A new approach to space-charge-limited conduction theory

Abstract

We describe a new method for obtaining numerical solutions to the single-carrier conduction problem (including diffusion) in insulators. The method is illustrated by treating the space-charge-limited current problem in the case where both electrodes are ohmic, and traps in the insulator are assumed to be absent, or shallow, or exponentially distributed in energy. Transformation of the conduction equation to express charge density as a function of field, followed by straightforward numerical solution, gives the current and voltage parametrically as functions of the field at the charge density minimum. For voltages less than a few tenths of a volt the current is given by j ∝ U/d^2l+1, and at rather high voltages the standard result j ∝ U^l+1/d^2l+1 is valid. Simple formulae, valid except at very low voltages, are derived for the position and height of the potential maximum.