Modelling of photoinduced discharge of photoreceptors under pulsed photoexcitation: small and large signal xerographic time-of-flight analysis

Abstract

A general theoretical model for the photoinduced discharge of a charged photoreceptor is developed by considering non-dispersive charge transport in a high-resistivity semiconductor (insulator in the dark), point form representations of Ohm's law, Gauss's law and Maxwell's equations for the total current, and the trapping and release rate equations. The rate equations incorporate arbitrary strengths of trapping, release, and trap saturation for a single level of traps. In contrast to most previous works, the trap filling effect is fully incorporated into the model which allows its effects to be studied. These equations were combined to create a single general second-order nonlinear partial differential equation which governs the behaviour of the electric field during photoinduced discharge. The general differential equation for the field was then solved numerically using boundary conditions that are representative of pulsed illumination. Solutions were obtained under low injection (0.1% of surface charge) and high injection (10%, 50%, and 99% of surface charge) conditions. Trapping parameters in the model could be adjusted to represent a wide range of trapping conditions including trap saturation. In each case, the time evolution of the discharge was monitored by calculating the trapped and untrapped charge densities at regular intervals throughout the discharge. By differentiating the calculated surface voltage V, the rate discharge dV/dt was also monitored, because it is an experimentally accessible quantity that is widely used in xerographic time-of flight measurements. Results obtained under low injection conditions demonstrated that the dispersion in the charge packet increased with larger values of the mobility reduction factor and smaller values of the trapping and release rates, and r, respectively. Increased charge packet dispersion was seen to cause increased dispersion in dV/dt near the transit time. The temporal spread of arrival times analytically predicted by the Schmidlin equation was found to be in good agreement with the present model in the small signal mode. High injection results illustrated that the dispersion of the charge packet and |dV/dt| increased dramatically with increased injection strength. Under extremely high injection, the dispersion is primarily determined by the amount of injection. The effect of trap saturation under high injection conditions was also investigated. Increased trap saturation caused the packet to become more spread out during the early stages of the discharge. This caused significant decay in |dV/dt| before the shallow-trap controlled transit time, but did not significantly affect the overall dispersion in |dV/dt|.