Modeling the effect of small gaps in surface-enhanced Raman spectroscopy

The electromagnetic mechanism of surface-enhanced Raman spectroscopy (SERS) involves plasmon enhancement of the optical-frequency electric fields on the surfaces of silver or gold (or sometimes other) nanoparticles where molecules that exhibit Raman scattering are located. It has long been recognized that the largest electric fields are associated with small gaps (∼1 nm) between two or more nanoparticles (including fused particle structures) that are 20-100 nm in size. Recent advances in electromagnetic theory calculations, which we overview in this article, provide a clear quantitative picture of the SERS enhancement associated with this effect. These advances include: (1) recognition of the nanoparticle structures that give the highest enhancement factors for a given gap size; (2) determination of the dependence of enhancement factor on gap size in the small-gap limit; (3) the use of finite-element methods, rather than cubic grid-based methods, to evaluate enhancement factors; (4) evaluation of the dipole reradiation effect on enhancement factors for small gaps; and (5) the use of nonlocal dielectric functions to describe a material's electrodynamic response. These advances have demonstrated that the "hot spots" for 1 nm or smaller gaps often have a multipolar plasmon resonance character, reflecting the short propagating plasmon wavelength that exists in them. This leads to SERS excitation spectra that are not correlated with extinction or scattering spectra. In addition, these results show that the electromagnetic SERS enhancement factor has an approximate 1/gap ² dependence on gap (size) for optimally chosen particles.