Electron-Hole Pair Excitation

Head-Gordon and Tully [264] used the Golden Rule expression 

In order to evaluate the influence of phonon versus electron friction it is necessary to have models which include both aspects. Although many models for electron-hole pair excitation are available, most of these do not also consider the phonon excitation, and they are therefore not able to discriminate between the two processes. The model which is proposed by Metiu and coworkers [256] as well as Billing [262] assumes that the effective charge on the incoming molecule or adsorbate through Coulomb interaction with the metal-electrons excites these from levels below to levels above the Fermi level. Below we describe the semiclassical model proposed by Billing. This model has a collision-oriented aspect and treats the excitation processes to infinite order. 

One obvious question is whether the nuclear and electronic motion can be separated in the fashion which is done in most models for molecule surface scattering and also in the above-mentioned treatment of electron-hole pair excitation. The traditional approach is to invoke a Born-Oppenheimer approximation, i.e., one defines adiabatic potential energy surfaces on which the nuclear dynamics is solved — either quantally or classically. In the Bom-Oppenheimer picture the electrons have had enough time to readjust to the nuclear positions. Thus the nuclei are assumed to move infinitely slowly. For finite speed, nonadiabatic corrections therefore have to be introduced. Thus, before comparison with experimental data is carried out we have to consider whether nonadiabatic processes are important. Two types of nonadiabatic processes are possible—one is nonadiabatic transitions in the gas phase from the lower adiabatic to the upper surface (as discussed in Chapter 4). The other is the nonadiabatic excitation of electrons in the metal through electron-hole pair excitation. 

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Using this model they have tried to look at important chemical processes at metal surfaces to deduce the role of electronic nonadiabaticity. In particular, they have tried to evaluate the importance of electron-hole-pair excitation in scattering, sticking and surface mobility of CO on a Cu(100) surface.36,37 Those studies indicated that the magnitude of energy transferred by coupling to the electron bath was significantly less than that coupled to phonons. Thus the role of electron-hole-pair excitation in... 

However, a very limited number of studies focused on the effect of solvent dynamics on electron transfer reactions at electrodes.Smith and Hynes" introduced the effect of electronic friction (arising from the interaction between the excited electron hole pairs in the metal electrode) and solvent friction (arising from the solvent dynamic [relaxation] effect) in the electron transfer rate at metallic electrodes. The consideration of electron-hole pair excitation in the metal without illumination by light seems unrealistic. 

In chemisorbed systems, the molecular orbitals of the adsorbate are mixed with the electronic states of the substrate, producing strong adsorption bonds, i.e. the frequency of the adsorbate mode is well above the highest phonon frequency of the substrate. The relaxation of these vibrational excited states via emission of substrate phonons has only a low probability, because many phonons have to be enoitted during the decay. Non-radiative damping by electron-hole pair excitation appears to be the dominant relaxation path in these systems. 

The strength of the lattice instability near the Fermi vector depends on the magnitude of the electron-phonon coupling and on the phase space available for electron-hole pair excitation around 2kf. Thus, a reconstructive surface phase transition has to fulfill the following requirements in order to be ascribed to an electronically driven lattice instability ... 

Hence the leading term in a single mode transition, i.e. the damping of the mode i of frequency Qi from the first excited level into the ground state by electron-hole pair excitation is given by the first term (see for example [36]) ... 

Recent experiments determining the so-called chemicurrent [111] have provided some information on the importance of electron-hole pair excitation in adsorption processes. Using thin films deposited on n-type Si(l 1 1) as a Schottky diode device, the nonadiabatically generated electron-hole pairs upon both atomic and molecular chemisorption create the chemicurrent which can be measured [111, 112]. It has been estimated that for example in the NO adsorption on Ag one quarter of the adsorption energy is dissipated to electron-hole pairs. Adsorption-induced electron-hole pair creation has also been found for other metal substrates, such as Au, Pt, Pd, Cu, Ni and Fe, and even for semiconductors such as GaAs and Ge [112, 113]. 

Since DFT calculations are in principle only applicable for the electronic ground state, they cannot be used in order to describe electronic excitations. Still it is possible to treat electronic exciations from first principles by either using quantum chemistry methods [114] or time-dependent density-functional theory (TDDFT) [115,116], First attempts have been done in order to calculate the chemicurrent created by an atom incident on a metal surface based on time-dependent density functional theory [117, 118]. In this approach, three independent steps are preformed. First, a conventional Kohn-Sham DFT calculation is performed in order to evaluate the ground state potential energy surface. Then, the resulting Kohn-Sham states are used in the framework of time-dependent DFT in order to obtain a position dependent friction coefficient. Finally, this friction coefficient is used in a forced oscillator model in which the probability density of electron-hole pair excitations caused by the classical motion of the incident atom is estimated. 

Hopster H, Raue R, Kisker E et al (1983) Evidence for spin-dependent electron-hole-pair excitations in spin-polarized secondary-electron emission from Ni(l 10). Phys Rev Lett 50 70... 

As the region near an X-ray absorption edge is scanned in energy, the ejected photoelectron sequentially probes the empty electronic levels of the material. Theoretically, interest in core-state excitation has developed considerably since the work of Mahan (179) and Nozieres and De Dominicis (219) on the singular response of the conduction electrons (in metals) to the sudden potential created by removal of a core electron. The resulting electron-hole pair excitations lead to a threshold edge asymmetry. 

We are concerned with low-energy processes (near the Fermi energy). Consequently, the only pertinent wave vectors of electron-hole pair excitations will be those close to q = 0 and 2fcF since the electron-hole pair excitation energy is zero for these vectors in the one-dimensional noninteracting electron gas. The Fourier transform of the Coulomb interaction will contain terms near q = 0 and q = 2k which are approximated by... 

A feature of peculiar importance in one dimension is that long wavelength charge or spin-density-wave oscillations constructed by the combination of electron-hole pair excitations at low energy form extremely stable excitations... 

Other interesting treatments of the solid motion have been developed in which the motion of the solid s atoms is described by quantum mechanics [Billing and Cacciatore 1985, 1986]. This has been done for a harmonic solid in the context of treatment of the motion of the molecule by classical mechanics and use of a TDSCF formalism to couple the quantum and classical subsystems. The impetus for this approach is the fact that, if the entire solid is treated as a set of coupled harmonic oscillators, the quantum solution can be evaluated directly in an operator formalism. Then, the effect of solid atom motion can be incorporated as an added force on the gas molecule. Another advantage is the ability to treat the harmonic degrees of freedom of the solid and the harmonic electron -hole pair excitations on the same footing. The simplicity of such harmonic degrees of freedom can also be incorporated into the previously defined path-integral formalism in a simple manner to yield influence functionals (Feynman and Hibbs 1965). 

A different approach was described by Otto et al. and Burstein et al. Their Adatom Model postulates an extra Raman enhancement mechanism for adsorbates at active sites of atomic scale roughness . The adatom acts as an element of small or atomic scale roughness causing localired breakdown in the selection rules for electron-hole pair excitation. The model is based on a Raman scattering mechanism by charge transfer (cf. Fig. 7). An electron on the metal side is excited from... 

Consider the injection of a classical monochromatic electromagnetic wave of frequency co into a 3D PBG material by means of a single-mode waveguide channel. Suppose this waveguide channel contains a small active region of optically excitable two-level systems (confined electron-hole pair excitations or atoms) with a radiative transition at frequency [Pg.326]

Recombination electron/hole pairs Excited electrons and photo-generated holes are unstable species that can recombine quickly during the recombination, they can release energy in a nonproductive form as heat or photons. 

Notice that the expression (/ I IO) on the left-hand side of Eq. (33) describes the reaction of the electronic system on the excitation caused by the Coulombic interaction (see the integral Vd l). On the other hand, the matrix element on the right-hand side of Eq. (33) characterizes only the primary excitation process. Therefore Eq. (33) describes the resonance. The characteristic property of this energy equation is presence of the poles for the one-electron excitation energies As-j fj -y If it exists the solution Ep(q) (cf. Eq. (25)), which is much larger than any Aejjj -y can be considered as the energy of a plasmon. If such a collective state exists it results from a constructive interaction of many electron-hole pair excitations with small individual energy contributions. 

Fig. 2. Electron-hole pair continuum for Fermi liquid with crystal-field levels for local moments superposed. When the Kondo coupling is strong, there will be considerable admixture of the crystal-field and electron-hole pair excitations, resulting in a broadening or even elimination of sharp features in the local moment density of states.

Juaristi Jl, Alducin M, Diez-Muino R, Busnengo HF, Salin A (2008) Role of electron-hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces. Phys Rev Lett 100 116102... 

The modified hydrodynamic dielectric constant of Eq. (5.61) is a useful first approximation and allows estimating the importance of non-locality. However, it takes into account at the lowest order only the dependence on q. In particular, it lacks an effect which is, very likely, important for the determination of the molecule decay rate the excitation of electron-hole pairs. Such excitations are a way to transfer energy from the molecule to the metal, and then to dissipate such energy since the excited electron-hole pairs recombine mainly non-radiatively. Both energy and momentum must be conserved in the excitation of electron-hole pairs. Two sources can supply the momentum needed for the electron-hole pair excitation one is the spatial variation of the oscillating electric field acting in the metal and the other is the metal surface potential, which is able to provide momentum in the direction perpendicular to the surface. When the electric field is originated by a molecule which is far from the metal, the excitation of electron-hole pairs due to the field spatial... 

When the molecule is close to the metal, the spatially inhomogeneous field can carry the needed momentum. To take into account these electron-hole pair excitations and, more generally, to improve the description of the q-dependence of the dielectric constant, one can use a modified Lindhard-Mermin electric permittivity [84, 85], The Lindhard-Mermin dielectric function is the Lindhard function... 

As in the liquid, evaluating the two additional terms exactly is as difficult as the original problem. However, because of their physical interpretation it is possible to provide simple yet realistic approximations for them. In practice, one sometimes solves the equations of motion not only for the molecular degrees of freedom but also for those surface atoms to which they are directly coupled. Only the rest of the solid is averaged over. This structureless, pillow-like description of the environment has enabled the method of classical trajectories to be applied not only to reactions at the surface but also in solution. Unique to the surface is the need to allow for electron-hole pair excitations. 

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