Three-Dimensional Time-Domain Finite-Element Simulation of Dielectric Breakdown Based on Nonlinear Conductivity Model

Dielectric breakdown during high-power operation is hazardous to electric and electronic devices and systems. During the breakdown process, the bound charges break free and are pushed to move by the force of high-intensity fields. As a result, a reduction in the resistance of an insulator can be observed, and a portion of the insulator becomes electrically conductive. Such a process can be described as the change of conductivity of the dielectric, which in this case, is a nonlinear function of the electric field. In this paper, the nonlinear conductivity is incorporated into Maxwell's equations, and the resulting nonlinear equation is solved using the time-domain finite-element method together with Newton's method (NM). The Jacobian matrix required in the NM is analytically derived to obtain a numerical solution with good accuracy and efficiency. A fixed-point method is also presented to provide numerical solutions as a validation for the NM. Several numerical examples are presented to demonstrate the capability of the proposed algorithm and the nonlinear effect caused by the nonlinear conductivity.