Modeling of current distribution in zinc oxide varistors using Voronoi network and finite element method

Nonuniform current distribution inside varistor ceramics is a key factor influencing its performance and failures. Therefore understanding, modeling and predicting of current distribution in varistor ceramics is of crucial significance. This paper proposes a numerical model for simulation of nonuniform electric current distribution inside zinc oxide varistors. A numerical model is based on physical modeling of the varistor's grain-structured geometry presented by Voronoi network using finite element method (FEM) simulation. The presented method is solving complete electric field inside the modeled geometry and therefore provides a more physically accurate approach for better understanding and predicting nonuniform current distribution in the varistor. In order to properly establish a FEM model a novel approach in defining grain boundary characteristic is proposed. Thus, a macroscopic model of the varistor microstructure has been developed and the grain micro-junction boundary characteristic has been derived. The simulation results of nonuniform current distribution in a varistor agree well with measurement results for a typical ZnO varistor. The presented model enables investigation of influences of varistor geometry (shapes, sizes) and material properties on the current distribution. A new mathematical expression for varistor I-V characteristic based on Lambert function is proposed.