Energy-dependent carrier masses of zinc blende semiconductors: Solved using the Kane approximation

Abstract

The mathematical expressions for the effective carrier masses of zinc blende semiconductors are derived, with particular emphasis on their dependence on carrier energy. In this work, Hamiltonian matrix diagonalization is employed to obtain the band energies, followed by the Kane approximation to derive analytical expressions for energy-dependent effective masses. Unlike conventional approaches that assume constant effective mass near the band edge, the present formulation explicitly accounts for band non-parabolicity. InAs and GaAs are used as representative examples to verify consistency between the derived expressions and calculated band structures. The results provide a physically transparent and analytically tractable framework for modeling carrier transport in high-speed electronic and optoelectronic devices.