The Theory of Surface-Enhanced Raman Spectroscopy on Organic Semiconductors: Graphene

Drawing on a theoretical expression previously derived for general semiconductor substrates, we examine the surface-enhancement of the Raman signal (SERS) when the substrate is chosen to be monolayer graphene. The underlying theory involves vibronic coupling, originally proposed by Herzberg and Teller. Vibronic coupling of the allowed molecular transitions with the charge-transfer transitions between the molecule and the substrate has been shown to be responsible for the SERS enhancement in semiconductor substrates. We then examine such an expression for the Raman enhancement in monolayer graphene, which is dependent on the square of the derivative of the density of states of the graphene. On integration, we find that the discontinuity of the density-of-states function leads to a singularity in the SERS intensity. Knowledge of the location of this resonance allows us to maximize the Raman intensity by careful alignment of the doping level of the graphene substrate with the charge-transfer transition.