Thermal transport in suspended silicon membranes measured by laser-induced transient gratings

Abstract

Studying thermal transport at the nanoscale poses formidable experimental challenges due both to the physics of the measurement process and to the issues of accuracy and reproducibility. The laser-induced transient thermal grating (TTG) technique permits non-contact measurements on nanostructured samples without a need for metal heaters or any other extraneous structures, offering the advantage of inherently high absolute accuracy. We present a review of recent studies of thermal transport in nanoscale silicon membranes using the TTG technique. An overview of the methodology, including an analysis of measurements errors, is followed by a discussion of new findings obtained from measurements on both "solid" and nanopatterned membranes. The most important results have been a direct observation of non-diffusive phononmediated transport at room temperature and measurements of thickness-dependent thermal

2D Phononic Crystals: Progress and Prospects in Hypersound and Thermal Transport Engineering

“…As a consequence, thermal conductivity in nanostructures and PnCs is mainly governed by diffuse scattering. In thin films, a direct link between their thickness and thermal conductivity has been observed, and is well described by the Fuchs–Sondheimer model . An experimental reconstruction of the MFP contribution to thermal conductivity shows that the main contribution stems from phonons with MFPs in the 100 nm–10 µm range in agreement with first‐principles calculations .…”

Directional Phonon Suppression Function as a Tool for the Identification of Ultralow Thermal Conductivity Materials

“…For example, first-principles calculations of silicon show that half of the heat is carried by phonons with MFPs larger than one micron67, supporting the strong phonon suppression observed in porous materials with microscale pores8. In addition, very low thermal conductivities have been measured in many nanostructures, including nanoporous materials891011121314, nanowires1516 and thin films17, corroborating the use of such material systems for thermoelectric applications.…”

Diffusive Phonons in Nongray Nanostructures

“…On the other side, electrons have MFPs that are typically as small as a few nanometers thus their size effects are mostly negligible [6]. Notable nanostructures, including thin films [7], nanowires [8,9], and porous materials [10][11][12][13][14][15], show a significant suppression in thermal conductivity with respect to the bulk, holding promises for high-efficiency thermal energy conversion.In the case of materials with wide bulk MFP distribution, K(Λ), the effective thermal conductivity (κ eff ) can be conveniently computed by κ eff /κ bulk = B 0 (Λ)S(Kn)dΛ, where κ bulk is the bulk thermal conductivity, Kn = Λ/L c is the Knudsen number, S(Kn) is the material-independent, suppression function [16], andis a bulk material property, which can be computed from first-principles [17]. This approach, which we refer to as the "non-interacting model," treats phonons with different MFPs separately, with the diffusive regime (i.e., for short Kns) as described by standard Fourier's law; on the other hand, the suppression function associated with ballistic phonons (i.e., with large Kns) is S(Kn) ≈ Kn −1 , arising from the MFPs in the nanostructure being limited b L c .…”

“…We note a deviation from S(Λ) around Kn ≈ 1. In this last part, we calculate the thermal conductivity of a recently fabricated porous Si membrane in which strong phonon size effects were observed [15]. The sample is 340 nm thick and has circular pores with diameter of 135 nm and periodicity of L = 206 nm.…”

“…(a) The suppression function, S(Λ), the isotropic suppression function, SISO(Λ), and the diffusive suppression function, SD(Λ), for the structure presented in[15]. (b) The thermal flux profile.…”