Phonon-assisted carrier transport across a grain boundary

A general theory of phonon-assisted transition of majority carriers across a grain boundary (GB) is formulated with the GB angle as a variable. It is found that the bulk relaxation time in the crystalline region and the transition time at the GB are the important parameters that determine the transmission coefficient of carriers across the GB. Using the proposed model, an n-type polycrystalline silicon is employed as an example in a numerical calculation