Quasi-ballistic Phonon Transport Research Articles

Anisotropy Reversal of Thermal Conductivity in Silicon Nanowire Networks Driven by Quasi-Ballistic Phonon Transport.

Nanostructured semiconductors promise functional thermal management for microelectronics and thermoelectrics through a rich design capability. However, experimental studies on anisotropic in-plane thermal conduction remain limited, despite the demand for directional heat dissipation. Here, inspired by an oriental wave pattern, a periodic network of bent wires, we investigate anisotropic in-plane thermal conduction in nanoscale silicon phononic crystals with the thermally dead volume. We observed the anisotropy reversal of the material thermal conductivity from 1.2 at 300 K to 0.8 at 4 K, with the reversal temperature of 80 K mediated by the transition from a diffusive to a quasi-ballistic regime. Our Monte Carlo simulations revealed that the backflow of the directional phonons induces the anisotropy reversal, showing that the quasi-ballistic phonon transport introduces preferential thermal conduction channels with anomalous temperature dependence. Accordingly, the anisotropy of the effective thermal conductivity varied from 2.7 to 5.0 in the range of 4-300 K, indicating an anisotropic heat manipulation capability. Our findings demonstrate that the design of nanowire networks enables the directional thermal management of electronic devices.

Suppressed phonon conduction by geometrically induced evolution of transport characteristics from Brownian motion into Lévy flight

Despite extensive research on quasi-ballistic phonon transport, anomalous phonon transport is still observed in numerous nanostructures. Herein, we investigate the transport characteristics of two sets of samples: straight beams and nanoladders comprising two straight beams orthogonally connected with bridges. A combination of experiments and analysis with a Boltzmann transport model suggests that the boundary scattering within the bridges considerably dictates the distribution of phonon mean free paths, despite its negligible contribution to the net heat flux. Statistical analysis of those boundary scatterings shows that phonons with large axial angles are filtered into bridges, creating dead spaces in the line-of-sight channels. Such redistribution induces Lévy walk conduction along the line-of-sight channels, causing the remaining phonons within the bridges to exhibit Brownian motion. Phonon conduction in the nanoladders is suppressed below that of the straight beams with equivalent cross-sectional areas due to trapped phonons within the bridges. Our work reveals the origin of unusual thermal conductivity suppression at the nanoscale, suggesting a method to modulate phonon conduction via systematic nanostructuring.

Quasiballistic phonon transport from first principles

At short length scales phonon transport is ballistic: the thermal resistance of semiconductors and insulators is quantized and length independent. At long length scales, on the other hand, transport is diffusive and resistance arises as a result of the scattering processes experienced by phonons. In many cases of interest, however, these two transport regimes coexist. Here we propose a first-principles approach to treat quasiballistic phonon transport where diffusive and ballistic phonons receive separate theoretical treatments. Partitioning the overall phonon population for a given transport length is performed examining the mean free paths obtained from the solution of the Boltzmann transport equation and allowing only diffusive phonons to participate in anharmonic phonon-phonon scattering processes. We present results for Si and diamond, discussing the crossover from ballistic to diffusive transport as the length scale and/or the temperature increases and compute the relative contribution of ballistic and diffusive phonons to the thermal conductance in each transport condition.

Enhanced Thermoelectric Performance of As-Grown Suspended Graphene Nanoribbons.

Conventionally, graphene is a poor thermoelectric material with a low figure of merit (ZT) of 10-4-10-3. Although nanostructuring was proposed to improve the thermoelectric performance of graphene, little experimental progress has been accomplished. Here, we carefully fabricated as-grown suspended graphene nanoribbons with quarter-micron length and ∼40 nm width. The ratio of electrical to thermal conductivity was enhanced by 1-2 orders of magnitude, and the Seebeck coefficient was several times larger than bulk graphene, which yielded record-high ZT values up to ∼0.1. Moreover, we observed a record-high electronic contribution of ∼20% to the total thermal conductivity in the nanoribbon. Concurrent phonon Boltzmann transport simulations reveal that the reduction of lattice thermal conductivity is mainly attributed to quasi-ballistic phonon transport. The record-high ratio of electrical to thermal conductivity was enabled by the disparate electron and phonon mean free paths as well as the clean samples, and the enhanced Seebeck coefficient was attributed to the band gap opening. Our work not only demonstrates that electron and phonon transport can be fundamentally tuned and decoupled in graphene but also indicates that graphene with appropriate nanostructures can be very promising thermoelectric materials.

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.

Recent progress in the concurrent atomistic-continuum method and its application in phonon transport

Abstract

A Generalized Enhanced Fourier Law

A generalized enhanced Fourier law (EFL) that accounts for quasi-ballistic phonon transport effects in a formulation entirely in terms of physical observables is derived from the Boltzmann transport equation. It generalizes the previously reported EFL from a gray phonon population to an arbitrary quasi-ballistic phonon mode population, the chief advantage being its formulation in terms of observables like the heat flux and temperature, in a manner akin to the Fourier law albeit rigorous enough to describe quasi-ballistic phonon transport.

Modeling ballistic effects in frequency-dependent transient thermal transport using diffusion equations

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 thermal transport. Our analytical solutions are found to compare excellently to rigorous numerical results of the phonon Boltzmann transport equation. The correct physical boundary conditions can be different from those traditionally used and are paramount for accurately capturing ballistic effects. To illustrate the technique, we consider a simple model problem using two different, commonly used heating conditions. We demonstrate how this framework can easily handle detailed material properties, by considering the case of bulk silicon using a full phonon dispersion and mean-free-path distribution. This physically transparent approach provides clear insights into the nonequilibrium physics of quasi-ballistic phonon transport and its impact on thermal transport properties.

Thermal Transport in Single-Layer MoS2and Black Phosphorus Transistors

Ballistic thermal conductance in single-layer MoS2 and black phosphorus (BP) is calculated based on the phonon dispersion. In single-layer MoS2, the ballistic thermal conductance is almost isotropic of a value of $10.7\times 10^{8}$ W/ $\text{m}^{2}\text{K}$ ; while in single-layer BP, the in-plane ballistic thermal conductance is anisotropic with a value of $12.8\times 10^{8}$ W/ $\text{m}^{2}\text{K}$ in the zigzag direction and $7.1\times 10^{8}$ W/ $\text{m}^{2}\text{K}$ in the armchair direction. Thermal transport behaviors at both steady state and transient state in double-gated MOSFET-like transistors with single-layer MoS2 and BP used as the channel material are studied. The conventional Fourier’s law with contact temperatures as the boundary conditions and modified boundary conditions that can capture quasi-ballistic phonon transport effects are used. The simulation results show that Fourier’s law with contact temperatures as the boundary conditions underestimate the peak temperature rise by 64% in single-layer MoS2 transistors and 56% in single-layer BP transistors when the channel length is comparable to the phonon mean free path. And the strong anisotropic thermal properties of single-layer BP lead to higher temperature rise in the armchair direction than that in the zigzag direction.

Measuring Phonon Mean Free Path Distributions by Probing Quasiballistic Phonon Transport in Grating Nanostructures.

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.

Radial quasiballistic transport in time-domain thermoreflectance studied using Monte Carlo simulations

Recently, a pump beam size dependence of thermal conductivity was observed in Si at cryogenic temperatures using time-domain thermal reflectance (TDTR). These observations were attributed to quasiballistic phonon transport, but the interpretation of the measurements has been semi-empirical. Here, we present a numerical study of the heat conduction that occurs in the full 3D geometry of a TDTR experiment, including an interface, using the Boltzmann transport equation. We identify the radial suppression function that describes the suppression in heat flux, compared to Fourier's law, that occurs due to quasiballistic transport and demonstrate good agreement with experimental data. We also discuss unresolved discrepancies that are important topics for future study.

Influence of Heat Source Size on Phonon Transport in Thin Silicon Film

Energy transfer is mainly governed by the phonon transport in dielectric films. The polarization and dispersion of the phonons alter the thermal resistance of the film as the film size becomes comparable to the mean path of the substrate material. This is because of the quasi-ballistic behavior of the transport characteristics. In this case, the ballistic phonons do not undergo scattering in the film while suppressing the thermal resistance increase across the film. In the present study, the quasi-ballistic phonon transport and the effect of heat source size on the phonon transport characteristics are investigated in the two-dimensional silicon film. The heat source is located at one edge of the film while other edges assumed to be at uniform temperature. Since the Knudsen number is small (∼1), the Boltzmann transport equation is solved numerically, incorporating the polarization and dispersion of phonons, to obtain phonon intensity distribution in the film. Equivalent equilibrium temperature is introduced to assess the phonon intensity distribution in the film. The transient behavior of the phonon transport is incorporated in the analysis to predict the time to reach steady state value of equivalent temperature in the film. It is found that the size of the heat source has a significant effect on the phonon transport in the film. The effective thermal conductivity reduces significantly as the heat source size reduces.

Phonon Dominated Heat Conduction Normal to Mo/Si Multilayers with Period below 10 nm

Thermal conduction in periodic multilayer composites can be strongly influenced by nonequilibrium electron-phonon scattering for periods shorter than the relevant free paths. Here we argue that two additional mechanisms-quasiballistic phonon transport normal to the metal film and inelastic electron-interface scattering-can also impact conduction in metal/dielectric multilayers with a period below 10 nm. Measurements use the 3ω method with six different bridge widths down to 50 nm to extract the in- and cross-plane effective conductivities of Mo/Si (2.8 nm/4.1 nm) multilayers, yielding 15.4 and 1.2 W/mK, respectively. The cross-plane thermal resistance is lower than can be predicted considering volume and interface scattering but is consistent with a new model built around a film-normal length scale for phonon-electron energy conversion in the metal. We introduce a criterion for the transition from electron to phonon dominated heat conduction in metal films bounded by dielectrics.

Thermal conductivity of bulk and thin-film silicon: A Landauer approach

The question of what fraction of the total heat flow is transported by phonons with different mean-free-paths is addressed using a Landauer approach with a full dispersion description of phonons to evaluate the thermal conductivities of bulk and thin film silicon. For bulk Si, the results reproduce those of a recent molecular dynamic treatment showing that about 50% of the heat conduction is carried by phonons with a mean-free-path greater than about 1 μm. For the in-plane thermal conductivity of thin Si films, we find that about 50% of the heat is carried by phonons with mean-free-paths shorter than in the bulk. When the film thickness is smaller than ∼0.2 μm, 50% of the heat is carried by phonons with mean-free-paths longer than the film thickness. The cross-plane thermal conductivity of thin-films, where quasi-ballistic phonon transport becomes important, is also examined. For ballistic transport, the results reduce to the well-known Casimir limit [H. B. G. Casimir, Physica 5, 495–500 (1938)]. These results shed light on phonon transport in bulk and thin-film silicon and demonstrate that the Landauer approach provides a relatively simple but accurate technique to treat phonon transport from the ballistic to diffusive regimes.