Nondiffusive Thermal Transport Research Articles

Thermal transport exceeding bulk heat conduction due to nonthermal micro/nanoscale phonon populations

While classical size effects usually lead to a reduced effective thermal conductivity, we report here that nonthermal phonon populations produced by a micro/nanoscale heat source can lead to enhanced heat conduction, exceeding the prediction from Fourier's law. 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 that predicted by the heat diffusion equation; however, if the source predominantly produces low-frequency acoustic phonons with long mean free paths, it may get significantly cooler than that predicted by the heat equation, yielding an enhanced heat transport beyond bulk heat conduction.

Monte Carlo study of temperature-dependent non-diffusive thermal transport in Si nanowires

Non-diffusive thermal transport has gained extensive research interest recently due to its important implications on fundamental understanding of material’s phonon mean free path distributions and many nanoscale energy applications. In this work, we systematically investigate the role of boundary scattering and nanowire length on the non-diffusive thermal transport in thin silicon nanowires by rigorously solving the phonon Boltzmann transport equation (BTE) using a variance reduced Monte Carlo technique across a range of temperatures. The simulations use the complete phonon dispersion and spectral lifetime data obtained from first-principle density function theory calculations as input without any adjustable parameters. Our BTE simulation results show that the nanowire length plays an important role in determining the thermal conductivity of silicon nanowires. In addition, our simulation results suggest significant phonon confinement effect for the previously measured silicon nanowires. These findings are important for a comprehensive understanding of microscopic non-diffusive thermal transport in silicon nanowires.

Nondiffusive thermal transport and prediction of the breakdown of Fourier’s law in nanograting experiments

An appropriate heat conduction model is indispensable for experimental data analysis in nanothermometry in order to extract parameters of interests and to achieve a fundamental understanding of phonon-mediated heat transfer in nanostructures and across interfaces. Recently, nanoscale periodic metallic gratings are used as a group of distributed heaters as well as transducers in nanothermometry. However, in this technique, there are coupled hotspot-size-dependent effective thermal conductivity (ETC) and hotspot-size-dependent thermal interface resistivity, which posts a challenge for experimental data analysis using Fourier’s law that fails to extract both ETC and thermal interface resistivity simultaneously. To overcome this challenge, a novel two-parameter nondiffusive heat conduction (TPHC) model, which has been successfully applied to data analysis in different types of pump-probe experiments, is applied to analyze laser-induced nondiffusive heat transfer in nanoscale metallic grating experiments. Since the hotspot-size-dependent ETC is automatically captured by the TPHC model, the hotspot-size-dependent interface resistivity becomes the only parameter to be determined from experiments through data fitting. Thus, the hotspot-size-dependent thermal interface resistivity can be determined from experiments without the impact from the hotspot-size-dependent ETC. Currently, there is a lack of a criterion to predict when Fourier’s law breaks down in nanoscale heat transfer. To fill this gap, a criterion based the TPHC model is identified to predict the valid range of Fourier’s law, which is validated in both theoretical analyses and nanoscale metallic grating experiments.

Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films

The phonon Boltzmann transport equation (BTE) is widely utilized to study non-diffusive thermal transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat transport for nanostructures in multi-dimensional transport geometries, and will assist the probing of the mean free path distribution of materials via transient grating experiments.

Nondiffusive Thermal Transport Increases Temperature Rise in RRAM Filaments

Thermal transport in resistive random-access memory (RRAM) is modeled in the set state, where the conductive filament (CF) is approximated by an infinitely long cylinder embedded in crystalline rutile TiO2, a prototypical RRAM material. Determination of the phonon mean free path (MFP) spectrum in TiO2 shows that MFPs are similar to the CF radius, indicating that thermal transport is nondiffusive. We develop an analytical solution to the Boltzmann transport equation (BTE) to model the nondiffusive thermal transport in TiO2 and find that the surface temperature rise of the CF predicted by the BTE is larger than that predicted by the heat diffusion equation (e.g., $4\times $ larger for a 1 nm CF radius in a device operating at a temperature of 300 K). We propose a suppressed, effective TiO2 thermal conductivity to more accurately predict the CF temperature rise with the heat diffusion equation.

Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring non-diffusive transport. By utilizing the known Fourier solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime.

Monte Carlo study of non-diffusive relaxation of a transient thermal grating in thin membranes

The impact of boundary scattering on non-diffusive thermal relaxation of a transient grating in thin membranes is rigorously analyzed using the multidimensional phonon Boltzmann equation. The gray Boltzmann simulation results indicate that approximating models derived from previously reported one-dimensional relaxation model and Fuchs-Sondheimer model fail to describe the thermal relaxation of membranes with thickness comparable with phonon mean free path. Effective thermal conductivities from spectral Boltzmann simulations free of any fitting parameters are shown to agree reasonably well with experimental results. These findings are important for improving our fundamental understanding of non-diffusive thermal transport in membranes and other nanostructures.

Experimental Evidence of Non-Diffusive Thermal Transport in Si and GaAs

ABSTRACTThe length-scales at which thermal transport crosses from the diffusive to ballistic regime are of much interest particularly in the design and improvement of nano-structured materials. In this work, we demonstrate that the departure from diffusive transport has been observed in Si and GaAs using an optical transient thermal grating technique where an arbitrary, experimentally set length scale can be imposed on a material. In a transient thermal grating experiment, crossed laser pulses interfere creating a well-defined periodic absorption and temperature profile. A probe beam is diffracted from this transient grating and length-scale dependent thermal transport properties can be determined from the signal decay. As the length scale is decreased to lengths shorter than the mean free paths of heat carrying phonons, quasi-ballistic heat transport effects become apparent allowing us to map out length scales and mean free paths relevant to nondiffusive thermal transport in Si and GaAs.