Broadening of Plasmonic Resonance Due to Electron Collisions with Nanoparticle Boundary: а Quantum Mechanical Consideration

Abstract

1 We present a quantum mechanical approach to calculate broadening of plasmonic resonances in metallic nanostructures due to collisions of electrons with the surface of the structure. The approach is applicable if the characteristic size of the structure is much larger than the de Broglie electron wavelength in the metal. The approach can be used in studies of plasmonic properties of both single nanoparticles and arrays of nanoparticles. Energy conservation is insured by a self-consistent solution of Maxwell's equations and our model for the photon absorption at the metal boundaries. Consequences of the model are illustrated for the case of spheroid nanoparticles and results are in good agreement with earlier theories. In particular, we show that the boundary-collision broadening of the plasmonic resonance in spheroid nanoparticles can depend strongly on the polarization of the impinging light. 1 A. V. Uskov P.N. Lebedev Physical Institute,

Landau damping of surface plasmons in metal nanostructures

“…We stress that in a system with dispersive dielectric function, where the mode energy is U rather than ω [70], the standard transition rate must by rescaled by the factor ω/2U [69]. Calculation of Q s (and, hence, of Γ s ) hinges on the transition matrix element M αβ , which has so far been evaluated, either analytically or numerically, only for several simple geometries permitting separation of variables [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]68]. For general-shape systems, evaluation of M αβ presents an insurmountable challenge of finding, with a good accuracy, the three-dimensional electron wave functions oscillating rapidly, with the Fermi wavelength period λ F , on the system size scale L ≫ λ F .…”

“…We consider the case when excitation energy ω is much larger than the electron level spacing, so that, in the absence of phonon and impurity scattering, the electron transition to the state ψ β (r) with energy ǫ β = ǫ α + ω requires momentum transfer to the interface. A direct evaluation of M αβ , so far carried out only for some simple geometries [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]68], requires the knowledge of ψ α in the entire system volume. We note, however, that for a typical plasmon frequency ω ≪ E F , where E F is the Fermi energy in the metal, the momentum transfer q ∼ ω/v F takes place in a region of size ξ nl ∼ /q ∼ v F /ω, so that, for characteristic system size L ≫ v F /ω, the e-h pair excitation takes place in a close proximity to the interface (see Fig.…”

“…In subsequent quantum-mechanical studies carried within random phase approximation (RPA) [45][46][47][48][49][50][51] and timedependent local density approximation (TDLDA) [52][53][54][55][56][57][58][59] approaches, a more complicated picture has emerged involving the role of confining potential and nonlocal effects. These are dominant at the spatial scale ξ nl = v F /ω that defines the characteristic length for nonlocal effects [60,61] (e.g., for noble metals, v F /ω < 1 nm in the plasmon frequency range), whereas for larger systems with L ≫ v F /ω (i.e., several nm and larger), they mainly affect the overall magnitude of γ sp , while preserving intact its size dependence [56,58].…”

“…The major roadblock in the way of carrying this program forward has so far been the lack of any quantummechanical model for evaluation of γ s in a nanostructure of arbitrary shape. Due to the complexity of electronic states in general-shape confined systems, calculations of γ s were performed, within RPA [44][45][46][47][48][49][50][51] and TDLDA [52][53][54][55][56][57][58][59] approaches, only for some simple (mostly spherical) geometries. For general shape systems, the surface scattering rate was suggested, within the classical scattering (CS) model [62][63][64][65][66], in the form γ cs = Av F /L, where L is interpreted as the ballistic scattering length in a classical cavity, while the phenomenological constant A accounts for the effects of surface potential, electron spillover, and dielectric environment.…”

Broadband infrared absorption enhancement by electroless-deposited silver nanoparticles

“…It is important to highlight the position distribution, which is completely random but in particular gives rise to dimers or groups of particles very close to each other (if not overlapping), with even nanometersized gaps. In principle, nonlocal effects may enhance the absorption too [68][69][70].…”