Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers

TL;DR

This paper establishes fundamental theoretical upper limits on the enhancement achievable in surface-enhanced Raman scattering (SERS) for arbitrary-shaped nanostructures, depending on material properties and geometry.

Contribution

It derives analytical bounds on SERS enhancement based on scatterer shape, size, and material, providing a benchmark for future nanostructure design.

Findings

Silver is optimal in visible wavelengths.

Aluminum outperforms in near-UV.

Simple geometries do not reach the bounds.

Abstract

The low efficiency of Raman spectroscopy can be overcome by placing the active molecules in the vicinity of scatterers, typically rough surfaces or nanostructures with various shapes. This surface-enhanced Raman scattering (SERS) leads to substantial enhancement that depends on the scatterer that is used. In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterers, depending only on its material constants and the separation distance from the molecule. According to our metric, silver is optimal in visible wavelengths while aluminum is better in the near-UV region. Our general analytical bound scales as the volume of the scatterer and the inverse sixth power of the distance to the active molecule. Numerical computations show that simple geometries fall short of the bounds, suggesting further design opportunities for future improvement. For periodic scatterers, we use two formulations to discover different bounds, and the tighter of the two always must apply. Comparing these bounds suggests an optimal period depending on the volume of the scatterer.