Lowering of grain-boundary barrier heights by grain curvature

A model is presented for the potential barrier height at grain boundaries in polycrystalline semiconductors, which takes into account a curved grain boundary under equilibrium and nonequilibrium conditions, assuming flat quasi-Fermi levels. An analytical method to calculate the reduction of the potential barrier due to the grain curvature, without using the depletion approximation, is developed and applied to compute the barrier lowering as a function of the bulk doping concentration, interface state density, and the grain radius in silicon. The barrier height can vary along a grain boundary, due to different local curvatures, being lowest at corners of grains.