Fractional Model of Multiple Trapping with Charge Leakage: Transient Photoconductivity and Transit–Time Dispersion

Abstract

The model of multiple trapping into energy-distributed states is a successful tool to describe the transport of nonequilibrium charge carriers in amorphous semiconductors. Under certain conditions, the model leads to anomalous diffusion equations that contain time fractional derivatives. From this perspective, the multiple-trapping model can be used to interpret fractional transport equations, formulate initial and boundary conditions for them, and to construct numerical methods for solving fractional kinetic equations. Here, we shortly review the application of fractional multiple-trapping equations to problems of transient photoconductivity relaxation and transit–time dispersion in the time-of-flight experiment and discuss the connection of the multiple-trapping model with generalized fractional kinetic equations. Different types of charge leakage are discussed. The tempered fractional relaxation is obtained for recombination via localized states and distributed order equations arise for the non-exponential density of states presented as a weighted mixture of exponential functions. Analytical solutions for photocurrent decay in transient photoconductivity and time-of-flight experiments are provided for several simplified situations.