Finite-element formulation for anodic bonding

An anodic bond is modeled as a moving non-material line forming the intersection of three material surfaces representing the unbonded conductor, the unbonded insulator, and the bonded interface. The component mass balance equations, Gauss' law, and the linear momentum equations are cast in a finite-element formulation, which is used to predict the evolution of the sodium ion concentration, electric potential, and stress during the anodic bonding of Pyrex glass and silicon. The method is applicable to the viscoplasticity of solid electrolytes, and the volume and interface free energies can be modified to model electromechanical interface phenomena such as debonding, space charge accumulation and sliding at grain boundaries in ionic crystals, and a cohesive zone theory of piezoelectric fracture.