Kinetics of xerographic discharge by surface charge injection

Abstract

Using a novel and very simple method, a complete formal solution is presented for the kinetics of discharge (surface potential versus time) of a xerographic photoreceptor under the following conditions. (i) The discharge is effected entirely by charge injected or generated at one surface. The kinetics of injection is arbitrary. Included as special cases are instantaneous injection (e.g., under flash exposure) and injection at a rate proportional to the quantum efficiency of charge generation (e.g., under exposure at constant intensity). (ii) Charge transport is well described by a mobility law without diffusion, trapping, or dispersion. In the case of instantaneous injection explicit analytical solutions are given for constant, power-law, exponential, and Poole-Frenkel mobility laws and general relationships are pointed out among solutions for different thicknesses, initial or final potentials, or parameters in the mobility law. These properties can be used to diagnose whether an experimentally observed discharge is limited by the kinetics of injection or transport. They also form the basis of a graphical method for predicting the course of any discharge with instantaneous injection, using a single master plot for the appropriate mobility law. Along the way, several nonstandard formulas relating the surface potential to the space-charge density are discussed.