Abstract
Heat conduction in semiconductors and dielectrics depends upon their phonon mean free paths that describe the average travelling distance between two consecutive phonon scattering events. Nondiffusive phonon transport is being exploited to extract phonon mean free path distributions. Here, we describe an implementation of a nanoscale thermal conductivity spectroscopy technique that allows for the study of mean free path distributions in optically absorbing materials with relatively simple fabrication and a straightforward analysis scheme. We pattern 1D metallic grating of various line widths but fixed gap size on sample surfaces. The metal lines serve as both heaters and thermometers in time-domain thermoreflectance measurements and simultaneously act as wire-grid polarizers that protect the underlying substrate from direct optical excitation and heating. We demonstrate the viability of this technique by studying length-dependent thermal conductivities of silicon at various temperatures. The thermal conductivities measured with different metal line widths are analyzed using suppression functions calculated from the Boltzmann transport equation to extract the phonon mean free path distributions with no calibration required. This table-top ultrafast thermal transport spectroscopy technique enables the study of mean free path spectra in a wide range of technologically important materials.
Highlights
Λ are the phonon mode dependent specific heat, group velocity and MFP, respectively, is the key metric to describe the contributions of phonons with different MFPs to heat transport under the relaxation time approximation8. kaccum(Λ *), yielding the contributions of phonons with MFPs less than a threshold value Λ *, essentially describes the distribution of phonon MFPs contributing to a material’s thermal conductivity
An emerging optical desk-top approach focuses on utilizing quasiballistic phonon transport, created when characteristic length scales become comparable to the phonon MFPs, to map out the MFP distributions[2,3,4,5,6]
The described thermal conductivity spectroscopy technique is a general method for studying phonon MFPs in a wide range of materials
Summary
Λ are the phonon mode dependent specific heat, group velocity and MFP, respectively, is the key metric to describe the contributions of phonons with different MFPs to heat transport under the relaxation time approximation8. kaccum(Λ *), yielding the contributions of phonons with MFPs less than a threshold value Λ *, essentially describes the distribution of phonon MFPs contributing to a material’s thermal conductivity. In quasiballistic transport where the heat source dimension is comparable with some phonon MFPs (Fig. 1(b)), long-MFP phonons do not experience scattering as inherently assumed by Fourier’s law and no local thermal equilibrium can be established, leading to the breakdown of the heat diffusion theory[29]. Measuring diffraction of an extreme UV probe[2,15], predominantly sensitive to the photothermally induced surface displacement, largely alleviates the problems associated with electronic excitation and moderate substrate heating Another nontrivial challenge is the mapping of experimentally measured effective thermal conductivities to the phonon MFP distribution in the material under study. The approach of ref. 7 requires the fabrication of membranes spanning a broad range of thicknesses commensurate with the phonon MFPs, making it impractical as a generic MFP spectroscopy tool
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