Tight-binding Central Interaction Model for the Band Structure of Silicon

Abstract

We consider a simple tight-binding model involving all interactions between first and second nearest-neighbour (n.n.) bonds in the diamond lattice. We show that the band structure may be solved analytically in the central approximation in which all second n.n. bond interactions of the same type, for example all bonding: bonding or all bonding: antibonding interactions, are considered equal. The k dependence of the solution is given in terms of the corresponding s-band eigenvalues, which are determined by the topology of the structure.