Spectral phonon mean free path and thermal conductivity accumulation in defected graphene: The effects of defect type and concentration

Abstract

The spectral phonon properties in defected graphene have been unclear due to the lack of advanced techniques for predicting the phonon-defect scattering rate without fitting parameters. Taking advantage of the extended phonon normal mode analysis, we obtained the spectral phonon relaxation time and mean free path (MFP) in defected graphene and studied the impacts of three common types of defects: Stone-Thrower-Wales (STW) defect, double vacancy (DV), and monovacancy (MV). The phonon-STW defect scattering rate is found to have no significant frequency dependence, and as a result, the relative contribution of long-wavelength phonons sharply decreases. In contrast, the phonon scattering by DVs or MVs exhibits a frequency dependence of ${\ensuremath{\tau}}_{p\ensuremath{-}d}^{\ensuremath{-}1}\ensuremath{\sim}{\ensuremath{\omega}}^{1.1\ensuremath{-}1.3}$ except for a few long-wavelength phonons, revisiting the traditionally used $\ensuremath{\sim}{\ensuremath{\omega}}^{4}$ dependence. We note that although MV-defected graphene has the lowest thermal conductivity as compared to the other two defected graphene samples at the same defect concentration, it has a portion of phonons with the longest MFP. The contribution from the long-MFP and long-wavelength phonons does not decrease much as the vacancy concentration increases. STW defect and MV block more out-of-plane modes than in-plane modes, while DV has less bias for which mode to block. As the MV concentration increases from 0 to 1.1%, the relative contribution from out-of-plane modes decreases from 30% to 18%, while that of the transverse acoustic mode remains at around 30%. These findings of spectral phonon properties can provide more insight than the effective properties and benefit the prospective phononic engineering.