Spatially resolved determination of thermal conductivity by Raman spectroscopy

We review the Raman shift method as a non-destructive optical tool to investigate the thermal conductivity and demonstrate the possibility to map this quantity with a micrometer resolution by studying thin film and bulk materials for thermoelectric applications. In this method, a focused laser beam both thermally excites a sample and undergoes Raman scattering at the excitation spot. The temperature dependence of the phonon energies measured is used as a local thermometer. We discuss that the temperature measured is an effective one and describe how the thermal conductivity is deduced from single temperature measurements to full temperature maps, with the help of analytical or numerical treatments of heat diffusion. We validate the method and its analysis on three- and two-dimensional single crystalline samples before applying it to more complex Si-based materials. A suspended thin mesoporous film of phosphorus-doped laser-sintered S{{i}₇₈}G{{e}₂₂} nanoparticles is investigated to extract the in-plane thermal conductivity from the effective temperatures, measured as a function of the distance to the heat sink. Using an iterative multigrid Gauss-Seidel algorithm the experimental data can be modelled yielding a thermal conductivity of 0.1 W/m K after normalizing by the porosity. As a second application we map the surface of a phosphorus-doped three-dimensional bulk-nanocrystalline Si sample which exhibits anisotropic and oxygen-rich precipitates. Thermal conductivities as low as 11 W/m K are found in the regions of the precipitates, significantly lower than the 17 W/m K in the surrounding matrix. The present work serves as a basis to more routinely use the Raman shift method as a versatile tool for thermal conductivity investigations, both for samples with high and low thermal conductivity and in a variety of geometries.