Analytical model of dynamic secondary electron emission of insulators under electron irradiation

Abstract

We developed an analytical model of dynamic secondary electron (SE) emission of an insulator under electron irradiation. In this model, the interaction between surface charge accumulation and SE emission is considered. The surface charge accumulation is determined by the difference between the incident and emission currents. The surface potential is then calculated using a capacitance model. In a negative charging process, the landing energy of primary electrons (PEs) and the corresponding SE emission yield (SEY) are upgraded according to the surface potential. In a positive charging process, the effect of a surface barrier on SE emission is considered in the calculation of dynamic SEY. Differential equations for the surface potential and SEY and their analytic solutions are obtained and verified using measurement data for both positive and negative charging processes. Charging speed and the saturation of surface potential are analyzed. The positive charging process is found to be faster than the negative charging process. An equivalent circuit is presented and the time constant and its dependence on both irradiation conditions and material properties are discussed.