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Modelling of photoinduced discharge of double-layer photoreceptors: general formulation and small signal xerographic time-of-flight analysis

The decay of the surface potential on a charged insulating film, which is inhomogeneous across its thickness, is theoretically analysed by considering the injection of surface charges into the bulk and their subsequent transport through the film towards the grounded substrate. The present analysis models xerographic discharge that involves unipolar transport. It is assumed that during transport the carriers interact with a monoenergetic set of traps from which there may be release. A second-order partial differential equation is derived for the electric displacement D(x,t) which describes the time evolution of D at any point in the sample. This partial differential equation is numerically solved for the xerographic time-of-flight (XTOF) condition which requires the injection of a small fraction of the surface charges into the film by pulsed photoinjection. The sample is assumed to be composed of a double-layer photoreceptor type device where the first layer has a lower drift mobility than the second layer. The drift mobility, trapping and release times as well as the dielectric constant vary across the interface from one layer to the other. The numerical calculations provide insight into the interpretation of XTOF signals obtained from double-layer devices and demonstrate that the main peak in the photocurrent is due to prolonged injection into the second layer as a result of dispersion in the first layer.