On the Description of Covalent Bonds in Diamond Lattice Structures by a Simplified Tight-Binding Approximation

Abstract

The simplest possible tight-binding approximation, using sp hybridized bonds and nearest neighbors overlaps, is used to describe the band structure of diamond, silicon, and germanium. This crude approximation has the great advantage of giving explicit and simple formulas for the Bloch functions and E(k) curves in the whole reciprocal space, as a function of two parameters: an overlap integral λ and an sp promotion energy ε. The general band structure is discussed as a function of ε/λ. The influence of sp hybridization on the band structure, covalent character of the valence electrons, optical and x-ray spectra are discussed. It is shown how the energy gap should be related to cohesive energy and pressure. The reasonable agreement with experiment of these various predictions shows the usefulness of the method to understand in a rough and somewhat qualitative way general properties of covalent bonds in crystals.