Electronic structure and some related properties of InSb using a k→⋅π→ method and Green's function technique

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 Γ6c and the degenerate valence band Γ8v 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 Γ7v 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.

► Electronic structure is studied in non-parabolic limits for InSb.
► We use hybridization of k→⋅π→ method and Green's function technique.
► Effective mass is calculated as a function of temperature and magnetic field.
► Effective g-factor is calculated as a function of temperature and photon field.
► Satisfactory agreement with experimental results, wherever available, is obtained.