Nonparabolicity of the conduction band in GaAs

The technique of resonant Raman scattering is used in a magnetic field to determine interband magneto-optical transitions in GaAs(001) from enhancements of the 1-LO- and 2-LO-phonon intensities due to resonances with Landau levels. The experiments were performed far above the ${\mathit{E}}_0$ fundamental gap, where corrections due to Coulomb effects can be neglected. We observed incoming, outgoing, and intermediate resonances involving only heavy-mass valence levels. These levels can be described rather accurately by solving an 8×8 k⋅p matrix with 30 Pidgeon-Brown blocks, and therefore, the observed nonlinearities in the fan plots of laser energy ħ${\mathrm{\omega }}_{\mathit{l}}$ versus magnetic field B for transitions with Landau quantum numbers n can be attributed to the nonparabolicity of the ${\mathrm{\Gamma }}_6^{\mathit{c}}$ conduction band of GaAs. A simple formula for the bulk ${\mathrm{\Gamma }}_6^{\mathit{c}}$ dispersion is deduced from a two-band model with only one parameter to fit the fan plots for different scattering configurations and types of resonances. This yields an experimental determination of the conduction-band dispersion and effective mass in the region from 100 meV up to about 300 meV above the ${\mathit{E}}_0$ fundamental gap. Our results compare favorably with 16×16 k⋅p and pseudopotential calculations.