A first step was made here towards the development of a continuum field formulation for coupled diffusion and mechanics in polycrystalline solids. The bases of the formulation were lattice-level mechanisms, from which a continuum thermodynamic description of processes at μm-length scales was built. In the case of self-diffusion, the compositional problem was posed in terms of a binary vacancy-atom mixture. Isotropic linear elasticity and isothermal conditions were assumed. Coupled constitutive relationships for composition and mechanics were formally derived from the underlying thermodynamic principles. Coupling arose upon applying the governing partial differential equations for each sub-problem. Under applied tractions or intrinsic stresses, the atoms usually diffused from surfaces having a compressive normal traction, to those having a relatively tensile normal traction. Flow was mediated by electric fields, via the electromigration mechanism. In the case of metal interconnect lines in integrated circuit devices, the results of the microscopic processes were reflected by phenomena such as diffusional creep, hillock formation, grain growth, grain boundary motion, void formation and void evolution. A computational framework which was based upon the finite-element method was developed in order to solve the coupled equations.

A Lattice-Based Micromechanical Continuum Formulation for Stress-Driven Mass Transport in Polycrystalline Solids. K.Garikipati, L.Bassman, M.Deal: Journal of the Mechanics and Physics of Solids, 2001, 49[6], 1209-37