Two-band analysis of hole mobility and Hall factor for heavily carbon-doped p-type GaAs

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Abstract
We solve a pair of Boltzmann transport equations based on an interacting two‐isotropic‐band model in a general way first to get transport parameters corresponding to the relaxation time. We present a simple method to calculate effective relaxation times, separately for each band, which compensate for the inherent deficiencies in using the relaxation time concept for polar optical–phonon scattering. Formulas for calculating momentum relaxation times in the two‐band model are presented for all the major scattering mechanisms of p‐type GaAs for simple, practical mobility calculations. In the newly proposed theoretical framework, first‐principles calculations for the Hall mobility and Hall factor of p‐type GaAs at room temperature are carried out with no adjustable parameters in order to obtain direct comparisons between the theory and recently available experimental results. In the calculations, the light‐hole‐band nonparabolicity is taken into account on the average by the use of energy‐dependent effective mass obtained from the k⋅p method and valence‐band anisotropy is taken partly into account by the use the Wiley’s overlap function.. The calculated Hall mobilities show a good agreement with our experimental data for carbon‐doped p‐GaAs samples in the range of degenerate hole densities. The calculated Hall factors show rH=1.25–1.75 over hole densities of 2×1017–1×1020 cm−3.