Analysis and modeling of residual stress in diamond thin film deposited by the hot-filament chemical vapor deposition process

Transcription

1 Analysis and modeling of residual stress in diamond thin film deposited by the hot-filament chemical vapor deposition process Seung I. Cha and Soon H. Hong Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, 373- Kusung-dong, Yusung-gu, Taejon, , Korea (Received 6 October 2000; accepted 0 April 200) The effect of microstructure on residual stress in diamond thin film was investigated. The diamond thin film was deposited by the hot filament chemical vapor deposition process with hydrogen/methane precursor gas and followed by annealing at 50 C for 30 min. The residual stresses of the diamond thin film were measured by Raman spectroscopy. A model to estimate the residual stress was proposed on the basis of grain boundary relaxation mechanism and microstructural analysis of diamond thin film. It is confirmed that the residual stress in diamond thin film is proportional to a microstructural factor, / [D( f + )] /2, where D is the grain size of diamond and f is the volume ratio of nondiamond carbon/diamond. I. INTRODUCTION In recent years, diamond thin film has been the most promising material in various fields of industry and science because of the outstanding properties of diamond such as high thermal conductivity, low electric conductivity, high wear resistance, and wide band gap. Moreover, the application areas become even broader with the advance of diamond deposition technology at low pressure. In spite of these numerous potential application areas, the issues on the residual stress in diamond thin film have not been clearly understood. Numerous researchers have been investigating the measurement and analysis of residual stress in diamond thin film. 9 Windischmann et al. investigated the residual stress of diamond thin film by the curvature measurement technique based on Stoney s equation. They measured the variation of residual stress in diamond thin film deposited by microwave plasma chemical vapor deposition (MPCVD) process according to the substrate temperature and methane volume fraction in precursor gas. Their analysis stated that the nondiamond carbon and hydrogen impurities in diamond thin film induced the compressive residual stress and grain size refinements, increasing tensile residual stress by the grain boundary relaxation mechanism. Chalker et al. 3 investigated the residual stress of diamond thin film deposited by the hot-filament chemical vapor deposition (HFCVD) process by x-ray diffraction (XRD). They reported that the residual tensile stress is caused by the misfit stress at the interface between diamond and substrate. Chiou 4 explained that the grain boundary caused tensile residual stress in diamond thin film. Kuo et al. 5 found that the presence of nondiamond carbon within the diamond lattice induced the compressive stresses. Schwarzbach et al. 8 and Baglio et al. 6 issued grain size effects on the residual stress. It is generally accepted that the tensile stress increases with decreasing grain size by the grain boundary relaxation mechanisms, and the nondiamond carbon induces compressive stress in diamond thin film. However, in spite of the understanding about the origin of residual stresses in diamond thin film, the quantitative analyses to estimate the residual stress in diamond thin film have not been established yet. In this study, the effect of grain size and nondiamond carbon in diamond thin film on residual stress was investigated by experimental measurements and theoretical modeling. The microstructures of deposited diamond thin films were observed under various conditions of deposition process and annealing treatment. The dependence of residual stress on microstructural factors was analyzed to estimate the residual stress in diamond thin film. II. EXPERIMENTAL PROCEDURES Diamond thin films were deposited on the Si substrate by the HFCVD process heated by tungsten filaments. The (00) Si single crystal wafers with thickness of 0.5 mm, which were pretreated with fine diamond powders by an ultrasonic vibrator to seed the diamond particles, were used as substrates. The distance between the substrate and the tungsten filaments was fixed as 7 mm. The temperature of the substrate was maintained at 000 C during the deposition process. The deposition J. Mater. Res., Vol. 6, No. 7, Jul Materials Research Society 953

2 time was 0 h. Hydrogen gas mixed with a controlled amount of methane was used as a precursor gas for deposition of diamond thin films. The volume fraction of methane in the precursor gas was controlled from.5% to 3.0%. Total gas pressure in HFCVD system was maintained at 40 torr, and the gas flow rate was fixed as 00 sccm. At these deposition conditions, the thickness of diamond thin film was about 3 m regardless of the methane volume fraction in the precursor gas. The deposited diamond thin films were annealed at 50 C for 30 min to investigate the effect of annealing treatment on the residual stress. To prevent the oxidation of diamond thin film, the samples were sealed in a quartz tube vacuumed to 0 6 torr, and these were followed by annealing. The microstructure of diamond thin films was observed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The residual stress and content of nondiamond carbon were measured by the Raman spectroscopy.,2 III. RESULTS AND DISCUSSION A. Microstructure evolution of deposited diamond thin film Surface morphology of deposited diamond thin films was found to be closely dependent on the deposition conditions. Strong facets were formed on the surface of diamond thin films as shown in Fig. A strong () facet was developed when the volume fraction of methane in precursor gas was above 2.5%. However, the surface morphology showed irregular shape and surface facets disappeared when the volume fraction of methane in precursor gas was below 2.5%. As the volume fraction of methane increased in precursor gas, more strong facets were developed. These results were not in agreement with others reports on the microstructure of diamond thin film. 3 5 Strong facets were reported when the volume fraction of methane was 0.5.0%, and the facets disappeared when the volume fraction of methane increased over.5%. Figures 2(a) and 2(b) exhibit the variations of grain size and the ratio of nondiamond carbon/diamond in deposited diamond thin film with increasing methane volume fraction, respectively. The nondiamond carbon content in thin film was analyzed by the peak intensity ratio obtained from the Raman spectroscopy. The grain size of diamond increased as the volume fraction of methane in precursor gas increased from 0.5 to 2.0 m, as shown in Fig. 2(a). It is shown in Fig. 2(b) that the nondiamond carbon/diamond volume ratios decreased as the volume fraction of methane in precursor gas increased from 0.5% to 2.5%. However, the ratio of nondiamond carbon/diamond increased when the volume fraction of methane in the precursor gas was 3.0%. FIG.. SEM micrographs of surface of diamond thin film deposited on Si at 000 C for 0 h with CH 4 H 2 ratio of (a).5%, (b) 2%, (c) 2.5%, and (d) 3%. 954 J. Mater. Res., Vol. 6, No. 7, Jul 200

3 B. Analysis of residual stresses of diamond thin film FIG. 2. (a) The variation of average grain size and (b) the variation of nondiamond carbon/diamond volume ratio in diamond thin films deposited at 000 C for 0 h coinciding with CH 4 /H 2 ratio changes. The surface morphologies of annealed diamond thin films are shown in Fig. 3. The surface facets of diamond thin film deposited at the volume fraction of the methane in precursor gas of 2.5% developed considerably with the increase in annealing time at 50 C. The development of a strong () facet is due to the lowering of the surface energy during annealing treatment. In contrast to these results, for the diamond thin film deposited at the volume fraction of methane of 3.0% in the precursor gas, the surface morphologies did not change by annealing because the () facet had already been formed during the deposition process. The grain size of annealed diamond thin film increased with the increasing annealing time, as shown in Fig. 4(a). However, the grain size of diamond thin film deposited at the volume fraction of methane of 3.0% in the precursor gas decreased when the annealing time was over 30 min. Figure 4(b) depicts that the nondiamond carbon/diamond ratios increased with increased annealing time. It seems that the increasing ratio of nondiamond carbon/diamond resulted from the phase transition of diamond into graphite at high temperature. Measured residual stress values by Raman spectroscopy with the increasing volume fraction of methane in precursor gas and the annealing time at 50 C are shown in Fig. 5. Figure 5(a) shows that the compressive residual stress increased as the methane volume fraction in the deposition process increased. Comparing the relationship between the residual stress and the volume ratio of nondiamond carbon/diamond, the compressive residual stress increased as the volume ratio of nondiamond carbon/diamond decreased. These results were in contrast to those of the other researches that reported the increase of compressive residual stress as the contents of impurities, such as nondiamond carbon, increased.,5 Furthermore, the compressive residual stress increased with the increasing grain size of diamond. These results agreed with the findings that the tensile residual stress decreased with an increase in grain size of diamond by the grain boundary relaxation model. 4,6,8 In the case of annealed diamond thin films, there were considerable changes in residual stress. In diamond thin film deposited at the volume fraction of methane of 2.5% in precursor gas, residual stress increased up to the annealed time of min, and then decreased and was saturated with the increased annealing time. When the volume fraction of methane was 3.0% in the precursor gas, residual stress decreased with the increased annealing time up to min, and then increased and saturated with further increased annealing time. Considering the changes of the nondiamond carbon content by annealing diamond thin films, the residual stress changes during annealing treatments did not depend on the nondiamond carbon in diamond thin films. Also, compared to the grain size changes during annealing treatment, it was found that the residual stress did not depend on only the grain size change. Thus, the combined effect of the grain size and nondiamond carbon contents in diamond thin film must be considered in analysis of the residual stress in diamond thin films. C. Modeling of residual stress in diamond thin film The residual stress in thin films generally can be divided into two components, i.e., intrinsic stress and extrinsic stress. To obtain the intrinsic stress, the thermal strain between diamond thin film and Si substrate can be estimated based on the following equation: th = T2 Ti diamond Si dt, () J. Mater. Res., Vol. 6, No. 7, Jul

4 FIG. 3. SEM micrographs of the diamond thin films deposited with methane volume fraction of 2.5% and 3.0% after annealing at 50 C for various times: (a) 2.5%, as deposited; (b) 2.5%, min; (c) 2.5%, 5 min; (d) 2.5%, 30 min; (e) 3.0%, as deposited; (f) 3.0%, min; (g) 3.0%, 5 min; and (h) 3.0%, 30 min. where diamond indicates the thermal expansion coefficient and Si indicates the thermal expansion coefficient of Si substrate. In Eq. (), the calculated thermal stress was compressive 720 MPa, and therefore the intrinsic stress in diamond thin film was tensile. To understand the intrinsic stress of diamond thin film, numerous explanations have been attempted, but no quantified model is available yet. In many cases the tensile intrinsic stresses were explained by grain boundary relaxation, and compression intrinsic stresses by impurities, especially nondiamond carbon because of its large molar volume. 9 To analyze the combined effect of grain size and nondiamond carbon on the residual stress in diamond thin film, we performed microstructure modeling performed. In modeling, we simplified the microstructure of diamond thin film, as shown in Fig. 6(a), into the array of rectangular shaped columnar diamond grains with nondiamond carbon phase between the diamond grains, as shown in Fig. 6(b). The residual stress in diamond thin films was calculated by Hoffman s grain boundary relaxation model. 6,7 Applying this model, the conditions of low diffusion rate, no plastic deformation, and columnar grain structure were required. The diamond thin film used in this study was perfectly satisfactory for applying the grain boundary relaxation model. In the grain boundary relaxation model, the residual stress was generated by filling the intergrain spacing with elastically deformed diamond grains during grain boundary formation. Thus, to calculate the residual stress, the equilibrium intergrain spacing in which the diamond 956 J. Mater. Res., Vol. 6, No. 7, Jul 200

5 begins to elastically deform, have to be obtained by calculating the free energy per unit area before the grain boundary formed as follows: E = E D + d 2 8 Dt D + 8 Dt G. (2) Where D and d are the grain size of diamond and graphite, respectively, and t is thickness of thin film. E 0 is internal energy of grains and D and G the are surface energy of diamond grains and graphite, respectively. If the grain boundary is formed by elastic extension and filling the intergrain spacing, the free energy is calculated as follows: E 2 = E D + d 2 8 Dt D G + t E D 2, (3) where D G is the grain boundary energy of diamond and graphite. The equilibrium intergrain spacing can be obtained when the energy values before and after the grain boundary formation are the same. It is expressed as follows: = D.5 D + d 0.5 E 2 D + 2 G 2 D G 0.5. (4) If all surface energy difference terms were represented by, the stress by filling the intergrain spacing could be calculated as follows: = D D + d E (5) The value calculated by Eq. (4) was about nm. This agreed with other researchers calculation from stress. 9 With the volume ratio of nondiamond carbon/diamond f, measured by Raman spectroscopy, and geometrical calculation in the microstructural model, the width of nondiamond carbon layer d can be obtained as a function of D and f: d = D + f. (6) FIG. 4. (a) The variation of average grain size and (b) nondiamond carbon/diamond volume ratio of diamond thin films deposited at 000 C with methane volume fractions of 2.5% and 3.0% with annealing time at 50 C in vacuum. FIG. 5. The residual stresses of diamond thin films measured by the Raman spectroscopy method: (a) as-deposited and (b) annealed at 50 C in vacuum condition. J. Mater. Res., Vol. 6, No. 7, Jul

6 FIG. 6. (a) TEM micrographs of diamond thin film deposited at 000 C for 0 h with methane volume fraction of 2.0% and (b) schematic illustration showing microstructure model of diamond thin films to calculate the residual stress. Using Eq. (6) in Eq. (5), we can obtain the residual stress as a function of diamond grain size and volume ratio of nondiamond carbon/diamond as in Eq. (7): = E D + f (7) In Eq. (7), the stress was not a function of thickness or other factors. Therefore, Eq. (7) could be simplified by introducing two constants, A and C, as follows: A = D( + f ) + C. (8) In the above equation, the constant A is dependent on the material properties, i.e., elastic modulus and surface energy, and the constant C is extrinsic stress, which implies thermal stress between diamond and substrate or diamond and interlayer materials. To prove this model and FIG. 7. Plot of residual stress in diamond thin films versus /[D( + f )] /2. Solid symbols represent as-deposited and open symbols represent annealed specimens. The line shows calculated values from modified Hoffman s model. calculation, the residual stress and /[D( + f )] /2 were plotted in Fig. 7. As shown in Fig. 7, all stress values from different conditions were arranged in one line. By fitting the experimental data, the constant A is obtained in a range from to Pa m /2, and the constant C is obtained as.2 GPa. The value of the constant A obtained by fitting the experimental data agreed with the calculated value, i.e., Pa m /2, under the assumption that the grain boundary was only diamond or graphite. But the constant C was larger than the thermal stress calculated by Eq. (). This was the reason why, in extrinsic stress, there was another origin of compressive stress that would contain some impurities like hydrogen that existed in the diamond grain. But the important feature of this work was that the major factors of residual stress in diamond thin film were only two factors, that is, grain size and nondiamond carbon content. In the investigation of residual intrinsic stress by microstructure modeling, the role of nondiamond carbon, in residual stress of diamond thin film, was shown to be different from others results. In general, the nondiamond carbon was regarded as the origin of compressive residual stress because it has a larger molar volume than that of diamond and it has been well explained in the experimental data. However, in this case, nondiamond carbon existed in the grain boundaries of diamond. 7 The nondiamond carbon in the grain boundaries of diamond could fill the gap between diamond grains when the grain boundaries form. Another role of nondiamond carbon was the modification of grain boundary energies. IV. CONCLUSIONS The residual stress of diamond thin film was investigated by the Raman spectroscopy method. As a result, the major factors inducing residual stress in diamond thin film include thermal stress, grain size, and nondiamond 958 J. Mater. Res., Vol. 6, No. 7, Jul 200

7 carbon content. To analyze these effects on residual stress in diamond thin film, a microstructure model was used. As a result, we could find out the microstructure factor /[D( + f )] /2 that is linearly dependent on residual stress in diamond thin film. The other parameters affecting the residual stress were the only factors that changed these major factors. In this case, the role of nondiamond carbon to residual stress of diamond thin film was to fill intergrain space and to modify the surface energy of diamond grains. REFERENCES. H. Windischmann, G.F. Epps, Y. Cong, and R.W. Collins, J. Appl. Phys. 63, 223 (99). 2. H. Guo and M. Alam, Thin Solid Film 22, 73 (992). 3. P.R. Chalker, A.M. Jones, C. Johnston, and I.M. Buckley-Golder, Surf. Coat. Technol. 47, 365 (99). 4. Y.H. Chiou, C.T. Hwang, M.Y. Han, J.H. Jou, Y.S. Chang, and H.C. Shih, Thin Solid Film 253, 9 (994). 5. C.T. Kuo, C.R. Lin, and H.M. Lien, Thin Solid Film , 254 (996). 6. J.A. Bablio, B.C. Farnsworth, S. Hankin, G. Hamill, and D. O Neil, Thin Solid Film 22, 80 (992). 7. W. Wang, K. Liao, J. Gao, and A. Liu, Thin Solid Film 25, 74 (992). 8. D. Schwarzbach, R. Haubner, and B. Lux, Diamond Rel. Mater. 3, 757 (994). 9. S.K. Choi and H.M. Choi, J. Vac. Sci. Technol. A 4, 65 (996). 0. P.M. Fabis, Thin Solid Film 288, 93 (996).. M.H. Grimsditch, Phys. Rev. B 32, 90 (985). 2. H. Bopart, Phys. Rev. B 32, 423 (985). 3. K. Kobashi, K. Nishimura, K. Miyata, K. Kumagai, and A. Nakaue, J. Mater. Res. 5, 2469 (990). 4. C.C. Chiu, Y. Liou, and Y.D. Juang, Thin Solid Film 260, 8 (995). 5. S.C. Sharma, M. Green, R.C. Hyer, C.A. Dark, T.D. Black, A.R. Chourasia, D.R. Chopra, and K.K. Mishra, J. Mater. Res. 5, 2424 (990). 6. R.W. Hoffman, Phys. Thin Film 3, 2 (966). 7. W.D. Nix and B.M. Clemens, J. Mater. Res. 4, 3467 (999). J. Mater. Res., Vol. 6, No. 7, Jul