Theory of electron–hole kinetics in amorphous semiconductors under illumination: Application to solar cells

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Abstract
A general kinetic theory of the generation and recombination of electron–hole pairs for an illuminated amorphous semiconductor with an arbitrary distribution of gap states is presented. The basic assumptions of the theory are first, that sharp mobility edges separate localized states from extended states, and second that the localized states can communicate with each other only via the extended states. In the limit that mobile carriers are concentrated at the band edges, the coupled nonlinear integral equations for the occupation functions can be reduced to quadratures. The theory is applied to calculate the current–voltage characteristic of amorphous silicon solar cells, in the ‘‘lumped circuit’’ model where the spatial dependence is neglected. The open circuit voltage, the fill factor and the upper limit for the solar conversion efficiency of such devices are calculated as functions of the gap density of states.