We present a formally exact solution of the multiple-scattering-theory (MST) equations for the case of semi-infinite and coherent doubly semi-infinite materials. For the case of semi-infinite materials (surfaces), we also present an alternative approach based upon the embedded-cluster method, which can be numerically as accurate as the exact method but is computationally easier to implement. The methods presented here satisfy the correct boundary conditions associated with semi-infinite materials and thus constitute a proper generalization of the Green-function formalism as applied to bulk systems, to the treatment of surfaces and interfaces. Specifically, the lack of translational invariance in directions perpendicular to the surface or interface is handled through the solution of a self-consistent equation for the scattering matrix, describing exactly the interaction of any chosen plane near the surface or interface with the rest of the material. The formalism is free of the introduction of extraneous conditions such as the artificial truncation of the free-particle propagator or the range of electron hopping elements, or the use of a complex potential. Furthermore, being based on a first-principles, MST Green-function method, the formalism is applicable to the treatment of a large number of physically important problems such as surface and/or interface regions formed by pure materials or concentrated alloys, the study of impurities of diverse kinds near such a region, and many others. Results for one-dimensional model systems as well as realistic three-dimensional materials are presented. The advantages, convergence properties, and restrictions of the formalisms are discussed and further work, currently in progress, is commented upon.

• Received 2 January 1990

DOI:https://doi.org/10.1103/PhysRevB.42.3798