Electron-defect scattering

Since the number of phonons increases with temperature, the electron-phonon and phonon-phonon scattering are temperature dependent. The number of defects is temperature independent and correspondingly, the mean free path for phonon defect and electron defect scattering does not depend on temperature. 

The thermal conductivity of a pure metal is lowered by alloying, whether the alloy formed is a single phase (solid solution) or multiphase mixture. There are several reasons for this. First, electrons are scattered by crystal imperfections and solute atoms (electron-defect scattering). Second, a substantial portion of the thermal conductivity in alloys, in contrast to that of pure metals, is by phonons, Kph (phonons are the sole contribution in electrically insulating solids) and phonons are also scattered by defects. Finally, electron-phonon interactions limit both Kei and Kp. ... 

The bandwidth of UPS features contains information on electron/hole-phonon/vi-bration interaction, electron (hole) lifetime, and electron-defect scattering provided... 

Electron-defect scattering. Real surfaces always contain a nonnegUgible amount of defects, such as steps or impurity atoms. The associated electron-defect scattering mainly changes the electron momentum. If we regard a phonon as a distortion of the ideal lattice, it is in many aspects similar to electron-phonon scattering. 

The effect of electron-defect scattering has been studied in photoemission by Kevan [71, 122]. For the Shockley surface state, an increase in the linewidth with... 

Defects might also be created by thermal excitations through anharmonic effects. In such cases, special care has to be taken to separate the contributions from electron-phonon and electron-defect scattering [123]. 

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 ... 

Electron dynamic scattering must be considered for the interpretation of experimental diffraction intensities because of the strong electron interaction with matter for a crystal of more than 10 nm thick. For a perfect crystal with a relatively small unit cell, the Bloch wave method is the preferred way to calculate dynamic electron diffraction intensities and exit-wave functions because of its flexibility and accuracy. The multi-slice method or other similar methods are best in case of diffraction from crystals containing defects. A recent description of the multislice method can be found in [8]. 

Compared with the momentum of impinging atoms or ions, we may safely neglect the momentum transferred by the absorbed photons and thus we can neglect direct knock-on effects in photochemistry. The strong interaction between photons and the electronic system of the crystal leads to an excitation of the electrons by photon absorption as the primary effect. This excitation causes either the formation of a localized exciton or an (e +h ) defect pair. Non-localized electron defects can be described by planar waves which may be scattered, trapped, etc. Their behavior has been explained with the electron theory of solids [A.H. Wilson (1953)]. Electrons which are trapped by their interaction with impurities or which are self-trapped by interaction with phonons may be localized for a long time (in terms of the reciprocal Debye frequency) before they leave their potential minimum in a hopping type of process activated by thermal fluctuations. 

Crystallographic defects, in general, are also electronic defects. In metals, they provide scattering centers for electrons, increasing the... 

The effect of backward defect scattering is more subtle. There are coupled flow equations for t-1, gt, and Kp [see Eq. (12) for its definition]. The main effect of the disorder is to generate an effective electron backward scattering proportional to t 1 that subtracts to gt and accordingly acts to decrease Kp. There are three possible sets of fixed points. 

Gjpnnes, J. Disorder and defect scattering, thermal diffuse scattering, amorphous materials. In Electron Diffraction Techniques, Cowley, J.M., Ed. Oxford University Press New York, 1993 Vol. 2, 223-259. 

It has been shown that the spin-Hall effect may arise from various spin-orbit couphngs, such as a spin-orbit (SO) interaction induced by the electron-impurity scattering potential,a Rashba SO conphng in two-dimensional systems, etc. Murakami et al. also predicted a nonvanishing spin-Hall cnrrent (AHC) in a perfect Luttinger bnlk p -type semiconductors (no impurities or defects)." Experimental observations of the spin-Hall effect have been reported recently in a n -type bnlk semiconductor and in a two-dimensional heavy-hole system. ... 

Presently, methods are being developed that focus on the use of superresolution confocal Raman microscopy (CRM), electron back-scattered diffraction (EBSD), and, in combination with high-resolution XRD, to identify and measure the stress distributions of structures and defects that control... 

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],... 

FIGURE 8.2 Thermal conductivity of aluminum and copper as a function of temperature [3]. Note that at low temperature, the thermal conductivity increases linearly with temperature. In this regime, defect scattering dominates and the mean free path is independent of temperature. The thermal conductivity in this regime depends on the purity of the sample. The linear behavior arises from the linear relation between the electronic heat capacity and temperature. As the temperature is increased, phonon scattering starts to dominate and the mean free path reduces with increasing temperature, lb a large extent, the thermal conductivity of a metal is independent of the purity of the sample. 

In pure metals the electron-phonon interaction is inversely proportional to the number of thermal phonons Te-ph 7 [1]. This result is valid for pure limit 97- / 1 qr is thermal phonon wave vector, / is the electron mean free path) [2,3]. In dirty limit qt / 1) electrons mostly scatter from defects and impurities and the electron-phonon interaction demonstrates more complicated behavior. According to the theoretical analysis made by Thouless [4] and Reizer [3] the relaxation time is proportional to T Te.pf x T ) in the case of full phonon drag of scattering centers. 

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