Effects of energy dissipation on anisotropic materials

A model and its simulations are presented to describe the effects of energy dissipation on anisotropic systems. When the current electromigration is constant, energy dissipation depends on lattice constants, resistivity, and the angles along the longitudinal and transversal directions. It is shown that an orientation variation of the grain can significantly influence the energy dissipation for some anisotropic materials. Based on calculations for the grain model, the mechanism of grain growth and microstructure evolution under electromigration is explained. Theoretical implications about material selection and reliability are derived.