Charge injection and conduction on the surface of insulators

Abstract

We have calculated numerically the flow of charge onto an insulator surface by injection from an electrode touching the surface, using conformal mapping in conjunction with the boundary element method. We have assumed that the driving fields are due to the electrodes and to the surface charge itself, while the natural conductivity of the surface is negligible. We have considered three geometries used experimentally. In general, we find that for strong injection, the surface charge is confined to the region close to the injecting electrode, that the absorption current behaves as I∝t−γ,γ∼1/3, and that the absorption and resorption currents do not exhibit mirror symmetry. Furthermore, if the active electrode can inject charges of either sign, then on shorting the electrodes a counter charge is injected, which leads to a more rapid discharge at early times but does not give rise to a current reversal (anomalous current). Materials of higher dielectric constant store more surface charge. We compare our results with previous calculations and with existing experimental work.