Drude-Sommerfeld model

The decay of the nanoparticle plasmons can be either radiative, ie by emission of a photon, or non-radiative (Figure 7.5). Within the Drude-Sommerfeld model the plasmon is a superposition of many independent electron oscillations. The non-radiative decay is thus due to a dephasing of the oscillation of individual electrons. In terms of the Drude-Sommerfeld model this is described by scattering events with phonons, lattice ions, other conduction or core electrons, the metal surface, impurities, etc. As a result of the Pauli exclusion principle, the electrons can be excited into empty states only in the CB, which in turn results in electron-hole pair generation. These excitations can be divided into inter- and intraband excitations by the origin of the electron either in the d-band or the CB (Figure 7.5) [15]. 

Figure 3. Energy diagram for free electrons in a metal. The positive background charge of the core ions leads to a potential energy well with respect to the energy of the electron in vacuum vac- The averaged kinetic energy of the free electrons is indicated with dashed lines 3/2 k%T according to the Drude model, and 3/5 according to the Sommerfeld model. The electrochemical potential of the electrons in the metal [Fermi level] is also indicated.

T. Sommerfeld and K. D. Jordan, /. Phys. Chem. A, 109, 11531-11538 (2005). Quantum Drude Oscillator Model for Describing the Interaction of Excess Electrons with Water Clusters An Application to (H20)jj. 

Optical properties of metal nanoparticles embedded in dielectric media can be derived from the electrodynamic calculations within solid state theory. A simple model of electrons in metals, based on the gas kinetic theory, was presented by Drude in 1900 [9]. It assumes independent and free electrons with a common relaxation time. The theory was further corrected by Sommerfeld [10], who incorporated corrections originating from the Pauli exclusion principle (Fermi-Dirac velocity distribution). This so-called free-electron model was later modified to include minor corrections from the band structure of matter (effective mass) and termed quasi-free-electron model. Within this simple model electrons in metals are described as... 

At the present time, by far the most useful non-empirical alternatives to Cl are the methods based on density functional theory (DFT) . The development of DFT can be traced from its pre-quantum-mechanical roots in Drude s treatment of the electron gas" in metals and Sommerfeld s quantum-statistical version of this, through the Thomas-Fermi-Dirac model of the atom. Slater s Xa method, the laying of the formal foundations by... 

Sommerfeld A (1916) The Drude dispersion theory from the standpoint of Bohr s model, and the constitution of hydrogen, oxygen, and nitrogen. Ann Phys 51 1... 

In 1933, Arnold Sommerfeld and Hans Bethe revised the Drude model. Their more complete, quantum mechanical theory goes under the name of the free electron... 

Over the course of history, pure metal has been described by a variety of models. The initial model, attributable to Drude, considered the metal to comprise a gas of electrons enveloping positive ions in a constant potential. Drude applies Maxwell-Boltzmann statistics to that electron gas. In fact, as the electrons are fermions, it is most appropriate to apply Fermi-Dirac statistics to them, as Sommerfeld did in his model, still using a constant potential. Unlike with molecules, though, because of their low mass, the electrons cannot be used for the approximation of the classic limit statistics given by ... 

Fowler proposed a theory in 1931 which showed that the photoelectric current variation with light frequency could be accounted for by the effect of temperature on the number of electrons available for emission, in accordance with the distribution law of Sommerfeld s theory of metals. Sommerfeld s theory (1928) had resolved some of the problems surrounding the original models for electrons in metals. In classical Drude theory, a metal had been envisaged as a three-dimensional potential well (or box) containing a gas of freely mobile electrons. This adequately explained their high electrical and thermal conductivities. However, because experimentally it is found that metallic electrons do not show a gaslike heat capacity, the Boltzman distribution law is inappropriate. A Fermi-Dirac distribution function is required, consistent with the need that the electrons obey the Pauli exclusion principle, and this distribution function has the form... 

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