Phonon thermal conductivity of graphene (original) (raw)
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A physics-based flexural phonon-dependent thermal conductivity model for single layer graphene
2012
In this paper, we address a physics-based closed-form analytical model of flexural phonon-dependent diffusive thermal conductivity (κ) of suspended rectangular single layer graphene sheet. A quadratic dependence of the out-of-plane phonon frequency, generally called flexural phonons, on the phonon wave vector has been taken into account to analyze the behavior of κ at lower temperatures. Such a dependence has further been used for the determination of second-order three-phonon Umklapp and isotopic scatterings. We find that these behaviors in our model are best explained through the upper limit of Debye cutoff frequency in the second-order three-phonon Umklapp scattering of the long phonon waves that actually remove the thermal conductivity singularity by contributing a constant scattering rate at low frequencies and note that the out-of-plane Gruneisen parameter for these modes need not be too high. Using this, we clearly demonstrate that κ follows a T 1.5 and T −2 law at lower and higher temperatures in the absence of isotopes, respectively. However in their presence, the behavior of κ sharply deviates from the T −2 law at higher temperatures. The present geometry-dependent model of κ is found to possess an excellent match with various experimental data over a wide range of temperatures which can be put forward for efficient electro-thermal analyses of encased/supported graphene.
On the accuracy of classical and long wavelength approximations for phonon transport in graphene
Journal of Applied Physics, 2011
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. V
Lattice thermal conductivity of pristine and doped (B,N) Graphene
2020
In this paper, the effect of B and N doping on the phonon induced thermal conductivity of graphene has been investigated. This study is important when one has to evaluate the usefulness of electronic properties of B and N doped graphene. We have performed the calculations by employing density functional perturbation theory(DFPT) to calculate the inter-atomic forces=force constants of pristine/doped graphene. Thermal conductivity calculations have been carried out by making use of linearized Boltzmann transport equations (LBTE) under single-mode relaxation time approximation (RTA). The thermal conductivity of pristine graphene has been found to be of the order of 4000W/mK at 100K, which decreases gradually with an increase in temperature. The thermal conductivity decreases drastically by 96 % to 190 W/mK when doped with 12.5 % B and reduces by 99 % to 30 W/mK with 25 % B doping. When graphene is doped with N, the thermal conductivity decreases to 4 W/mK and 55 W/mK for 12.5 % and 25 ...
Thermal Transport in Graphene Nanostructures: Experiments and Simulations
Graphene, Ge/iii-V, and Emerging Materials For Post-Cmos Applications 2, 2010
Thermal transport in graphene and graphene nanostructures have been studied experimentally and theoretically. Methods and previous work to measure and calculate the thermal conductivities of graphene and related nanostructures are briefly reviewed. We demonstrate that combining Raman spectroscopy for thermometry and electrical transport for Joule heating is an effective approach to measure both graphene thermal conductivity and graphenesubstrate interface thermal resistance. This technique has been applied to a variety of exfoliated or CVD-grown graphene samples (both suspended and substrate-supported), yielding values comparable with those measured using all-optical or all-electrical techniques. We have also employed classical molecular dynamics simulation to study thermal transport in graphene nanostructures and suggest such structures may be used as promising building blocks for nanoscale thermal engineering.
Mechanism of thermal conductivity reduction in few-layer graphene
2011
Using the linearized Boltzmann transport equation and perturbation theory, we analyze the reduction in the intrinsic thermal conductivity of few-layer graphene sheets accounting for all possible three-phonon scattering events. Even with weak coupling between layers, a significant reduction in the thermal conductivity of the out-of-plane acoustic modes is apparent. The main effect of this weak coupling is to open many new three-phonon scattering channels that are otherwise absent in graphene. However, reflection symmetry is only weakly broken with the addition of multiple layers, and ZA phonons still dominate thermal conductivity. We also find that reduction in thermal conductivity is mainly caused by lower contributions of the higher-order overtones of the fundamental out-of-plane acoustic mode. The results compare remarkably well over the entire temperature range with measurements of graphene and graphite.
Planar phonon anisotropy, and a way to detect local equilibrium temperature in graphene
Applications in Engineering Science, 2023
The effect of inclusion of the planar phonon anisotropy on thermo-electrical behavior of graphene is analyzed. Charge transport is simulated by means of Direct Simulation Monte Carlo technique coupled with numerical solution of the phonon Boltzmann equations based on deterministic methods. The definition of the crystal lattice local equilibrium temperature is investigated as well and the results furnish possible alternative approaches to identify it starting from measurements of electric current density, with relevant experimental advantages, which could help to overcome the present difficulties regarding thermal investigation of graphene. Positive implications are expected for many applications, as the field of electronic devices, which needs a coherent tool for simulation of charge and hot phonon transport; the correct definition of the local equilibrium temperature is in turn fundamental for the study, design and prototyping of cooling mechanisms for graphene-based devices.
Dynamic response of graphene to thermal impulse
Physical Review B, 2011
A transient molecular dynamics technique is developed to characterize the thermophysical properties of two-dimensional graphene nanoribbons (GNRs). By directly tracking the thermal-relaxation history of a GNR that is heated by a thermal impulse, we are able to determine its thermal diffusivity quickly and accurately. We study the dynamic thermal conductivity of various length GNRs of 1.99 nm width. Quantum correction is applied in all of the temperature calculations and is found to have a critical role in the thermal-transport study of graphene. The calculated specific heat of GNRs agrees well with that of graphite at 300.6 and 692.3 K, showing little effect of the unique graphene structure on its ability to store thermal energy. A strong size effect on GNR's thermal conductivity is observed and its theoretical values for an infinite-length limit are evaluated by data fitting and extrapolation. With infinite length, the 1.99-nm-wide GNR has a thermal conductivity of 149 W m −1 K −1 at 692.3 K, and 317 W m −1 K −1 at 300.6 K. Our study of the temperature distribution and evolution suggests that diffusive transport is dominant in the studied GNRs. Non-Fourier heat conduction is observed at the beginning of the thermal-relaxation procedure. Thermal waves in GNR's in-plane direction are observed only for phonons in the flexural direction (ZA mode). The observed propagation speed (c = 4.6 km s −1 ) of the thermal wave follows the relation of c = v g / √ 2 (v g is the ZA phonon group velocity). Our thermal-wave study reveals that in graphene, the ZA phonons transfer thermal energy much faster than longitudinal (LA) and transverse (TA) modes. Also, ZA↔ZA energy transfer is much faster than the ZA↔LA/TA phonon energy transfer.
Journal of Computational and Theoretical Transport, 2018
The importance of the correct determination of the relaxation times, entering the electron-phonon coupling, is crucial for a proper evaluation of the rise of the crystal lattice temperature induced by a flow of electrons that undergo an external electric field. We describe the crystal heating by simulating the dynamics of all the phonon branches, i.e. acoustic, optical, K and Z phonons in a suspended monolayer graphene. At each time step the charge transport is determined by means of a direct simulation Monte Carlo procedure while the evolution of the phonon distributions is evaluated by counting the emission and absorption processes in the electron-phonon scatterings. For several applied electric fields and for several positive Fermi energies, the behaviors of the crystal lattice temperature, obtained with different models of the relaxation times, are compared and discussed. The contribution of each type of phonon is highlighted as well.