Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes

Abstract

Knowledge of the mean-free-path distribution of heat-carrying phonons is key to understanding phononmediated thermal transport. We demonstrate that thermal conductivity measurements of thin membranes spanning a wide thickness range can be used to characterize how bulk thermal conductivity is distributed over phonon mean free paths. A noncontact transient thermal grating technique was used to measure the thermal conductivity of suspended Si membranes ranging from 15-1500 nm in thickness. A decrease in the thermal conductivity from 74-13% of the bulk value is observed over this thickness range, which is attributed to diffuse phonon boundary scattering. Due to the well-defined relation between the membrane thickness and phonon mean-free-path suppression, combined with the range and accuracy of the measurements, we can reconstruct the bulk thermal conductivity accumulation vs. phonon mean free path, and compare with theoretical models.

Thermal transport size effects in silicon membranes featuring nanopillars as local resonators

“…We observe, expectedly, k Memb to drop significantly with decreasing d due to dispersion modification as well as the reduction of phonon mean free paths (MFP) caused by diffuse boundary scattering at the surfaces as a result of their reconstruction at the equilibrium state [23]. These effects been studied experimentally in the literature in the context of a thin silicon layer on a substrate [24], freestanding silicon membranes [12,25], and also silicon nanowires [26]. The k NPM curves are observed to similarly increase with increasing unit-cell size (due to increasing thickness) until gradual saturation.…”

Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

“…The suppression function provides the ability to extend the notion of thermal conductivity beyond the diffusive regime in which it is defined from Fourier's law [21,23]. By utilizing the suppression function for a given experimental geometry, one can obtain the material's phonon MFP distribution from the experimentally measured thermal conductivity [5,6,12,23]. To obtain the effective thermal conductivity, the thermal signal from the experiment is fitted to the results of the Fourier law.…”

“…The thermal conductivity accumulation function has been utilized as an elegant metric for understanding which MFP phonons contribute predominantly to thermal transport in a material [13][14][15]. Various experimental tools such as time-domain thermoreflectance (TDTR) [4,6,8,12,16,17], frequency-domain thermoreflectance (FDTR) [18,19], and transient thermal grating (TTG) [3,5,7,20] techniques have been extensively utilized recently in order to probe and observe nondiffusive transport by using ultrafast time scales or ultrashort length scales and gain key insight into the material's MFP spectrum.When the length scales in a system become comparable to the MFPs in a material, the effective thermal conductivity is reduced compared to its bulk, diffusive limit value [21,22]. A suppression function S ω is used to quantify this reduction or suppression of thermal conductivity, defined as…”

“…In particular, there has been a growing interest recently in developing numerical and analytical solutions to the BTE to model thermal transport in phonon spectroscopy experiments [1][2][3][4][5][6][7][8][9][10][11][12] to extract phonon mean free path (MFP) distribution. The thermal conductivity accumulation function has been utilized as an elegant metric for understanding which MFP phonons contribute predominantly to thermal transport in a material [13][14][15].…”

Role of thermalizing and nonthermalizing walls in phonon heat conduction along thin films

“…The thermal conductivity reduction due to boundary scattering of phonons is conventionally treated using the Fuchs-Sondheimer theory, which was first derived for electron boundary scattering independently by Fuchs [7] and Reuter and Sondheimer [8] and was later extended to phonon boundary scattering in several works [9][10][11]. Fuchs-Sondheimer theory is widely used to interpret experiments but makes an important assumption that the diffusely scattered part of the phonon spectrum at a partially specular wall is at a local thermal equilibrium with the wall -the thermalizing boundary condition.…”