Experimental Study on the Photoelastic Coefficient and Its Wavelength Dispersion for Quantitative Imaging of Residual Strain in Commercial SiC Substrates

Abstract

The absolute difference between two photoelastic coefficients $\left| {p_{11} - p_{12} } \right|$ and its wavelength dispersion have been experimentally studied in commercially available (0001) 4H silicon carbide substrates by using originally developed imaging polariscopes (xIPs) with different light-source wavelengths ($\lambda$ = 630 nm, 940 nm, and 1200 nm). The simple three-point bending test was adopted to measure the distribution of birefringence $\left| {\Delta {\text{n}}} \right|$ in a small beam under an external load. Additionally, numerical simulation was performed to accurately estimate the distribution of $\left| {\sigma_{1} - \sigma_{2} } \right|$ in the beam, even with its size restriction. The value of $\left| {p_{11} - p_{12} } \right|$ was evaluated by regression analysis on the value pairs of $\left| {\sigma_{1} - \sigma_{2} } \right|$ and $\left| {\Delta {\text{n}}} \right|$ examined under various external loads. In order to avoid the effect of residual strain in the sample, the regression analysis was performed at many positions over the sample rather than a few representative points as is adopted conventionally. The value of $\left| {p_{11} - p_{12} } \right|$ was obtained as 0.040, 0.090 and 0.13 at wavelengths of 630 nm, 940 nm, and 1200 nm, respectively. The wavelength dispersion revealed inverse correlation with photon energy and suggested that $\left| {p_{11} - p_{12} } \right|$ may become close to zero at a certain wavelength shorter than 630 nm, implying a technical trade-off between the sensitivity of the photoelastic effect and the signal-to-noise ratio in polariscopic photometry, which is useful for considering the optimal wavelength in quantitative strain imaging with photoelastic technique.