Theory of strain effects on the Raman spectrum of Si-Ge core-shell nanowires

An analytical model is introduced to compute the Raman spectrum of Si-Ge core shell nanowires. For the calculation of the strain, the materials are assumed to be elastically isotropic. It is argued that the largest components of the strain tensor are not significantly affected by this approximation. The phonon modes in the presence of strain are calculated using the known deformation potential tensors for Si and Ge. Predictions are made for Si-Ge and Ge-Si core-shell nanowires with axes along the 〈 011 〉 and 〈 111 〉 crystallographic directions. The results are presented in a way that makes it very simple to compare with experimental data and to extend the calculation to cases in which the shell consists of a Si_1-xGe _x alloy.