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

Dhruv Singh, Purdue University
Jayathi Murthy, Birck Nanotechnology Center, Purdue University
Timothy S. Fisher, Birck Nanotechnology Center, Purdue University

Date of this Version



Journal of Applied Physics: Volume 110, Issue 11


Copyright (2011) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics: Volume 110, Issue 11 and may be found at . The following article has been submitted to/accepted by the Journal of Applied Physics. Copyright (2011) Dhruv Singha, Jayathi Y. Murthy, and Timothy S. Fisher. This article is distributed under a Creative Commons Attribution 3.0 Unported License.


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. (C) 2011 American Institute of Physics. [doi:10.1063/1.3665226]


Nanoscience and Nanotechnology