Analytic modeling of the discharge of a unipolar photoconductor

The discharge of a photoconductor under open-circuit boundary conditions (e.g., xerographic discharge) is investigated for the case in which only one carrier (e.g., holes) is mobile. Bulk recombination is taken into account. A general solution for the electric field and analytic expressions for the surface potential are obtained for the case of flash illumination. The space and time evolution in the limit of low-intensity illumination exhibits remarkable scaling properties and is governed by a single nonlinear differential equation in one variable. A criterion is derived for predicting whether flash illumination will produce a larger or smaller discharge than a slower illumination with the same total number of photons.