Intergranular barrier height fluctuations in polycrystalline semiconductors

Abstract

The punctual character and random nature of the impurity positions in depletion regions lead to inhomogeneities that can significantly affect the potential intergranular barriers at polycrystalline semiconductors and, in general, of potential barriers at any semiconductor interface. This would reflect in Arrhenius plots for the electrical conductivity that become curved due to fluctuations of the intergranular barrier heights. Experimental results for polycrystalline tin oxide can be fitted assuming thermionic emission conduction at grain boundaries with a Gaussian distribution of barrier height fluctuations. However, resorting to a computational numerical model, we found that spatial fluctuations in barrier heights due to the discreteness of the donors and their statistical distribution at the depletion region differ from a Gaussian distribution. The type of obtained fluctuations, considering thermionic emission conduction, cannot explain the Arrhenius plots for the electrical conductivity found experimentally, especially at low temperature. Conversely, the tunneling contribution to conduction, without resorting to fluctuations, presents the observed trends.