Mesoscopic Modelling of Mechanically-Modulated Electrical Conductivity in Zinc Oxide Varistors

Abstract

An electromechanically-coupled model for the simulation of electric current flow in zinc oxide varistors is presented. The model is based on an equivalent circuit representation of the varistor microstructure, where the grain boundaries are modelled as non-linear resistors in the circuit. This approach extends previous circuit models by including the effect of mechanical stress on grain boundary conductivity. The three-dimensional mechanical stress distribution in the material is calculated by the finite element method (FEM). 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 polarisation. Finally, the electric current flow patterns and the bulk conductivity of the material are computed using a non-linear 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 microstructural properties and on the mechanical stress condition of the material. The effect of residual thermal stress in polycrystalline structures on the electrical conductivity is also considered. Just as in the case of applied stress, the electrical conductivity is highly sensitive to the accumulation of thermal stress within the material. Furthermore, the effect of the inverse piezoelectric effect is examined and accounted for in the computation of the macroscopic varistor characteristics.