Electron states at planar and stepped semiconductor surfaces

We develop a method to study electronic properties of planar and stepped semiconductor surfaces. The method, based on the Bethe-Peierls approximation, deals with tight-binding Hamiltonians, and since it works in a real-space representation, avoids numerical integrations in $k$ space to get the density of states. We calculate the electronic density of states at steps in the (11) surface in the honeycomb lattice as well as in the (111) surface of a covalent semiconductor (Si,Ge). Our results in the latter case are in good agreement with ultraviolet photoemission data.