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Numerical Simulation of Surface Diffusion Controlled Motion and Shape Change of Electromigration Voids

Published online by Cambridge University Press:  15 February 2011

O. Kraft,
U. E. Mockl and
E. Arzt
O. Kraft
Affiliation:
now at Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305-2205
U. E. Mockl
Affiliation:
Max-Planck-Institut ftir Metallforschung and Institut ftir Metallkunde der Universitdt, Seestr. 71, D-70174 Stuttgart, Germany
E. Arzt
Affiliation:
Max-Planck-Institut ftir Metallforschung and Institut ftir Metallkunde der Universitdt, Seestr. 71, D-70174 Stuttgart, Germany
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Abstract

In order to simulate void motion and shape change of electromigration voids a numerical model was developed in which electromigration-driven diffusion on the void surfaces is assumed to act as the primary transport mechanism. The simulation describes the motion and shape evolution of a "two-dimensional void" having a simple initial shape in an isotropic medium. The current density distribution in the vicinity of a void was calculated by the application of a finite element method. Subsequently, the void shape changes by surface diffusion were examined using a finite difference scheme which includes the influence of gradients in curvature along the void surface. The model has been extended to allow other diffusion pathways, such as grain boundaries. The often observed faceting of voids and the formation of slit-like voids are discussed on the basis of simulations in which anisotropic surface tension and anisotropic surface diffusivity were assumed.

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