Nonlocal Transport and Cuspidal Surface Mobility in Semiconductors

The curious cuspidal behavior of the surface mobility formulas of Greene, Frankl, and Zemel for nearly flat bands has been emphasized by Flietner, who also noted the omission of a size-effect transport term. He gave revised formulas showing higher surface mobility values and no cusp. We show that Grenee, Frankl, and Zemel actually omitted a pair of size-effect terms, that these very nearly cancel, and that, therefore, the corresponding thick-sample surface mobility formulas are correct. We also show that the cusp is a characteristic of transport in the nonlocal case (mean free path comparable to Debye screening length) where band bending cannot be treated as a small perturbation.