Micro-Raman spectroscopy stress measurement method for porous silicon film

Micro-Raman Spectroscopy (MRS) is an effective stress measurement method. Generally, the application of MRS for stress measurement requires the quantitative relationship between Raman shift and stress based on the material of the objects to be measured. In this paper, a theoretical investigation of Raman stress measurement for porous silicon (PS) material was presented. First, the mathematical expressions for the Raman shift and stress components of transversely isotropic material were deduced by analyzing the transversely isotropic characteristics of porous silicon material and applying the secular equation of lattice dynamics for diamond-type crystal. Meanwhile, the nanoindentation technique and digital speckle correlation method were introduced to detect the elastic moduli and Poisson's ratio of porous silicon material, respectively. Subsequently, the Raman shift to stress coefficients of porous silicon material, as well as their regularity varying with PS porosity, are achieved by substituting the material parameters determined in the experiments into the analytic relationship acquired through deductions. Using these coefficients, the distribution of residual stress along the thickness direction in the PS-film/Si-substrate structure was measured.