Permittivity Model Selection Based on Size and Quantum-Size Effects in Gold Films

  • Iuliia Riabenko V.N. Karazin Kharkiv National University, School of radiophysics, biomedical electronics and computer systems, Kharkiv, Ukraine; Institute of Quantum Optics, Leibniz University Hannover, Hannover, Germany
  • Sergey Shulga V.N. Karazin Kharkiv National University, School of radiophysics, biomedical electronics and computer systems, Kharkiv, Ukraine
  • Nikolai А. Makarovskii V.N. Karazin Kharkiv National University, School of Physics, Kharkiv, Ukraine
  • Konstantin Beloshenko V.N. Karazin Kharkiv National University, School of radiophysics, biomedical electronics and computer systems, Kharkiv, Ukraine
Keywords: Permittivity, Mie theory, Hampe-Shklyarevsky model, Absorption spectra, Plasma absorption band, Gold granules


The article is focused on optical properties of nanostructures containing spherical gold nanoparticles of various radii. We explore correlation between the particle radius and the choice of permittivity model applied to describe optical absorption spectra of gold granules. The experiments show splitting of the absorption band of granular gold films to form a second absorption peak. The first peak is associated with the phenomenon of plasmon resonance, while the second one reflects quantum hybridization of energy levels in gold. Quantum effects are shown to prevail over size effects at a granule diameter of about 5-6 nm. The Mie theory gives a rigorous solution for the scattered electromagnetic field on a sphere taking into account optical properties of the latter, however, it does not specify the criteria for selecting a model to calculate dielectric permittivity. Both calculations and experiments confirm the limiting diameter of gold nanoparticles where the Hampe-Shklyarevsky model is applied. Meanwhile, this model is still unable to predict the splitting of the plasma absorption band. The data presented in the article can be used for a predetermined local field enhancement in composite media consisting of a biolayer and metal nanoparticles. The conducted research provides a deeper understanding of the influence of a terahertz high-intensity electromagnetic field localized in the space on quantum dots.


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How to Cite
Riabenko, I., Shulga, S., MakarovskiiN. А., & Beloshenko, K. (2023). Permittivity Model Selection Based on Size and Quantum-Size Effects in Gold Films. East European Journal of Physics, (3), 406-412.