Stress effects on the Raman spectrum of an amorphous material: Theory and experiment on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>a</mml:mi></mml:math>-Si:H

Abstract

Strain in a material induces shifts in vibrational frequencies. This phenomenon 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 the 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 $\ensuremath{\epsilon}$ and found peak shifts $\mathrm{\ensuremath{\Delta}}\ensuremath{\omega}=\left(\ensuremath{-}460\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\right)\mathrm{Tr}\phantom{\rule{4pt}{0ex}}\ensuremath{\epsilon}$. 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 $\ensuremath{-}510\ifmmode\pm\else\textpm\fi{}120\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. 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.