Conduction model covering non-degenerate through degenerate polycrystalline semiconductors with non-uniform grain-boundary potential heights based on an energy filtering model

We propose a new conduction model associated with thermionic emission of carriers over potential barriers at grain boundaries, which is applicable to non-degenerate through degenerate polycrystalline semiconductors. We first assume the grain-boundary potential barriers of a uniform height and derive an analytical expression of the electrical conductivity on the basis of an energy filtering model with fully incorporating the Fermi-Dirac distribution of carriers. We then introduce fluctuations of the potential barrier height as a Gaussian distribution into the model. It is shown that the non-linear curves of Arrhenius plots of electrical conductivity in various polycrystalline semiconductors (Si, CdS, CdSe, ZnO, WO3, In2Se3) in literature are well fitted using the model with the effect of fluctuations taken into account, being regardless of whether carriers are degenerate or non-degenerate, without assuming other conduction mechanisms such as tunneling and variable range hopping.