Raman scattering from Ge-Si core-shell nanowires: Validity of analytical strain models

The Raman scattering spectra from Ge-Si core-shell nanowires have been computed using two alternative strain models: A simple analytical approach that assumes cylindrical symmetry and isotropic elastic constants, and a more realistic method that incorporates the actual nanowire geometry and the cubic-symmetry elastic constants of Si and Ge. The results show that the simple analytical model provides qualitatively correct descriptions of the strain and Raman spectra. In particular, both calculations predict that the strain is essentially uniform within the core section of the nanowire, suggesting that core Raman spectra are ideal for strain characterization. The quantitative agreement between the two methods is also surprisingly good, making it possible to use simple analytical expressions to estimate the strain in nanowires with errors not exceeding 10.