COHERENT-POTENTIAL APPROXIMATION WITH THE CONTINUED-FRACTION FORMALISM

We present a general approach to perform coherent-potential electronic-structure calculations of semiconductor alloys within the coherent-potential approximation, using continued fractions for the representation of the relevant Green's-function matrix elements. Starting from a tight-binding representation of the constituent-semiconductor Hamiltonian, it is shown how to evaluate self-consistently a large number of continued-fraction coefficients by means of the construction of an appropriate biorthonormal basis set. A simplified procedure for situations in which groups of energy bands can be treated independently is also proposed. With respect to other approaches in the literature, our procedure presents some special formal and technical advantages that should allow much more manageable treatment of semiconductor alloys.