Neglecting Diffusion in Space-Charge-Limited Currents

Abstract

In most work dealing with space‐charge‐limited currents, the diffusive contribution to the current is neglected. The classic steady‐state problem was handled by Mott and Gurney. For their problem of the perfect insulator it is well known that diffusion dominates near the injecting contact but, after some critical distance, drift dominates, and it is consistent to neglect diffusion. For the case of transient SCLC the mathematical validity of neglecting diffusion has not been shown. The purpose of this work is to show that for times greater than a critical time and distances greater than a critical distance the diffusive term can consistently be neglected. The solutions found by Mark and Helfrich and by Many and Rakavy for injection of electrons into an insulator under an applied voltage pulse have been shown to be correct under the above conditions. The interesting result is that the critical parameters are related to geometrical parameters by the ratio of the thermal voltage kT/q to the applied voltage. We therefore find that for signals large compared to kT/q, the neglect of diffusion is valid over most of the range of time and distance associated with the problem.