Nonequilibrium behavior of depletion, inversion, and accumulation grain boundaries

The recombination velocity of polysilicon grain boundaries is calculated from the Shocley-Read-Hall formula, taking into account the balance of charges for nonequilibrium conditions. The calculation is not restricted to grain boundaries in depletion, but applies to the full range of band bending. The results show the existence of significant differences in the nonequilibrium behavior of depletion, inversion, and accumulation grain boundaries. For depletion/inversion grain boundaries, the recombination velocity is small and nearly independent of excitation for both low- and high-state densities, whereas medium-state densities show high recombination velocities and a strong injection dependence. Accumulation grain boundaries always provide lower recombination velocities than depletion/inversion grain boundaries and they do not show any dependence upon excitation. In order to verify the theoretical excitation dependences, several n⁺-p and p⁺-n solar cells prepared from polycrystalline bulk material have been investigated under various insolation conditions. For the n⁺-p cells, deviations from a linear dependence of the short circuit current upon intensity were observed, whereas the p⁺-n cells showed a precisely linear dependence, indicating depletion/inversion grain boundaries in p-type, but accumulation grain boundaries in n-type polysilicon.