Experimental evidence of nanometer-scale confinement of plasmonic eigenmodes responsible for hot spots in random metallic films

We report on the identification and nanometer scale characterization over a large energy range of random, disorder-driven, surface plasmons in silver semicontinuous films embedded in silicon nitride. By performing spatially resolved electron energy loss spectroscopy experiments, we experimentally demonstrate that these plasmons eigenmodes arise when the films become fractal, leading to the emergence of strong electrical fields (“hot spots”) localized over few nanometers. We show that disorder-driven surface plasmons strongly depart from those usually found in nanoparticles, being strongly confined and randomly and densely distributed in space and energy. Beyond that, we show that they have no obvious relation with the local morphology of the films, in stark contrast with surface plasmon eigenmodes of nanoparticles.

Figure 1

(a) HAADF images of areas i to iii, where silver appears bright. (b) Log-log plot of the perimeters of the metal clusters found in each area as a function of their surfaces. Red, blue, and green dots relate, respectively, to the areas i, ii, and iii. For small clusters, the perimeter roughly scales with the square root of the surface, which is characteristic of Euclidian shapes. The slope increases for large clusters, as expected for fractal shapes.

Figure 2

(a) HAADF images of areas i–iii. (b) EEL probability local spectra (colored) corresponding to the probe positions indicated in (a) and mean EEL probability spectra (grey) obtained by averaging the set of spectra acquired in the whole area. The dashed boxes demarcate some low-energy and high-energy regimes. (c) Spatial variations of the EEL probability at the energy loss values of 1.0 and 1.4 eV (low-energy regime) and 2.8 and 3.2 eV (high-energy regime). The superimposed contour line is the sample morphology profile obtained from the HAADF images.

Figure 3

(a) Histograms of the percentage of pixels in areas i to iii in which a peak with a given central energy was found, weighted by the amplitude of the peaks. (b) Map combining the amplitude (in height) and central energy (through a color code) of the peaks whose central energy is between 0.8 and 1.5 eV. A pixel is blanked when no peak was found in this spectral range.

Figure 4

(a) HAADF image of a large semicontinuous area slightly before the percolation threshold. (b) Maps of the energy and amplitude of the peaks whose central energy is between 1.0 and 1.8 eV. When no peak is found in these spectral ranges, the pixel is either blanked if the local material is silver, or greyed if the local material is silicon nitride. The superimposed contour line is the sample profile obtained from the HAADF image. The black circles stress two different eigenmodes.

Figure 5

(a) HAADF images of a semicontinuous area and of a small structural detail indicated by the white square. (b) EEL probability local spectra corresponding to the probe positions indicated in (a). (c) Maps of the amplitude (left), central energy (middle), and FWHM (right) of the peaks whose central energy is found within two 0.05 eV wide energy windows centered at 1.30 (top) and 1.60 eV (bottom). When no peak is found in these spectral ranges, the pixel is either blanked if the local material is silver, or greyed if the local material is silicon nitride. (d) Spatial extension of some eigenmodes measured in the semicontinuous area of (a) as a function of their eigenenergy. (e) Red: damping rate of some eigenmodes measured in the semicontinuous area of (a) as a function of their eigenenergy. The black dotted line shows the instrumental limitation imposed by the spectral resolution of the measurement. Black: Half FWHM as a function of the central energy of the EMLDOS peaks obtained after numerical simulation performed in a similar area.