Optical absorption in highly strained Ge/SiGe quantum wells: The role of $Γ→Δ$ scattering

We report the observation of the quantum-confined Stark effect in Ge/SiGe multiple quantum well heterostructures grown on Si_0.22Ge_0.78 virtual substrates. The large compressive strain in the Ge quantum well layers caused by the lattice mismatch with the virtual substrate results in a blue shift of the direct absorption edge, as well as a reduction in the Γ-valley scattering lifetime because of strain-induced splittings of the conduction band valleys. We investigate theoretically the Γ-valley carrier lifetimes by evaluating the $Γ→L$ and $Γ→Δ$ scattering rates in strained Ge/SiGe semiconductor heterostructures. These scattering rates are used to determine the lifetime broadening of excitonic peaks and the indirect absorption in simulated absorption spectra, which are compared with measured absorption spectra for quantum well structures with systematically varied dimensions. We find that $Γ→Δ$ scattering is significant in compressively strained Ge quantum wells and that the Γ-valley electron lifetime is less than 50 fs in the highly strained structures reported here, where $Γ→Δ$ scattering accounted for approximately half of the total scattering rate.