Generalized Wannier functions at interfaces: Stacking faults in silicon

A variational method suitable to compute the generalized Wannier functions (GWF) of a crystal with defects is presented. The scheme is applied to study the structural and electronic properties of stacking faults in silicon. Since no model Hamiltonian is used, this is the first time that GWF are self-consistently determined. The minimization of the total energy causes very small relaxations of the ionic layers at the fault. Our results for the energies of formation are in satisfactory agreement with experimental data. Once we have obtained the Hamiltonian, the band structure is calculated giving some interface states. The available experimental information on states at the fundamental gap of these imperfect crystals is discussed.