Theory of Space‐Charge‐Limited Currents in Thin Semiconductor Layers

The current flowing in a thin semiconductor layer between two knife‐like contacts located on the same side of the layer is analyzed using a model in which the thicknesses of the layer and the electrodes are taken to be negligible compared with the separation of the electrodes. Since the excess density of mobile charge in the layer is controlled by the transversal component of the electric field, side effects play a dominant part in the model. The calculated current‐voltage characteristic shows a transition from ohmic to space‐charge‐limited behaviour at increasing voltages. The space‐charge‐limited current at higher voltages is inversely proportional to the square of the electrode distance. This dependence was found experimentally by Polke, Stuke and Vinaricky. The effect of traps is taken into account by means of a simple model. If empty traps are present at zero electric field, the theory yields a threshold potential beyond which the current starts flowing.