Length dependent thermal conductivity measurements yield phonon mean free path spectra in nanostructures

Cooling Dynamics of Individual Gold Nanodisks Deposited on Thick Substrates and Nanometric Membranes

The cooling dynamics of individual gold nanodisks synthesized using colloidal chemistry and deposited on solid substrates with different compositions and thicknesses were investigated using optical time-resolved spectroscopy and finite-element modeling. Experiments demonstrate a strong substrate-dependence of these cooling dynamics, which require the combination of heat transfer at the nanodisk/substrate interface and heat diffusion in the substrate. In the case of nanodisks deposited on a thick sapphire substrate, the dynamics are found to be mostly limited by the thermal resistance of the gold/sapphire interface, for which a value similar to that obtained in the context of previous experiments on sapphire-supported single gold nanodisks produced by electron beam lithography is deduced. In contrast, the cooling dynamics of nanodisks supported by nanometric silica and silicon nitride membranes are much slower and largely affected by heat diffusion in the membranes, whose efficiency is strongly reduced as compared to the thick sapphire case.

Mean Free Path Suppression of Low-Frequency Phonons in SiGe Nanowires

Accurate measurements of the size-dependent lattice thermal conductivity (κ_l) of alloy nanostructures are challenging but help to address outstanding questions on the effects of atomic disorder and surface roughness on low-frequency vibrational modes in functional materials. Here, we report sensitive κ_l measurements of multiple segments of the same individual SiGe nanowires. In contrast to a previous report of ballistic thermal transport over several microns in SiGe nanowires, the obtained κ_l are nearly independent of the segment length from 2 to 10 μm and the temperature between 150 and 300 K. The results are in agreement with a theoretical calculation based on the virtual crystal approximation of the vibrational modes as phonons with mean free paths suppressed by purely diffuse surface scattering. The findings inform continuing theoretical efforts for understanding the roles of different types of vibrational modes in thermal transport in disordered thermoelectric and electronic materials.

Strain tuned high thermal conductivity in boron phosphide at nanometer length scales - a first-principles study

Breakdown of Fourier law of heat conduction at nanometer length scales significantly diminishes thermal conductivity, leading to challenges in thermal management of nanoelectronic applications. In this work we demonstrate using first-principles computations that biaxial strain can enhance k at a nanoscale in boron phosphide (BP), yielding nanoscale k values that exceed even the bulk k value of silicon. At a length scale of L = 200 nm, k of 4% biaxially strained BP is enhanced by 25% to a value of 150.4 W m-1 K-1, relative to 120 W m-1 K-1 computed for unstrained BP at 300 K. The enhancement in k at a nanoscale is found to be due to the suppression of anharmonic scattering in the higher frequency range where phonon meanfreepaths are in nanometers, mediated by an increase in the phonon band gap in strained BP. Such a suppression in scattering enhances the meanfreepaths in the nanometer regime, thus enhancing nanoscale k. First-principles computations based on deriving harmonic and anharmonic force interactions from density-functional theory are used to provide detailed understanding of the effect in terms of individual scattering channels.

Controlling Thermal Conductivity in Mesoporous Silica Films Using Pore Size and Nanoscale Architecture

This work investigates the effect of wall thickness on the thermal conductivity of mesoporous silica materials made from different precursors. Sol-gel- and nanoparticle-based mesoporous silica films were synthesized by evaporation-induced self-assembly using either tetraethyl orthosilicate or premade silica nanoparticles. Since wall thickness and pore size are correlated, a variety of polymer templates were used to achieve pore sizes ranging from 3-23 nm for sol-gel-based materials and 10-70 nm for nanoparticle-based materials. We found that the type of nanoscale precursor determines how changing the wall thickness affects the resulting thermal conductivity. The data indicate that the thermal conductivity of sol-gel-derived porous silica decreased with decreasing wall thickness, while for nanoparticle-based mesoporous silica, the wall thickness had little effect on the thermal conductivity. This work expands our understanding of heat transfer at the nanoscale and opens opportunities for tailoring the thermal conductivity of nanostructured materials by means other than porosity and composition.

Quasi-Ballistic Heat Conduction due to Lévy Phonon Flights in Silicon Nanowires

Future of silicon-based microelectronics depends on solving the heat dissipation problem. A solution may lie in a nanoscale phenomenon known as ballistic heat conduction, which implies conduction of heat without heating the conductor. However, attempts to demonstrate this phenomenon experimentally are controversial and scarce, whereas its mechanism in confined nanostructures is yet to be fully understood. Here, we experimentally demonstrate quasi-ballistic heat conduction in silicon nanowires (NWs). We show that the ballisticity is the strongest in short NWs at low temperatures but weakens as the NW length or temperature is increased. Yet, even at room temperature, quasi-ballistic heat conduction remains visible in short NWs. To better understand this phenomenon, we probe directions and lengths of phonon flights. Our experiments and simulations show that the quasi-ballistic phonon transport in NWs is essentially the Lévy walk with short flights between the NW boundaries and long ballistic leaps along the NW. Thus, we conclude that ballistic heat conduction is present in silicon even at room temperature in sufficiently small nanostructures and may yet improve thermal management in silicon-based microelectronics.

Thermal conductivity of amorphous SiO2 thin film: A molecular dynamics study

Amorphous SiO₂ (a-SiO₂) thin films are widely used in integrated circuits (ICs) due to their excellent thermal stability and insulation properties. In this paper, the thermal conductivity of a-SiO₂ thin film was systematically investigated using non-equilibrium molecular dynamics (NEMD) simulations. In addition to the size effect and the temperature effect for thermal conductivity of a-SiO₂ thin films, the effect of defects induced thermal conductivity tuning was also examined. It was found that the thermal conductivity of a-SiO₂ thin films is insensitive to the temperature from −55 °C to 150 °C. Nevertheless, in the range of the thickness in this work, the thermal conductivity of the crystalline SiO₂ (c-SiO₂) thin films conforms to the T^−α with the exponent range from −0.12 to −0.37, and the thinner films are less sensitive to temperature. Meanwhile, the thermal conductivity of a-SiO₂ with thickness beyond 4.26 nm has no significant size effect, which is consistent with the experimental results. Compared with c-SiO₂ thin film, the thermal conductivity of a-SiO₂ is less sensitive to defects. Particularly, the effect of spherical void defects on the thermal conductivity of a-SiO₂ is followed by Coherent Potential model, which is helpful for the design of low-K material based porous a-SiO₂ thin film in microelectronics.

Reduced Thermal Transport in the Graphene/MoS2/Graphene Heterostructure: A Comparison with Freestanding Monolayers

The thermal conductivity of the graphene-encapsulated MoS₂ (graphene/MoS₂/graphene) van der Waals heterostructure is determined along the armchair and zigzag directions with different twist angles between the layers using molecular dynamics (MD) simulations. The differences in the predictions relative to those of the monolayers are analyzed using the phonon power spectrum and phonon lifetimes obtained by spectral energy density analysis. The thermal conductivity of the heterostructure is predominantly isotropic. The out-of-plane phonons of graphene are suppressed because of the interaction between the adjacent layers that results in the reduced phonon lifetime and thermal conductivity relative to monolayer graphene. The occurrence of an additional nonzero phonon branch at the Γ point in the phonon dispersion curves of the heterostructure corresponds to the breathing modes resulting from stacking of the layers in the heterostructure. The thermal sheet conductance of the heterostructure being an order of magnitude larger than that of monolayer MoS₂, this van der Waals material is potentially suitable for efficient thermal packaging of photoelectronic devices. The interfacial thermal conductance of the graphene/MoS₂ bilayer as a function of the heat flow direction shows weak thermal rectification.

Heat guiding and focusing using ballistic phonon transport in phononic nanostructures

Unlike classical heat diffusion at macroscale, nanoscale heat conduction can occur without energy dissipation because phonons can ballistically travel in straight lines for hundreds of nanometres. Nevertheless, despite recent experimental evidence of such ballistic phonon transport, control over its directionality, and thus its practical use, remains a challenge, as the directions of individual phonons are chaotic. Here, we show a method to control the directionality of ballistic phonon transport using silicon membranes with arrays of holes. First, we demonstrate that the arrays of holes form fluxes of phonons oriented in the same direction. Next, we use these nanostructures as directional sources of ballistic phonons and couple the emitted phonons into nanowires. Finally, we introduce thermal lens nanostructures, in which the emitted phonons converge at the focal point, thus focusing heat into a spot of a few hundred nanometres. These results motivate the concept of ray-like heat manipulations at the nanoscale.

Length Scale of Diffusive Phonon Transport in Suspended Thin Silicon Nanowires

Recent experimental advances have revealed that the mean free path (mfp) of phonons contributing significantly to thermal transport in crystalline semiconductors can be several microns long. Almost all of these experiments are based on bulk and thin film materials and use techniques that are not directly applicable to nanowires. By developing a process with which we could fabricate multiple electrically contacted and suspended segments on individual heavily doped smooth Silicon nanowires, we measured phonon transport across varying length scales using a DC self-heating technique. Our measurements show that diffusive thermal transport is still valid across O(100) nm length scales, supporting the diffuse nature of phonon-boundary scattering even on smooth nanowire surfaces. Our work also showcases the self-heating technique as an important alternative to the thermal bridge technique to measure phonon transport across short length scales relevant to mapping the phonon mfp spectrum in nanowires.

An electrical probe of the phonon mean-free path spectrum

Most studies of the mean-free path accumulation function (MFPAF) rely on optical techniques to probe heat transfer at length scales on the order of the phonon mean-free path. In this paper, we propose and implement a purely electrical probe of the MFPAF that relies on photo-lithographically defined heater-thermometer separation to set the length scale. An important advantage of the proposed technique is its insensitivity to the thermal interfacial impedance and its compatibility with a large array of temperature-controlled chambers that lack optical ports. Detailed analysis of the experimental data based on the enhanced Fourier law (EFL) demonstrates that heat-carrying phonons in gallium arsenide have a much wider mean-free path spectrum than originally thought.

Impact of Phonon Surface Scattering on Thermal Energy Distribution of Si and SiGe Nanowires

Thermal transport in nanostructures has attracted considerable attention in the last decade but the precise effects of surfaces on heat conduction have remained unclear due to a limited accuracy in the treatment of phonon surface scattering phenomena. Here, we investigate the impact of phonon-surface scattering on the distribution of thermal energy across phonon wavelengths and mean free paths in Si and SiGe nanowires. We present a rigorous and accurate description of phonon scattering at surfaces and predict and analyse nanowire heat spectra for different diameters and surface conditions. We show that the decrease in the diameter and increased roughness and correlation lengths makes the heat phonon spectra significantly shift towards short wavelengths and mean free paths. We also investigate the emergence of phonon confinement effects for small diameter nanowires and different surface scattering properties. Computed results for bulk materials show excellent agreement with recent experimentally-based approaches that reconstruct the mean-free-path heat spectra. Our phonon surface scattering model allows for an accurate theoretical extraction of heat spectra in nanowires and contributes to elucidate the development of critical phonon transport modes such as phonon confinement and coherent interference effects.

Temperature-Dependent Mean Free Path Spectra of Thermal Phonons Along the c-Axis of Graphite

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 measurements of c-axis phonon MFP spectra in graphite at a variety of temperatures using time-domain thermoreflectance measurements of graphite flakes with variable thickness. Our results indicate that c-axis phonon MFPs have values of a few hundred nanometers at room temperature and a much narrower distribution than in isotropic crystals. At low temperatures, phonon scattering is dominated by grain boundaries separating crystalline regions of different rotational orientation. Our study provides important new insights into heat transport and phonon scattering mechanisms in graphite and other anisotropic van der Waals solids.

Robustly Engineering Thermal Conductivity of Bilayer Graphene by Interlayer Bonding

Graphene and its bilayer structure are the two-dimensional crystalline form of carbon, whose extraordinary electron mobility and other unique features hold great promise for nanoscale electronics and photonics. Their realistic applications in emerging nanoelectronics usually call for thermal transport manipulation in a controllable and precise manner. In this paper we systematically studied the effect of interlayer covalent bonding, in particular different interlay bonding arrangement, on the thermal conductivity of bilayer graphene using equilibrium molecular dynamics simulations. It is revealed that, the thermal conductivity of randomly bonded bilayer graphene decreases monotonically with the increase of interlayer bonding density, however, for the regularly bonded bilayer graphene structure the thermal conductivity possesses unexpectedly non-monotonic dependence on the interlayer bonding density. The results suggest that the thermal conductivity of bilayer graphene depends not only on the interlayer bonding density, but also on the detailed topological configuration of the interlayer bonding. The underlying mechanism for this abnormal phenomenon is identified by means of phonon spectral energy density, participation ratio and mode weight factor analysis. The large tunability of thermal conductivity of bilayer graphene through rational interlayer bonding arrangement paves the way to achieve other desired properties for potential nanoelectronics applications involving graphene layers.