Universal phonon mean free path spectra in crystalline semiconductors at high temperature

Abstract

Thermal conductivity in non-metallic crystalline materials results from cumulative contributions of phonons that have a broad range of mean free paths. Here we use high frequency surface temperature modulation that generates non-diffusive phonon transport to probe the phonon mean free path spectra of GaAs, GaN, AlN, and 4H-SiC at temperatures near 80 K, 150 K, 300 K, and 400 K. We find that phonons with MFPs greater than 230 ± 120 nm, 1000 ± 200 nm, 2500 ± 800 nm, and 4200 ± 850 nm contribute 50% of the bulk thermal conductivity of GaAs, GaN, AlN, and 4H-SiC near room temperature. By non-dimensionalizing the data based on Umklapp scattering rates of phonons, we identified a universal phonon mean free path spectrum in small unit cell crystalline semiconductors at high temperature.

Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments

“…Our results are relevant for efforts to use TDTR and FDTR as a MFP spectroscopy technique 1,4,24 . Observations of Fourier theory failure in the through-plane and in-plane direction are both sensitive to the MFP distribution of solids (Fig.…”

“…On the other hand, the observation of Minnich et al 4 that L A of Si depends on w 0 below 100 K was related to a failure of Fourier theory in the in-plane direction. That Fourier theory fails anisotropically has direct implications for the interpretations of prior experiments that assumed Fourier theory failed isotropically in three-dimensional heat-transfer problems 1,4,7,24 , see Supplementary Note 1 and Supplementary Figs 1 and 2.…”

“…Prior experimental studies that observed a dependence of L A on f emphasized the importance of temperature profile length scales being comparable to MFPs 1,6,24 . As we demonstrate in more detail in subsequent sections, another factor causing L A to deviate from L B in the through-plane direction is interfacialphonon scattering.…”

Characteristic length of phonon transport within periodic nanoporous thin films and two-dimensional materials

“…Similar phonon MFP spectra can also be found in many other materials. 54,55 Therefore, the provided K Ã Pore curve can be accurate for nanoporous thin films of a variety of materials, such as oxides and nitrides.…”

A new regime of nanoscale thermal transport: Collective diffusion increases dissipation efficiency

“…Recent work has shown that the rate of heat dissipation from a heat source is reduced significantly below that predicted by Fourier's law for diffusive heat transfer when the characteristic dimension of the heat source is smaller than the mean free path (MFP) of the dominant heat carriers (phonons in dielectric and semiconductor materials) (1)(2)(3)(4)(5)(6). However, a complete fundamental description of nanoscale thermal transport is still elusive, and current theoretical efforts are limited by a lack of experimental validation.…”