Numerical and analytic methods for the study of disordered alloy surfaces

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Abstract
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.