Surface properties of a network model of electrons in solids

Surface properties of a network model of electrons in solids are discussed. In the model, electrons are restricted to move along lines connecting node points of a periodic network. Each node point on the network corresponds to an atom. A potential well is introduced for each atom or node point so that as the depth of the potential becomes large, one has the tight binding model and, as the potential vanishes and the number of node points increases, one has the Sommerfeld free electron model. Exact wave functions and energy levels have been obtained elsewhere for the model when periodic boundary conditions are applied.When free boundaries are introduced, a band of surface states develops. Its depth of penetration into the crystal as a function of wave number is investigated. The edges of the surface energy bands are located and their density of states is calculated.