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The diffusion equation for an illuminated Schottky barrier is solved for a finite lifetime of photoinjected minority carriers within the barrier. The general solutions are related to parabolic cylinder functions when diffusivity and mobility are constant. These solutions are subject to the usual boundary conditions that at the surface the minority carrier current is proportional to the carrier density and that at the barrier/bulk interface the carrier density and its gradient are continuous. The photoconversion efficiency for a given impurity concentration is completely defined by three parameters: the charge transfer rate at the surface, the optical absorptivity, and the carrier lifetime. These calculations are applicable to many of the oxide semiconductors used as anodes in photoelectrolysis.
H. S. Jarrett (1981) studied this question.