Numerical and analytic methods for the study of disordered alloy surfaces

We report exact, numerically simulated, and analytic calculations of the density of states (DOS) at or near the surface of semi-infinite substitutionally disordered alloys in the tight-binding approximation to the Hamiltonian. The exact DOS is obtained through a recursion method, which is applicable to systems of any dimensionality, and yields results which possess the desirable analytic and convergence properties. Both the surface generalization of the coherent-potential approximation (CPA) and of the embedded-cluster method (ECM) are used to calculate averaged and partial DOS s and to compare them with the exact results. As is the case with bulk alloys, the CPA yields a smooth overall description of the exact spectra, while the ECM properly reproduces much of the structure of the DOS even when used with relatively small clusters of atoms. A discussion of the work and its possible utility is given.