Fractal nanostructures with the Hilbert curve geometry as a SERS substrate

TL;DR

This paper proposes a novel SERS substrate based on fractal Hilbert curve geometries, demonstrating unique dielectric responses and resonance behaviors in doped semiconductor nanostructures with potential applications in enhanced Raman scattering.

Contribution

It introduces a new fractal-based substrate design for SERS, analyzing its dielectric properties and resonance shifts through theoretical modeling of Hilbert curve geometries.

Findings

Dielectric response varies with frequency, showing dimensional crossover.

Resonance shifts to lower frequencies as trapping potential depth increases.

Fractal geometry influences charge distribution and optical properties.

Abstract

We suggest a new type of substrates for the Surface Enhanced Raman Scattering measurements with the geometry based on self-similar fractal space filling curves. As an example, we have studied theoretically the dielectric response properties of doped semiconductor nanostructures, where the conducting electrons are trapped in the effective potential having the geometry of the Hilbert curve. We have found that the system may exhibit the induced charge distribution specific for either two dimensional or one dimensional systems, depending on the frequency of the external applied field. We have demonstrated that with the increasing of the depth of the trapping potential the resonance of the system counterintuitively shifts to lower frequencies.