Collisions electron-phonon

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

An elementary treatment of the free-electron motion (see, e.g., Kittel, 1962, pp. 107-109) shows that the damping constant is related to the average time t between collisions by y = 1 /t. Collision times may be determined by impurities and imperfections at low temperatures but at ordinary temperatures are usually dominated by interaction of the electrons with lattice vibrations electron-phonon scattering. For most metals at room temperature y is much less than oip. Plasma frequencies of metals are in the visible and ultraviolet hu>p ranges from about 3 to 20 eV. Therefore, a good approximation to the Drude dielectric functions at visible and ultraviolet frequencies is... 

Equation 6.22 predicts that electronic conductivity is dependent on the electron relaxation time. However, it suggests no physical mechanisms responsible for controlling this parameter. Since electrons exhibit wave-particle duahty, scattering events could be suspected to play a part. In a perfect crystal, the atoms of the lattice scatter electrons coherently so that the mean-free path of an electron is infinite. However, in real crystals there exist different types of electron scattering processes that can limit the electron mean-free path and, hence, conductivity. These include the collision of an electron with other electrons (electron-electron scattering), lattice vibrations, or phonons (electron-phonon scattering), and impurities (electron-impurity scattering). 

Photoelectron spectroscopy of valence and core electrons in solids has been useful in the study of the surface properties of transition metals and other solid-phase materials. When photoelectron spectroscopy is performed on a solid sample, an additional step that must be considered is the escape of the resultant photoelectron from the bulk. The analysis can only be performed as deep as the electrons can escape from the bulk and then be detected. The escape depth is dependent upon the inelastic mean free path of the electrons, determined by electron-electron and electron-phonon collisions, which varies with photoelectron kinetic energy. The depth that can be probed is on the order of about 5-50 A, which makes this spectroscopy actually a surface-sensitive technique rather than a probe of the bulk properties of a material. Because photoelectron spectroscopy only probes such a thin layer, analysis of bulk materials, absorbed molecules, or thin films must be performed in ultrahigh vacuum (<10 torr) to prevent interference from contaminants that may adhere to the surface. 

The velocity relevant for transport is the Fermi velocity of electrons. This is typically on the order of 106 m/s for most metals and is independent of temperature [2], The mean free path can be calculated from i = iyx where x is the mean free time between collisions. At low temperature, the electron mean free path is determined mainly by scattering due to crystal imperfections such as defects, dislocations, grain boundaries, and surfaces. Electron-phonon scattering is frozen out at low temperatures. Since the defect concentration is largely temperature independent, the mean free path is a constant in this range. Therefore, the only temperature dependence in the thermal conductivity at low temperature arises from the heat capacity which varies as C T. Under these conditions, the thermal conductivity varies linearly with temperature as shown in Fig. 8.2. The value of k, though, is sample-specific since the mean free path depends on the defect density. Figure 8.2 plots the thermal conductivities of two metals. The data are the best recommended values based on a combination of experimental and theoretical studies [3],... 

Electron-electron. At room temperature the mean distance between electron-electron collisions is about 10 times that of electron-phonon collisions so electron-phonon scattering is dominant. 

The classical theory of absorption in dielectric materials is due to H. A. Lorentz and in metals it is the result of the work of P. K. L. Drude. Both models treat the optically active electrons in a material as classical oscillators. In the Lorentz model the electron is considered to be bound to the nucleus by a harmonic restoring force. In this manner, Lorentz s picture is that of the nonconductive dielectric. Drude considered the electrons to be free and set the restoring force in the Lorentz model equal to zero. Both models include a damping term in the electron s equation of motion which in more modem terms is recognized as a result of electron-phonon collisions. 

The quantity F is related to the mean time between electron collisions with lattice vibrations. T (i.e., to the problem of electron-phonon scattering). By considering the motion of electrons able to make collisions with lattice vibrations in an electric field E having radian frequency o), it is straightforward to show that the average velocity is... 

In recent decades the thinking of physicists has largely been dominated by attempts to describe systems in terms of linear differential equations and their solutions. Deviations fi om their harmonic behaviour, which lead to non-linear terms in the differential equations, have been treated as perturbations by introducing interactions between the quasi-particles, correspond to the harmonic solutions (electron-electron and electron-phonon collisions, etc.). The idea of the soliton concept is to solve the non-linear differential equations, not by numerical approximations but analytically and to associate new quasi-particles wifli exact solutions, the solitons. 

If electron-phonon interactions proceed along the substrate s surface or approach the surface from beneath, these interactions can induce further emissions from the periphery of the vaporized region. Owing to the lower energies involved, these emissions can be in the form of complete intact molecular species. This spike-based mechanism differentiates itself from cooperative motion by the fact that the former describes a superposition of events by individual atoms/ions making up the lattice, i.e. overlapping collisions within a single collision cascade, as opposed to a cooperative motion of many adjacent atoms. 

The development of ultrashort laser pulses down to pulse durations of 5 x 10 s has opened access to studies of extremely fast transient phenomena. Examples are the relaxation of electrons in semiconductors after their excitation by a short light pulse. The electrons excited with a definite energy tuo into the conduction band thermalize within 10 s by electron-phonon collisions (Figure 10). With a much longer decay constant, they recombine with holes in the valence band before they can be excited again by the next pulse. Such time-resolved studies give important information on the limiting processes for the maximum speed of computers. 

Dephasing is another important broadening process for spectral lines of adsorbates. Elastic collisions of phonons and conduction electrons with adsorbed atoms or molecules disrupt the phases of their induced dipole moments and thus provide surface-specific pathways for phase relaxation. If an adsorbed particle can be considered as a two-level system, both the lifetime of its excited state, T, and the dephasing time, T, contribute to the spectral linewidth 7 as ... 

On an ideally flat metal surface the SEW absorption is related to the electron collisions with phonons, impurities and other electrons. Surface roughness introduces an additional decay path for the SEWs. The reason for this is twofold. 

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