Electronic structure and some related properties of InSb using a [formula omitted] method and Green's function technique

Abstract

We develop a k → ⋅ π → theory, where π → is the momentum operator in the presence of the spin–orbit interaction, for the narrow gap III–V semiconductor InSb. It is based on an eight-band k → ⋅ π → model where the interaction between conduction band Γ 6 c and the degenerate valence band Γ 8 v is treated exactly within the Luttinger–Kohn representation. The eigen values and eigen functions are obtained for the band edge states. These are then used to treat the spin–orbit split valence band Γ 7 v using perturbation theory. We also derive a theory for the magnetic field-dependent electron energy by obtaining an expression for the thermodynamic potential in first order in field in the presence of spin–orbit interaction, following Green's function approach. The field-dependent part of the band energy is expressed in terms of the effective g-factor. We apply the theory to calculate the band edge electronic effective mass as a function of temperature and applied magnetic field and the effective g-factor as a function of temperature and photon energy. Three variants of the energy gap as a function of temperature are considered. Results obtained using the gaps from thermal expansion and lattice dilatation agree better with experiment than those using the optical gap.