Anisotropic optical phonon scattering of holes in cubic semiconductors

Abstract

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.

Anisotropy in Ultrafast Carrier and Phonon Dynamics in p-Type Heavily Doped Si

“…[1][2][3] Several previous studies have suggested that the anisotropy of carrier distributions is closely related to the generation of coherent phonons. 1,[4][5][6] Dolguikh et al theoretically showed that the anisotropy in Si originates from the non-parabolic energy dispersion of valence bands. 4) In the valence bands, at k ¼ 0, the energy surfaces of the heavy and light hole bands are characterized by a parabolic shape.…”

“…1,[4][5][6] Dolguikh et al theoretically showed that the anisotropy in Si originates from the non-parabolic energy dispersion of valence bands. 4) In the valence bands, at k ¼ 0, the energy surfaces of the heavy and light hole bands are characterized by a parabolic shape. 7) Away from k ¼ 0, the energy dispersion is no longer parabolic due to mixing among the three valence bands.…”

“…7) They found that the anisotropy is essential for an accurate description of the carrier-phonon scattering rate in Si. 4) The anisotropy should be revealed when the inter-valence band transition away from k ¼ 0 occurs. 8,9) Such transitions are allowed when the Fermi energy is lowered with p-type doping.…”