Analysis of Quasi-Ballistic Phonon Transport Based on Transient Thermal Grating and the Boltzmann Transport Equation

Studying heat conduction in semiconductors at the micro/nano scale is crucial for further optimizing heat dissipation of electronics. Transient thermal grating (TTG) is a noncontact technique for investigating thermal transport properties of semiconductors. The traditional scheme to extract the thermal diffusivity from the TTG measurements is based on the diffusion equation. At length scales comparable to or even shorter than the mean free paths (MFPs) of phonons, this framework breaks down. Although previous work has proposed a method of theoretical analysis for multidimensional quasi-ballistic thermal transport of phonons in TTG with an analytic solution to the Boltzmann transport equation (BTE), the feasibility of applying this solution to TTG measurements to extract the contribution of phonons to heat conduction has not been tested experimentally. In this work, we selected germanium as the demonstration material and extracted the contribution of phonons with various MFPs to heat conduction successfully based on the TTG experiment data and the solution to the 2-dimensional (2D) BTE. This work not only verifies the viability of this method but also provides an important guide for future research on micro/nano scale heat conduction in semiconductors.