Coupled Simulation of Current Flow and Residual Thermal Stress in ZnO Varistors

An electromechanically coupled modeling framework for the simulation of electric current flow in ZnO varistors is developed. The model is based on an equivalent circuit representation of the varistor microstructure with grain boundaries represented by nonlinear resistor branches of the circuit. This approach extends on previous circuit models by including the effect of mechanical stress on grain boundary conductivity. In this article, we consider, in particular, the effect of residual thermal stress in polycrystalline structures on electrical conductivity. The distribution of this stress throughout the material is computed by finite element method (FEM) simulations. Then, each grain boundary conductivity is determined by applying a self-consistent model for the trapped interface charge induced by piezoelectric polarization. Finally, the electric current flow patterns and the bulk conductivity of the material are computed using the nonlinear circuit model. The simulated I-V characteristics reveal a significant sensitivity of the electrical conductivity to internal thermal stress within the material. Furthermore, for realistic ZnO microstructures, the simulations demonstrate the effect of current concentration along thin conducting paths depending on the mechanical stress condition of the material.