Infrared absorption in ${\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}}_{1-x}{\mathrm{Ge}}_x/\mathrm{Si}$ quantum wells

The infrared intersubband optical transitions in SiGe/Si quantum wells is theoretically examined. We have used the $8\times 8,$ $12\times 12,$ and $14\times 14$ $\mathbf{k}\cdot \mathbf{p}$ Hamiltonians taking into account both the p-like first conduction band and the s-like second conduction band to calculate wave functions and energy dispersion of the valence band of ${\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}}_{0.8}{\mathrm{Ge}}_{0.2}/\mathrm{Si}$ quantum wells. We discuss intersubband absorption in the valence band and we show that the p-p interaction favors intersubband transitions for an optical polarization parallel to the layer plane $(x$ polarization). For z polarization, both s-p and p-p interactions play the same footing role in intervalence band transitions.