Renormalization formalism in the theory of the electronic structure of superlattices: Application to silicon superlattices

A renormalization formalism for the calculation of electronic states in nontrivial superlattices is discussed for the first time. Starting from a microscopic tight-binding description of the crystal electron Hamiltonian using localized orbitals, we show how the renormalization techniques are implemented and easily applied to the study of superlattices of arbitrary width. As an example of the renormalization procedure, we consider silicon crystals in the presence of an additional superlattice potential in the [001] direction. We study the dependence of the energy gap upon superlattice width, and describe how relevant parameters drive the change from an indirect- to direct-band-gap material. Moreover, a peculiar effect due to zone folding of inequivalent valleys in the conduction band is found. The advantages of the present procedure relative to other computational tools available from the literature are discussed.