Mesoscopic modeling of the mechanically tunable electrical conductivity of ZnO varistors

An electromechanically coupled model for the simulation of electric current flow in ZnO varistors is presented. The model is based on an equivalent circuit representation of the varistor microstructure, where the grain boundaries are modeled as nonlinear resistors in the circuit. This approach extends on previous circuit models by including the effect of mechanical stress on grain boundary conductivity. The 3D mechanical stress distribution in the material is calculated by the finite element method. Using this distribution, the electrical resistance of each grain boundary 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 IV-characteristics reveal a significant sensitivity of electrical conductivity to applied stress. For 2D and 3D ZnO varistor models, the simulations demonstrate the effect of current concentration along thin conducting paths depending on microstructure properties and on the mechanical stress condition of the material.