Effects of interface-potential nonuniformities on carrier transport across silicon grain boundaries

In an experimental investigation of electronic transport across individual grain boundaries in cast silicon, we have recently arrived at the conclusion that the diffusion potential at the grain boundary may in many cases exhibit appreciable variation over the boundary plane. The present paper describes an interpretation of the experimental observations in terms of a Gaussian distribution of interface potential over the grain-boundary surface, and a majority carrier transport to the boundary which is diffusion limited. In the grain boundaries studied the mean value of the diffusion potential was found to vary from 〈Vd〉 ≂0.70 to 〈Vd〉 ≂0.32 eV and the standard deviation from σ≂0 to σ≂0.11 eV. These values were derived from the change in activation energy with temperature. For the particular grain boundaries with spatial uniformity (σ≂0) excellent agreement of the characteristics with an emission/diffusion model of majority-carrier transport is obtained. It is concluded (i) that it is not generally proper to assume that grain boundaries in cast silicon are spatially uniform and (ii) that the Gaussian distribution model provides a satisfactory first approximation to the spatial variation in grain boundaries.