0
Research Papers: Micro/Nanoscale Heat Transfer

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

[+] Author and Article Information
Paul Plachinda

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

Professor
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

## Abstract

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.

<>
Your Session has timed out. Please sign back in to continue.

## Figures

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

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

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.

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

Fig. 5

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

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections