Conduction electron energy relaxation

By using the same approach as Giuffrida, Darugar et al. prepared Cu NPs from the Cu(acac)2 precursor and studied time-resolved transient absorption phenomena for nanoparticles of 12 and 30 nm. The conduction electron energy relaxation was found to be faster in the smaller particles, whereas fluorescence showed an opposite trend [151]. 

In direct gap GaAs, an excited electron at the bottom of the conduction band can relax spontaneously back into a hole in the valence band by emitting a photon at the band gap energy. This electron-hole radiative recombination process can only occur in Si if momentum is conserved, i.e., the excited electron wave vector must be reduced to zero. This, in pure Si, occurs via the transfer of momentum to a phonon that is created with equal and opposite wave vector to that of the initial state in the conduction band. Such a three-body process is quite inefficient compared with direct gap recombination.1218 This is why Si is such a poor light emitter. 

An impurity atom in a solid induces a variation in the potential acting on the host conduction electrons, which they screen by oscillations in their density. Friedel introduced such oscillations with wave vector 2kp to calculate the conductivity of dilute metallic alloys [10]. In addition to the pronounced effect on the relaxation time of conduction electrons, Friedel oscillations may also be a source of mutual interactions between impurity atoms through the fact that the binding energy of one such atom in the solid depends on the electron density into which it is embedded, and this quantity oscillates around another impurity atom. Lau and Kohn predicted such interactions to depend on distance as cos(2A pr)/r5 [11]. We note that for isotropic Fermi surfaces there is a single kp-value, whereas in the general case one has to insert the Fermi vector pointing into the direction of the interaction [12,13]. The electronic interactions are oscillatory, and their 1 /r5-decay is steeper than the monotonic 1 /r3-decay of elastic interactions [14]. Therefore elastic interactions between bulk impurities dominate the electronic ones from relatively short distances on. 

The photophysical origin of plasmonic heating can be attributed to the nonradia-tive relaxation of the optically excited conduction electrons, whose energies then diffuse into the metal lattice (electron-phonon coupling) and are dissipated as heat into the surrounding medium (phonon-phonon interactions).71-73 Under ideal conditions, the nanoparticle temperature can be estimated by the following equation 73... 

As other semiconductors, QDs are characterized by a certain band gap between their valence and conduction electron bands.20 When a photon having an excitation energy exceeding the semiconductor band gap is absorbed by a QD, electron-hole pairs are generated (electrons are excited from the valence to the conduction band) and the recombination of electron-hole pairs (the relaxation of the excited state) results in the emission of the measured fluorescence light. 

For a deviation from the equilibrium with the background radiation, predictions for the distribution of electrons and holes axe possible under certain assumptions which are justified in most realistic cases. A typical assumption is, for example, that the electrons in the conduction band scatter frequently with vibrating atoms in such a way that the times for momentum relaxation and energy relaxation are short compared to their lifetime in the conduction band, after which they are annihilated in a recombination reaction with a hole. Under these conditions, the distribution of the electrons over the states in the conduction band results in a larger entropy than in any other distribution for the same number of electrons and the same temperature. 

In order to account for such a mechanism, photochemical excitation of a semiconductor surface might induce the promotion of an electron from the valence band to the conduction band. Since relaxation of the high-energy electron is inhibited by the absence of intra-states, if the lifetime of this photo generated electron-hole pair is sufficiently long to allow the interfacial electron transfer from an accumulation site to an electron acceptor, as well as the interfacial electron transfer from an adsorbed organic donor to the valence-band hole, the irradiated semiconductor can simultaneously catalyze both oxidation and reduction reactions in a fashion similar to multifunctional enzymes reactions [232]. 

After core hole formation, relaxation in the valence orbitals can give rise to promotion of valence electrons into unoccupied levels. If this reorganization is fast, and the energy required for this transition is not available to the primary photoelectron, shake-up satellites can show up on the low kinetic energy (high p) side of the main peak. Further loss lines can be created if the photoelectron passing the solid excites group oscillation of the conduction electrons (plasmon loss). 

A detailed study of the N2 emission rates has been carried out by Morrill et al (1998). In this study, the quasistatic electric field model (Pasko et al, 1997) was used to calculate the electric fields, and the solution to Boltzmann s equation was used to calculate the electron energy distribution function as a fimction of altitude. Results for excitation of seven triplet states of N2 are shown in Fig. 12 at A = 65 and 75 km. The temporal diuation of the excitations may be understood in terms of the faster relaxation (higher conductivity see Fig. 9) of the E field at the higher altitude. 

Here, r = t( f) is the relaxation time of those conduction electrons which have acquired the additional momentum hSkx on the Fermi surface and relax back to thermal equilibrium after the electric field is switched off. This relaxation process is an inelastic scattering process in which the electrons which occupy a state A on the Fermi surface, that is, which have wavevectors kp, are scattered into unoccupied states B on the Fermi surface (Fig. 8.5). This scattering can be with a phonon, with a statistical lattice defect, or with an impurity. In a simple metal, the scattering occurs only for the electrons at the Fermi energy, and thus only those electrons which move with the Fermi velocity determine the mobility, and together with it and the concentration n of all the charge carriers, then limit the specific conductivity. 

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