Metal-insulator transitions in tetrahedral semiconductors under lattice change

Although most insulators are expected to undergo insulator to metal transition on lattice compression, tetrahedral semiconductors Si, GaAs and InSb can become metallic on compression as well as by expansion. We focus on the transition by expansion which is rather peculiar; in all cases the direct gap at F point closes on expansion and thereafter a zero-gap state persists over a wide range of lattice constant. The solids become metallic at an expansion of 13% to 15% when an electron Fermi surface around L-point and a hole Fermi surface at Gamma-point develop. We provide an understanding of this behavior in terms of arguments based on symmetry and simple tight-binding considerations. We also report results on the critical behavior of conductivity in the metal phase and the static dielectric constant in the insulating phase and find common behavior. We consider the possibility-of excitonic phases and distortions which might intervene between insulating and metallic phases.