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Strain in a material induces shifts in vibrational frequencies, which is aprobe of the nature of the vibrations and interatomic potentials, and can beused to map local stress/strain distributions via Raman microscopy. This methodis standard for crystalline silicon devices, but due to lack of calibrationrelations, it has not been applied to amorphous materials such as hydrogenatedamorphous silicon (a-Si:H), a widely studied material for thin-filmphotovoltaic and electronic devices. We calculated the Raman spectrum of a-Si:H\ab initio under different strains $\epsilon$ and found peak shifts $\Delta\omega = \left( -460 \pm 10\ \mathrm{cm}^{-1} \right) {\rm Tr}\ \epsilon$. Thisproportionality to the trace of the strain is the general form for isotropicamorphous vibrational modes, as we show by symmetry analysis and explicitcomputation. We also performed Raman measurements under strain and found aconsistent coefficient of $-510 \pm 120\ \mathrm{cm}^{-1}$. These resultsdemonstrate that a reliable calibration for the Raman/strain relation can beachieved even for the broad peaks of an amorphous material, with similaraccuracy and precision as for crystalline materials.

Stress effects on the Raman spectrum of an amorphous material: theory and experiment on a-Si:H