Polarized off-axis Raman spectroscopy: A technique for measuring stress tensors in semiconductors

Abstract

A characterization technique was developed for measuring the complete tensor nature of stress fields in semiconductors. By combining incident light tilted away from the normal axis with polarization of the incident and scattered beams, any Raman-active optical phonon mode can be selectively studied. Once the frequencies and intensities of these phonons are known, the complete stress tensor can be determined. Using this concept, a general, systematic theory and methodology for implementing polarized off-axis Raman spectroscopy was developed that took into account realistic effects which would be encountered in an actual experiment. This methodology was applied to mechanically deformed silicon wafers. By applying loads in different configurations across the wafer, various types of stress were created including tension, compression, and shear. The polarized off-axis Raman technique was validated by comparing its results to both analytic calculations based upon the theory of elasticity and to direct measurements of the wafer curvature using a laser deflection method.