Research Papers: Micro/Nanoscale Heat Transfer

Thermal Conductivity of Graphene Nanoribbons: Effect of the Edges and Ribbon Width

[+] Author and Article Information
Paul Plachinda

Graduate Research Assistant
Department of Physics,
Portland State University,
Portland, OR 97201
e-mail: plachind@pdx.edu

David Evans

Program Manager
Sharp Laboratories of America, Inc.,
Camas, WA 98607
e-mail: devans@sharplabs.com

Raj Solanki

Department of Physics,
Portland State University,
Portland, OR 97201
e-mail: solanki@pdx.edu

We use the “crystallographic” definition of the Fourier transform, i.e., F[f(x)]=-+f(x)exp(-2πikx)dx.

Original definition of the Fejér kernel Fn-1(x)=sin2(nx/2)/sin2(x/2), the Fejér kernel has a property: 12π-ππFn(x)dx=1.

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 9, 2011; final manuscript received February 21, 2012; published online October 5, 2012. Assoc. Editor: Pamela M. Norris.

J. Heat Transfer 134(12), 122401 (Oct 05, 2012) (7 pages) doi:10.1115/1.4006297 History: Received August 09, 2011; Revised February 21, 2012

We have calculated thermal conductance of graphene nanoribbons (GNRs) and their dependence on the type of ribbon edge termination (zigzag or armchair) and the width of the ribbon, which ranges from 50 Å to 50 μm. Our model incorporates the effect of edge roughness and includes edge roughness correlation functions for both types of termination. The dependence of thermal conductance on the width of the ribbons and relative contribution of different scattering mechanisms are also analyzed by means of the Green’s function approach to the edge scattering. High temperature thermal conductance of the nanoribbons was found to be 0.15 nW/K and 0.18 nW/K (corresponding to thermal conductivity, 4641 and 5266 W/mK, respectively, for 10 μm long GNRs) which is in a good agreement with the experimental results.

Copyright © 2012 by ASME
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Grahic Jump Location
Fig. 1

Cuts along two directions a graphene sheet, to produce zigzag (horizontal gray, or red in the online version) and armchair (vertical and oblique dark grey, or green and blue in the online version) terminations of the GNRs

Grahic Jump Location
Fig. 2

(a) Phonon dispersion relations, (b) ballistic transmission function, and (c) phonon density of states for the Γ–M (zigzag) (left) and Γ–K (armchair) (right) directions in graphene

Grahic Jump Location
Fig. 3

Shape functions and their Fourier transforms. (a) Shape function for the armchair boundary, (b) shape function for the zigzag boundary, (c) Fourier transform of the shape function for the armchair boundary, and (d) Fourier transform of the shape function for the zigzag boundary.

Grahic Jump Location
Fig. 4

Scaled attenuation coefficient (mW4/a3L)t-n,m for armchair (a) and zigzag (b) types of boundary as a function of k-vector: solid—from mode m = 0 to mode −n, n = 0, …, 2; dashed—from mode m = 1 to mode −n, n = 0, …, 2; and dashed-dotted—from mode m = 2 to mode −n, n = 0, …, 2

Grahic Jump Location
Fig. 5

Thermal conductance of armchair (a) and zigzag (b) types of boundary as function of temperature




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