RESUMEN
The stress-driven grain
boundary diffusion problem is 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 nonlocality, complex geometry, and singularities in the
stress tensor have left open such mathematical questions as existence of
solutions and compatibility of boundary conditions. In this paper and its
companion, we address these issues and establish a firm mathematical foundation
for this problem. We use techniques from semigroup
theory to prove that the problem is well posed and that the stress field
relaxes to a steady state distribution which, in the nondegenerate
case, balances the electromigration force along grain
boundaries. Our analysis shows that while the role of electromigration
is important, it is the interplay among grain growth, stress generation, and
mass transport that is responsible for the diffusive nature of the problem. Electromigration acts as a passive driving force that
determines the steady state stress distribution, but it is not responsible for
the dynamics that drive the system to steady state. We also show that stress
singularities may develop near grain boundary junctions; however, stress
components directly involved in the diffusion process remain finite for all
time. Thus, we have identified a mechanism by which large "hidden"
stresses may develop that are not directly involved in the diffusion process
but may play a role in void nucleation and stress-induced damage. [ABSTRACT
FROM AUTHOR]