Size-mismatch disorder at the surface of semiconductors

We study the effects of size-mismatch disorder on the surface relaxation of semiconductor solid solutions. Assuming a Kirkwood-type potential, we obtain an analytic solution for the nearest-neighbor distances and their distributions as a function of the distance from the surface as well as the displacements at the (111) and (100) surfaces. This solution is also valid for bond-mismatch disorder and is checked against computer simulations for two-dimensional triangular networks along (10) and (11) surfaces. Predictions are made for the topography of the (111) surface of a SiGe alloy.