The integro‐differential equations predicting transient decay of space‐charge currents in media

摘要

A pair of coupled, nonlinear integro‐differential equations, which exactly describe the transient current produced by the drift and collection of a swarm of space charge in a medium between two electrodes, has been derived for a single charge carrier species using a field‐independent mobility model. The equations represent the solution of the mathematical problem involving arbitrary space‐charge sizes and distributions coupled with the effects of the inherent time constants of the physical system. Computer‐generated numerical solutions, for the special case of the initial charge distributions which correspond to steady‐state currents, are reported. The equations under these conditions can be decoupled to form a stiff third‐order differential equation. The numerical results indicate a possible scheme for correcting transient current waveforms, which are distorted by space‐charge fields, in order to obtain the proper, ideal times of flight needed for true mobility measurements.