Residual stresses in chemical vapour deposited diamond films

Diamond and Related Materials 9 Ž2000. 1739᎐1743

Residual stresses in chemical vapour deposited diamond films U

Qi Hua Fana, , J. Gracio ´ b, E. Pereiraa a

b

Department of Physics, Uni¨ ersity of A¨ eiro, 3810 A¨ eiro, Portugal Department of Mechanical Engineering, Uni¨ ersity of A¨ eiro, 3810 A¨ eiro, Portugal

Abstract In this paper we report the determination of residual stresses in diamond films grown on SiŽ100. using a plate bending theory and a bi-metal theory combined with micro-Raman spectroscopy. Raman spectra show that with an increase in the film thickness, the characteristic diamond line shifts from higher wave numbers Ž) 1332 cmy1 . to lower Ž- 1332 cmy1 ., indicating a change of compressive to tensile bi-axial stress with increase in the film thickness. A plate bending theory and a bi-metal theory are used to determine the distribution of the stress induced by the thermal mismatch. The modelled results show that the bi-axial stress decreases linearly along the film growth direction and the stress at the filmrsubstrate interface decreases when the film becomes thicker. The difference from the Raman results is attributed to intrinsic stress. 䊚 2000 Elsevier Science S.A. All rights reserved. Keywords: Diamond film; Stress; Raman spectroscopy

1. Introduction The superior properties of chemical vapour deposited ŽCVD. diamond films make them attractive in many potential applications w1᎐4x. In order to obtain reliable diamond coatings, residual stresses must be identified and controlled. Generally such stresses are composed of two sources, namely, intrinsic stress and thermal stress. Structural mismatch between the film and substrate and defects within the film are responsible for intrinsic stress while thermal stress originates from the difference in the thermal expansion coefficients of the film and substrate. Residual stresses have been evaluated by a number of techniques, including substrate curvature, X-ray diffraction and micro-Raman spectroscopy w5᎐9x, among which the micro-Raman spectroscopy is most commonly used. For a perfect diamond crystal without any external stress, its face-centred cubic symmetry results in a triply degenerate first order phonon. As the wave vector of the incident radiation is considerably smaller U

Corresponding author. E-mail address: [email protected] ŽQ.H. Fan..

than the Brillouin zone extension, single phonon or first order Raman scattering produces information about phonons near the zone centre Ž k s 0.. The first order Raman peak for diamond appears at 1332 cmy1 . The effects of external stress on the Raman spectrum have been discussed by a few authors w9᎐11x. It is known that under compressive or tensile stresses the diamond Raman line shifts to higher or lower frequency respectively. A hydrostatic stress only produces a shift since the diamond cubic symmetry is preserved, while an anisotropic stress can change the crystallographic symmetry and lift the three-fold degeneracy either completely or partially, leading to a split of the Raman line. The degree of the shift and splitting of the Raman spectra depends on the magnitude of the stress. It is necessary to note that residual stress evaluated by the above-mentioned techniques is actually a sum of thermal stress and intrinsic stress. Therefore, the nature of the residual stress is determined by the nature and relative magnitude of these two stress components. For example, residual stress in CVD diamond films grown on Si has been reported as both tensile and compressive, depending on the CVD techniques and growth conditions w12᎐16x. This implies that many fac-

0925-9635r00r$ - see front matter 䊚 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 0 . 0 0 2 8 4 - 3

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Q.H. Fan et al. r Diamond and Related Materials 9 (2000) 1739᎐1743

tors affect stresses in CVD diamond films. In order to understand the origination and to determine the stress components, intensive studies have been performed by different authors, using in-situ and ex-situ measurements w12᎐20x. In this paper we propose a simplified method for evaluating residual stresses in diamond films by using a plate bending theory and a bi-metal theory combined with micro-Raman spectroscopy. With this method, intrinsic stress induced by the structural mismatch and by the film growth strain is distinguished from thermal stress. The stress evolution with the film growth is also discussed.

2. Experimental details Substrates used for diamond deposition were asreceived SiŽ100., being mirror polished on one side. They were 0.3 mm thick and were cut into 5 = 5 mm2 squares. An ASTeX PDS18 microwave plasma CVD system was used for diamond synthesis. The deposition conditions were as follows: microwave power, 3400 W; gas pressure: 100 torr; gas flow rate: 475 sccm consisting of 450 sccm H2 and 25 sccm CH4 . The substrate temperature, being controlled mainly by the microwave power, was approximately 850⬚C. Under these deposition conditions the diamond films appear almost transparent and are therefore called ‘white grade’. Diamond films with different thicknesses were obtained by simply changing the deposition time. A Renishaw 2000 micro-Raman system with a 633-nm He᎐Ne laser was used to characterize the diamond films. At this laser wavelength, the non-diamond carbon phases scatter more effectively than diamond due to a resonance effect w21x. It is therefore useful in characterizing diamond films of ‘good’ quality. The Renishaw Raman system works in two modes: main mode and extended mode. In the main mode the grating does not rotate and therefore yields a high repeatability of 0.1 cmy1 in the spectrum. Raman spectra obtained in the main mode allows an accurate comparison of the diamond line shift. All Raman spectra in this work were taken in the main mode and a Type IIa bulk diamond was used to calibrate the peak position. For each sample five different points along the surface diagonal were measured and their average Raman shift was used in evaluation of the residual stress.

Fig. 1. Raman spectra taken from diamond films of different thickness deposited on Si. Ža. 1.7 ␮m, Žb. 4.0 ␮m, Žc. 11 ␮m, Žd. 23 ␮m, Že. 48 ␮m.

signals for diamond phase and non-diamond phases changes with increase in the film thickness. Therefore, a variation in the growth strain with the film evolution may occur. In thinner films, the diamond Raman line shifts to wave numbers higher than 1332 cmy1 , corresponding to a compressive stress, while in thicker films it shifts to lower wave numbers, corresponding to a tensile stress. The change in the nature of the residual stress indicates a possible variation in the nature and relative magnitude of intrinsic stress and thermal stress. It is noted that all samples show slight curvature with the film on the convex side. It is known that the Raman shift is proportional to bi-axial stress ␴ in the diamond films with relationships shown as follows w9x: ␴ s y 1.08 Ž ␯s y ␯0 . Ž GPa . for a singlet phonon

Ž1.

␴ s y 0.384 Ž ␯d y ␯0 . Ž GPa . for a doublet phonon

Ž2.

where ␯0 s 1332 cmy1 , ␯s is the observed maximum of the singlet in the spectrum and ␯d the maximum of the doublet. In many films, the splitting of the Raman line is not obvious. In this case, the observed peak position ␯m is assumed locating at the centre between the singlet ␯s and doublet ␯d , i.e. ¨ m s Ž1r2.Ž ¨ s q ¨ d . w22x. From Eqs. Ž1. and Ž2. we obtain ␴ s y 0.567 Ž ␯m y ␯0 . Ž GPa .

3. Results and discussion Diamond films with thicknesses of 1.7᎐48 ␮m were deposited on the Si substrate. Typical Raman spectra taken from some of these films and corresponding diamond line position are shown in Fig. 1 and Table 1, respectively. It can be seen that the intensity of Raman

for unsplitted peak

Ž3.

Using Eqs. Ž1. ᎐ Ž3., residual stress in the diamond films is obtained, as given in Table 1. As mentioned before, the residual stress evaluated from Raman spectra is a sum of intrinsic stress and thermal stress. In order to distinguish the two stress

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Table 1 Curvature radius R calculated from bi-metal theory and residual stresses calculated from the plate-bending theory and from the diamond Raman line shift. ŽIntrinsic stress is derived from the difference of these two stresses . Film thickness d f Žmm. Raman shift Žcmy1 . Stress ␴ evaluated from Raman spectra ŽGPa. Curvature radius R calculated from bi-metal theory Žmm. Bending stress Ž ␴f s axq b . in film: component a ŽGPa mmy1 . Bending stress Ž ␴f s axq b . in film: component b ŽGPa. Bending stress at film surface ŽGPa. ␴surf s a) d f q b Mean bending stress a in film ŽGPa. ␴m s Ž1r2.Ž ␴surf q b . Intrinsic stress ␴i ŽGPa. ␴i s ␴ y ␴m

0.0017 1332.43 y0.244

0.004 1332.33 y0.189

0.011 1331.93 0.038

0.023 1331.73 0.151

0.048 1331.60 0.227

2002.669

939.042

440.640

295.390

233.393

0.564

1.202

2.562

3.822

4.837

y1.285

y1.158

y0.889

y0.646

y0.460

y1.283

y1.153

y0.861

y0.558

y0.228

y1.284

y1.156

y0.875

y0.602

y0.344

1.040

0.968

0.915

0.755

0.570

components, we first consider the effect of the thermal mismatch. Assuming the diamond film and the Si substrate behave as a bi-metal plate, as shown in Fig. 2, the difference in the thermal expansion coefficients will induce stresses in both the film and the substrate and will lead to the coatingrsubstrate bending upon cooling from the deposition temperature to room temperature. From bi-metal theory w23x, the radius of curvature, R, is given by: Fig. 2. An illustration of the bi-metal bending plate.

1 s R

6 Ž ␣s y ␣f .Ž Td y Tr .Ž 1 q m . 2 1 h 3 Ž 1 q m . 2 q Ž 1 q mn . m2 q mn

ms

df ds

Ž5.

ns

Efr Ž 1 y ␯f . Esr Ž 1 y ␯s .

Ž6.

ž

Ž4.

/

From plate-bending theory, we can obtain the stresses ␴f and ␴s in the film and substrate, respectively w23,25x.

where ␣s s 3.5 Ky1 , ␣f s 2.0 Ky1 are average values of thermal expansion coefficients for Si and diamond in a temperature range from Tr s 25⬚C Žroom temperature. to Td s 850⬚C Ždeposition temperature., ds and df are substrate thickness and film thickness, Es s 170 GPa, Ef s 1050 GPa are Young’s modulus of Si and diamond, and ␯s s 0.42, ␯f s 0.07 are their Poisson’s ratio, respectively. The calculated curvature radius R is given in Table 1. It should be noted that the thermal expansion coefficients for Si and diamond change with temperature. This should be considered for more accurate calculation. Furthermore, plastic deformation in Si at high temperature occurs. This may cause some error in determining the curvature radius with the bi-metal theory, although the thermal mismatch between Si and diamond becomes small at high temperature ranges w24x.

␴f s

Y d3 q Ys ds3 d 1 y f f q Yf xy f R 2 6 df Ž df q ds .

␴s s

3 3 d 1 Yf df q Ys ds q Ys x q s R 6 ds Ž df q ds . 2

ž

ž

/

/

Ž7.

Ž8.

where x is the distance from the filmrsubstrate interface, Yf s EfrŽ1 y ␯f ., Ys s EsrŽ1 y ␯s .. Table 1 and Fig. 3 show the stresses calculated from Eq. Ž7.. Two features can be observed. First, the absolute value of the stress decreases linearly from the filmrsubstrate interface to the film surface, i.e. ␴f s axq b, where a Y d 1 Yf d f3 q Ys ds3 s f and bs y q Yf f . Second, the R R 6 d f Ž df q ds . 2 absolute value of the stress at the filmrsubstrate interface, xs 0, decreases with increasing the film thickness. However, the stress difference along the film depth is small if we compare the stress at the filmrsubstrate interface, ␴f Ž xs 0., with the stress at the film surface, ␴f Ž x s df ., especially in thinner films Ž- 23 ␮m.. We therefore consider a mean bending

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creases with increasing the film thickness. Recall the Raman spectra shown in Fig. 1, we may propose that the intrinsic stress is proportional to the non-diamond phases and defects in the CVD diamond films.

4. Conclusions

Fig. 3. Residual stresses evaluated from Raman spectra Ž=., calculated from the bi-metal theory and plate bending theory Ž䉫, I, ^., and derived intrinsic stress Ž)..

stress ␴m , which is an average value of the stress ␴f through the film depth, i.e. ␴m s Ž1r2.w ␴f Ž xs 0. q ␴f Ž x s df .x. From Eq. Ž7. we get ␴m s

Y d3 q Ys ds3 1 y f f R 6 df Ž df q ds .

Ž9.

The calculated mean bending stress is also shown in Table 1 and Fig. 3. It is worth pointing out that the Raman spectra are actually a superposition of contribution from different depths of a film. Since the residual stresses change along the film growth direction, it is expected that the Raman shift contributed from layers of different depths is not the same and the signal intensity is also different due to absorption loss. Details have been discussed in a previous work w26x. However, considering the fact that the diamond films used in this work have a transparent quality, we may assume that the Raman line shift reflects a mean stress in the film. Furthermore, as can be seen in Table 1 and Fig. 3, the relative value of the stress evaluated from Raman spectra is much higher than the bending stress induced by the thermal mismatch. This is true even for a thicker film, e.g. 48 ␮m. Therefore, the above assumption is expected to yield reasonable accuracy in evaluation residual stresses in the diamond films deposited on the Si substrates. Note that the stress obtained from Eq. Ž9. is an effect of thermal mismatch. Thus, intrinsic stress ␴i can be derived from the difference in the stresses evaluated from Raman spectra Ž ␴ . and from the bimetal theory and the plate bending theory Ž ␴m ., ␴i s ␴ y ␴m

Ž 10 .

Obviously, the result is an average intrinsic stress in the film. From Table 1 and Fig. 3, it can be seen that the derived intrinsic stress is tensile in nature. It de-

Residual stresses in CVD diamond films deposited on SiŽ100. substrates are evaluated. The diamond Raman line shift reflects a combination of intrinsic stress and thermal stress. The thermal stress distribution in the film is modelled using a plate bending theory and a bi-metal theory, showing that the bi-axial stress decreases linearly along the film growth direction. The stress at the filmrsubstrate interface is compressive in nature and decreases when the film becomes thicker. The stress modelled is quite different from that evaluated by Raman spectroscopy. The difference is, therefore, attributed to intrinsic stress, probably originating from structure mismatch between the diamond and Si and from a variation in microstructure of the film with its growth evolution.

Acknowledgements The authors would like to thank Mr A. Fernandes for his help in experiments. NATO research project SFS-PO-OPTOELECT ‘Diamond Film Technology’ is acknowledged. One of the authors ŽQ.H.F.. would like to thank Fundac¸˜ ao para a Ciencia e a Tecnologia ˆ ŽPortugal. for financial support. References w1x J.E. Field, in: J.E. Field ŽEd.., Properties of Natural and Synthetic Diamond, Academic Press, San Diego, CA, 1992, p. 667. w2x J.C. Angus, C.C. Hayman, Science 241 Ž1988. 913. w3x K.E. Spear, J. Am. Ceram. Soc. 72 Ž1989. 171. w4x W.A. Yarbrough, R. Messier, Science 247 Ž1990. 688. w5x G.G. Stoney, Proc. R. Soc. Lond. Ser. A 82 Ž1909. 172. w6x K. Roll, J. Appl. Phys. 47 Ž1976. 3224. w7x B.D. Cullity, Elements of X-ray Diffraction, Addison-Wesley, Reading, MA, 1978, p. 447. w8x D.S. Knight, W.B. White, J. Mater. Res. 4 Ž1989. 385. w9x J.W. Ager, M.D. Drory, Phys. Rev. B 48 Ž1993. 2601. w10x S. Ganesan, A.A. Maradudin, J. Oitmaa, Ann. Phys. 56 Ž1970. 556. w11x M.H. Grimsditch, E. Anastassakis, M. Cardona, Phys. Rev. B 18 Ž1978. 901. w12x P.R. Chalker, A.M. Jones, C. Johnston, I.M. Buckley-Golder, Surf. Coat. Technol. 47 Ž1991. 365. w13x H. Windischmann, G.F. Epps, Y. Cong, R.W. Collins, J. Appl. Phys. 69 Ž1991. 2231. w14x J.A. Baglio, B.C. Farnsworth, S. Hankin, G. Hamill, D. O’Neil, Thin Solid Films 212 Ž1992. 180. w15x N.S. Van Damme, D.C. Nagle, S.R. Winzer, Appl. Phys. Lett. 58 Ž1991. 2919.

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