Anisotropic optical phonon scattering of holes in cubic semiconductors

The formula for the nonpolar optical phonon scattering rate of holes in cubic semiconductors is obtained in the case of strong valence band anisotropy. The deformation potential approximation is used. A three-band, 6 × 6 , k ∙ p Luttinger-Kohn representation includes states belonging to the heavy, light, and split-off bands. Mixing with the latter causes strong anisotropy in the transition matrix elements as well as in the density of final states. The derived formula is recommended for silicon, where inter- and intravalence-band scattering rates are much more strongly anisotropic and have significantly different values than those estimated from the usual two-band 4 × 4 , "warped spheres" approximation that neglects the split-off band. Results for the more isotropic case of germanium are presented for comparison.