Interference effect on Raman spectrum of single layer graphene on SiO$_{2}$/Si

We studied the dependence of the Raman spectrum of graphene on the thickness of the SiO$_{2}$ layer. We prepared the single layer graphene samples with the various SiO$_{2}$ layer thicknesses ($\sim $240 to $\sim $388 nm) using micro-mechanical cleavage from the natural graphite and observed a strong variation of the Raman spectrum as a function of the thickness of SiO$_{2}$ layer. It is found that the intensity of Raman signal is strongly influenced by the interference due to multiple reflections in the graphene and SiO$_{2}$ layers. The Raman enhancement factor was calculated by taking into account the interference effect. The model calculation fits well with the experimental data. The interference also affects the Raman intensity ratio of the 2$D$ band to the $G$ band due to the difference in the wavelength of these signals. Moreover, we calculated the Raman enhancement factor as a function of the SiO$_{2}$ thickness and the excitation laser wavelength.