Dielectric relaxation in open circuit: Theory, simulations, and some experiments

Abstract

Static charge on insulating material surfaces may be a source of nuisance and an operational requirement in many devices. It induces a potential that evolves with time due to conduction and polarization processes in the dielectric. Here, we analyze, from a theoretical and experimental point of view, the response of an insulator subjected to a charging pulse, within the frame of linear system theory. The surface potential decay and the return voltage after a brief neutralization, which can be easily measured using an electrostatic probe, usually follow time power laws. We consider here a dielectric following the classical Cole–Cole response function in the frequency domain and derive an exact analytic formula for the potential decay, which involves a Mittag–Leffler function. The relationship between the potential decay and the absorption current when a constant voltage is applied on the dielectric is also analyzed. Experiments on several common insulating materials are analyzed according to this theory, using a numerical simulation with a two-cell model. Return voltage measurements are used to check which materials behave according to the linear model. We underline that an equivalent circuit using constant-phase elements, corresponding to several cells following the Cole–Cole response, can also represent dipolar motions in the dielectric as charge hopping between energy-distributed traps.