Effect of hydrostatic pressure on the Raman spectrum of ${\mathrm{Ge}}_n{\mathrm{Si}}_m$ multiple quantum wells with $n<~4$ and $m<~7$

We report a Raman study of the effects pressure has on the vibrational structure of ${\mathrm{Ge}}_n{\mathrm{Si}}_m$ multiple quantum wells (MQW’s) with $n<~4$ and $m<~7.$ Three primary phonon bands are studied: Ge-Ge within the germanium layers, Si-Si within the silicon layers, and the Ge-Si interface mode. Pressure shifts each of these bands consistent with a mode-Grüneisen constant of unity for all samples and laser excitations used. We observe resonance effects with the confined Ge-like $E_1$ transition for the ${\mathrm{Ge}}_4{\mathrm{Si}}_5$ sample. The transition is near 2.4 eV at ambient pressure and blueshifts at $\approx 4\pm 1$ meV/kbar. This pressure coefficient is smaller than the corresponding quantity in bulk germanium. This is attributed to the fact that silicon dictates the in-plane contraction of the Ge layer that is at a smaller rate than the corresponding quantity in bulk germanium. We see no evidence of resonance enhancement in samples with thinner Ge layers in each MQW period. This implies that at least four Ge atoms are necessary to form the states producing the $E_1$ transition, consistent with previous studies. An additional feature seen in the spectra near $310\hspace{0.5em}{\mathrm{cm}}^{-1}$ is identified by the pressure study to be 2TA Raman scattering from silicon.