SMALL-CRYSTAL APPROACH TO ORDERED SEMICONDUCTOR COMPOUNDS

A small-crystal approximation is proposed for the calculation of the electronic energy levels of ordered semiconductor compounds. The method yields the exact spectrum of a tight-binding Hamiltonian for a 16-site cluster with periodic boundary conditions and 5 orbitals per site: The spectrum corresponds to the sampling of the fcc Brillouin zone at eight high-symmetry points. The formalism is applied to estimate the electronic contribution to the formation energy of 15 ordered structures of GaxAl1-xAs and InxGa1-xP and 22 GeSi compounds. All studied alloys are found to have lower electronic energies than the segregated systems. The role played by the electronic energy in the ordering mechanisms of these semiconductors is discussed. © 1990 The American Physical Society.