A recently developed enhanced Fourier law is applied to the problem of extracting thermal properties of materials from frequency-domain thermoreflectance (FDTR) experiments. The heat transfer model comprises contributions from two phonon channels; one a high-heat-capacity diffuse channel consisting of phonons of mean free path (MFP) less than a threshold value, and the other a low-heat-capacity channel consisting of phonons with MFP higher than this value that travel quasi-ballistically over length scales of interest. The diffuse channel is treated using the Fourier law, while the quasi-ballistic channel is analyzed using a second-order spherical harmonic expansion of the phonon distribution function. A recent analysis of FDTR experimental data suggested the use of FDTR in deriving large portions of the MFP accumulation function; however, it is shown here that the data can adequately be explained using our minimum-parameter model, thus highlighting an important limitation of FDTR experiments in exploring the accumulation function of bulk matter.
To develop effective thermal management strategies for GaN transistors, it is essential to accurately predict the device junction temperature. Since the width of the heat generation in the devices is comparable to phonon mean free paths of GaN, phonon ballistic transport exists and can significantly affect the heat transport process, which necessitates a thorough understanding of the influence of the phonon ballistic effects in GaN transistors. In this paper, the ballistic-diffusive phonon transport in GaN-on-SiC devices is examined by measuring the hotspot temperature using the thermoreflecta…
The maximum output power of GaN-based high-electron mobility transistors is limited by high channel temperature induced by localized self-heating which degrades device performance and reliability. With generated heat fluxes within these devices reaching magnitude close to ten times of that at the sun surface, chemical vapor deposition (CVD) diamond is an attractive candidate to aid in the extraction of this heat in order to keep the operating temperatures of these high power electronics as low as possible. Due to the observed inhomogeneous structure, CVD diamond membranes exhibit a 3D anisotro…
In this work, we develop a numerical fitting routine to extract multiple thermal parameters using frequency-domain thermoreflectance (FDTR) for materials having non-standard, non-semi-infinite geometries. The numerical fitting routine is predicated on either a 2-D or 3-D finite element analysis that permits the inclusion of non semi-infinite boundary conditions, which can not be considered in the analytical solution to the heat diffusion equation in the frequency domain. We validate the fitting routine by comparing it to the analytical solution to the heat diffusion equation used within the wi…
Thermal resistances from interfaces impede heat dissipation in micro/nanoscale electronics, especially for high-power electronics. Despite the growing importance of understanding interfacial thermal transport, advanced thermal characterization techniques which can visualize thermal conductance across buried interfaces, especially for nonmetal-nonmetal interfaces, are still under development. This work reports a dual-modulation-frequency TDTR mapping technique to visualize the thermal conduction across buried semiconductor interfaces for beta-Ga2O3-SiC samples. Both the beta-Ga2O3 thermal condu…
Anisotropic thermal properties are of both fundamental and practical interests, but remain challenging to characterize using conventional methods. In this work, a new metrology based on asymmetric beam time-domain thermoreflectance (AB-TDTR) is developed to measure three-dimensional anisotropic thermal transport by extending the conventional TDTR technique. Using an elliptical laser beam with controlled elliptical ratio and spot size, the experimental signals can be exploited to be dominantly sensitive to measure thermal conductivity along the cross-plane or any specific in-plane directions. A…
Many materials have anisotropic thermal conductivity, with diverse applications such as transistors, thermoelectrics, and laser gain media. Yet measuring the thermal conductivity tensor of such materials remains a challenge, particularly for materials lacking in-plane symmetry (i.e., transversely anisotropic materials). This paper demonstrates thermal conductivity tensor measurements for transversely anisotropic materials, by extending beam-offset frequency-domain thermoreflectance (BO-FDTR) methods which had previously been limited to transversely isotropic materials. Extensive sensitivity an…
The Boltzmann transport equation (BTE) has proven indispensable in elucidating quasiballistic heat dynamics. Experimental observations of nondiffusive thermal transients, however, are interpreted almost exclusively through purely diffusive formalisms that merely extract "effective" Fourier conductivities. Here, we build upon stochastic transport theory to provide a characterisation framework that blends the rich physics contained within BTE solutions with the convenience of conventional analyses. The multidimensional phonon dynamics are described in terms of an isotropic Poissonian flight proc…
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 ph…
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 a microscopic perspective, interfacial phonon transport is described by transmission and reflection coefficients, analogous to the well-known Fresnel coefficients for light. However, these coefficients have never been directly measured, and thermal transport processes at interfaces remain poorly understood despite considerable effort. Here, we report the first measurements of the Fresnel transmission coef…
Heat transfer across interfaces of graphene and polar dielectrics (e.g. SiO2) could be mediated by direct phonon coupling, as well as electronic coupling with remote interfacial phonons (RIPs). To understand the relative contribution of each component, we develop a new pump-probe technique, called voltage-modulated thermoreflectance (VMTR), to accurately measure the change of interfacial thermal conductance under an electrostatic field. We employed VMTR on top gates of graphene field-effect transistors and find that the thermal conductance of SiO2/graphene/SiO2 interfaces increases by up to ΔG…
We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively s…
We study nondiffusive thermal transport by phonons at small distances within the framework of the Boltzmann transport equation (BTE) and demonstrate that the transport is significantly affected by the distribution of phonons emitted by the source. We discuss analytical solutions of the steady-state BTE for a source with a sinusoidal spatial profile, as well as for a three- dimensional Gaussian hot spot, and provide numerical results for single crystal silicon at room temperature. If a micro/nanoscale heat source produces a thermal phonon distribution, it gets hotter than predicted by the heat …
The mean-free path (MFP) accumulation function for the effective thermal conductivity, introduced by Dames and Chen is a compact, universal and highly useful summary of the effect of ballistic thermal transport on the effective thermal conductivity measured by various experiments. The frequency domain thermoreflectance (FDTR) experiment is especially well suited to its determination. Extraction of the accumulation function from this experiment uses the thermal penetration depth (TPD) of phonons at each frequency as a cut-off for classifying phonons as ballistic or diffusive at that frequency. …
It is generally understood that Fourier's law does not describe ballistic phonon transport, which is important when the length of a material is similar to the phonon mean-free-path. Using an approach adapted from electron transport, we demonstrate that Fourier's law and the heat equation do capture ballistic effects, including temperature jumps at ideal contacts, and are thus applicable on all length scales. Local thermal equilibrium is not assumed, because allowing the phonon distribution to be out-of-equilibrium is important for ballistic and quasi-ballistic transport. The key to including t…
Artificially engineered 2D materials offer unique physical properties for thermal management, surpassing naturally occurring materials. Here, using van der Waals epitaxy, we demonstrate the ability to engineer extremely insulating ultra-thin thermal metamaterials based on crystalline lattice-mismatched Bi2Se3/MoSe2 superlattices and graphene/PdSe2 heterostructures with exceptional thermal resistances (70-202 m^2K/GW) and ultralow cross-plane thermal conductivities (0.01-0.07 Wm^-1K^-1) at room temperature, comparable to those of amorphous materials. Experimental data obtained using frequency-d…
Understanding ballistic phonon transport effects in transient thermoreflectance experiments and explaining the observed deviations from classical theory remains a challenge. Diffusion equations are simple and computationally efficient but are widely believed to break down when the characteristic length scale is similar or less than the phonon mean-free-path. Building on our prior work, we demonstrate how well-known diffusion equations, namely the hyperbolic heat equation and the Cattaneo equation, can be used to model ballistic phonon effects in frequency-dependent periodic steady-state therma…
For a thermal conductivity that is spatially uniform and independent of temperature, Fourier's law of heat transfer predicts a curl-free heat-flux. In the quasi-ballistic phonon transport regime, where the Fourier law breaks down, it has been proven starting from the Boltzmann transport equation that the constitutive relation for the heat-flux contains a solenoidal (circulatory) term with zero divergence and non-zero curl. In this paper we show how to reduce the effective thermal conductivity of a material with dimensions on the same scale as the phonon mean-free path, by exploiting the soleno…
Previous studies have predicted the failure of Fourier's law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regimes only by this phenomenon. In this work, the transient heat propagation in homogeneous thermal system is studied based on the phonon Boltzmann transport equation (BTE) under the Callaway model. Given a quasi-one or quasi-two (three) dimensional s…
Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier's Law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier's Law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement…
Heat conduction in graphite has been studied for decades because of its exceptionally large thermal anisotropy. While the bulk thermal conductivities along the in-plane and cross-plane directions are well known, less understood are the microscopic properties of the thermal phonons responsible for heat conduction. In particular, recent experimental and computational works indicate that the average phonon mean free path (MFP) along the c-axis is considerably larger than that estimated by kinetic theory, but the distribution of MFPs remains unknown. Here, we report the first quantitative measurem…
Nanoconfinement induces many intriguing non-Fourier heat conduction phenomena that have been extensively studied in recent years, such as the nonlinear temperature profile inside the devices, the temperature jumps near the contacts, and the finite-size effects. The understanding of these phenomena, however, has been a matter of debate over the past two decades. In this work, we demonstrate a unified phonon interpretation of non-Fourier heat conduction which can help to understand these phenomena by a mode-to-mode correspondence between the non-equilibrium molecular dynamics (NEMD) simulations …
In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels of description. Transport of heat is formulated within kinetic theory of polarized phonons, kinetic theory of unpolarized phonons, hydrodynamics of polarized phonons, and hydrodynamics of unpolarized phonons. These various levels of description are linked by Poisson reductions, where no linearizations are made. Consequently, we obtain a new phonon hydrodynamics that contains convective terms dependent on vorticity of the heat flux, which are missing in the standard theories of phonon hydrodynam…
