Topics in Particle and Dispersion Science

 
Fig. 1. The spectra of contributions to the real part, ε', of the dielectric function for silver. The thick green curve (data file) is the measured dielectric function. The red curve (data file) is the free-electron dielectric function ε'_free (calculated from the Drude model, for example, Kreibig U and Vollmer 1995, Sect. 2.1.1). The blue curve (data file) is the interband contribution, χ'_IB. Redrawn by permission after Ehrenreich H and Philipp 1962.

In the Rayleigh limit (relative particle size x << 1; for example, van de Hulst HC 1981, section 6.1) for spherical particles in air (or vacuum), the plasmon resonance occurs when the real part of the dielectric function, ε' of the particle material equals -2 (this value depends on particle shape). This graph shows a significant shift in the resonance wavelength towards lower energy due to the interband contribution (blue). Such a wavelength shift occurs for all the noble metals. For example, if we take only the free-electron contribution to ε' (red) to estimate the plasmon resonance energy (wavelength, λ) of silver, then ε' = ε'_free = -2 at the energy, E, of ~5.3 eV (λ ~220 nm; assuming that the surrounding medium is air, with ε_m = 1). But using the measured dielectric function (green) to find the plasmon energy yields ε' = ε'_free + χ'_IB = -2 when E ~3.3 eV (λ ~344 nm).

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