Raman measurements of uniaxial strain in silicon nanostructures

Abstract

The strain-shift coefficient used to convert Raman shifts to strain depends on multiple factors including phonon deformation potentials (PDPs). PDPs have been reported for silicon, which differ by 30%. This leads to varying strain-shift-coefficients. Using the wrong strain-shift coefficient affects the strain determined. The discrepancies in the reported PDPs were previously ascribed to surface stress relaxation and the opacity of the material to the laser radiation. This paper shows that surface orientation and scattering geometry are major factors behind the PDPs discrepancies. The work further demonstrates that different PDPs are required to accurately characterize transverse optical and longitudinal optical Raman modes. The effects of sample geometry and stress have also been studied. State of the art devices use nanowires and thin films under large values of uniaxial stress; however, previous experiments to determine PDPs and strain-shift coefficients in silicon have been limited to bulk material and stress only in the range 0–2 GPa. In this work, the strain-shift coefficient of silicon nanostructures is determined for a large range of geometries and applied stress values (0–4.5 GPa). Strain in the samples has been measured using three independent techniques: analytical calculations, finite element simulations, and by direct visual inspection of the samples elongation using scanning electron microscopy. Raman shifts have been measured using 458 nm and 364 nm laser radiations. The combination of these techniques and the large number of samples (up to 85) has allowed the accurate determination of the strain-shift coefficient for the technologically important (100) silicon surface.