Raman scattering from fully strained Ge_1-xSn_x (x≤0.22) alloys grown on Ge(001)2×1 by low-temperature molecular beam epitaxy

Fully strained single-crystal Ge_1-xSn_x alloys (x≤0.22) deposited on Ge(001)2×l by low-temperature molecular beam epitaxy have been studied by Raman scattering. The results are characterized by a Ge-Ge longitudinal optical (LO) phonon line, which shifts to lower frequencies with increasing x. Samples capped with a 200-Å-thick Ge layer exhibit a second Ge-Ge LO phonon line whose position remains close to that expected from bulk Ge. For all samples, capped and uncapped, the frequency shift Δω_GeSn of the Ge-Ge LO phonon line from the G_1-xSn_x layer, with respect to the position for bulk Ge, is linear with the Sn fraction x(Δω_GeSn= -76.8x cm^-1) over the entire composition range. Using the elastic constants, the Grüneisen parameter, and the shear phonon deformation parameter for Ge, we calculate the contribution of compressive strain to the total frequency shift to be Δω_strain=63.8x cm^-1. Thus, the LO phonon shift in Ge_1-xSn_x due to substitutional-Sn-induced bond stretching in fully relaxed alloys is estimated to be Δω_bond = - 140.6x cm^-1.