Decay of Electrostatic Surface Potential on Insulators via Charge Injection, Transport and Trapping

Abstract

Decay of the surface potential on an initially corona charged insulator via charge injection, transport and trapping is theoretically examined and a general partial differential equation is derived for the space and time dependence of the electric field E(x, t) in terms of the charge carrier mobility, µ, trapping time, τ′, and the trap capture coefficient Ct. The present formulation specifically takes into account that as deep trapping proceeds, the rate of trapping decreases due to trap filling. The numerical solution of this differential equation gives the instantaneous electric field, E(x, t), profiles in the sample which can be integrated to obtain the time evolution of the surface potential, V(t), rate of discharge, dV/dt, final residual potential, Vr, and also the fraction of traps filled as a function of µ, τ′ and Ct. Two experimental conditions are considered. (a) The time dependence of the electric field, E(0, t), at the surface is well defined by the charge injection process, which in the present case, corresponds to a weak step illumination. (b) The spatial dependence of the initial field, E(x, 0), is well defined by an appropriate short light pulse illumination at t=0.