Stacking-induced phonon transport engineering of siligene

Tunable phonon transport properties of two-dimensional materials are desirable for effective heat management in various application scenarios. Here, we demonstrate by first-principles calculations and Boltzmann transport theory that the lattice thermal conductivity of siligene could be efficiently engineered by forming various stacking configurations. Unlike few-layer graphene, the stacked siligenes are found to be covalently bonded along the out-of-plane direction, which leads to unique dependence of the thermal conductivity on both the stacking order and layer number. Due to the restricted flexural phonon scattering induced by the horizontal reflection symmetry, the AA stacking configuration of bilayer siligene exhibits obviously higher thermal conductivity compared with the AB stacking. In addition, we observe increasing thermal conductivity with the layer number, as evidenced by the reduced phonon scattering phase space and Grüneisen parameter. Interestingly, the Fuchs-Sondheimer model works well for the thickness-dependent thermal conductivity of stacked siligenes.

Large Mechanosensitive Thermoelectric Enhancement in Metallo-Organic Magnetic Molecules

Organic materials are promising candidates for thermoelectric cooling and energy harvesting at room temperature. However, their electrical conductance (G) and Seebeck coefficient (S) need to be improved to make them technologically competitive. Therefore, radically new strategies need to be developed to tune their thermoelectric properties. Here, we demonstrate that G and S can be tuned mechanically in paramagnetic metallocenes, and their thermoelectric properties can be significantly enhanced by the application of mechanical forces. With a 2% junction compression, the full thermoelectric figure of merit is enhanced by more than 200 times. We demonstrate that this is because spin transport resonances in paramagnetic metallocenes are strongly sensitive to the interaction between organic ligands and the metal center, which is not the case in their diamagnetic analogue. These results open a new avenue for the development of organic thermoelectric materials for cooling future quantum computers and generating electricity from low-grade energy sources.

Towards Optimizing Width Modulation for Maximum Thermoelectric Efficiency

Maximizing thermoelectric efficiency is typically addressed as identical to minimizing parasitic thermal conduction. Such an approach relies on the assumption that the adopted strategy mainly affects phonons, leaving electrons intact, and is not justified in many cases of non-uniform nanostructures such as width-modulated nanowaveguides, where both electrons and phonons are significantly affected by width modulation. Here, we address the question of maximizing the thermoelectric efficiency of this class of metamaterials by exploring the effect of the modulation extent on both electron and phonon transport. We investigated the effect of increasing modulation degree on the thermoelectric efficiency, considering the cases of (a) a two-QD modulation and (b) multiple-QD modulations in periodic and aperiodic sequences. We show that the thermoelectric efficiency depends on the coupling between the modulation units and the interplay between periodicity and aperiodicity in the modulation profile. We reveal that the maximization of the thermoelectric power factor is for periodic width-modulation, whereas the maximization of the thermoelectric efficiency is for aperiodic width-modulation profiles that form quasi-localized states for electrons. Our work provides new insight that can be used to optimize width modulation for maximum thermoelectric efficiency.

Lattice thermal conductivity of embedded nanoparticle composites: the role of particle size distribution

Nanoparticles embedded within a crystalline solid serve as impurity phonon scattering centers that reduce lattice thermal conductivity, a desirable result for thermoelectric applications. Most studies of thermal transport in nanoparticle-laden composite materials have assumed the nanoparticles to possess a single size. If there is a distribution of nanoparticle sizes, how is thermal conductivity affected? Moreover, is there a best nanoparticle size distribution to minimize thermal conductivity? In this work, we study the thermal conductivity of nanoparticle-laden composites through a molecular dynamics approach which naturally captures phonon scattering processes more rigorously than previously used analytical theories. From thermal transport simulations of a systematic variety of nanoparticle configurations, we empirically formulate how nanoparticle size distribution, particle number density, and volume fraction affect the lattice thermal conductivity. We find at volume fractions below 10%, the particle number density is by far the most impactful factor on thermal conductivity and at fractions above 10%, the effect of the size distribution and number density is minimal compared to the volume fraction. In fact, upon comparisons of configurations with the same particle number density and volume fractions, the lattice thermal conductivity of a single nanoparticle size can be lower than that of a size distribution which contradicts intuitions that a single size would attenuate phonon transport less than a spectrum of sizes. The random alloy, which can be considered as a single size configuration of maximum particle number density where the nanoparticle size is equal to the lattice constant, is the most performant in thermal conductivity reduction at volume fractions below 10%. We conclude that nanoparticle size distribution only plays a minor role in affecting lattice thermal conductivity with the particle number density and volume fraction being the more significant factors that should be considered in fabrication of nanoparticle-laden composites for potential improved thermoelectric performance.

Engineering Heat Transport Across Epitaxial Lattice-Mismatched van der Waals Heterointerfaces

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 thermal metamaterials based on atomically thin lattice-mismatched Bi2Se3/MoSe2 superlattices and graphene/PdSe2 heterostructures with exceptional thermal resistances (70-202 m2 K/GW) and ultralow cross-plane thermal conductivities (0.012-0.07 W/mK) at room temperature, comparable to those of amorphous materials. Experimental data obtained using frequency-domain thermoreflectance and low-frequency Raman spectroscopy, supported by tight-binding phonon calculations, reveal the impact of lattice mismatch, phonon-interface scattering, size effects, temperature, and interface thermal resistance on cross-plane heat dissipation, uncovering different thermal transport regimes and the dominant role of long-wavelength phonons. Our findings provide essential insights into emerging synthesis and thermal characterization methods and valuable guidance for the development of large-area heteroepitaxial van der Waals films of dissimilar materials with tailored thermal transport characteristics.

Origin of Ultralow Thermal Conductivity in Metal Halide Perovskites

Resulting from their remarkable structure-property relationships, metal halide perovskites have garnered tremendous attention in recent years for a plethora of applications. For instance, their ultralow thermal conductivities make them promising candidates for thermoelectric and thermal barrier coating applications. It is widely accepted that the "guest" cations inside the metal halide framework act as "rattlers", which gives rise to strong intrinsic phonon resistances, thus explaining the structure-property relationship dictating their ultralow thermal conductivities. In contrast, through systematic atomistic simulations, we show that this conventionally accepted "rattling" behavior is not the mechanism dictating the ultralow thermal conductivities in metal halide perovskites. Instead, we show that the ultralow thermal conductivities in these materials mainly originate from the strongly anharmonic and mechanically soft metal halide framework. By comparing the thermal transport properties of the prototypical fully inorganic CsPbI₃ and an empty PbI₆ framework, we show that the addition of Cs⁺ ions inside the nanocages leads to an enhancement in thermal conductivity through vibrational hardening of the framework. Our extensive spectral energy density calculations show that the Cs⁺ ions have well-defined phase relations with the lattice dynamics of the "host" framework resulting in additional pathways for heat conduction, which is in disagreement with the description of the individual "rattling" of guests inside the framework that has been widely assumed to dictate their ultralow thermal conductivities. Furthermore, we show that an efficient strategy to control the heat transfer efficacy in these materials is through the manipulation of the framework anharmonicity achieved via strain and octahedral tilting. Our work provides the fundamental insights into the lattice dynamics that dictate heat transfer in these novel materials, which will ultimately help guide their further advancement in the next-generation of electronics such as in thermoelectric and photovoltaic applications.

Decoding the phonon transport of structural lubrication at silicon/silicon interface

Although the friction characteristics under different contact conditions have been extensively studied, the mechanism of phonon transport at the structural lubrication interface is not extremely clear. In this paper, we firstly promulgate that there is a 90°-symmetry of friction force depending on rotation angle at Si/Si interface, which is independent of normal load and temperature. It is further found that the interfacial temperature difference under incommensurate contacts is much larger than that in commensurate cases, which can be attributed to the larger interfacial thermal resistance (ITR). The lower ITR brings greater energy dissipation in commensurate sliding, and the reason for that is more effective energy dissipation channels between the friction surfaces, making it easier for the excited phonons at the washboard frequency and its harmonics to transfer through the interface. Nevertheless, the vibrational frequencies of the interfacial atoms between the tip and substrate during the friction process do not match in incommensurate cases, and there is no effective energy transfer channel, thus presenting the higher ITR and lower friction. Eventually, the number of excited phonons on contact surfaces reveals the amount of frictional energy dissipation in different contact states.

Theoretical Prediction of Thermoelectric Performance for Layered LaAgOX (X = S, Se) Materials in Consideration of the Four-Phonon and Multiple Carrier Scattering Processes

Inspired by the experimental achievement of layered LaCuOX (X = S, Se) with superior thermoelectric (TE) performance, the TE properties of Ag-based isomorphic LaAgOX are systemically investigated by the first-principles calculation. The LaAgOS and LaAgOSe are direct semiconductors with wide bandgaps of ≈2.50 and ≈2.35 eV. Essential four-phonon and multiple carrier scattering mechanisms are considered in phonon and electronic transport calculations to improve the accuracy of the figure-of-merit (ZT). The p-type LaAgOX (X = S, Se) shows excellent TE performance on account of the large Seebeck coefficient originated from the band convergency and low thermal conductivity caused by the strong phonon-phonon scattering. Consequently, the optimal ZTs along the out-of-plane direction decrease in the order of n-type LaAgOSe (≈2.88) > p-type LaAgOSe (≈2.50) > p-type LaAgOS (≈2.42) > n-type LaAgOS (≈2.27) at 700 K, and the optimal ZTs of ≈1.16 and ≈1.29 are achieved for p-type LaAgOS and LaAgOSe at the same temperature. The present work would provide a deep insight into the phonon and electronic transport properties of LaAgOX (X = S, Se), but also could shed light on the way for the rational design of state-of-the-art heteroanionic materials for TE application.

Phonon transport mechanism of HfO2ultrathin film with temperature-correction full-band Monte Carlo simulation

Hafnium dioxide (HfO₂) has been widely used in microelectronics nowadays and commonly withstands extremely high temperatures, so the investigation of its thermodynamic properties is particularly essential. This paper develops a temperature-correction full-band Monte Carlo (TFMC) method to investigate the HfO₂ultrathin film. The phonon dynamics parameters of HfO₂are calculated based on the first-principles method. TFMC can better describe the phonon cumulative distribution function in different temperatures by modifying the phonon relaxation time and heat capacity. The thermal conductivity of HfO₂ultrathin film is calculated based on the above method and is in good agreement with the literature. It is observed that the optical phonons in HfO₂ultrathin film are prominent in the phonon heat transport, which is quite different from the mechanism in common semiconductor materials. Combined with the full-band diffuse mismatch model, the Si-based HfO₂ultrathin film is studied. It is found that the existence of the interface with substrates improves the thermodynamic properties of the ultrathin film, which provides a reference for the selection of substrate materials.

Ultrafast Dynamics of Demagnetization in FeMn/MnGa Bilayer Nanofilm Structures via Phonon Transport

Superdiffusive spin transport has been proposed as a new mechanism of ultrafast demagnetization in layered magnetic nanostructures and demonstrated experimentally. However, it is unknown if it is possible for phonon transport to occur and manipulate ultrafast demagnetization. Here, we explore the ultrafast dynamics of demagnetization of an antiferromagnet/ferromagnet bilayer nanostructure, of a FeMn/MnGa bilayer film prepared by molecular beam epitaxy. Ultrafast dynamics of a two-step demagnetization were observed through the time-resolved magneto-optical Kerr effect. The first-step fast component of the two-step demagnetization occurred within ~200 fs, while the second-step slow component emerged in a few tens of picoseconds. For a single MnGa film, only the ultrafast dynamics of the first-step fast demagnetization were observed, revealing that the second-step slow demagnetization originates from interlayer phonon transport. A four-temperature model considering phonon transport was developed and used to effectively reproduce the observed ultrafast dynamics of two-step demagnetization. Our results reveal the effect of phonon transport on demagnetization for the first time and open up a new route to manipulate ultrafast demagnetization in layered magnetic structures.

Electronic and transport properties of semimetal ZrBeSi crystal: a first-principles study

In recent years, semimetals have aroused people's research interest. Here, we systematically study phonon and electronic transport properties of the ZrBeSi with semimetal character by using the first-principles calculations together with the Boltzmann transport theory. Calculated lattice thermal conductivities of the ZrBeSi alongaandcaxes are 31.3 W (m · K)^-1and 56.0 W (m · K)^-1at room temperature, respectively, which are larger than the most semiconductors and semimetals. By comparing with other semimetals, we find that the larger lattice thermal conductivity of ZrBeSi is due to its smaller Grüneisen parameter, which indicates the weaker phonon scattering. Main contributions to the lattice thermal conductivities alongaandcaxis come from the acoustic branches, and conversely, the contributions of optical branches are very small. In addition, we calculate the Seebeck coefficient and the electron thermal conductivity of ZrBeSi based on the relaxation time approximation. The electronic transport properties of ZrBeSi exhibit strong anisotropy in bothaandbdirections. Calculated electronic thermal conductivities of pristine ZrBeSi alongaandcaxes are 8.8 W (m · K)^-1and 9.7 W (m · K)^-1at room temperature, respectively. Furthermore, we also obtain the figure of meritZTon the basis of phonon and electron transport. The obtainedZTalongcaxis reaches a maximum of 0.11 at 900 K, demonstrating that ZrBeSi has a generalZT, but it has good heat conduction ability. Our research will help to understand the transport properties of semimetals and expand the application of semimetals to heat conduction devices. At the same time, it also provides some reference for the future experimental work.

Molecular Dynamics Simulation on In-Plane Thermal Conductivity of Graphene/Hexagonal Boron Nitride van der Waals Heterostructures

Graphene, hexagonal boron nitride (h-BN), and their heterostructures are promising thermal interface materials due to the outstanding thermal properties of graphene and h-BN. For the heterostructures, extensive work has mainly focused on the thermal transport of two-dimensional (2D) graphene/h-BN (GBN) in-plane heterostructures in which graphene and h-BN are bonded at the interface. In this study, we investigate the thermal conductivity of three-dimensional (3D) GBN van der Waals (vdW) heterostructures by means of nonequilibrium molecular dynamics (NEMD) simulations. Unlike the 2D GBN in-plane heterostructure, the 3D GBN vdW heterostructure consists of three layers where graphene is sandwiched by two h-BN sheets via vdW forces. Various techniques, including hydrogen-functionalization, vacancy defects, tensile strain, interlayer coupling strength, layer numbers of h-BN, size effect, and temperature, are extensively explored to find an effective route for the modulation of the thermal conductivity. It is found that the thermal conductivity of the triple-layer GBN vdW heterostructure is very sensitive to these extrinsic factors. Of these, hydrogen-functionalization is the most effective method. A low hydrogen coverage of 1% in the sandwiched graphene can lead to 55% reduction in the thermal conductivity of the vdW heterostructure. Vacancy defects on graphene exert a more significant effect on the thermal conductivity reduction for the vdW heterostructure than B or N vacancies in the outer h-BN layers. This work reveals the physical mechanism for manipulating the thermal transport along the GBN vdW heterostructures via structural modification and provides a useful guideline for designing novel thermal management devices based on the GBN vdW heterostructures.

Lattice Instability and Ultralow Lattice Thermal Conductivity of Layered PbIF

Understanding the interplay between various design strategies (for instance, bonding heterogeneity and lone pair induced anharmonicity) to achieve ultralow lattice thermal conductivity (κ_l) is indispensable for discovering novel functional materials for thermal energy applications. In the present study, we investigate layered PbXF (X = Cl, Br, I), which offers bonding heterogeneity through the layered crystal structure, anharmonicity through the Pb²⁺ 6s² lone pair, and phonon softening through the mass difference between F and Pb/X. The weak interlayer van der Waals bonding and the strong intralayer ionic bonding with partial covalent bonding result in a significant bonding heterogeneity and a poor phonon transport in the out-of-plane direction. Large average Grüneisen parameters (≥2.5) demonstrate strong anharmonicity. The computed phonon dispersions show flat bands, which suggest short phonon lifetimes, especially for PbIF. Enhanced Born effective charges are due to cross-band-gap hybridization. PbIF shows lattice instability at a small volume expansion of 0.1%. The κ_l values obtained by the two channel transport model are 20-50% higher than those obtained by solving the Boltzmann transport equation. Overall, ultralow κ_l values are found at 300 K, especially for PbIF. We propose that the interplay of bonding heterogeneity, lone pair induced anharmonicity, and constituent elements with high mass difference aids the design of low κ_l materials for thermal energy applications.

Microwave Synthesis and Enhanced Thermoelectric Performance of p-Type Bi0.90Pb0.10Cu1-xFexSeO Oxyselenides

BiCuSeO oxyselenide, one of the best oxygen-containing thermoelectric materials, is promising with great potential applications. In this work, we present a high ZT of >1.3 in Bi_0.90Pb_0.10Cu_0.96Fe_0.04SeO fabricated via microwave synthesis and subsequent spark plasma sintering (SPS). We added 3-4 atom % Fe to the Pb-doped BiCuSeO to regulate the hole carrier concentration and mobility to 0.8-1.0 × 10²⁰ cm^-3 and ∼40 cm² V^-1 S^-1, respectively, achieving moderate electrical conductivity, high Seebeck coefficient, and low carrier thermal conductivity simultaneously in a dual-doped sample. Under the synergistic enhancement by stress field, dislocation, and nanophase, the lattice thermal conductivity of Bi_0.90Pb_0.10Cu_0.96Fe_0.04SeO is limited to 0.24-0.49 W m^-1 K^-1 at 300-873 K. The development of efficient preparation methods for high-performance thermoelectric materials is significant to promote the application of thermoelectric conversion technology.

Phonon hydrodynamics in crystalline materials

Phonon hydrodynamics is an exotic phonon transport phenomenon that challenges the conventional understanding of diffusive phonon scattering in crystalline solids. It features a peculiar collective motion of phonons with various unconventional properties resembling fluid hydrodynamics, facilitating non Fourier heat transport. Hence, it opens up several new avenues to enrich the knowledge and implementations on phonon physics, phonon engineering, and micro and nanoelectronic device technologies. This review aims at covering a comprehensive development as well as the recent advancements in this field via experiments, analytical methods, and state-of-the-art numerical techniques. The evolution of the topic has been realized using both phenomenological and material science perspectives. Further, the discussions related to the factors that influence such peculiar motion, illustrate the capability of phonon hydrodynamics to be implemented in various applications. A plethora of new ideas can emerge from the topic considering both the physics and the material science axes, navigating toward a promising outlook in the research areas around phonon transport in non-metallic solids.

Tuning the Thermal Transport of Hexagonal Boron Nitride/Reduced Graphene Oxide Heterostructures

Tuning the thermal properties of materials is considered to be of crucial significance for improving the performance of electronic devices. Along these lines, the development of van der Waals (vdW) heterostructures becomes an effective solution to affect the thermal transport mechanisms. However, vdW interactions usually block phonon transport, which leads to a reduction in thermal conductivity. In this work, we experimentally demonstrate a large enhancement in the thermal conductivity of a vdW heterostructure composed of few-layer hexagonal boron nitride (h-BN) and reduced graphene oxide (RGO). By controlling the reduction temperature of RGO and changing the thickness of h-BN, the thermal conductivity of the RGO is increased by nearly 18 times, namely, from 91 to 1685 W m^-1 K^-1. Photothermal scanning imaging is used to reveal the changes in the heat transfer and temperature distribution of the h-BN/RGO heterostructure. Both photothermal scanning and Raman spectroscopy experiments show that the vdW interaction between h-BN and RGO can greatly increase the thermal conductivity of RGO, which is in contrast to the conventional understanding that vdW interaction reduces thermal conductivity. Our work paves the way for the manipulation of the thermal conductivity of two-dimensional (2D) heterostructures, which could be of great significance for future nanoelectronic circuits.

Degenerated Hole Doping and Ultra-Low Lattice Thermal Conductivity in Polycrystalline SnSe by Nonequilibrium Isovalent Te Substitution

Tin mono-selenide (SnSe) exhibits the world record of thermoelectric conversion efficiency ZT in the single crystal form, but the performance of polycrystalline SnSe is restricted by low electronic conductivity (σ) and high thermal conductivity (κ), compared to those of the single crystal. Here an effective strategy to achieve high σ and low κ simultaneously is reported on p-type polycrystalline SnSe with isovalent Te ion substitution. The nonequilibrium Sn(Se1- x Tex ) solid solution bulks with x up to 0.4 are synthesized by the two-step process composed of high-temperature solid-state reaction and rapid thermal quenching. The Te ion substitution in SnSe realizes high σ due to the 103 -times increase in hole carrier concentration and effectively reduced lattice κ less than one-third at room temperature. The large-size Te ion in Sn(Se1- x Tex ) forms weak SnTe bonds, leading to the high-density formation of hole-donating Sn vacancies and the reduced phonon frequency and enhanced phonon scattering. This result-doping of large-size ions beyond the equilibrium limit-proposes a new idea for carrier doping and controlling thermal properties to enhance the ZT of polycrystalline SnSe.

Nonequilibrium Green's function method for phonon heat transport in quantum system

Phonon heat transport property in quantum devices is of great interesting since it presents significant quantum behaviors. In the past few decades, great efforts have been devoted to establish the theoretical method for phonon heat transport simulation in nanostructures. However, modeling phonon heat transport from wavelike coherent regime to particlelike incoherent regime remains a challenging task. The widely adopted theoretical approach, such as molecular dynamics, semiclassical Boltzmann transport equation, captures quantum mechanical effects within different degrees of approximation. Among them, Non-equilibrium Green's function (NEGF) method has attracted wide attention, as its ability to perform full quantum simulation including many-body interactions. In this review, we summarized recent theoretical advances of phonon NEGF method and the applications on the numerical simulation for phonon heat transport in nanostructures. At last, the challenges of numerical simulation are discussed.

Thermal transport in beta-gallium oxide thin-films using non-gray Boltzmann transport equation

Phonon transport inβ-Ga₂O₃thin films and metal-oxide field effect transistors (MESFETs) are investigated using non-gray Boltzmann transport equations (BTEs) to decipher the effect of ballistic-diffusive phonon transport. The effects of domain size, and energy dissipation to various phonon modes and subsequent phonon-phonon energy exchange on the thermal transport and temperature distribution is investigated using non-gray BTE. Our analysis deciphered that domain size plays a major role in thermal transport inβ-Ga₂O₃but energy dissipation to various phonon modes and subsequent phonon-phonon energy exchange does not affect the temperature field significantly. Phonon transport inβ-Ga₂O₃MESFETs on diamond substrate is investigated using coupled non-gray BTE and Fourier model. It is established that the ballistic effects need to be considered for devices withβ-Ga₂O₃layer thickness less than 1 μm. A non-gray phonon BTE model should be used near hotspot in the thinβ-Ga₂O₃layer as the Fourier model may not give accurate temperature distribution. The results from this work will help in understanding the mechanism of phonon transport in theβ-Ga₂O₃thin films and energy efficient design of its FETs.

Strain-tunable lattice thermal conductivity of the Janus PtSTe monolayer

Using first-principles calculations and Boltzmann transport theory, we study the effect of biaxial tensile strain on phonon transport in a Janus PtSTe monolayer. The band gap between the optical and acoustic phonon branches shrinks with increasing strain, resulting in a highly nonlinear monotonic decrease in the lattice thermal conductivity. That reduction reaches close to an order of magnitude when the gap disappears completely under high strains (>8%). This behavior is attributed to a strong enhancement of the anharmonic scattering of acoustic phonons due to the band overlap. Our findings underscore the potential of strain engineering as a class of methods to tune the thermal transport properties of two-dimensional (2D) Janus nanomaterials.

Directional thermal channeling: A phenomenon triggered by tight packing of heat sources

Understanding nanoscale thermal transport is critical for nano-engineered devices such as quantum sensors, thermoelectrics, and nanoelectronics. However, despite overwhelming experimental evidence for nondiffusive heat dissipation from nanoscale heat sources, the underlying mechanisms are still not understood. In this work, we show that for nanoscale heat source spacings that are below the mean free path of the dominant phonons in a substrate, close packing of the heat sources increases in-plane scattering and enhances cross-plane thermal conduction. This leads to directional channeling of thermal transport-a novel phenomenon. By using advanced atomic-level simulations to accurately access the lattice temperature and the phonon scattering and transport properties, we finally explain the counterintuitive experimental observations of enhanced cooling for close-packed heat sources. This represents a distinct fundamental behavior in materials science with far-reaching implications for electronics and future quantum devices.

Phononic Thermal Transport along Graphene Grain Boundaries: A Hidden Vulnerability

While graphene grain boundaries (GBs) are well characterized experimentally, their influence on transport properties is less understood. As revealed here, phononic thermal transport is vulnerable to GBs even when they are ultra-narrow and aligned along the temperature gradient direction. Non-equilibrium molecular dynamics simulations uncover large reductions in the phononic thermal conductivity (κp ) along linear GBs comprising periodically repeating pentagon-heptagon dislocations. Green's function calculations and spectral energy density analysis indicate that the origin of the κp reduction is hidden in the periodic GB strain field, which behaves as a reflective diffraction grating with either diffuse or specular phonon reflections, and represents a source of anharmonic phonon-phonon scattering. The non-monotonic dependence with dislocation density of κp uncovered here is unaccounted for by the classical Klemens theory. It can help identify GB structures that can best preserve the integrity of the phononic transport.

Thermoelectric Properties of Strained β-Cu2Se

In recent years, the high-temperature phase of Cu₂Se, namely, β-Cu₂Se, has attracted increasing attention due to its outstanding thermoelectric efficiency. The Cu ions in β-Cu₂Se show a distinct ion-liquid behavior between the framework of a Se ion lattice. Many experimental operations may lead to a discrepancy in the lattice structure. Experimentally synthesized β-Cu₂Se was p-type, and a thermoelectric device needs both p-type and n-type materials with a close figure of merit. Studying the effect of strain and the possibility of n-type β-Cu₂Se is essential. Utilizing first-principles calculations and molecular dynamics simulations, we investigate the thermoelectric performance of strained β-Cu₂Se. The results show that the n-type β-Cu₂Se can exhibit superior zT values like the p-type one. Applying compressive strain is an effective way to promote the power factor. The tensile strain will lead to a low lattice thermal conductivity and thus boost the p-type zT values. The predicted maximum zT values for n-type and p-type β-Cu₂Se can reach 1.65 and 1.71 at 800 K, respectively. Considering the fact that applying strain is challenging in experiments, we propose a feasible strategy to manipulate the lattice structure and carrier type: doping halogen elements. Our results provide a guide for Cu₂Se-based thermoelectric devices.

Thermal Conductivity of Aluminum Scandium Nitride for 5G Mobile Applications and Beyond

Radio frequency (RF) microelectromechanical systems (MEMS) based on Al_1-xSc_xN are replacing AlN-based devices because of their higher achievable bandwidths, suitable for the fifth-generation (5G) mobile network. However, overheating of Al_1-xSc_xN film bulk acoustic resonators (FBARs) used in RF MEMS filters limits power handling and thus the phone's ability to operate in an increasingly congested RF environment while maintaining its maximum data transmission rate. In this work, the ramifications of tailoring of the piezoelectric response and microstructure of Al_1-xSc_xN films on the thermal transport have been studied. The thermal conductivity of Al_1-xSc_xN films (3-8 W m^-1 K^-1) grown by reactive sputter deposition was found to be orders of magnitude lower than that for c-axis-textured AlN films due to alloying effects. The film thickness dependence of the thermal conductivity suggests that higher frequency FBAR structures may suffer from limited power handling due to exacerbated overheating concerns. The reduction of the abnormally oriented grain (AOG) density was found to have a modest effect on the measured thermal conductivity. However, the use of low AOG density films resulted in lower insertion loss and thus less power dissipated within the resonator, which will lead to an overall enhancement of the device thermal performance.

Strategies for Manipulating Phonon Transport in Solids

In this review, we summarize the recent efforts on manipulating phonon transport in solids by using specific techniques that modify their phonon thermal conductivity (i.e., specific heat, phonon group velocity, and mean free path) and phonon thermal conductance (i.e., transmission probability and density of states). The strategies discussed for tuning thermal conductivity are as follows: large unit cell approach and liquid-like conduction for maneuvering specific heat; rattler, mini-bandgap, and phonon confinement for manipulating phonon group velocity; nanoparticles, nanosized grains, coated grains, alloy (isotope) scattering, selection rules in phonon dispersion, Grüneisen parameter, lone-pair electronics, dynamic disorder, and local static distortion for restricting mean free path. We have also included the discussion on tuning phonon thermal conductance, as thermal conduction can be viewed as a transmission process. Additionally, phonon filtering, ballistic transport, and waveguiding are discussed to alter density of states and transmission probability. We hope this review can bring meaningful insights to the researchers in the field of phonon transport in solids.

Anharmonic, dimensionality and size effects in phonon transport (2017J. Phys.: Condens. Matter29 505703)

Corrigendum to 2017J. Phys.: Condens. Matter29505703.

Effective Lorenz Number of the Point Contact between Silver Nanowires

Electrical and thermal transport through metal point contacts, a key issue in the design and operation of various engineering devices, is of great recent interest. The effective Lorenz number (L), which relates the thermal to electrical conductance of point contacts, could provide valuable information on the relative contribution of electrons and phonons to thermal transport. Through measuring electrical and thermal transport across point contacts between silver nanowires, we report that L significantly deviates from the Sommerfeld value by up to 5.2 times and exhibits nonmonotonic variation with temperature. Analyses show that these observations are due to the more important phonon contribution to the thermal conductance of the point contact as Sharvin resistance greatly hinders electron transport, which is further confirmed by the size dependence of L with a higher value for a smaller contact size. These results provide critical insights into engineering designs involving point contacts between metal nanostructures.

Achieving Out-of-Plane Thermoelectric Figure of Merit ZT = 1.44 in a p-Type Bi2Te3/Bi0.5Sb1.5Te3 Superlattice Film with Low Interfacial Resistance

Recently, low-dimensional superlattice films have attracted significant attention because of their low dimensionality and anisotropic thermoelectric (TE) properties such as the Seebeck coefficient, electrical conductivity, and thermal conductivity. For these superlattice structures, both electrons and phonons show highly anisotropic behavior and exhibit much stronger interface scattering in the out-of-plane direction of the films compared to the in-plane direction. However, no detailed information is available in the literature for the out-of-plane TE properties of the superlattice-based films. In this report, we present the out-of-plane Seebeck coefficient, thermal conductivity, and electrical properties of p-type Bi₂Te₃/Bi_0.5Sb_1.5Te₃ (bismuth telluride/bismuth antimony telluride, BT/BST) superlattice films in the temperature range of 77-500 K. Because of the synergistic combination of the energy filtering effect and low interfacial resistance of the superlattice structure, an impressively high ZT of 1.44 was achieved at 400 K for the 200 nm-thick p-type BT/BST superlattice film, corresponding to a 43% ZT enhancement compared to the pristine p-BST films with the same thickness.

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.

Quantum Phonon Transport in Nanomaterials: Combining Atomistic with Non-Equilibrium Green's Function Techniques

A crucial goal for increasing thermal energy harvesting will be to progress towards atomistic design strategies for smart nanodevices and nanomaterials. This requires the combination of computationally efficient atomistic methodologies with quantum transport based approaches. Here, we review our recent work on this problem, by presenting selected applications of the PHONON tool to the description of phonon transport in nanostructured materials. The PHONON tool is a module developed as part of the Density-Functional Tight-Binding (DFTB) software platform. We discuss the anisotropic phonon band structure of selected puckered two-dimensional materials, helical and horizontal doping effects in the phonon thermal conductivity of boron nitride-carbon heteronanotubes, phonon filtering in molecular junctions, and a novel computational methodology to investigate time-dependent phonon transport at the atomistic level. These examples illustrate the versatility of our implementation of phonon transport in combination with density functional-based methods to address specific nanoscale functionalities, thus potentially allowing for designing novel thermal devices.

Controllable Seebeck Coefficients of a Metal-Diffused Aluminum Oxide Layer via Conducting Filament Density and Energy Filtering

We investigate the intrinsic thermoelectric (TE) properties of the metal-diffused aluminum oxide (AO) layer in metal/AO/metal structures, where the metallic conducting filaments (CFs) were locally formed in the structures via an electrical breakdown (EBD) process as shown by resistive switching memory devices, by directly measuring cross-plane Seebeck coefficients on the CF-containing insulating AO layers. The results showed that the Seebeck coefficients of the CF-containing AO layer in metal/AO/metal structures were influenced by the generation of the metallic CFs, which is due to the diffusion of the metal into the insulating AO layers when exposed to a temperature gradient in the direction of the cross plane of the sample. In addition, the increase in the Seebeck coefficients of the CF-containing AO layer when the number of EBD-processed patterns was increased is satisfactorily explained by the low-energy carrier (i.e., minority carriers) filtering through the metal-oxide interfacial barriers in the metal/AO/metal structures.

Direct Probing of Cross-Plane Thermal Properties of Atomic Layer Deposition Al2O3/ZnO Superlattice Films with an Improved Figure of Merit and Their Cross-Plane Thermoelectric Generating Performance

There is a recent interest in semiconducting superlattice films because their low dimensionality can increase the thermal power and phonon scattering at the interface in superlattice films. However, experimental studies in all cross-plane thermoelectric (TE) properties, including thermal conductivity, Seebeck coefficient, and electrical conductivity, have not been performed from these semiconducting superlattice films because of substantial difficulties in the direct measurement of the Seebeck coefficient and electrical conductivity. Unlike the conventional measurement method, we present a technique using a structure of sandwiched superlattice films between two embedded heaters as the heating source, and electrodes with two Cu plates, which directly enables the investigation of the Seebeck coefficient and electrical conductivity across the Al₂O₃/ZnO superlattice films, prepared by the atomic layer deposition method. Used in combination with the promising cross-plane four-point probe 3-ω method, our measurements and analysis demonstrate all cross-plane TE properties of Al₂O₃/ZnO superlattice films in the temperature range of 80 to 500 K. Our experimental methodology and the obtained results represent a significant advancement in the understanding of phonons and electrical transports in nanostructured materials, especially in semiconducting superlattice films in various temperature ranges.

Tuning phonon transport spectrum for better thermoelectric materials

The figure of merit of thermoelectric materials can be increased by suppressing the lattice thermal conductivity without degrading electrical properties. Phonons are the carriers for lattice thermal conduction, and their transport can be impeded by nanostructuring, owing to the recent progress in nanotechnology. The key question for further improvement of thermoelectric materials is how to realize ultimate structure with minimum lattice thermal conductivity. From spectral viewpoint, this means to impede transport of phonons in the entire spectral domain with noticeable contribution to lattice thermal conductivity that ranges in general from subterahertz to tens of terahertz in frequency. To this end, it is essential to know how the phonon transport varies with the length scale, morphology, and composition of nanostructures, and how effects of different nanostructures can be mutually adopted in view of the spectral domain. Here we review recent advances in analyzing such spectral impedance of phonon transport on the basis of various effects including alloy scattering, boundary scattering, and particle resonance.

Ultralow Thermal Conductivity and Mechanical Resilience of Architected Nanolattices

Creating materials that simultaneously possess ultralow thermal conductivity, high stiffness, and damage tolerance is challenging because thermal and mechanical properties are coupled in most fully dense and porous solids. Nanolattices can fill this void in the property space because of their hierarchical design and nanoscale features. We report that nanolattices composed of 24- to 182-nm-thick hollow alumina beams in the octet-truss architecture achieved thermal conductivities as low as 2 mW m^-1 K^-1 at room temperature while maintaining specific stiffnesses of 0.3 to 3 MPa kg^-1 m³ and the ability to recover from large deformations. These nanoarchitected materials possess the same ultralow thermal conductivities as aerogels while attaining specific elastic moduli that are nearly 2 orders of magnitude higher. Our work demonstrates a general route to realizing multifunctional materials that occupy previously unreachable regions within the material property space.

Manipulation of Phonon Transport in Thermoelectrics

For several decades, thermoelectric advancements have largely relied on the reduction of lattice thermal conductivity (κ_L ). According to the Boltzmann transport theory of phonons, κ_L mainly depends on the specific heat, the velocity, and the scattering of phonons. Intensifying the scattering rate of phonons is the focus for reducing the lattice thermal conductivity. Effective scattering sources include 0D point defects, 1D dislocations, and 2D interfaces, each of which has a particular range of frequencies where phonon scattering is most effective. Because acoustic phonons are generally the main contributors to κ_L due to their much higher velocities compared to optical phonons, many low-κ_L thermoelectrics rely on crystal structure complexity leading to a small fraction of acoustic phonons and/or weak chemical bonds enabling an overall low phonon propagation velocity. While these thermal strategies are successful for advancing thermoelectrics, the principles used can be integrated with approaches such as band engineering to improve the electronic properties, which can promote this energy technology from niche applications into the mainstream.

First-Principle-Based Phonon Transport Properties of Nanoscale Graphene Grain Boundaries

The integrity of phonon transport properties of large graphene (linear and curved) grain boundaries (GBs) is investigated under the influence of structural and dynamical disorder. To do this, density functional tight-binding (DFTB) method is combined with atomistic Green's function technique. The results show that curved GBs have lower thermal conductance than linear GBs. Its magnitude depends on the length of the curvature and out-of-plane structural distortions at the boundary, having stronger influence the latter one. Moreover, it is found that by increasing the defects at the boundary, the transport properties can strongly be reduced in comparison to the effect produced by heating up the boundary region. This is due to the large reduction of the phonon transmission for in-plane and out-of-plane vibrational modes after increasing the structural disorder in the GBs.

Promising Thermoelectric Bulk Materials with 2D Structures

Given that more than two thirds of all energy is lost, mostly as waste heat, in utilization processes worldwide, thermoelectric materials, which can directly convert waste heat to electricity, provide an alternative option for optimizing energy utilization processes. After the prediction that superlattices may show high thermoelectric performance, various methods based on quantum effects and superlattice theory have been adopted to analyze bulk materials, leading to the rapid development of thermoelectric materials. Bulk materials with two-dimensional (2D) structures show outstanding properties, and their high performance originates from both their low thermal conductivity and high Seebeck coefficient due to their strong anisotropic features. Here, the advantages of superlattices for enhancing the thermoelectric performance, the transport mechanism in bulk materials with 2D structures, and optimization methods are discussed. The phenomenological transport mechanism in these materials indicates that thermal conductivities are reduced in 2D materials with intrinsically short mean free paths. Recent progress in the transport mechanisms of Bi₂ Te₃ -, SnSe-, and BiCuSeO-based systems is summarized. Finally, possible research directions to enhance the thermoelectric performance of bulk materials with 2D structures are briefly considered.

Phonon Speed, Not Scattering, Differentiates Thermal Transport in Lead Halide Perovskites

Thermal management plays a critical role in the design of solid state materials for energy conversion. Lead halide perovskites have emerged as promising candidates for photovoltaic, thermoelectric, and optoelectronic applications, but their thermal properties are still poorly understood. Here, we report on the thermal conductivity, elastic modulus, and sound speed of a series of lead halide perovskites MAPbX₃ (X = Cl, Br, I), CsPbBr₃, and FAPbBr₃ (MA = methylammonium, FA = formamidinium). Using frequency domain thermoreflectance, we find that the room temperature thermal conductivities of single crystal lead halide perovskites range from 0.34 to 0.73 W/m·K and scale with sound speed. These results indicate that regardless of composition, thermal transport arises from acoustic phonons having similar mean free path distributions. A modified Callaway model with Born von Karmen-based acoustic phonon dispersion predicts that at least ∼70% of thermal conductivity results from phonons having mean free paths shorter than 100 nm, regardless of whether resonant scattering is invoked. Hence, nanostructures or crystal grains with dimensions smaller than 100 nm will appreciably reduce thermal transport. These results are important design considerations to optimize future lead halide perovskite-based photovoltaic, optoelectronic, and thermoelectric devices.

Phonon Transport through Nanoscale Contact in Tip-Based Thermal Analysis of Nanomaterials

Nanomaterials have been actively employed in various applications for energy and sustainability, such as biosensing, gas sensing, solar thermal energy conversion, passive radiative cooling, etc. Understanding thermal transports inside such nanomaterials is crucial for optimizing their performance for different applications. In order to probe the thermal transport inside nanomaterials or nanostructures, tip-based nanoscale thermometry has often been employed. It has been well known that phonon transport in nanometer scale is fundamentally different from that occurred in macroscale. Therefore, Fourier’s law that relies on the diffusion approximation is not ideally suitable for describing the phonon transport occurred in nanostructures and/or through nanoscale contact. In the present study, the gray Boltzmann transport equation (BTE) is numerically solved using finite volume method. Based on the gray BTE, phonon transport through the constriction formed by a probe itself as well as the nanoscale contact between the probe tip and the specimen is investigated. The interaction of a probe and a specimen (i.e., treated as a substrate) is explored qualitatively by analyzing the temperature variation in the tip-substrate configuration. Besides, each contribution of a probe tip, tip-substrate interface, and a substrate to the thermal resistance are analyzed for wide ranges of the constriction ratio of the probe.

Nonperturbative Quantum Nature of the Dislocation-Phonon Interaction

Despite the long history of dislocation-phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and their capability of dealing with thermal transport phenomena for bulk material only. Here by utilizing a fully quantized dislocation field, which we called a "dislon", a phonon interacting with a dislocation is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime, which are reducible to classical results. A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. For instance, a renormalized phonon naturally resolves the decade-long debate between dynamic and static dislocation-phonon scattering approaches, as two limiting cases. In particular, at nanoscale, both the dynamic and static approaches break down, while the present renormalization approach remains valid by capturing the size effect, showing good agreement with lattice dynamics simulations.

Temperature and Thickness Dependences of the Anisotropic In-Plane Thermal Conductivity of Black Phosphorus

The anisotropic basal-plane thermal conductivities of thin black phosphorus obtained from a new four-probe measurement exhibit much higher peak values at low temperatures than previous reports. First principles calculations reveal the important role of crystal defects and weak thickness dependence that is opposite to the case of graphene and graphite due to the absence of reflection symmetry in puckered phosphorene.

The Role of Interfacial Electronic Properties on Phonon Transport in Two-Dimensional MoS2 on Metal Substrates

We investigate the role of interfacial electronic properties on the phonon transport in two-dimensional MoS₂ adsorbed on metal substrates (Au and Sc) using first-principles density functional theory and the atomistic Green's function method. Our study reveals that the different degree of orbital hybridization and electronic charge distribution between MoS₂ and metal substrates play a significant role in determining the overall phonon-phonon coupling and phonon transmission. The charge transfer caused by the adsorption of MoS₂ on Sc substrate can significantly weaken the Mo-S bond strength and change the phonon properties of MoS₂, which result in a significant change in thermal boundary conductance (TBC) from one lattice-stacking configuration to another for same metallic substrate. In a lattice-stacking configuration of MoS₂/Sc, weakening of the Mo-S bond strength due to charge redistribution results in decrease in the force constant between Mo and S atoms and substantial redistribution of phonon density of states to low-frequency region which affects overall phonon transmission leading to 60% decrease in TBC compared to another configuration of MoS₂/Sc. Strong chemical coupling between MoS₂ and the Sc substrate leads to a significantly (∼19 times) higher TBC than that of the weakly bound MoS₂/Au system. Our findings demonstrate the inherent connection among the interfacial electronic structure, the phonon distribution, and TBC, which helps us understand the mechanism of phonon transport at the MoS₂/metal interfaces. The results provide insights for the future design of MoS₂-based electronics and a way of enhancing heat dissipation at the interfaces of MoS₂-based nanoelectronic devices.

First-Principles Prediction of Ultralow Lattice Thermal Conductivity of Dumbbell Silicene: A Comparison with Low-Buckled Silicene

The dumbbell structure of two-dimensional group IV material offers alternatives to grow thin films for diverse applications. Thermal properties are important for these applications. We obtain the lattice thermal conductivity of low-buckled (LB) and dumbbell (DB) silicene by using first-principles calculations and the Boltzmann transport equation for phonons. For LB silicene, the calculated lattice thermal conductivity with naturally occurring isotope concentrations is 27.72 W/mK. For DB silicene, the calculated value is 2.86 W/mK. The thermal conductivity for DB silicene is much lower than LB silicene due to stronger phonon scattering. Our results will induce further theoretical and experimental investigations on the thermoelectric (TE) properties of DB silicene. The size-dependent thermal conductivity in both LB and DB silicene is investigated as well for designing TE devices. This work sheds light on the manipulation of phonon transport in two-dimensional group IV materials by dumbbell structure formed from the addition of adatoms.

Thermal Transport in Silicon Nanowires at High Temperature up to 700 K

Thermal transport in silicon nanowires has captured the attention of scientists for understanding phonon transport at the nanoscale, and the thermoelectric figure-of-merit (ZT) reported in rough nanowires has inspired engineers to develop cost-effective waste heat recovery systems. Thermoelectric generators composed of silicon target high-temperature applications due to improved efficiency beyond 550 K. However, there have been no studies of thermal transport in silicon nanowires beyond room temperature. High-temperature measurements also enable studies of unanswered questions regarding the impact of surface boundaries and varying mode contributions as the highest vibrational modes are activated (Debye temperature of silicon is 645 K). Here, we develop a technique to investigate thermal transport in nanowires up to 700 K. Our thermal conductivity measurements on smooth silicon nanowires show the classical diameter dependence from 40 to 120 nm. In conjunction with Boltzmann transport equation, we also probe an increasing contribution of high-frequency phonons (optical phonons) in smooth silicon nanowires as the diameter decreases and the temperature increases. Thermal conductivity of rough silicon nanowires is significantly reduced throughout the temperature range, demonstrating a potential for efficient thermoelectric generation (e.g., ZT = 1 at 700 K).

Simultaneous Thermoelectric Property Measurement and Incoherent Phonon Transport in Holey Silicon

Block copolymer patterned holey silicon (HS) was successfully integrated into a microdevice for simultaneous measurements of Seebeck coefficient, electrical conductivity, and thermal conductivity of the same HS microribbon. These fully integrated HS microdevices provided excellent platforms for the systematic investigation of thermoelectric transport properties tailored by the dimensions of the periodic hole array, that is, neck and pitch size, and the doping concentrations. Specifically, thermoelectric transport properties of HS with a neck size in the range of 16-34 nm and a fixed pitch size of 60 nm were characterized, and a clear neck size dependency was shown in the doping range of 3.1 × 10(18) to 6.5 × 10(19) cm(-3). At 300 K, thermal conductivity as low as 1.8 ± 0.2 W/mK was found in HS with a neck size of 16 nm, while optimized zT values were shown in HS with a neck size of 24 nm. The controllable effects of holey array dimensions and doping concentrations on HS thermoelectric performance could aid in improving the understanding of the phonon scattering process in a holey structure and also in facilitating the development of silicon-based thermoelectric devices.

Realization of Room-Temperature Phonon-Limited Carrier Transport in Monolayer MoS2 by Dielectric and Carrier Screening

By combining a high-κ dielectric substrate and a high density of charge carriers, Coulomb impurities in MoS2 can be effectively screened, leading to an unprecedented room-temperature mobility of ≈150 cm(2) V(-1) s(-1) and room-temperature phonon-limited transport in a monolayer MoS2 transistor for the first time.

Phonon-interface scattering in multilayer graphene on an amorphous support

The recent studies of thermal transport in suspended, supported, and encased graphene just began to uncover the richness of two-dimensional phonon physics, which is relevant to the performance and reliability of graphene-based functional materials and devices. Among the outstanding questions are the exact causes of the suppressed basal-plane thermal conductivity measured in graphene in contact with an amorphous material, and the layer thickness needed for supported or embedded multilayer graphene (MLG) to recover the high thermal conductivity of graphite. Here we use sensitive in-plane thermal transport measurements of graphene samples on amorphous silicon dioxide to show that full recovery to the thermal conductivity of the natural graphite source has yet to occur even after the MLG thickness is increased to 34 layers, considerably thicker than previously thought. This seemingly surprising finding is explained by long intrinsic scattering mean free paths of phonons in graphite along both basal-plane and cross-plane directions, as well as partially diffuse scattering of MLG phonons by the MLG-amorphous support interface, which is treated by an interface scattering model developed for highly anisotropic materials. Based on the phonon transmission coefficient calculated from reported experimental thermal interface conductance results, phonons emerging from the interface consist of a large component that is scattered across the interface, making rational choice of the support materials a potential approach to increasing the thermal conductivity of supported MLG.