Conduction electrons in GaAs: Five-levelk⋅ptheory and polaron effects

Properties of conduction electrons in GaAs are described theoretically using a five-level k⋅p model, which consistently accounts for inversion asymmetry of the material. The dispersion relation E(k) is computed and it is shown that the conduction band is both nonparabolic and nonspherical. The energy dependence of the electron effective mass, the energy-momentum relation in the forbidden gap, and the spin splitting of the band are calculated. Analytical expressions for the band-edge effective mass, the spin splitting, and the Landé factor $g^{\mathrm{*}}$ are presented, taking explicitly into account an interband matrix element of the spin-orbit interaction. A five-level P⋅p theory for the conduction band in the presence of an external magnetic field is developed. Resonant and nonresonant effects due to polar electron–optic-phonon interaction are included in the theory. The spin g value of conduction electrons is calculated as a function of energy and magnetic field. Spin-doublet splitting of the cyclotron resonance and the cyclotron-resonance-mass anisotropy are described. A comparison of the theory with experimental data of various authors is used to determine important band parameters for GaAs. It is shown that away from the band edge the polaron effects in GaAs are comparable to the band-structure effects.