Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness

Abstract

Surface plasmon polariton (SPP) resonance spectra for noble metals (Au, Ag, and Cu) were comprehensively studied in the Kretschmann attenuated total reflection (ATR) geometry, in the wavelength (λ) range from 300 to 1000 nm with the angle of incidence (θ) ranging from 45 to 60° and the film thickness (d) ranging from 41 to 76 nm. The experimental plasmon resonance spectra were reproduced by a calculation that included the broadening effects as follows: (1) the imaginary part of the bulk dielectric constant, (2) the thickness-dependent radiative coupling of the SPP at the metal–air interface to the prism, (3) the lack of conservation of the wavevector parallel to the interface kx(k||) caused by the surface roughness, (4) scanning λ at a fixed θ (changing both energy and kx at the same time) over the SPP dispersion relation. For Au and Ag, the experimental results were in good agreement with the calculated results using the bulk dielectric constants, showing no film thickness dependence of the plasmon resonance energy. A method to extract the true width of the plasmon resonance from raw ATR spectra is proposed and the results are rigorously compared with those expected from the bulk dielectric function given in the literature. For Au and Ag, the width increases with energy, in agreement with that expected from the relaxation of bulk free electrons including the electron–electron interaction, but there is clear evidence of extra broadening, which is more significant for thinner films, possibly due to relaxation pathways intrinsic to plasmons near the interface. For Cu, the visibility of the plasmon resonance critically depends on the evaporation conditions, and low pressures and fast deposition rates are required. Otherwise, scattering from the surface roughness causes considerable broadening of the plasmon resonance, resulting in an apparently fixed resonance energy without clear incident angle dependence. For Cu, the observed plasmon dispersion agrees well with that expected from the bulk dielectric function even with nominal oxidation of the surface, but the widths at long wavelengths are much larger than those theoretically expected.