Heavy-hole scattering by confined nonpolar optical phonons in a singleSi1−xGex/Siquantum well

Abstract

Intrasubband and intersubband scattering rates of heavy holes are obtained due to confined nonpolar optical phonons in a ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ quantum well with Si barriers. Guided and interface Ge-Si and Ge-Ge modes and unconfined Si-Si modes are considered. A continuum model is used for the two components of the ionic displacement of confined vibrations: the uncoupled $s$-polarized TO mode and the hybrid of the LO and $p$-polarized TO modes. The guided mode is obtained using the model of a quantum well with infinitely rigid barriers and the interface mode is derived from the hydrodynamic boundary conditions. While the total intersubband scattering rates are reduced as a result of confinement, the opposite is found for the intrasubband scattering. Depending on the well width and Ge content, the intersubband scattering rates are reduced by a factor of 2-4 with respect to their values for no confinement. Thus one would expect comparable enhancement in the intersubband lifetimes crucial to the population inversion in a ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x/\mathrm{Si}$ intersubband laser.