  Core-shell Ge-SixGe1-x 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-shell, and bare Ge NWs. We find that
the Ge-Ge mode frequency is diameter-independent in GeNWs with a value similar
to that of bulk Ge, 300.5 cm-1. 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.
