Grain boundary diffusion due to stress and electromigration

Jon Wilkening, Courant Institute of Mathematical Sciences, New York University

In this talk, I will describe a continuum model of mass transport phenomena in microelectronic circuits due to high current densities (electromigration) and gradients in normal stress along grain boundaries. The model involves coupling many different equations and phenomena, and difficulties such as non-locality, stiffness, complex geometry, and singularities in the stress tensor near corners and junctions make the problem difficult to analyze rigorously and simulate numerically.

I will also describe a singularity capturing least squares finite element method we developed to model this problem numerically. The numerical results provided unexpected insight about the structure of the problem, which ultimately led to a rigorous proof of well-posedness using techniques from semigroup theory.

Abstract Author(s): Jon Wilkening