Light-hole to heavy-hole acoustic phonon scattering rate

A superlattice consisting of periods of $90\AA \hspace{0.5em}{\mathrm{Si}}_{0.7}{\mathrm{Ge}}_{0.3}$ quantum wells and 50 Å Si barriers on a $\mathrm{}\left(100\right)\mathrm{}\hspace{0.5em}{\mathrm{Si}}_{0.81}{\mathrm{Ge}}_{0.19}$ buffer is investigated for the purpose of designing Si-based terahertz intersubband lasers using the feature of inverted light-hole effective mass. It has been shown that the energy subband dispersion curve of this structure demonstrates a region of inverted light-hole effective mass. Since the energy separation between the two lowest subbands that are also of different type is below the optical phonon energy, acoustic phonon scattering is an important nonradiative process and is therefore studied. Our result indicates that the intersubband phonon scattering process is much weaker between different types of subband. For the particular structure of interest, this scattering rate is about 0.5/ns, corresponding to an intersubband lifetime of 2 ns, which is much longer than the typical lifetime of 1 ps when it is between subbands of the same kind.