A lattice-based micromechanical continuum formulation for stress-driven mass transport in polycrystalline solids

This work represents a first step toward the development of a continuum field formulation for the coupled phenomena of diffusion and mechanics in polycrystalline solids. The basis of the formulation lies in lattice-level mechanisms, from which a continuum thermodynamic description of processes at micron length scales is developed. Considering self-diffusion, the composition problem is posed in terms of a binary vacancy-atom mixture. For mechanics, isotropic linear elasticity and isothermal conditions are assumed. The coupled constitutive relations for composition and mechanics are formally derived from the underlying thermodynamic principles. When applied to governing partial differential equations for each subproblem, the coupled nature is realized. Under applied tractions or intrinsic stress, the atoms diffuse - in general from surfaces with compressive normal traction to those with relatively tensile normal traction. The flow is mediated by electric fields via the mechanism of electromigration. In the case of metal interconnect lines in integrated circuit devices, the results of these microscopic processes are manifested in phenomena such as diffusional creep, hillock formation, grain growth, grain boundary motion, void formation and void evolution. These phenomena have a significant impact on the function, performance and failure of interconnect lines. A computational framework based on the finite element method has been developed to solve the coupled equations. Several numerical examples are presented and comparisons with analytical results are provided where the latter are available. (C) 2001 Elsevier Science Ltd. All rights reserved.