On Estimating the $G$-peak shift in graphene Raman spectra

The frequency shift of the Raman $G$ peak of epitaxial graphene due to the interaction with a substrate described by effective bond force constant $k$ is investigated using the model of two coupled oscillators. The relative $G$-peak shift is shown to be $\Delta\omega(G)/\omega(G)\propto k/k_{0g}$, where $k_{0g}$ is the bond-stretching force constant of single-layer graphene. Assuming $k\propto P$ and $k\propto -T$, where $P$ and $T$ are the pressure and temperature, and the $k$ variation to be dominant, we qualitatively explain the experimental dependences of $\Delta\omega(G)$ on $P$ and $T$. The effect of the substrate on the $G$-peak broadening in epitaxial graphene is discussed.