Effect of indirect interband absorption in Ge/SiGe quantum wells

The effect of the indirect interband absorption both below and above the direct gap in Ge/SiGe quantum-well (QW) structures is theoretically investigated in comparison to the direct interband absorption. The theoretical formula for the indirect interband absorption is derived based on the second-order time-dependent perturbation theory. The direct interband absorption is calculated by summing the bound-state exciton contribution based on the variational method and the QW continuum-state contribution in the consideration of the valence band mixing effect and a Sommerfeld excitonic enhancement factor. The calculated indirect interband absorption parabolically increases below the direct bandgap and shows a stair-step-like gradual increase above the direct bandgap. The calculated optical absorption spectra at room temperature are compared with the experimental results measured by Kuo [Nature 437, 1334 (2005)]. Although the indirect interband absorption is very small below the direct bandgap, the contribution of the gradually increasing indirect interband absorption is significant at the high transition energy above the direct bandgap.