Raman analysis of three-dimensionally graded stress tensor components in sapphire

Abstract

An improved method of confocal/polarized Raman spectroscopy is proposed, which enables the determination of the full set of tensor components in three dimensionally graded stress fields in sapphire single-crystal. From the experimental side, the proposed method employs a simple back-scattered configuration for the optical microprobe and relies on the experimental knowledge of the matrix of piezospectroscopic (PS) coefficients of sapphire (i.e., the proportionality constants relating the frequency shifts of individual Raman bands to the magnitude of an uniaxial stress applied along different crystallographic directions). From the theoretical side, the complete set of stress tensor components were generally expressed as a function of the PS coefficients for any unknown multiaxial stress state by means of the Euler transformation matrix, leading to a system of linear equations; such equations link each stress component to the experimentally observed spectral shifts of different Raman bands. The proposed PS method does not require a direct knowledge of the secular equation, but local crystallographic orientations should be retrieved from polarized Raman intensities. With probe averaging effects being systematically removed by probe deconvolutive routines, the PS method is shown to correctly resolve multiaxial stress tensor fields with steep gradients in space.