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Proceedings of Symposium on Energy Engineering in the 21<sup>st</sup> Century (SEE2000) Volume I-IV

ISSN:
1-56700-132-7 (Print)

SELF-SIMILAR GROWTH OF A COMPOUND LAYER IN THIN-FILM BINARY DIFFUSION COUPLES

Huifang Zhang
Mechanical Engineering Department, Louisiana State University Baton Rouge, LA 70803-6413, USA

Harris Wong
Mechanical Engineering Department, Louisiana State University Baton Rouge, LA 70803-6413, USA

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. This growth process is important in electronic materials processing and in synthesis of high-temperature materials using multilayer films. 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. An asymptotic solution valid for small concentration gradients is derived and agrees with the numerical results.