Characterization of strain in core-shell nanowires: a Raman spectroscopy study

Raman scattering from Ge-Si core-shell nanowires is investigated theoretically and experimentally. A theoretical model that makes it possible to extract quantitative strain information from the measured Raman spectra is presented for the first time. Geometrical and elastic simplifications are introduced to keep the model analytical, which facilitates comparison with experimental results. In particular, the nanowires are assumed to be cylindrical, and their elastic constants isotropic. The simple analytical model is subsequently validated by performing numerical calculations using realistic nanowire geometries and cubic, anisotropic elastic constants. The comparison confirms that the analytic model is an excellent approximation that greatly facilitates quantitative Raman work, with expected errors in the strain determination that do not exceed 10%. Experimental Raman spectra of a variety of core-shell nanowires are presented, and the strain in the nanowires is assessed using the models described above. It is found that all structures present a significant degree of strain relaxation relative to ideal, fully strained Ge-Si core-shell structures. The analytical models are modified to quantify this strain relaxation.