MODELING OF PHOTO-INDUCED DISCHARGE IN AMORPHOUS SEMICONDUCTORS
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The characteristics of charge transport in amorphous materials are of great importance because they determine the perfomance of xerographic devices. Transport in amorphous materials is dramatically affected by the presence of localized states in the mobility gap. In order to design efficient photoreceptor materials, a detailed understanding of trapping processes in amorphous materials is required. Considerable work has been performed in this area. However, no complete model for photo-induced discharge in the presence of arbitrary trapping and carrier injection exists. In this work, a general theoretical model for photo-induced discharge in amorphous materials is developed from the point form representations of Ohm's Law, Gauss' Law, Maxwell's equation for the total current and the trapping rate equation. The rate equation incorporates arbitrary strengths of trapping, release, and trap saturation for a single level of traps. These equations' were combined to create a' second-order nonlinear partial differential equation which governs the behaviour of the electric field during photo-induced discharge. The differential equation was then solved numerically using boundary conditions which are representative of pulsed-illumination. Solutions were obtained under low injection (0.1%) and high injection (10%, 50%, and 90%) conditions. Trapping parameters which are representative of shallow traps were used. In each case, the mechanics of the simulated discharge were monitored by calculating the trapped and untrapped charge densities at regular intervals throughout the discharge. The rate of change of the surface voltage, dV/dt, was also monitored, because it is an experimentally accessible quantity that provides insight into trapping processes. Results obtained under low injection conditions demonstrated that the dispersion in the charge packet increased with larger values of the mobility reduction factor 6 and smaller values of the trapping and release rates, 0) and r. Increased charge packet dispersion was seen to cause increased dispersion. in dV/dt near the transit time. The temporal spread.of arrival times predicted by the Schmidlin equation was found to be in good agreement with simulation results.