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Raman scattering, AFM and nanoindentation characterisation of diamond films obtained by hot filament CVD
Diamond and Related Materials 13 (2004) 266–269
Raman scattering, AFM and nanoindentation characterisation of diamond films obtained by hot filament CVD I.B. Yanchuka,*, M.Ya. Valakha, A.Ya. Vul’b, V.G. Golubevb, S.A. Grudinkinb, N.A. Feoktistovb, A. Richterc, B. Wolfc a
Institute of Semiconductor Physics NAS Ukraine, Prospect Nauki 45, 03028 Kiev, Ukraine b Ioffe Physico-Technical Institute RAS, 194021 St.Petersburg, Russia c University of Applied Sciences Wildau, Bahnhofstrasse 1, D-15745 Wildau, Germany
Abstract In this work, structure and mechanical properties of diamond films fabricated by HFCVD on silicon substrates with nanodiamond seeding were investigated. Raman spectroscopy was used to characterise the diamond phase content, crystalline quality and source of stresses in these films. Topography, hardness and Young’s modulus were studied by scanning force microscopy (SFM) and nanoindentation methods. It has been ascertained that for the diamond films grown on silicon substrates with nanodiamond seeding hardness and crystalline quality is higher than for films on scratched silicon. The diamond films demonstrate Raman upshift with respect to natural diamond, indicating presence of internal compressive stress. It was shown that various types of impurities and defects induce compressive stresses in the diamond grains. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: Diamond film; Nanodiamond precursor; Raman scattering; SFM; Nanoindentation
1. Introduction It is well known that the nucleation process critically determines the film structure, morphology, defect formation. In most CVD methods, diamond nucleation on non-diamond substrates without substrate pre-treatment is usually very difficult and slow w1x. The common technological idea of many methods aimed to nondiamond substrate pre-treatment is the change of heterogeneous growth to homogeneous one. It can be realised due to preliminary deposition of diamond crystallites on the substrate surface. Authors w1,2x offered the methods to create nucleation centres, which consist of preliminary deposition of diamond nanoparticles (nanodiamond seeding) onto silicon substrate. Nanodiamond seeding has advantage over conventional scratching method and other nucleation methods for high speed formation of continuous diamond films, possibility of the low temperature growth and deposition films on substrates with various strengths of chemical affinity to carbon w3,4x. However, we have little information regarding structure *Corresponding author. Tel.: q380-44-265-8303; fax: q380-44265-8550. E-mail address: [email protected] (I.B. Yanchuk).
and mechanical properties of diamond films grown with nanodiamond seeding. The main purpose of this work is the investigation of structure and hardness of diamond films fabricated by hot filament CVD on silicon using for substrate pretreatment the nanodiamond seeding and conventional substrate scratching method. We have employed Raman scattering, scanning force microscopy and nanoindentation methods to evaluate phase composition, crystalline quality, residual stresses, nanohardness (hardness of single diamond grain) and Young’s modulus. The results from these techniques were used to elucidate sources of stresses in the films and influence of substrate pretreatment methods on film’s crystalline quality and hardness. 2. Experimental details Diamond films were prepared from hydrogen–methane mixture using the HF-CVD method. The deposition process parameters were chosen so as to provide a maximum content of the diamond phase in the films w5x. For all set of experiments, the gas mixture pressure in the reaction chamber was maintained at 48 Torr,
0925-9635/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2003.11.001
I.B. Yanchuk et al. / Diamond and Related Materials 13 (2004) 266–269
methane concentration was 1%, hydrogen concentration was 99%, substrate temperature was kept at 750 8C, the filament temperature was 2200 8C. The gas flow rate was changed in the ranges 300–500 sccm. As substrate, we used optically polished silicon (100). For pretreatment process, the nanodiamonds with particles size 4–5 nm were prepared using a commercial detonation carbon synthesised from a trinitrotoulene–hexogen mixture. The nanodiamond powder was extracted from the detonation carbon by oxidation with 50% nitric acid at 220 8C in an autoclave w6x. Nucleation centres were created by deposition of nanodiamonds from isopropyl suspension with the nanodiamond powder concentration close to 1 wt.% onto the substrates. Another part of silicon substrates was scratched with a diamond powder of 1 mm grain size. The growth time for these films lasted 4–6 h. The structure of the films was studied using the Raman scattering spectroscopy. The Raman spectra were detected at room temperature using a double monochromator, a cooled photomultiplier employing standard photon counting technique and an Arq laser with ls 488 nm for excitation. Topography and hardness of the films were investigated using scanning force microscopy in combination with depth sensing nanoindentation. The experimental equipment consists of a HYSITRON Triboscope attached to a Nanoscope IV scanning force microscope of digital instruments (now VEECO). The system design guarantees that the penetration of the hardness probe is perpendicular to the surface of the specimen, in contrast to cantilever-based nanoindentation with an unchanged SFM. 3. Results Depicted in Fig. 1a is the Raman spectrum of the diamond film (the gas flow rate 500 sccm) with the thickness 2 mm prepared on the silicon substrate scratched with diamond powder (the sample 500S). In the spectrum, one can observe the narrow symmetrical diamond peak at 1335.4 cmy1 with FWHM 7.0 cmy1, which corresponds to a zone centre mode of T2g symmetry. Besides, the wide band G-peak centred at 1529 cmy1 is seen. The diamond peak developed over the background of the weak wide band in the range 1250– 1400 cmy1 is the so-called D-peak. The presence of Dand G-peaks reflects the presence of sp2-bonded carbon w7 x . In order to study the influence of pre-treatment of the surface on the diamond film structure in more detail, the diamond films were deposited at the same conditions and the gas flow rate 300 sccm with a film thickness of 4 mm onto silicon substrates seeded with nanodiamond powder (samples 300ND) and the scratched ones (sample 300S).
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Fig. 1. Raman spectra of the diamond films: (a) 500S film on the scratched silicon substrate grown at gas flow rate 500 sccm; (b) 300S film on the scratched silicon substrate and (c) 300ND film on the silicon substrates seeded with nanodiamonds grown at gas flow rate 300 sccm.
SFM data showed that the surface of both types of films is formed by rising diamond grains. The lateral dimension of grains is here approximately 1–2 mm, and their height is close to 500 nm. Our measurements of nanohardness performed on separate diamond grains (Fig. 2a,b) showed that in films of both types, nanohardness increased with the depth of indenter penetration into the films. In the first case, this effect is more pronounced and reaches values up to 55 GPa at the depth of 20 nm, while in the second case – 36 GPa at 50 nm depth. When measuring the indentation Young’s modulus in the film with nanodiamond precursors, we also revealed growth of this value up to 450 GPa with the film depth (Fig. 3a). For the second type films, Young’s modulus even decreases with depth (Fig. 3b). 4. Discussion Starting from the G-peak position and intensity ratio I(D)yI(G) and using the amorphisation trajectory w7x, it is possible to estimate the content and order degree of sp2-bonded atoms. As in the Raman spectra of the sample 500S, the G-peak has its position at 1529 cmy1 and I(D)yI(G)s0.64, one can deduce that the film contains an observable fraction of amorphous graphite.
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Fig. 2. Hardness H in diamond grain vs. contact depth of films (a) 300ND and (b) 300S.
In the spectrum of the sample 300ND (Fig. 1c), the Dpeak is absent, while the weak G-peak is shifted to the high-frequency side. In the Raman spectra of the samples 300S and 300ND, we could not determine G-peak parameters, therefore, it was impossible to estimate the sp2 fraction in general. In Raman spectra of all the samples, we could observe upshift of the diamond peak and the increased FWHM in the film as compared to its position in natural diamond (1332.3 cmy1 and 2 cmy1, respectively) w8x. The reason of this upshift is caused by compressive stress. Using the given pressure coefficient as1.9 cmy1 yGPa in Ref. w8x, the stress magnitudes s in the films can be evaluated (see Fig. 1). The estimated stresses s can be represented as a sum of the thermal stress sTH caused by the difference between thermal expansion coefficients of diamond and substrates, stresses sMIS caused by the misfit of diamond and substrate crystal lattices, and internal stresses 8sIN that can be assigned to various sources such as impurities and structural extended defects w8x. Therefore, in accordance with Ref. w8x, we suggest that the most probable origins of Dn are the intrinsic stress sources caused by various types of impurities and defects presented in the grown diamond films. The nitrogen impurities, silicon and especially the sp2-type bonding of the graphitic phase may support these defects. It is noteworthy that stress magnitudes correlate with the diamond peak halfwidth. Widening the diamond peak is related to scattering of phonons on
Fig. 3. Young’s modulus E in diamond grain vs. contact depth of films (a) 300ND and (b) 300S.
I.B. Yanchuk et al. / Diamond and Related Materials 13 (2004) 266–269
impurities and defects in diamond crystallites w8x. It means that the diamond peak up-shift value and its halfwidth depend on the amount of defects and impurities. Being based on what is said above, one can conclude that the films deposited on substrates seeded with nanodiamond have a more ordered diamond structure with less impurity quantity including amorphous graphite. These data correlate with nanohardness measurements. In accordance with model of geometrically necessary dislocations hardness H;h y1y2, where h is a penetration depth w9x. The nanohardness relation for samples 300ND and 300S is 1.7 at same load 5 mN. However, hardness relation is 1.9 with the given indentation depths for samples 300ND and 300S. It means that also other contributions to hardness except dislocation have to be considered. We suggest that presence of sp2-carbon in diamond grains is responsible for decreasing nanohardness. The Young’s modulus of diamond films is strongly dependent on the content of defects and impurities in the sample w10x. Therefore Young’s modulus of NDtype films is larger than that of S-type films. The indentation process from normal point force induces stresses in diamond film. Variation of Young’s modulus as a function of depth (Fig. 3) characterises evolution of these stresses. A decreasing Young’s modulus with depth (sample 300S) results in the spreading of stresses to the film surface, whereas an increasing Young’s modulus with depth (sample 300ND) results in diffusing stresses towards the interior of film w10x. These results are of importance for surface engineering of antifriction and wear resistance coatings. The observed increase of hardness with depth can be explained by partial graphitisation of the diamond film surface. Preliminary data obtained by us and using the ionisation spectroscopy methods confirm the fact. This coating is formed as a consequence of energetically favourable relaxation of sp3 dandling bonds to a C_ C sp2 configuration w11x. Surface of diamond grains is
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coated with a disordered layer of sp2 ysp3 hybridised carbon atoms, therefore, one can observe the above mentioned hardness growth. 5. Conclusion In the work effect of nanodiamond seeding on structure and mechanical properties of diamond films grown by HFCVD method on silicon substrates was examined by Raman scattering and SFM methods. It has been established that the films prepared with nanodiamond seeding consist of harder diamond grains and have higher crystalline quality than the films deposited onto the silicon substrates scratched with diamond powder. In the films deposited onto substrates with nanodiamond precursors, there is considerably less content of sp2hybridised carbon atoms. From Raman analysis of diamond films fabricated at the same substrate temperature it was assumed that the compressive internal stress in the diamond films grown at our process parameters is due to various types of impurities and defects presented in the diamond grains. References w1x H. Liu, D.S. Dandy, Diamond Relat. Mater. 4 (1995) 1173. w2x T. Yara, H. Makita, A. Hatta, T. Ito, A. Hiraki, Jpn. J. Appl. Phys. 34 (1995) 312. w3x A. Hiraki, Appl. Surf. Sci. 162–163 (2000) 326. w4x S.A. Grudinkin, V.G. Golubev, A.Ya. Vul’, Proceedings of International Conference Trends in Nanotechnology (TNT2001), September 3–7, Segovia, Spain, 2001, p. 225. w5x M.V. Baidakova, N.A. Feoktistov, V.G. Golubev, S.A. Grudinkin, V.G. Melehin, A.Ya. Vul’, et al., Semiconductors 36 (2002) 651. w6x A.E. Aleksinskii, M.V. Baidakova, A.Ya. Vul’, V.I. Siklitskii, Phys. Solid State 41 (1999) 688. w7x J. Robertson, Mater. Sci. Eng. R 37 (2002) 129. w8x L. Bergman, R.J. Nemanich, J. Appl. Phys. 78 (1995) 6709. w9x B. Wolf, A. Richter, New J. Phys. 5 (2003) 15.1. w10x A.E. Giannakopoulos, S. Sueresh, Int. J. Solids Struct. 34 (1997) 2357. w11x G.A.J. Amaratunga, J. Robertson, V.S. Veerasamy, W.I. Milne, D.R. McKenzie, Diamond Relat. Mater. 4 (1995) 637.
Raman scattering, AFM and nanoindentation characterisation of diamond films obtained by hot filament CVD I.B. Yanchuka,*, M.Ya. Valakha, A.Ya. Vul’b, V.G. Golubevb, S.A. Grudinkinb, N.A. Feoktistovb, A. Richterc, B. Wolfc a
Institute of Semiconductor Physics NAS Ukraine, Prospect Nauki 45, 03028 Kiev, Ukraine b Ioffe Physico-Technical Institute RAS, 194021 St.Petersburg, Russia c University of Applied Sciences Wildau, Bahnhofstrasse 1, D-15745 Wildau, Germany
Abstract In this work, structure and mechanical properties of diamond films fabricated by HFCVD on silicon substrates with nanodiamond seeding were investigated. Raman spectroscopy was used to characterise the diamond phase content, crystalline quality and source of stresses in these films. Topography, hardness and Young’s modulus were studied by scanning force microscopy (SFM) and nanoindentation methods. It has been ascertained that for the diamond films grown on silicon substrates with nanodiamond seeding hardness and crystalline quality is higher than for films on scratched silicon. The diamond films demonstrate Raman upshift with respect to natural diamond, indicating presence of internal compressive stress. It was shown that various types of impurities and defects induce compressive stresses in the diamond grains. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: Diamond film; Nanodiamond precursor; Raman scattering; SFM; Nanoindentation
1. Introduction It is well known that the nucleation process critically determines the film structure, morphology, defect formation. In most CVD methods, diamond nucleation on non-diamond substrates without substrate pre-treatment is usually very difficult and slow w1x. The common technological idea of many methods aimed to nondiamond substrate pre-treatment is the change of heterogeneous growth to homogeneous one. It can be realised due to preliminary deposition of diamond crystallites on the substrate surface. Authors w1,2x offered the methods to create nucleation centres, which consist of preliminary deposition of diamond nanoparticles (nanodiamond seeding) onto silicon substrate. Nanodiamond seeding has advantage over conventional scratching method and other nucleation methods for high speed formation of continuous diamond films, possibility of the low temperature growth and deposition films on substrates with various strengths of chemical affinity to carbon w3,4x. However, we have little information regarding structure *Corresponding author. Tel.: q380-44-265-8303; fax: q380-44265-8550. E-mail address: [email protected] (I.B. Yanchuk).
and mechanical properties of diamond films grown with nanodiamond seeding. The main purpose of this work is the investigation of structure and hardness of diamond films fabricated by hot filament CVD on silicon using for substrate pretreatment the nanodiamond seeding and conventional substrate scratching method. We have employed Raman scattering, scanning force microscopy and nanoindentation methods to evaluate phase composition, crystalline quality, residual stresses, nanohardness (hardness of single diamond grain) and Young’s modulus. The results from these techniques were used to elucidate sources of stresses in the films and influence of substrate pretreatment methods on film’s crystalline quality and hardness. 2. Experimental details Diamond films were prepared from hydrogen–methane mixture using the HF-CVD method. The deposition process parameters were chosen so as to provide a maximum content of the diamond phase in the films w5x. For all set of experiments, the gas mixture pressure in the reaction chamber was maintained at 48 Torr,
0925-9635/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2003.11.001
I.B. Yanchuk et al. / Diamond and Related Materials 13 (2004) 266–269
methane concentration was 1%, hydrogen concentration was 99%, substrate temperature was kept at 750 8C, the filament temperature was 2200 8C. The gas flow rate was changed in the ranges 300–500 sccm. As substrate, we used optically polished silicon (100). For pretreatment process, the nanodiamonds with particles size 4–5 nm were prepared using a commercial detonation carbon synthesised from a trinitrotoulene–hexogen mixture. The nanodiamond powder was extracted from the detonation carbon by oxidation with 50% nitric acid at 220 8C in an autoclave w6x. Nucleation centres were created by deposition of nanodiamonds from isopropyl suspension with the nanodiamond powder concentration close to 1 wt.% onto the substrates. Another part of silicon substrates was scratched with a diamond powder of 1 mm grain size. The growth time for these films lasted 4–6 h. The structure of the films was studied using the Raman scattering spectroscopy. The Raman spectra were detected at room temperature using a double monochromator, a cooled photomultiplier employing standard photon counting technique and an Arq laser with ls 488 nm for excitation. Topography and hardness of the films were investigated using scanning force microscopy in combination with depth sensing nanoindentation. The experimental equipment consists of a HYSITRON Triboscope attached to a Nanoscope IV scanning force microscope of digital instruments (now VEECO). The system design guarantees that the penetration of the hardness probe is perpendicular to the surface of the specimen, in contrast to cantilever-based nanoindentation with an unchanged SFM. 3. Results Depicted in Fig. 1a is the Raman spectrum of the diamond film (the gas flow rate 500 sccm) with the thickness 2 mm prepared on the silicon substrate scratched with diamond powder (the sample 500S). In the spectrum, one can observe the narrow symmetrical diamond peak at 1335.4 cmy1 with FWHM 7.0 cmy1, which corresponds to a zone centre mode of T2g symmetry. Besides, the wide band G-peak centred at 1529 cmy1 is seen. The diamond peak developed over the background of the weak wide band in the range 1250– 1400 cmy1 is the so-called D-peak. The presence of Dand G-peaks reflects the presence of sp2-bonded carbon w7 x . In order to study the influence of pre-treatment of the surface on the diamond film structure in more detail, the diamond films were deposited at the same conditions and the gas flow rate 300 sccm with a film thickness of 4 mm onto silicon substrates seeded with nanodiamond powder (samples 300ND) and the scratched ones (sample 300S).
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Fig. 1. Raman spectra of the diamond films: (a) 500S film on the scratched silicon substrate grown at gas flow rate 500 sccm; (b) 300S film on the scratched silicon substrate and (c) 300ND film on the silicon substrates seeded with nanodiamonds grown at gas flow rate 300 sccm.
SFM data showed that the surface of both types of films is formed by rising diamond grains. The lateral dimension of grains is here approximately 1–2 mm, and their height is close to 500 nm. Our measurements of nanohardness performed on separate diamond grains (Fig. 2a,b) showed that in films of both types, nanohardness increased with the depth of indenter penetration into the films. In the first case, this effect is more pronounced and reaches values up to 55 GPa at the depth of 20 nm, while in the second case – 36 GPa at 50 nm depth. When measuring the indentation Young’s modulus in the film with nanodiamond precursors, we also revealed growth of this value up to 450 GPa with the film depth (Fig. 3a). For the second type films, Young’s modulus even decreases with depth (Fig. 3b). 4. Discussion Starting from the G-peak position and intensity ratio I(D)yI(G) and using the amorphisation trajectory w7x, it is possible to estimate the content and order degree of sp2-bonded atoms. As in the Raman spectra of the sample 500S, the G-peak has its position at 1529 cmy1 and I(D)yI(G)s0.64, one can deduce that the film contains an observable fraction of amorphous graphite.
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Fig. 2. Hardness H in diamond grain vs. contact depth of films (a) 300ND and (b) 300S.
In the spectrum of the sample 300ND (Fig. 1c), the Dpeak is absent, while the weak G-peak is shifted to the high-frequency side. In the Raman spectra of the samples 300S and 300ND, we could not determine G-peak parameters, therefore, it was impossible to estimate the sp2 fraction in general. In Raman spectra of all the samples, we could observe upshift of the diamond peak and the increased FWHM in the film as compared to its position in natural diamond (1332.3 cmy1 and 2 cmy1, respectively) w8x. The reason of this upshift is caused by compressive stress. Using the given pressure coefficient as1.9 cmy1 yGPa in Ref. w8x, the stress magnitudes s in the films can be evaluated (see Fig. 1). The estimated stresses s can be represented as a sum of the thermal stress sTH caused by the difference between thermal expansion coefficients of diamond and substrates, stresses sMIS caused by the misfit of diamond and substrate crystal lattices, and internal stresses 8sIN that can be assigned to various sources such as impurities and structural extended defects w8x. Therefore, in accordance with Ref. w8x, we suggest that the most probable origins of Dn are the intrinsic stress sources caused by various types of impurities and defects presented in the grown diamond films. The nitrogen impurities, silicon and especially the sp2-type bonding of the graphitic phase may support these defects. It is noteworthy that stress magnitudes correlate with the diamond peak halfwidth. Widening the diamond peak is related to scattering of phonons on
Fig. 3. Young’s modulus E in diamond grain vs. contact depth of films (a) 300ND and (b) 300S.
I.B. Yanchuk et al. / Diamond and Related Materials 13 (2004) 266–269
impurities and defects in diamond crystallites w8x. It means that the diamond peak up-shift value and its halfwidth depend on the amount of defects and impurities. Being based on what is said above, one can conclude that the films deposited on substrates seeded with nanodiamond have a more ordered diamond structure with less impurity quantity including amorphous graphite. These data correlate with nanohardness measurements. In accordance with model of geometrically necessary dislocations hardness H;h y1y2, where h is a penetration depth w9x. The nanohardness relation for samples 300ND and 300S is 1.7 at same load 5 mN. However, hardness relation is 1.9 with the given indentation depths for samples 300ND and 300S. It means that also other contributions to hardness except dislocation have to be considered. We suggest that presence of sp2-carbon in diamond grains is responsible for decreasing nanohardness. The Young’s modulus of diamond films is strongly dependent on the content of defects and impurities in the sample w10x. Therefore Young’s modulus of NDtype films is larger than that of S-type films. The indentation process from normal point force induces stresses in diamond film. Variation of Young’s modulus as a function of depth (Fig. 3) characterises evolution of these stresses. A decreasing Young’s modulus with depth (sample 300S) results in the spreading of stresses to the film surface, whereas an increasing Young’s modulus with depth (sample 300ND) results in diffusing stresses towards the interior of film w10x. These results are of importance for surface engineering of antifriction and wear resistance coatings. The observed increase of hardness with depth can be explained by partial graphitisation of the diamond film surface. Preliminary data obtained by us and using the ionisation spectroscopy methods confirm the fact. This coating is formed as a consequence of energetically favourable relaxation of sp3 dandling bonds to a C_ C sp2 configuration w11x. Surface of diamond grains is
269
coated with a disordered layer of sp2 ysp3 hybridised carbon atoms, therefore, one can observe the above mentioned hardness growth. 5. Conclusion In the work effect of nanodiamond seeding on structure and mechanical properties of diamond films grown by HFCVD method on silicon substrates was examined by Raman scattering and SFM methods. It has been established that the films prepared with nanodiamond seeding consist of harder diamond grains and have higher crystalline quality than the films deposited onto the silicon substrates scratched with diamond powder. In the films deposited onto substrates with nanodiamond precursors, there is considerably less content of sp2hybridised carbon atoms. From Raman analysis of diamond films fabricated at the same substrate temperature it was assumed that the compressive internal stress in the diamond films grown at our process parameters is due to various types of impurities and defects presented in the diamond grains. References w1x H. Liu, D.S. Dandy, Diamond Relat. Mater. 4 (1995) 1173. w2x T. Yara, H. Makita, A. Hatta, T. Ito, A. Hiraki, Jpn. J. Appl. Phys. 34 (1995) 312. w3x A. Hiraki, Appl. Surf. Sci. 162–163 (2000) 326. w4x S.A. Grudinkin, V.G. Golubev, A.Ya. Vul’, Proceedings of International Conference Trends in Nanotechnology (TNT2001), September 3–7, Segovia, Spain, 2001, p. 225. w5x M.V. Baidakova, N.A. Feoktistov, V.G. Golubev, S.A. Grudinkin, V.G. Melehin, A.Ya. Vul’, et al., Semiconductors 36 (2002) 651. w6x A.E. Aleksinskii, M.V. Baidakova, A.Ya. Vul’, V.I. Siklitskii, Phys. Solid State 41 (1999) 688. w7x J. Robertson, Mater. Sci. Eng. R 37 (2002) 129. w8x L. Bergman, R.J. Nemanich, J. Appl. Phys. 78 (1995) 6709. w9x B. Wolf, A. Richter, New J. Phys. 5 (2003) 15.1. w10x A.E. Giannakopoulos, S. Sueresh, Int. J. Solids Struct. 34 (1997) 2357. w11x G.A.J. Amaratunga, J. Robertson, V.S. Veerasamy, W.I. Milne, D.R. McKenzie, Diamond Relat. Mater. 4 (1995) 637.