Micro-Raman spectroscopic analysis of single crystal silicon microstructures for surface stress mapping

In this paper, an experimental analysis using a micro-Raman spectroscope for surface stress distribution in single crystal silicon (SCS) microstructures is described. Specially developed tensile test equipment applies a uniaxial tensile stress on SCS specimens with a 270 nm-high, 4 µm2 convex structures in the gauge section. Raman spectra around the convex region are measured using an ultraviolet laser with an excitation line of 363.8 nm. The shape of the Raman spectrum on the flat surface is symmetrical, whereas that around the edge of the convex is asymmetrical due to the multi-stress condition. Two-curve fitting is adopted for the asymmetric spectrum obtained at the edge, and the stress distribution estimated by the two peak positions is much closer to finite element analysis (FEA) results than that obtained by the one peak position. In partial least squares (PLS) analysis that is performed at the edge of the convex section only, explanatory variables are Raman spectral parameters, such as peak position, peak intensity, and full width at half maximum, and the response variable is the FEA stress distribution. The plane stress distributions derived from PLS analyses on each component are in good agreement with that from FEA. The combination of micro-Raman spectroscopy and tensile testing enables us to directly determine the stress components as well as stress magnitudes on SCS microstructures.