Space-charge limited surface currents between two semi-infinite planar electrodes embedded in a uniform dielectric medium

Abstract We extend the one-dimensional space-charge limited current theory to a two-dimensional geometry where current flows in a thin layer between two coplanar semi-infinite electrodes. It is shown that the surface charge density in the gap between the electrodes is the finite Hilbert transform of the in-plane component of the electric field. This enables us to derive analytical expressions for the field and charge density for single carrier injection and for photo-carrier extraction by solving a non-linear integral equation for the field. The analytical expressions have been verified by numerical calculations. For the in-plane geometry, the one-dimensional Mott–Gurney equation J = 9 8 μ ∊ V 2 L 3 is replaced by a similar K = 2 π μ ∊ V 2 L 2 equation. For extraction of photo-generated carriers the one-dimensional J ∼ g 3 / 4 V 1 / 2 dependence is replaced by a K ∼ g 2 / 3 V 2 / 3 dependence, where g is the generation rate of photo-carriers. We also extend these results to take into account trapping. We show experimental evidence obtained with an organic photoconductor confirming the predicted voltage, width and generation dependencies.