Simple model for surface-enhanced Raman scattering from tilted silver nanorod array substrates

A modified Greenler’s model is proposed to interpret surface enhanced Raman scattering (SERS) for molecules adsorbed onto a tilted and aligned Ag nanorod array substrate. This model only considers molecules absorbed on the side walls of the nanorods and the Raman incident and collection configurations. It reveals that when the incident angle increases to an optimal angle, the SERS intensity reaches a maximum. With the increase in the nanorod tilting angles, the maximum SERS intensity almost does not change, but the optimal incident angle increases linearly. The underlayer thin film also plays an important role for SERS enhancement. In addition, the SERS intensity is closely related to the polarization of the excitation light. When the incident angle is smaller than $15°$, $s$ polarization excites stronger Raman signals; at other incident angles, $p$-polarization excitation contributes more Raman intensity. Those theoretical predictions are qualitatively consistent with our experimental observations.

Figure 1

(a) A top view SEM image and (b) a cross-section SEM image of Ag nanorod array substrate fabricated by the OAD technique.

Figure 2

(Color online) A schematic illustration of the modified Greenler’s model. (a) Case I—the dipole is in the incident plane; (b) Case II—the dipole is perpendicular to the incident plane. All the induced dipoles are perpendicular to the nanorod.

Figure 3

(Color online) The relative Raman intensity ${\eta }_{\text{Raman}}$ as a function of the incident angle $\theta$ calculated from the modified Greenler’s model for a Ag nanorod SERS substrate. The underlayer substrate is Ag, the excitation light is unpolarized, and the nanorod tiling angles are $\beta =63°$ (navy short-dashed curve), $65°$ (green short-dashed curve), $67°$ (blue dashed-dotted curve), $70°$ (red dashed curve), and $72°$ (black solid curve), respectively.

Figure 4

(Color online) The optimal incident angle ${\theta }_0$ as a function of Ag nanorod tilting angle $\beta$ under unpolarized excitation light.

Figure 5

(Color online) The relative Raman intensity ${\eta }_{\text{Raman}}$ as a function of incident angle $\theta$ for different underlayer thin films: (a) Ag thin film (red solid curve); (b) glass substrate (blue solid curve); and (c) no substrate (black solid curve). The nanorod tilting angle is fixed,$\beta =70°$.

Figure 6

(Color online) The polarization dependence SERS intensity at different incident angles $\theta =0°$ (navy filled circles), $15°$ (black filled squares), $30°$ (blue triangles), $45°$ (green pentagons), $60°$ (red stars), and $75°$ (orange diamonds), respectively. When the incident angles $\theta$ are smaller than $15°$, the SERS intensity reaches a maximum at polarization angle of $90°$ and $270°$. When the incident angles are bigger than $15°$, the SERS intensity reaches a maximum at polarization angles of $0°$ and $180°$.