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Analytical and Numerical Modeling of Surface Morphologies in Thin Films

Published online by Cambridge University Press:  15 February 2011

François Y. Genin
François Y. Genin*
Affiliation:
Lawrence Livermore National Laboratory, Chemistry and Materials Science Division, Livermore, California 94550.
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Abstract

Experimental studies have shown that strains due to thermal expansion mismatch between a film and its substrate can produce very large stresses in the film that can lead to the formation of holes and hillocks. Based on a phenomenological description of the evolution of a solid surface under both capillary and stress driving forces and for surface and grain boundary self-diffusion, this article provides, for the first time, analytical and numerical solutions for surface profiles of model geometries in polycrystalline thin films. The results can explain a variety of surface morphologies commonly observed experimentally and are discussed to give some practical insights on how to control the growth of holes and hillocks in thin films.

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References

REFERENCES

1 Chaudhari, P., J. Appl. Phys. 45, 4339 (1974).Google Scholar
2 Jackson, M. S. and Li, C. -Y., Acta Metall. 30, 1993 (1982).Google Scholar
3 Srolovitz, D. J. and Safran, S. A., J. Appl. Phys. 60, 247 (1986).Google Scholar
4 Srolovitz, D. J. and Safran, S. A., J. Appl. Phys. 60, 255 (1986).Google Scholar
5 Hackney, S. A., Scripta Metall. 22, 1273 (1988).Google Scholar
6 Jiran, E. and Thompson, C. V., J. Electron. Mat. 19, 1153 (1990).Google Scholar
7 Jiran, E. and Thompson, C. V., Thin Solid Films 208, 23 (1992).Google Scholar
8 Sanchez, J. E. Jr., and Artz, E., Scripta Metall. Mater. 27, 285 (1992).Google Scholar
9 Génin, F. Y., Mullins, W. W., Wynblatt, P., Acta Metall. 40, 3239 (1992).Google Scholar
10 Brandon, R. and Bradshaw, F. J., Royal Aircraft Est., Tech. Rep. No. 66095 (1966).Google Scholar
11 Lahiri, S. K. and Wells, O. C., Appl. Phys. Lett. 15, 234 (1969).Google Scholar
12 Lahiri, S. K., J. Appl. Phys. 41, 3172 (1970).Google Scholar
13 Dell’oca, C. J. and Learn, A. J., Thin Solid Films 8, R47 (1971).Google Scholar
14 Sato, K., Oi, T., Matsumaru, H., Okubo, T. and Nishimura, T., Metall. Trans. 2, 691 (1971).Google Scholar
15 Lahiri, S. K., J. Appl. Phys. 46, 2791 (1975).Google Scholar
16 Murakami, M., Thin Solid Films 55, 101 (1978).Google Scholar
17 Huang, H. -C. W., Chaudhari, P., Kircher, C. J. and Murakami, M., Phil. Mag. A 54, 583 (1986).Google Scholar
18 Kobayashi, T., Kitahara, H., ,and Hosokawa, N., J. Vac. Sci. Technol. A 5, 2088 (1987).Google Scholar
19 Yost, F. G., Scripta Metall. 23, 1323, (1989).Google Scholar
20 Kim, J. Y. and Hummel, R. E., Phys. Stat. Sol. A 122, 255 (1990).Google Scholar
21 Smith, U., Kristensen, N., Ericson, F. and Schweitz, J. -Å., J. Vac. Sci. Technol. A 9, 2527 (1991).Google Scholar
22 Ericson, F., Kristensen, N., Schweitz, J. -Å. and Smith, U., J. Vac. Sci. Technol. B 9, 58 (1991).Google Scholar
23 Chang, C. Y. and Vook, R. W., J. Vac. Sci. Technol. A 9, 559 (1991).Google Scholar
24 Murakami, M., J. Vac. Sci. Technol. A 9, 2469 (1991).Google Scholar
25 Aceto, S., Chang, C. Y., and Vook, R. W., Thin Solid Films 219, 80 (1992).Google Scholar
26 Gerth, D., Katzer, D. and Schwarzer, R., Mater. Sci. Forum 94–97, (edited by Abbruzzese, G. and Brozzo, P.), 557 (1992).Google Scholar
27 Mullins, W. W., J. Appl. Phys. 28, 333 (1957).Google Scholar
28 Mullins, W. W., J. Appl. Phys. 30, 77 (1959).Google Scholar
29 King, R. T. and Mullins, W. W., Acta Metall. 10, 601 (1962).Google Scholar
30 Nichols, F. A. and Mullins, W. W., Trans AIME 233, 1840 (1965).Google Scholar
31 Nichols, F. A., J. Appl. Phys. 37, 2805 (1966).Google Scholar
32 Mullins, W. W., in Metal Surfaces, ASM-AIME Seminar, Cleveland, Ohio, 1963.Google Scholar
33 Srolovitz, D. J., Acta Metall. 37, 621 (1989).Google Scholar
34 Thouless, M. D., Acta Metall. Mater. 41, 1057 (1993).Google Scholar
35 Génin, F. Y., Mullins, W. W., Wynblatt, P., Acta Metall. 41, 3541 (1993).Google Scholar
36 Spingarn, J. R. and Nix, W. D., Acta Metall. 26, 1389 (1978).Google Scholar
37 Chuang, T. -J., Kagawa, K. I., Rice, J. R. and Sills, L. B., Acta Metall. 27, 265 (1979).Google Scholar
38 Svoboda, J. and Riedel, H., Acta Metall. Mater. 43, 499 (1995).Google Scholar
39 Pan, J. and Cocks, A. C. F., Acta Metall. Mater. 43, 1395 (1995).Google Scholar
40 Herring, C., in Physics of Powder Metallurgy, edited by Kingston, W. E., McGraw-Hill, New York (1951).Google Scholar
41 Herring, C., J. Appl. Phys. 21, 437 (1950).Google Scholar
42 Mullins, W. W., Acta Metall. 6, 414 (1958).Google Scholar
43 Génin, F. Y., J. Appl. Phys. 77, (1995) in press.Google Scholar
44 Génin, F. Y., Acta Metall. Mater., in press.Google Scholar
45 Génin, F. Y. and Siekhaus, W. J., J. Appl. Phys. (submitted).Google Scholar
46 Venkatraman, R., Chen, S. and Bravman, J. C., J. Vac. Sci. Technol. A 9, 2536 (1991).Google Scholar
47 Gerth, D., Katzer, D. and Schwarzer, R., Mater. Sci. Forum 94–97 (edited by Abbruzzese, G. and Brozzo, P.), 557 (1992).Google Scholar
48 Zlatanovic, D. and Davinic, G., Vacuum 40, 157 (1990).Google Scholar
49 Pico, C. A. and Bonifield, T. D., J. Mater. Res. 8, 1010 (1993).Google Scholar
50 Grovenor, C. M. R., Hentzell, H. T. G. and Smith, D. A., Acta Metall. Mater. 32, 773 (1984).Google Scholar
51 Thompson, C. V., Floro, J. and Smith, H. I., J. Appl. Phys. 67, 4099 (1990).Google Scholar