Raman spectroscopy and strain mapping in individual Ge-Si$_x$Ge$_1$-$x$ core-shell nanowires
Core-shell Ge-SixGe1âx nanowires (NWs) are expected to contain large strain fields due to the lattice mismatch at the core-shell interface. Here we report the measurement of core strain in a NW heterostructure using Raman spectroscopy. We compare the Raman spectra, and the frequency of the Ge-Ge mode measured in individual Ge-Si0.5Ge0.5 core-shells, and bare Ge NWs. We find that the Ge-Ge mode frequency is diameter independent in Ge NWs with a value similar to that of bulk Ge, 300.5 cmâ1. On the other hand, Ge-Si0.5Ge0.5 core-shell nanowires reveal a strain-induced blue shift of the Ge-Ge mode, dependent on the relative core and shell thicknesses. Using lattice dynamical theory we determine the strain in the Ge core and show that the results are in good agreement with values calculated using a continuum elasticity model.