Diffusion-limited quasi Fermi level near a semiconductor grain boundary

The spatial variation of the quasi Fermi level near a semiconductor grain boundary in steady state is calculated for the case of diffusion-limited conductivity. For an n-type semiconductor this level changes only slightly on the negative-voltage side. On the positive-voltage side, the largest variation is near the boundary, and is closely parallel to the parabolic band bending there. The level at the grain boundary calculated here is compared to that for the thermionic emission case. Although the functional form is different, the value of the Fermi level is nearly the same for either case.