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.

Stress Measurements in Si and SiGe by Liquid-Immersion Raman Spectroscopy

“…(16), the relationship between the Raman wavenumber shifts is and the anisotropic biaxial stresses xx and yy are obtained as follows [35]: …”

“…Recently, the forbidden optical phonon modes, the TO phonon modes, were excited even under the (001) Si backscattering geometry, using a high-numerical aperture (NA) liquid-immersion lens [22][23][24]. If all of the three optical phonon modes are detectable, the unknown three components of a stress tensor in Si can be obtained in theory [25][26][27][28][29][30][31][32][33][34][35]. The high-NA liquid-immersion Raman spectroscopy has great potential for measuring the complicated stress states in Si with high spatial resolution.…”

Micro-Raman measurement of bending stresses in micromachined silicon flexures

“…The phenomenon of Raman scattering, and the effects of mechanical stress on the Raman spectrum of single-crystal silicon, have been extensively studied and documented [10]- [26]. The principal results pertinent to the analysis of the flexure are summarized below.…”

“…The other is to perform additional spectroscopic measurements involving the polarizations of, and the relative angles between, the incident and scattered radiation. Such studies are topics of current research [25], [26], [41]. The use of time-resolved spectroscopy to measure dynamic stresses in rotating micromachinery is also being explored.…”

μ-Raman spectroscopy characterization of LiNbO3 femtosecond laser written waveguides

“…The first relates to materials used in microelectronics and micro electro-mechanical (MEMS) manufacturing, [21][22][23][24][25][26][27][28][29][30][31][32] and the other relates to photonic materials. [33][34][35][36] These photonic materials are used as bulk material for the generation of optical and electro-optical circuits.…”