Electrical properties of grain boundaries in polycrystalline materials under intrinsic or low doping

Abstract

An analytical model is developed to study the electrical properties (electric field and potential distributions, potential energy barrier height and polarization phenomenon) of polycrystalline materials at intrinsic or low doping for detector and solar cell applications by considering an arbitrary amount of grain boundary charge and a finite width of grain boundary region. The general grain boundary model is also applicable to highly doped polycrystalline materials. The electric field and potential distributions are obtained by solving Poisson's equation in both depleted grains and grain boundary regions. The electric field and potential distributions across the detector are analysed under various doping, trapping and applied biases. The electric field collapses, i.e. a nearly zero-average electric field region exists in some part of the biased detector at high trapped charge densities at the grain boundaries. The model explains the conditions of existence of a zero-average field region, i.e. the polarization mechanisms in polycrystalline materials. The potential energy barrier at the grain boundary exists if the electric field changes its sign at the opposite side of the grain boundary. The energy barrier does not exist in all grain boundaries in the low-doped polycrystalline detector and it never exists in intrinsic polycrystalline detectors under applied bias condition provided that there is no charge trapping in the grain.