Effect of film corrugation on the optical phonon lifetime in graphene

We present results of a microRaman study of n-layer graphene films supported on $\sim $atomically flat mica, Si/SiO$_{2}$ (or varying roughness) and suspended above a trench. Using the Raman G-band line width \textit{$\Gamma $}$_{G }$, we find that the optical phonon lifetime \textit{$\tau \sim $1/$\Gamma $} decreases linearly with increasing rms substrate roughness $\delta $, and independent of the chemical composition of the substrate. In agreement with this general observation, we find that \textit{$\Gamma $}$_{G}$ for unsupported graphene is significantly higher (i.e., \textit{the q=0} optical phonon lifetime is significantly lower) than observed when the film is supported on mica. Correlating \textit{$\Gamma $}$_{G}$ with values obtained from supported films, we infer an inherent rms roughness \textit{$\delta \quad \sim $ 2 nm} for unsupported graphene, in reasonable agreement with recent STM reports that first suggested that graphene might prefer to spontaneously convert to a corrugated system. Our observations may then relate to the effect of the local bending of the sp$^{2}$ sheet on the electron-phonon interaction.