Simple analytical model of bias dependence of the photocurrent of metal-semiconductor-metal photodetectors.

The current-voltage (I-V) characteristics of metal-semiconductor-metal (MSM) photodetectors under various light intensities are examined. The current shows an initial increase followed by saturation and a subsequent sharp increase as bias increases. We propose a theoretical model for bias dependence in all regions of operation except for breakdown, based on drift collection of carriers in the depleted regions under the contacts and diffusion and recombination in the undepleted region. This is based on the solution of the diffusion equation in the undepleted area between the two contacts of the MSM structure. The solution is subject to boundary conditions on excess minority carriers at the cathode end and continuity of current at the anode end. The latter is written in terms of a parameter, denoted as effective diffusion length, which describes the collection efficiency of carriers at the anode. The closed-form solution thus derived corroborates with physical expectations in several limiting cases. To compare theory with experiment, we propose methods to extract parameters that are used to normalize the I-V curves and calculate depletion widths under different light intensities, from current- and capacitance-voltage measurements. A close match between experimental and theoretical results is observed, and possible breakdown mechanisms are discussed.