Transient transport in amorphous solids: An exact calculation

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Abstract
An exact analytic result that is valid at all times is obtained for the decay of the transient photocurrent in amorphous materials. The motion of the charge carriers across the sample is modeled by a biased continuous-time random walk, and the current is calculated for an arbitrary event-time distribution. This is a generalization of the earlier results of Shlesinger and of Scher and Montroll wherein the short- and long-time features in the decay of the photocurrent were obtained for long-tailed event-time distributions using certain approximate solutions and periodic boundary conditions. We impose physical boundary conditions, and our solution may be used with any type of event-time distribution modeling the carrier transport. We discuss in detail the transition from the short-time to the long-time form of the power-law decay for a temporally fractal event-time distribution. The main advantage in using this form is that it enables us to vary the power-law index continuously. It also serves to highlight the dependence of the magnitude of the transition time on the details of the clustering of event times.