Chengyun Hua

Length Dependent Thermal Conductivity Measurements Yield Phonon Mean Free Path Spectra in Nanostructures

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.

Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.

Importance of frequency-dependent grain boundary scattering in nanocrystalline silicon and silicon–germanium thermoelectrics

Nanocrystalline silicon and silicon-germanium alloys are promising thermoelectric materials that have achieved substantially improved figure of merits compared to their bulk counterparts. This enhancement is typically attributed to a reduction in lattice thermal conductivity by phonon scattering at grain boundaries. However, further improvements are difficult to achieve because grain boundary scattering is poorly understood, with recent experimental observations suggesting that the phonon transmissivity may depend on phonon frequency rather than being constant as in the commonly used gray model. Here, we examine the impact of frequency-dependent grain boundary scattering in nanocrystalline silicon and silicon-germanium alloys in a realistic 3D geometry using frequency-dependent variance-reduced Monte Carlo simulations. We find that the grain boundary may not be as effective as predicted by the gray model in scattering certain phonons, with a substantial amount of heat being carried by low frequency phonons with mean free paths longer than the grain size. Our result will help guide the design of more efficient thermoelectrics.

Experimental metrology to obtain thermal phonon transmission coefficients at solid interfaces

Interfaces play an essential role in phonon-mediated heat conduction in solids, impacting applications ranging from thermoelectric waste heat recovery to heat dissipation in electronics. From the microscopic perspective, interfacial phonon transport is described by transmission coefficients that link vibrational modes in the materials composing the interface. However, direct experimental determination of these coefficients is challenging because most experiments provide a mode-averaged interface conductance that obscures the microscopic detail. Here, we report a metrology to extract thermal phonon transmission coefficients at solid interfaces using ab initio phonon transport modeling and a thermal characterization technique, time-domain thermoreflectance. In combination with transmission electron microscopy characterization of the interface, our approach allows us to link the atomic structure of an interface to the spectral content of the heat crossing it. Our work provides a useful perspective on the microscopic processes governing interfacial heat conduction.

Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain

Quasiballistic heat conduction, in which some phonons propagate ballistically over a thermal gradient, has recently become of intense interest. Most works report that the thermal resistance associated with nanoscale heat sources is far larger than predicted by Fouriers law; however, recent experiments show that in certain cases the difference is negligible despite the heaters being far smaller than phonon mean-free paths. In this work, we examine how thermal resistance depends on the heater geometry using analytical solutions of the Boltzmann equation. We show that the spatial frequencies of the heater pattern play the key role in setting the thermal resistance rather than any single geometric parameter, and that for many geometries the thermal resistance in the quasiballistic regime is no different than the Fourier prediction. We also demonstrate that the spectral distribution of the heat source also plays a major role in the resulting transport, unlike in the diffusion regime. Our work provides an intuitive link between the heater geometry, spectral heating distribution, and the effective thermal resistance in the quasiballistic regime, a finding that could impact strategies for thermal management in electronics and other applications.