Deep-Trapping Kinematics

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Abstract
An analytical treatment of the standard transport equations in the presence of deep traps is presented. The model assumed for the traps is one in which they can be characterized by a single trapping time, and the analysis is valid for arbitrarily strong trapping. The configuration treated is that appropriate to potential probe measurements. Carriers are introduced through photogeneration by highly absorbed illumination. An exact result is obtained relating the final potential resulting from the accumulated trapped space charge to the carrier range, or μT, product. This relationship is independent of the injection history and therefore of the complexities attendant with such surface phenomena as recombination and field‐dependent photogeneration. For continuous illumination, analytic results are obtained for the detailed space and time dependence of the trapped carriers and the resulting modification of the electric field. These results include the effects of a field‐dependent injection mechanism. Particular cases where the injection is proportional to the mth power of the field are treated, with m taking on the values 0, 0.5, 1, and 2.