  Strain in a material induces shifts in vibrational frequencies, which is a
probe of the nature of the vibrations and interatomic potentials, and can be
used to map local stress/strain distributions via Raman microscopy. This method
is standard for crystalline silicon devices, but due to lack of calibration
relations, it has not been applied to amorphous materials such as hydrogenated
amorphous silicon (a-Si:H), a widely studied material for thin-film
photovoltaic and electronic devices. We calculated the Raman spectrum of a-Si:H
\ab initio under different strains $\epsilon$ and found peak shifts $\Delta
\omega = \left( -460 \pm 10\ \mathrm{cm}^{-1} \right) {\rm Tr}\ \epsilon$. This
proportionality to the trace of the strain is the general form for isotropic
amorphous vibrational modes, as we show by symmetry analysis and explicit
computation. We also performed Raman measurements under strain and found a
consistent coefficient of $-510 \pm 120\ \mathrm{cm}^{-1}$. These results
demonstrate that a reliable calibration for the Raman/strain relation can be
achieved even for the broad peaks of an amorphous material, with similar
accuracy and precision as for crystalline materials.
