Phonon Transport In Graphene Research Articles

Thermal rectification effect of pristine graphene induced by vdW heterojunction substrate

As an effective means of thermal management, thermal rectification (TR) has been studied in a variety of complex asymmetric or heterogeneous structures. Due to experimental conditions, many complex structures cannot be realized easily, and the low-temperature thermal bath temperature far below room temperature does not conform to the actual application environment of the device. In this paper, we studied the thermal rectification inside graphene supported by a heterogeneous substrate of SiO2 and GaN alternately. Heat flux is easier to transfer from the graphene covered on the SiO2 side to the GaN side. When the temperature of the cold bath is maintained at 300 K, only the temperature of the high-temperature hot bath is changed, and the maximum TR rate is about 52%. TR rate can be tuned by heat source temperature and size, with heat source size of 2 nm and temperature above 450 K, the highest TR rate can be obtained. The phonon density of states and participation ratio reveal the influence of the substrate and position on the phonon transport in graphene. Besides, the spectral energy density analysis confirmed that the substrate effect caused the shift of the graphene flexural phonon mode and the reconstruction of the phonon spectrum, which was in good agreement with PDOS, and further explain the basic mechanism of TR from the scattering rate and the degree of localization.

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene.

The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics. In this paper, by considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers. The results indicate that the first one can be interpreted as a measure of how fast the system is trying to approach the local equilibrium, while the second one as the local equilibrium lattice temperature. We also provide the explicit expression of the macroscopic entropy density for the system of phonons, by which we theoretically explain the approach of the system toward equilibrium and characterize the nature of the equilibria, in the spatially homogeneous case.

Phonon transport in graphene based materials.

Graphene, due to its atomic layer structure, has the highest room temperature thermal conductivity k for all known materials. Thus, it is expected that graphene based materials are the best candidates for thermal management in next generation electronic devices. In this perspective, we first review the in-plane k of monolayer graphene and multilayer graphene obtained using experimental measurements, theoretical calculations and molecular dynamics (MD) simulations. Considering the importance of four-phonon scattering in graphene, we also compare the effects of three-phonon and four-phonon scattering on phonon transport in graphene. Then, we review phonon transport along the cross-plane direction of multilayer graphene and highlight that the cross-plane phonon mean free path is several hundreds of nanometers instead of a few nanometers as predicted using classical kinetic theory. Recently, hydrodynamic phonon transport has been observed experimentally in graphitic materials. The criteria for distinguishing the hydrodynamic from ballistic and diffusive regimes are discussed, from which we conclude that graphene based materials with a high Debye temperature and high anharmonicity (due to ZA modes) are excellent candidates to observe the hydrodynamic phonon transport. In the fourth part, we review how to actively control phonon transport in graphene. Graphene and graphite are often adopted as additives in thermal management materials such as polymer nanocomposites and thermal interface materials due to their high k. However, the enhancement of the composite's k is not so high as expected because of the large thermal resistance between graphene sheets as well as between the graphene sheet and matrix. In the fifth part, we discuss the interfacial thermal resistance and analyze its effect on the thermal conductivity of graphene based materials. In the sixth part, we give a brief introduction to the applications of graphene based materials in thermal management. Finally, we conclude our review with some perspectives for future research.

High thermal conductivity of graphene and structure defects: Prospects for thermal applications in graphene sheets

The utilization of thermal energy from different sources is an important development direction for conserving energy. With the development of technology, refined and rapid utilization of thermal energy is required. Traditional thermal conductive materials cannot meet the growing needs of human beings. Therefore, people pay attention to two-dimensional graphene film materials for their thermal conductivity. This review collects current modeling group of thermal transport on graphene, including non-equilibrium Green function (NEGF) theory, molecular dynamics (MD) simulations modeling and Boltzmann transport equation method. These models can well explain several phenomena of phonon transport in graphene. Further, structural defects were discussed and expounded the effect for graphene thermal conductivity, including doping, grain boundary and defects. Deeply understanding of defects on graphene, we can better grasp the thermal conductivity of graphene from the microscopic point of view.

A hierarchy of macroscopic models for phonon transport in graphene

In this work, we propose a hierarchy of macroscopic models for the description of phonon transport in graphene. They are devised starting from the phonon Boltzmann transport equation by using the moments method and the maximum entropy principle. The state variables are the phonon energy densities and the fluxes of integer powers of the energy. We underline that the full energy dispersion relations are used. We test the validity of the models by analysing the steady-state and dynamical thermal conductivity, and the heat transport in zigzag and armchair graphene nanoribbons under a fixed temperature gradient.

Revisiting phonon-phonon scattering in single-layer graphene

Understanding the mechanisms of thermal conduction in graphene is a long-lasting research topic, due to its high thermal conductivity. Peierls-Boltzmann transport equation (PBTE) based studies have revealed many unique phonon transport properties in graphene, but most previous works only considered three-phonon scatterings and relied on interatomic force constants (IFCs) extracted at 0 K. In this paper, we explore the roles of four-phonon scatterings and the temperature dependent IFCs on phonon transport in graphene through our PBTE calculations. We demonstrate that the strength of four-phonon scatterings would be severely overestimated by using the IFCs extracted at 0 K compared with those corresponding to a finite temperature, and four-phonon scatterings are found to significantly reduce the thermal conductivity of graphene even at room temperature. In order to reproduce the prediction from molecular dynamics simulations, phonon frequency broadening has to be taken into account when determining the phonon scattering rates. Our study elucidates the phonon transport properties of graphene at finite temperatures, and could be extended to other crystalline materials.

Size effect of thermal conductivity in monolayer graphene

We use the none quilibrium molecular dynamics method to investigate the thermal conductivity of both suspended and supported graphene at room temperature. Significant size (both length and wide) effect is observed in thermal conductivity of suspended monolayer graphene. And it is found that the thermal conductivity value would converge to a constant value as further increasing size. In the case of supported graphene, we find the thermal conductivity is much lower than that of its suspended counterpart, and the suppressed size effect on thermal transport is obtained. The underlying physics of the size effect on both suspended and supported graphene is investigated and presented in terms of phonon transport analysis. These results show the nature of phonon transport in graphene and provide a useful guide for tailoring and engineering of the thermophysical properties of graphene in thermo-electronic and photonic devices.

Effect of the Substrate on Phonon Properties of Graphene Estimated by Raman Spectroscopy

Low-temperature Raman studies of supported graphene are presented. A linear temperature dependence of 2D peak linewidths was observed with the coefficients of 0.036 and 0.033 cm $$^{-1}$$ /K for graphene on copper and glass substrates, respectively, while G peak linewidths remained unchanged throughout the whole temperature range. The different values observed for graphene on glass and copper substrates were explained in terms of the substrate effect on phonon–phonon and electron–phonon interaction properties of the material. The results of the present study can be used to consider substrate effects on phonon transport in graphene for nanoelectronic device engineering.

Hydrodynamic phonon transport in suspended graphene.

Recent studies of thermal transport in nanomaterials have demonstrated the breakdown of Fourier's law through observations of ballistic transport. Despite its unique features, another instance of the breakdown of Fourier's law, hydrodynamic phonon transport, has drawn less attention because it has been observed only at extremely low temperatures and narrow temperature ranges in bulk materials. Here, we predict on the basis of first-principles calculations that the hydrodynamic phonon transport can occur in suspended graphene at significantly higher temperatures and wider temperature ranges than in bulk materials. The hydrodynamic transport is demonstrated through drift motion of phonons, phonon Poiseuille flow and second sound. The significant hydrodynamic phonon transport in graphene is associated with graphene's two-dimensional features. This work opens a new avenue for understanding and manipulating heat flow in two-dimensional materials.

Investigation of two-dimensional lattice thermal transport in bilayer graphene using phonon scattering mechanism

Two-dimensional lattice thermal transport in bilayer graphene is investigated using phonon scattering mechanism. In the plane layer of carbon atoms the thermal conductivity (κ) is demonstrated by incorporating the phonon–defect, phonon–electron, phonon–grain boundaries, phonon–phonon umklapp scatterings and out-of-plane phonon scattering process in the model Hamiltonian. A typical T1.5 dependence of thermal conductivity observed at low temperatures (lower than 150K) is the resultant of various operating phonon scattering mechanisms. Above room temperatures, the thermal conductivity decreases and follows almost T−2 dependence which is an artifact of the dominant Umklapp phonon scattering at higher temperatures. The phonon peak appear at around 225K is due to the competition between the increase in the phonon population and decrease in phonon mean free path due to umklapp phonon scattering with increasing temperature. The results obtained from present model are in good agreement with the available experimental data and reflect the two-dimensional nature of phonon transport in graphene which is dominated by phonon scatterings.

The role of percolation and sheet dynamics during heat conduction in poly-dispersed graphene nanofluids

A thermal transport mechanism leading to the enhanced thermal conductivity of graphene nanofluids has been proposed. The graphene sheet size is postulated to be the key to the underlying mechanism. Based on a critical sheet size derived from Stokes-Einstein equation for the poly-dispersed nanofluid, sheet percolation and Brownian motion assisted sheet collisions are used to explain the heat conduction. A collision dependant dynamic conductivity considering Debye approximated volumetric specific heat due to phonon transport in graphene has been incorporated. The model has been found to be in good agreement with experimental data.

Dimensional dependence of phonon transport in freestanding atomic layer systems

Due to the fast development of nanotechnology, we have the capability of manipulating atomic layer systems such as graphene, hexagonal boron nitride and dichalcogenides. The major concern in the 2-dimensional nanostructures is how to preserve their exceptional single-layer properties in 3-dimensional bulk structures. In this study, we report that the extreme phonon transport in graphene is highly affected by the graphitic layer stacking based on experimental investigation of the thermal conduction in few-layer graphene, 1-7 layers thick, suspended over holes of various diameters. We fabricate freestanding axisymmetric graphene structures without any perturbing substrate, and measure the in-plane transport property in terms of thermal conduction by using Raman spectroscopy. From the difference in susceptibility to substrate effect, size effect on hot-spot temperature variation and layer number dependence of thermal conductivity, we show that the graphitic membranes with 2 or more layers have characteristics similar to 3-dimensional graphite, which are very different from those of 2-dimensional graphene membranes. This implies that the scattering of out-of-plane phonons by interlayer atomic coupling could be a key mechanism governing the intrinsic thermal property.

Thermal transport in graphene

The recent advances in graphene isolation and synthesis methods have enabled potential applications of graphene in nanoelectronics and thermal management, and have offered a unique opportunity for investigation of phonon transport in two-dimensional materials. In this review, current understanding of phonon transport in graphene is discussed along with associated experimental and theoretical investigation techniques. Several theories and experiments have suggested that the absence of interlayer phonon scattering in suspended monolayer graphene can result in higher intrinsic basal plane thermal conductivity than that for graphite. However, accurate experimental thermal conductivity data of clean suspended graphene at different temperatures are still lacking. It is now known that contact of graphene with an amorphous solid or organic matrix can suppress phonon transport in graphene, although further efforts are needed to better quantify the relative roles of interface roughness scattering and phonon leakage across the interface and to examine the effects of other support materials. Moreover, opportunities remain to verify competing theories regarding mode specific scattering mechanisms and contributions to the total thermal conductivity of suspended and supported graphene, especially regarding the contribution from the flexural phonons. Several measurements have yielded consistent interface thermal conductance values between graphene and different dielectrics and metals. A challenge has remained in establishing a comprehensive theoretical model of coupled phonon and electron transport across the highly anisotropic and dissimilar interface.

On the accuracy of classical and long wavelength approximations for phonon transport in graphene

This paper presents a critical evaluation of the approximations usually made in thermal conductivity modeling applied to graphene. The baseline for comparison is thermal conductivity computations performed using a rigorous calculation of three-phonon scattering events and accounting for the anharmonicity of interatomic forces. Three central assumptions that underlie published theories are evaluated and shown to compromise the accuracy of thermal conductivity predictions. It is shown that the use of classical phonon occupation statistics in place of the Bose-Einstein distribution causes the overprediction of specific heat and the underprediction of phonon relaxation time; for ZA phonons, the classical approximation can underpredict the relaxation time by a factor of approximately 2 at room temperature across a broad frequency band. The validity of the long wavelength (Klemens) approximation in evaluating the strength of phonon scattering events is also examined, and the findings indicate that thermal conductivity is significantly underpredicted when long-wavelength approximations are made, with the most significant discrepancy occurring for ZA phonons. The neglect of Normal processes in thermal conductivity computations is evaluated and shown to produce a diverging thermal conductivity with increasing size.

Thermal transport in graphene and effects of vacancy defects

We have performed molecular dynamics simulations to investigate phonon transport in graphene at 300 K with the Green-Kubo method. We show that the thermal conductivity (TC) of pristine graphene is $2903\ifmmode\pm\else\textpm\fi{}93$ W/mK, and the out-of-plane phonon mode contribution is $1202\ifmmode\pm\else\textpm\fi{}32$ W/mK. We further investigate thermal transport in graphene with different vacancy defect concentrations, and the TC shows that it is possible to achieve a maximum of a thousandfold reduction with a high defect density.

Lattice thermal conductivity of graphene flakes: Comparison with bulk graphite

The authors proposed a simple model for the lattice thermal conductivity of graphene in the framework of Klemens approximation. The Gruneisen parameters were introduced separately for the longitudinal and transverse phonon branches through averaging over phonon modes obtained from the first-principles. The calculations show that Umklapp-limited thermal conductivity of graphene grows with the increasing linear dimensions of graphene flakes and can exceed that of the basal planes of bulk graphite when the flake size is on the order of few micrometers. The obtained results are in agreement with experimental data and reflect the two-dimensional nature of phonon transport in graphene.