Analytical model for laser-induced transient grating measurements of thermal diffusivity in non-opaque materials

Abstract

The thermal transport and elastic properties of materials are often measured using the laser-induced transient grating spectroscopy (TGS) technique. The analysis of the TGS signal usually involves fitting well-known expressions, derived assuming the limiting cases of opaque or transparent materials, to the measured data. In this paper, the system of thermoelastic equations is analytically solved for an isotropic homogeneous material assuming finite laser penetration depth, which is an important consideration when the penetration depth is on the order of the acoustic wavelength. The need to use such a solution is discussed and compared to the expression for opaque material. The solution is benchmarked against TGS signal measured on single-crystal silicon with {100} surface orientation and is found to significantly improve the accuracy of the calculated thermal diffusivity as compared to using the expression for opaque material.