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Micro/Nanoscale Heat Transfer

# The Phonon Thermal Conductivity of Single-Layer Graphene From Complete Phonon Dispersion Relations

[+] Author and Article Information
Yunfeng Gu

College of Electronic and Mechanical Engineering, Nanjing Forestry University, Nanjing 210037, People’s Republic of China; Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, Key Laboratory of MEMS of China Educational Ministry,  Southeast University, Nanjing, 210096, People’s Republic of China

Zhonghua Ni, Minhua Chen, Kedong Bi

Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, Key Laboratory of MEMS of China Educational Ministry,Southeast University, Nanjing, 210096, People’s Republic of Chinayunfeichen@seu.edu.cn

Yunfei Chen1

Jiangsu Key Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, Key Laboratory of MEMS of China Educational Ministry,Southeast University, Nanjing, 210096, People’s Republic of Chinayunfeichen@seu.edu.cn

1

Corresponding author.

J. Heat Transfer 134(6), 062401 (May 09, 2012) (8 pages) doi:10.1115/1.4005743 History: Received September 02, 2010; Revised October 07, 2011; Published May 09, 2012

## Abstract

In this paper, the phonon scattering mechanisms of single-layer graphene are investigated based on the complete phonon dispersion relations. According to the selection rules that a phonon scattering process should obey the energy and momentum conservation conditions, the relaxation rates of combining and splitting umklapp processes can be calculated by integrating the intersection lines between different phonon mode surfaces in the phonon dispersion relation space. The dependence of the relaxation rates on the wave vector directions is presented with a three-dimensional surface over the first Brillouin zone. It is found that the reason for the optical phonons contributing little to heat transfer is attributed to the strong umklapp processes but not to their low phonon group velocities. The combining umklapp scattering processes involving the optical phonons mainly decrease the acoustic phonon thermal conductivity, while the splitting umklapp scattering processes of the optical phonons mainly restrict heat conduction by the optical phonons themselves. Neglecting the splitting processes, the optical phonons can contribute more energy than that carried by the acoustic phonons. Based on the calculated phonon relaxation time, the thermal conductivities contributed from different mode phonons can be evaluated. At low temperatures, both longitudinal and in-plane transverse acoustic phonon thermal conductivities have $T2$ temperature dependence, and the out-of-plane transverse acoustic phonon thermal conductivity is proportion to $T3/2$. The calculated thermal conductivity is on the order of a few thousands W/(m K) at room temperature, depending on the sample size and the edge roughness, and is in agreement well with the recently measured data in the temperature range from about 350 K to 500 K.

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## Figures

Figure 8

The temperature dependence of the acoustic phonon thermal conductivity and their approximate results

Figure 1

A schematic illustration of the possible (a) combining U process and (b) splitting U process for a phonon mode q. The wave vector q′ is in the BZ with the point Γ0 as its center and having a dash point line edge.

Figure 2

Phonon dispersion relations of the SLG in the triangular area ΔΓKM edged with the symmetry lines in the BZ. There are three acoustic phonon branches (LA, iTA, and oTA) and three optical phonon branches (LO, iTO, and oTO).

Figure 3

Construction for the interaction of three phonons: (a) the combining U process and (b) the splitting U process

Figure 4

The wave vector dependence of the relaxation rate of iTA phonons undergoing a combining U process (a) and a splitting U process (b) at 300 K

Figure 5

The frequency dependence of the relaxation rate of iTA phonons undergoing a combining U process at 300 K

Figure 6

A comparison between the total thermal conductivity calculated in this paper with those in previous literatures

Figure 7

The thermal conductivity as a function of temperature

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