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.
Similar content being viewed by others
References
P. Chaudhari, J. Appl. Phys. 45, 4339 (1974).
M. S. Jackson and C. -Y. Li, Acta Metall. 30, 1993 (1982).
D. J. Srolovitz and S. A. Safran, J. Appl. Phys. 60, 247 (1986).
D. J. Srolovitz and S. A. Safran, J. Appl. Phys. 60, 255 (1986).
S. A. Hackney, Scripta Metall. 22, 1273 (1988).
E. Jiran and C. V. Thompson, J. Electron. Mat. 19, 1153 (1990).
E. Jiran and C. V. Thompson, Thin Solid Films 208, 23 (1992).
J. E. Sanchez, Jr. and E. Artz, Scripta Metall. Mater. 27, 285 (1992).
F. Y. Génin, W. W. Mullins, P. Wynblatt, Acta Metall. 40, 3239 (1992).
R. Brandon and F. J. Bradshaw, Royal Aircraft Est., Tech. Rep. No. 66095 (1966).
S. K. Lahiri and O. C. Wells, Appl. Phys. Lett. 15, 234 (1969).
S. K. Lahiri, J. Appl. Phys. 41, 3172 (1970).
C. J. Dell’oca and A. J. Learn, Thin Solid Films 8, R47 (1971).
K. Sato, T. Oi, H. Matsumaru, T. Okubo and T. Nishimura, Metall. Trans. 2, 691 (1971).
S. K. Lahiri, J. Appl. Phys. 46, 2791 (1975).
M. Murakami, Thin Solid Films 55, 101 (1978).
H. -C. W. Huang, P. Chaudhari, C. J. Kircher and M. Murakami, Phil. Mag. A 54, 583 (1986).
T. Kobayashi, H. Kitahara, and N. Hosokawa, J. Vac. Sci. Technol. A 5, 2088 (1987).
F. G. Yost, Scripta Metall. 23, 1323, (1989).
J. Y. Kim and R. E. Hummel, Phys. Stat. Sol. A 122, 255 (1990).
U. Smith, N. Kristensen, F. Ericson and J. -Å. Schweitz, J. Vac. Sci. Technol. A 9, 2527 (1991).
F. Ericson, N. Kristensen, J. -Å. Schweitz and U. Smith, J. Vac. Sci. Technol. B 9, 58 (1991).
C. Y. Chang and R. W. Vook, J. Vac. Sci. Technol. A 9, 559 (1991).
M. Murakami, J. Vac. Sci. Technol. A 9, 2469 (1991).
S. Aceto, C. Y. Chang, and R. W. Vook, Thin Solid Films 219, 80 (1992).
D. Gerth, D. Katzer and R. Schwarzer, Mater. Sci. Forum 94–97, (edited by G. Abbruzzese and P. Brozzo), 557 (1992).
W. W. Mullins, J. Appl. Phys. 28, 333 (1957).
W. W. Mullins, J. Appl. Phys. 30, 77 (1959).
R. T. King and W. W. Mullins, Acta Metall. 10, 601 (1962).
F. A. Nichols and W. W. Mullins, Trans AIME 233, 1840 (1965).
F. A. Nichols, J. Appl. Phys. 37, 2805 (1966).
W. W. Mullins, in Metal Surfaces, ASM-AIME Seminar, Cleveland, Ohio, 1963.
D. J. Srolovitz, Acta Metall. 37, 621 (1989).
M. D. Thouless, Acta Metall. Mater. 41, 1057 (1993).
F. Y. Génin, W. W. Mullins, P. Wynblatt, Acta Metall. 41, 3541 (1993).
J. R. Spingarn and W. D. Nix, Acta Metall. 26, 1389 (1978).
T. -J. Chuang, K. I. Kagawa, J. R. Rice and L. B. Sills, Acta Metall. 27, 265 (1979).
J. Svoboda and H. Riedel, Acta Metall. Mater. 43, 499 (1995).
J. Pan and A. C. F. Cocks, Acta Metall. Mater. 43, 1395 (1995).
C. Herring, in Physics of Powder Metallurgy, edited by W. E. Kingston, McGraw-Hill, New York (1951).
C. Herring, J. Appl. Phys. 21, 437 (1950).
W. W. Mullins, Acta Metall. 6, 414 (1958).
F. Y. Génin, J. Appl. Phys. 77, (1995) in press.
F. Y. Génin, Acta Metall. Mater., in press.
F. Y. Génin and W. J. Siekhaus, J. Appl. Phys. (submitted).
R. Venkatraman, S. Chen and J. C. Bravman, J. Vac. Sci. Technol. A 9, 2536 (1991).
D. Gerth, D. Katzer and R. Schwarzer, Mater. Sci. Forum 94–97 (edited by G. Abbruzzese and P. Brozzo), 557 (1992).
D. Zlatanovic and G. Davinic, Vacuum 40, 157 (1990).
C. A. Pico and T. D. Bonifield, J. Mater. Res. 8, 1010 (1993).
C. M. R. Grovenor, H. T. G. Hentzell and D. A. Smith, Acta Metall. Mater. 32, 773 (1984).
C. V. Thompson, J. Floro and H. I. Smith, J. Appl. Phys. 67, 4099 (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Genin, F.Y. Analytical and Numerical Modeling of Surface Morphologies in Thin Films. MRS Online Proceedings Library 389, 83–94 (1995). https://doi.org/10.1557/PROC-389-83
Published:
Issue Date:
DOI: https://doi.org/10.1557/PROC-389-83