Deep-trapping kinematics of charge carriers in amorphous semiconductors: A theoretical and experimental study

There has been much recent interest in the determination of drift-mobility (μ) –lifetime (τ) products in amorphous semiconductors by various measurement techniques. Although most measurements have utilized time-of-flight types of transient-photoconductivity experiments, xerographic measurements have also been used, since they provide a clear measurement of the residual potential ${\mathit{V}}_{\mathit{R}}$, i.e., the electrostatic potential on the surface of a high-resistivity solid, due to trapped charges in the bulk. This paper identifies and critically examines the theoretical problems involved in the determination of μτ from such xerographic measurements. The deep-trapping model of Kanazawa and Batra, which relates the residual potential to the μτ product, is reformulated by specifically including the effect of the rate of trapping as being proportional to the instantaneous unoccupied density of traps. The latter description had been neglected in previous models of deep-trapping kinematics. A partial differential equation is derived that describes the space and time evolution of the electric field within the material.