Optimal design of gold nanomatryoshkas with embedded Raman reporters

- Classical vs quantum mechanical treatment of Au NMs with nm gaps is discussed.
- Analytical solutions have been obtained for the surface and volume averaged EM intensities.
- A detailed analysis of EM enhancement of Au NMs is given.
- The spectral dependence of EM enhancement on the Au NM structure has been studied. Optimal NM structures have been found for wavelengths of commercial Raman devices.

Gold multilayered nanoparticles (nanomatryoshkas, NMs), in which Raman molecules are embedded in a nanometer-sized gap between Au layers, have great potential in biomedical applications as highly efficient surface enhanced Raman scattering (SERS) probes. Compared to other SERS tags, the Raman molecules in Au NM are protected from environmental conditions and subjected to a strongly enhanced electromagnetic (EM) field in the gap. However, the SERS efficiency of Au NMs is multifactorial and depends on their structure, excitation wavelength, resonance properties and loading of Raman reporters, etc. Here, we report a detailed analysis of EM enhancement in Au(core)/Gap/Au(shell) NMs as a function of the core/gap/shell dimensions, the gap refractive index, and the excitation wavelength. The applicability of classical treatment is justified by discussion of recent studies on non-local and quantum tunneling effects in plasmonic dimers. Our optimization strategy is based on efficient rigorous solution for internal EM fields in a layered sphere and explicit analytical solutions for the surface and volume averaged EM intensities within a particular layer and around the NM. SERS enhancement is shown to be strongly dependent, in a resonance manner, on the core/gap/shell dimensions. For four wavelengths of commercial Raman devices 532, 633, 785, and 1064 nm, the optimal NM structures are found. Simulation data are discussed in the light of practical constrains and illustrated by experimental data on Au NMs with embedded 1,4 benzenedithiol (BDT) molecules that serve both as spacers and Raman reporters. The physical insights acquired from this study is hoped to pave the way for rational design of new SERS tags based on plasmonic field enhancement in the nanometer-sized gaps.