The effect of randomly distributed surface bumps on local field enhancements in surface enhanced Raman spectroscopy

Abstract

A model is presented for determining the enhancement of local electromagnetic fields which occurs close to rough metal surfaces through surface plasmon excitation. The model considers a random distribution of metal hemispheroids on a perfectly conducting flat plane. The electrodynamics of this system is described using the long wavelength approximation and with only the dipole coupling between different hemispheroids included. The square of the local field is averaged over all locations on the surface to provide an estimate of the enhancement in Raman intensity pertinent to surface enhanced Raman spectroscopy (SERS). Application is made to rough Ag, Cu, Au, Hg, and Pt surfaces, simulating the roughness produced by electrochemical anodization. For Ag, the roughness induced SERS enhancement is found to be about 102, with a weak dependence on wavelength down to 350 nm, where a sharp drop is observed. The variation of this result on the parameters which characterize the hemispheroid distributions is studied, including the variation with the distribution of hemispheroid heights and widths, with the number and arrangements of hemispheroids on the surface, with hemispheroid dielectric constant, and with hemispheroid coverage. Most of these parameters do not change the overall enhancement factors significantly, although the wavlength dependence of the enhancement does change significantly with hemispheroid coverage. The polarization of the local electric field close to the surface is studied, and found to be primarily perpendicular to the local surface for globally perpendicular applied fields. The SERS enhancement on Cu is found to be comparable to Ag for λ≳600 nm, with a drop in intensity by a factor of 5 at 600 nm. Au is similar to Cu, except that the drop occurs at 500 nm. Hg is similar to Ag in both the magnitude and frequency dependence of the enhancement, while Pt is uniformly smaller throughout the visible. All of these enhancements are ∼103 smaller than is seen experimentally using SERS, although the observed change in SERS intensity due to anodization does closely match the predictions of our model. Overall, we conclude that surface roughness probably contributes 102 to 103 to the overall enhancement with a frequency dependence which is close to that seen experimentally. This conclusion indicates that some other enhancement mechanism must be responsible for the remaining factor of 103 needed to explain the observed overall enhancement of 106.