Quantification method of stress depth distribution by micro-Raman spectroscopy for thin film nanomechanical resonator

Abstract

When stress and strain induced in a nanomechanical resonator are measured by micro-Raman spectroscopy, the analysis depth is longer than the thickness of the resonator. In cases where the resonator has stress depth distribution, the observed spectrum reflects the stress conditions at each depth and the shape of the spectrum deforms. We have developed a model of Raman spectrum formation and a method to quantify the stress depth distribution. The proposed model is expressed as a sum of several Voigt functions with individual intensities that depend on each depth and absorption characteristic, and the proposed quantification method applies nonlinear multiple regression analysis by using the model. We used this model to measure the Raman spectrum of a bent cantilever and calculate the stress depth distribution. We found that our model could obtain comparable results to those obtained by the finite element method.