Abstract
Thermal conductivity measurements over variable lengths on nanostructures such as nanowires provide important information about the mean free paths (MFPs) of the phonons responsible for heat conduction. However, nearly all of these measurements have been interpreted using an average MFP even though phonons in many crystals possess a broad MFP spectrum. Here, we present a reconstruction method to obtain MFP spectra of nanostructures from variable-length thermal conductivity measurements. Using this method, we investigate recently reported length-dependent thermal conductivity measurements on SiGe alloy nanowires and suspended graphene ribbons. We find that the recent measurements on graphene imply that 70% of the heat in graphene is carried by phonons with MFPs longer than 1 micron.
Highlights
We find that the recent measurements on graphene imply that 70% of the heat in graphene is carried by phonons with mean free paths (MFPs) longer than 1 micron
The measurements on graphene ribbons imply that MFPs are exceedingly long, with 70% of the heat being carried by phonons with MFPs longer than 1 micron
The original dispersion and relaxation times were calculated by density functional theory (DFT) by Jesus Carrete and N
Summary
Thermal conductivity measurements over variable lengths on nanostructures such as nanowires provide important information about the mean free paths (MFPs) of the phonons responsible for heat conduction. We present a reconstruction method to obtain MFP spectra of nanostructures from variable-length thermal conductivity measurements Using this method, we investigate recently reported length-dependent thermal conductivity measurements on SiGe alloy nanowires and suspended graphene ribbons. Information about MFPs was obtained by measuring the thermal conductivity over variable lengths of nanostructures such as nanotubes[7], graphene ribbons[15] and SiGe nanowires[16]. The MFP spectrum is obtained using the convex optimization method described in Ref. 20 We apply this approach to SiGe nanowires and graphene ribbons. K~ SðKnvÞf ðLvÞdLv~ L{1KðKnvÞFðLvÞdLv ð1Þ where Knv 5 Lv/L is the Knudsen Number, Lv is the MFP, L is the sample length along the direction of the temperature gradient, k denotes thermal conductivity as a function of length L, f(Lv) and
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