An empirical theory of isc and voc in the ZnzCd1−zS/Cu2S solar cell

Abstract

A simple empirical theory has been given for the short-circuit current (isc ) and the open-circuit voltage (voc ) of the ZnzCd1−zS/CU2S solar cell. The heterojunction band lineup at the interface is assumed to be determined by the pinning of the Fermi level at the collector surface by the copper impurity/cation vacancy level. Since the impurity level remains fixed with respect to the collector valence-band edge and the collector band gap goes up with z, such a pinning produces a potential barrier (‘‘spike’’) at the junction. The height of the spike increases with z. An estimate is made of the Cd impurity level in the emitter. This level is believed to act as the recombination center for electrons diffusing back to the emitter from the collector conduction band. These electrons would normally face a strong opposing field but because of an expected incipient Zener breadkdown of the potential barrier in the narrow highest field region they would face a substantially smaller opposing field. Zener breakdown field for CdS is known and for the mixed sulfide we have considered this field as a parameter obtained by fitting the voc values. The parameter, thus obtained, varies with z smoothly in a logarithmic scale and is within an order of magnitude of the Zener breakdown field for CdS. We have given some physical arguments to show that the Zener breakdown and consequent reduction of the field does not necessarily mean a widening of the depletion layer. While for CdS the known Zener breakdown field gives a value of voc in good agreement with the experiment, it is a measure of the expected correctness of the fitted values of this field that, in conjunction with the heights of the conduction-band spike, they give reasonable isc values. The generally consistent values of the parameters of the cell measured in different specimens are ascribed to the self-doping and self-compensating properties of the collector material. An explanation of the crossover of dark and light current-voltage characteristics for different types of cells has been given. Since it is futile to aim at any numerical accuracy in view of the uncertainties in some of the material parameters, the main emphasis has been on the explanation of the trends of the variation of the parameters with z. This explanation has been given in terms of a few physically reasonable assumptions. Although at least one experimental result tends to confirm the position of the recombination level, a few specific experiments have been suggested which would hopefully sustain the assumptions of the theory.