Abstract
The diffusion controlled growth of a compound phase AnB between two thin films of material A and B is studied with the nonlinear Kirkendall effect included. Previous models of the growth rate do not solve the diffusion equation, and thus do not fully utilize the predictive capability. This paper describes a self-similar transformation that reduces the nonlinear, time-dependent diffusion equation with two free boundaries into a nonlinear ordinary differential equation, which is solved numerically by a shooting method. It is found that the intrinsic diffusion coefficients of A and B in AnB can be determined from the positions of the interfaces without using the concentration profile. This provides a simpler method for measuring intrinsic diffusion coefficients.
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References
Mayer, J. W. and Lau, S. S. Electronic Materials Science: for integrated circuits in Si and GaAs, Macmillan, New York (1990).
Tu, K. N. Mayer, J. W. and Feldman, L. C. Electronic Thin Film Science, Macmillan, New York (1992).
Greer, A. L. Applied Surface Sci. 86, 329 (1995).
Greer, A. L. Materials Sci. Engineering A134, 1268 (1991).
Wohlert, S. and Bormann, R. J. Applied Phys. 85, 825 (1999).
Michaelsen, C. Yan, Z. H. and Bormann, R. J. Appl. Phys. 73, 2249 (1993).
Lin, J. H. and Chen, L. J. J. Appl. Phys. 77, 4425 (1995).
Shim, J. Y. Kwak, J. S. and Baik, H. K. Thin Solid Films 288, 309 (1996).
Munir, Z. A. High Temperature Sci. 27, 279 (1990).
Munir, Z. A. Metallurgical Transactions A 23A, 7 (1992).
Kidson, G. V. J Nuclear Materials 3, 21 (1961).
Wagner, C. Acta Metallurgica 17, 99 (1969).
Shatynski, S. R. Hirth, J. P. and Rapp, R. A. Acta Metallurgica 24, 1071 (1976).
Williams, D. S. Rapp, R. A. and Hirth, J. P. Metallurgical Transactions A 12A, 639 (1981).
Shewmon, P. G. Diffusion in Solids, McGraw-Hill, New York (1963).
H. Zhang, Master thesis, Louisiana State University (2000).
H. Zhang, and H. Wong, Acta Materialia (in press).
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Zhang, H., Wong, H. A Self-Similar Solution for the Growth Rate of a Compound Layer in Thin-Film Binary Diffusion Couples. MRS Online Proceedings Library 580, 309–314 (1999). https://doi.org/10.1557/PROC-580-309
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DOI: https://doi.org/10.1557/PROC-580-309