Piezoelectric Scattering in Semiconductors

The theory of the scattering of electrons by acoustic modes in piezoelectric semiconductors is generalized so as to properly take account of the anisotropic scattering probability. The Herring-Vogt approximate solution to the Boltzmann equation is used, which is accurate if the resulting relaxation-time tensor components do not differ by more than a factor of two or so. The other main simplifying assumption consists of treating the frequencies and polarizations of the acoustic modes by a simple approximation. The theory is applied to three symmetry classes of known piezoelectric semiconductors: zincblende and wurtzite symmetry (as typified by the III-V and II-VI compounds) and $\alpha$-quartz symmetry (as typified by selenium and tellurium). The electron mobility anisotropy calculated for CdS (based on the measured electroelastic properties and cyclotron-resonance masses) agrees quite well with the value deduced from experiment.