Reliability of Raman measurements of thermal conductivity of single-layer graphene due to selective electron-phonon coupling: A first-principles study

Abstract

Raman spectroscopy has been widely used to measure thermal conductivity ($\ensuremath{\kappa}$) of two-dimensional (2D) materials such as graphene. This method is based on a well-accepted assumption that different phonon polarizations are in near thermal equilibrium. However, in this paper, we show that, in laser-irradiated single-layer graphene, different phonon polarizations are in strong nonequilibrium, using predictive simulations based on first principles density functional perturbation theory and a multitemperature model. We first calculate the electron cooling rate due to phonon scattering as a function of the electron and phonon temperatures, and the results clearly illustrate that optical phonons dominate the hot electron relaxation process. We then use these results in conjunction with the phonon scattering rates computed using perturbation theory to develop a multitemperature model and resolve the spatial temperature distributions of the energy carriers in graphene under steady-state laser irradiation. Our results show that electrons, optical phonons, and acoustic phonons are in strong nonequilibrium, with the flexural acoustic (ZA) phonons showing the largest nonequilibrium to other phonon modes, mainly due to their weak coupling to other carriers in suspended graphene. Since ZA phonons are the main heat carriers in graphene, we estimate that neglecting this nonequilibrium leads to underestimation of thermal conductivity in experiments at room temperature by a factor of 1.35 to 2.6, depending on experimental conditions and assumptions used. Underestimation is also expected in Raman measurements of other 2D materials when the optical-acoustic phonon coupling is weak.