLC films grown by different techniques. It is also evident from the figure that E0 values are smaller for pulse plasma grown DLC films than RF grown DLC films, whereas for VHF grown DLC films, it lies between the values of RF grown DLC films and pulse plasma grown DLC films. These values of E0 were found to be in the range of 149–165 meV, 186–264 meV and 252–311 meV for DLC films grown using pulse, VHF and RF plasma techniques, respectively. Broad band tails are usually found in a-C:H, and the values of E0 are frequently over 500 meV w24x; but somewhat narrower tails (E0f150– 300 meV) have also been seen in a-C:H by Dischler et al. w25x and Schutte et al. w26x. The values of E0 in a highly tetrahedral hydrogenated amorphous carbon (taC:H) are found to be ;350 meV w27x. Thus, the values of E0 evaluated for DLC films grown by RF, VHF and Pulse plasma techniques in the present study, are found to be comparable to the values of E0 (150–500 meV) for DLC films reported in the literature w24–27x. Again, change in E0 values is found to be consistent with the variation of S values in these DLC films. Pulse plasma grown DLC films recorded smaller value of E0 than the cw discharge grown DLC films. This could mean pulsed discharge grown DLC films are less disordered than cw discharge grown DLC films. This is found to be consistent with the low values of S observed for the pulse plasma grown DLC films. It is also evident
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
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Fig. 1. (a) Variation of optical absorption coefficient (a) vs. photon energy (hn) for DLC films grown by rf technique; (b) Variation of optical absorption coefficient (a) vs. photon energy (hn) for DLC films grown by VHF pulse technique; and (c) Variation of optical absorption coefficient (a) vs. photon energy (hn) for DLC films grown by pulse technique.
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Fig. 2. Variation of Urbach energy (E0) vs. residual stress (S) for DLC films grown by various techniques.
from this figure that with the increase of S values, the values of E0 also increase, for all types of DLC films studied. Since E0 is a measure of disorder in the material and an increase in E0 values implies an increase of the disorder in the material. One can thus conclude that the S and the disorder of the material may be interrelated. From the analysis of the result of Fig. 2, a quantitative relationship between the values of E0 and S, was deduced as follows: E0sE00qmS
(7)
where, m is a constant which is the slope of the straight line drawn between E0 vs. S curve, E00 is a constant which represents the minimum E0 value in this type of material and is the intercept of the straight line of the E0 vs. S curve which corresponds to the zero S value. The values of E00 and m are found to be 140 meV and 37 GPaymeV, respectively. From these observations, it becomes clear that in the network of a-C:H reduction of E0 value less than 140 meV may not be possible. It is seen that a-C:H (DLC) films are highly disordered as compared to a-Si:H films. The values of E0 for c-Si and a-Si:H have been reported as 8.6 meV and 40 meV, respectively w28x. Further, the change in the observed values of E0 are found to be consistent with the change in the optical properties of DLC films of varying S values, i.e. with the increase of E0, the values of Eg decrease as shown in Fig. 3. However, there appears to be some small inconsistency in this behavior, which can, perhaps be attributed to the change of the technique for growing these films. In a study by O’Leary, it has been mentioned that Eg is found to be insensitive to the amount of
disorder w29x. In contrast, a quantitative relation between the values of Eg and E0 in a-Si:H films has been reported by Cody et al. w30x, which has also been confirmed by us w31x. It is found that the values of E0 decrease with the increase of Eg. Such quantitative relationship has earlier been reported by other groups w3,5,32x for a-Si:H, a-C:H and a-SiC:H systems. It is important to mention here that the value of Eg in all form of amorphous carbon is decided by p states. Since p states are weakly bound in a-C:H, they lie closer to the Fermi level compared to the s states. Consequently, the filled p states form the valence band and the empty p* states form the conduction band and thereby the size of Eg is determined. Whereas in a-Si:H system, Eg is decided entirely by the s states.
Fig. 3. Variation of Urbach energy (E0 ) vs. optical bandgap (Eg) for DLC films grown by various techniques.
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
It is reasonable to assume that S values for the films deposited at room temperature will mostly be governed by the structural disorder in the films, whereas the S values for the films deposited at higher temperatures, disorder may have two components i.e. structural and thermal disorder. In the case of rf self bias deposited DLC films, structural and thermal disorder are always present, even if there is no deliberate heating of the substrates, since substrates are anyway heated by ionic bombardment. Yamada et al. w33x, in a study of DLC films grown using rf self bias technique, found that as a result of the ion impact, Ts is found to increase and, thus it becomes difficult to maintain Td. Keeping this point in mind, Yamada et al. w33x have grown DLC films using a pulse plasma discharge technique. Earlier studies of DLC films grown by pulse plasma growth technique reported by us w20x, which shows that Ts does not raise due to the ionic bombardment, as during OFF time of the pulse, substrate gets cooled. Thus, in pulse plasma grown DLC films, at room temperature, only the structural disorder is expected to dominate. In the present study, we have estimated the rise of Ts for the rf self bias deposited DLC films from Fig. 4. It is to be noted that the energy of the bombarding ions on the substrate increases with the increase of applied power, which causes the enhancement of Ts. Fig. 4 indicates a rise in Ts from 30 to 80 8C kept at the cathode, with the change of self bias voltage from 0 to 400 V for the discharge, sustained using C2H2 gas. By estimating the values of Td from Fig. 4, at different self bias voltages and comparing it with the values of E0 corresponding to the DLC films grown at different self bias voltages from Table 1, one obtains the values of
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Table 1 Properties of DLC films grown using C2 H2 gas by RF (13.56 MHz), VHF (100 MHz) and pulse plasma techniques at constant pressure (25 mTorr) and flow rate (3.2 sccm) Sample No. Power density Self bias (Wycm2) voltage (V)
Residual E0 Eg Stress, S (meV) (eV) (GPa)
RF (13.56 MHz) CRF-7 0.10 CRF-8R 0.20 CRF-9R 0.30 DCRF-1 0.42
y98 y150 y250 y300
3.60 3.80 4.40 4.60
252 259 298 311
1.75 1.40 1.25 1.15
VHF (100 MHz) CHF-2 0.10 CHF-1 0.20 CHF-3 0.30 DCHF-5 0.10 DCHF-1 0.10 DCHF-3 0.10
y7.43 y19.95 y39.67 y(10q0) y(10q230) y(10q390)
1.70 1.75 1.99 1.70 2.20 2.90
196 202 242 204 244 264
1.55 1.45 1.40 1.60 1.55 1.60
Pulse CP-1 CP-2 CP-4 CP-3
– – – –
0.13 0.28 0.31 0.37
– 149 163 165
1.60 1.48 1.35 1.00
0.42 1.00 1.50 2.00
E0 at different temperatures. E0 values thus evaluated at different temperatures are shown in Fig. 5. It is evident from Fig. 5 that E0 increases with the increase of the Td. It is revealed from Fig. 5 that the minimum values of E0s140 meV is obtained for a temperature corresponding to 0 8C, which is found to be the same as that deduced from Eq. (7). This corresponds to the situation of absolutely no residual stress. From this result it is evident that the value of E0f140 meV evaluated,
Fig. 4. Variation of the substrate temperature vs. the self-bias voltage for the rf self bias deposited DLC films.
S. Kumar et al. / Diamond and Related Materials 12 (2003) 1576–1583
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Fig. 5. Variation of Urbach energy (E0) vs. the substrate temperature for the rf self bias deposited DLC films.
corresponds to the structural disorder only in the a-C:H family of materials. Thus, it becomes quite evident that there is a one-to-one correlation between the residual stress (S) and the disorder present in these films. From the present studies, it appears that in order to minimize the value of E0 in a-C:H films, deposition parameter should be chosen in such a way so that one can get minimum values of S. But we have seen in the present investigation that even pulse plasma grown DLC films with S values ranging from 0.1 to 0.4 GPa, show significantly higher values of E0, in the range of 140– 165 meV, compared to the lowest value of E0f40–50 meV obtained in a-Si:H films. Typical opto-electronic grade a-Si:H films grown using glow discharge technique, show S values in the range of 0.1–0.8 GPa with E0f50 meV w34x. These higher values of E0 obtained for a-C:H films may be due to the complex bonding arrangements of carbon than silicon, on account of its ability to form sp1, sp2 and sp3 hybridization. Further, carbon structure has more phonon assisted vibrations compared to silicon structure w35x that may also contribute to some part of the disorder in a-C:H films. Thus, from all that has been said so far it appears that a-C:H film with minimum value of E0f140 meV may be considered in quality as equivalent to a-Si:H films with E0f40 meV w28,36x. This minimum value of E0 observed in the a-Si:H and a-C:H may be the lower limit of the best quality material produced to date. E0s 8 meV has been observed to be the lower limit in case of c-Si w28x. 5. Conclusions The residual stress (S) and the Urbach energy (E0) of diamond-like carbon films have been discussed in
terms of disorder in the carbon network. A correlation has been observed to exist between the residual stress (S) and Urbach energy (E0) in these films. From the observed correlation, it is further inferred that the Urbach energy (E0) in DLC (a-C:H) films less than 140 meV may not be possible. Acknowledgments Authors are grateful to the Director, National Physical laboratory, New Delhi for his kind permission to publish this article and acknowledge with thanks Dr D. Sarangi and Dr C. Mukherjee, our past colleagues, for many valuable discussions. Authors also wish to acknowledge Department of Science and Technology, Govertment of India for providing financial assistance. References w1x J. Tauc, Mater. Res. Bull. 5 (1970) 721. w2x H. Oheda, Jpn. J. Appl. Phys. 18 (1979) 1973. w3x G.D. Cody, T. Tiedje, B. Abeles, B. Brooks, Y. Goldstein, Phys. Rev. Lett. 47 (1981) 1480. w4x M. Stutzmann, Appl. Phys. Lett. 47 (1985) 21. w5x T. Datta, J.A. Woollam, W. Notohamiprodjo, Phys. Rev. B 40 (1989) 5956. w6x A.B. Maity, M. Basu, S. Chaudhuri, A.K. Pal, J. Phys D:Appl. Phys. 28 (1995) 2547. w7x K. Enke, Thin Solid Films 80 (1981) 227. w8x C. Weissmantal, C. Schurer, F. Frohlich, P. Grau, H. Lehmann, Thin Solid Films 61 (1979) L5. w9x S.B. Desu, Phys. Stat. Sol. (a) 141 (1994) 119. w10x P. Hess, Thin Solid Films 241 (1994) 318. w11x J. Robertson, J. Non-Cryst. Solids 137–138 (1991) 825. w12x F.M. d’Heurle, J.M.E. Harper, Thin Solid Films 171 (1989) 81.
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