Electron-impurity scattering

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). 

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. ... 

Here rp(k) is the momentum relaxation time which is due to the electron-phonon and electron-impurity scattering,stands for the electron distribution functions of spin a, h(k) is the DP term which serves as an effective magnetic field and is composed of the Dresselhaus term [10] due to the bulk inversion asymmetry (BIA) and the Rashba term [11] due to the structure inversion asymmetry (SIA),... 

After some typical time, r, the electron will scatter off a lattice imperfection. This imperfection might be a lattice vibration or an impurity atom. If one assumes that no memory of the event resides after the scattering... 

The total electrical resistance at room temperature includes tire contribution from scattering of conduction electrons by the vacancies as well as by ion-core and impurity scattering. If the experiment is repeated at a number of high temperarnre anneals, then the effects of temperarnre on tire vacancy conuibu-tion can be isolated, since the other two terms will be constant providing that... 

The main scattering processes limiting the thermal conductivity are phonon-phonon (which is absent in the harmonic approximation), phonon defect, electron-phonon, electron impurity or point defects and more rare electron-electron. For both heat carriers, the thermal resistivity contributions due to the various scattering processes are additive. For... 

The lattice may be distorted because of several reasons as vacancies, interstitials, dislocations and impurities. These lattice defects cause the so-called impurity scattering which produces the term i ei. At low temperatures, i ei is the constant electronic thermal resistance typical of metals. 

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... 

The proportionality factor is the electron mobility, xn, which has units of square centimeters per volt per second. The mobility is determined by electron-scattering mechanisms in the crystal. The two predominant mechanisms are lattice scattering and impurity scattering. Because the amplitude of lattice vibrations increases with temperature, lattice scattering becomes the dominant mechanism at high temperatures, and therefore, the mobility decreases with increasing temperature. 

Theory predicts that the mobility decreases as T 3/2 because of lattice scattering (8). But because electrons have higher velocities at high temperatures, they are less effectively scattered by impurities at high temperatures. Consequently, impurity scattering becomes less important with increasing temperature. Theoretical models predict that the mobility increases as T3/2/nj, in which nx is the total impurity concentration (8). The mobility is related to the electron diffusivity, Dn, through the Einstein relation... 

Summary. We study how the single-electron transport in clean Andreev wires is affected by a weak disorder introduced by impurity scattering. The transport has two contributions, one is the Andreev diffusion inversely proportional to the mean free path i and the other is the drift along the transverse modes that increases with increasing . This behavior leads to a peculiar re-entrant localization as a function of the mean free path. 

Here we report how the single electron transport in Andreev wires at low temperatures T weak disorder introduced by impurity scattering assuming that inelastic processes are negligible. The Andreev wire is clean in the sense that the mean free path is much longer than the wire diameter, 3> a. 

The multiband superconductivity shows up only in the clean limit , where the single electron mean free path for the interband impurity scattering satisfies the condition / > hvF/Aav where vF is the Fermi velocity and Aav is the average superconducting gap [24,28,30,35],... 

The criterium that the mean free path should be larger than the superconducting coherence length must be met. This is a very strict condition that implies also that the impurity interband scattering rate yab should be very small yah (1/2 )(KB/ft)Tc. Therefore most of the metals are in the dirty limit where the interband impurity scattering mixes the electron wave functions of electrons on different spots on bare Fermi surfaces and it reduces the system to an effective single Fermi surface. 

Neutral shallow-impurity scattering is often discussed in papers about transport in TCO films at room temperature [87,88]. The mobility due to neutral impurity scattering was first derived by Erginsoy [89] who scaled the electron scattering at hydrogen atoms to that in a semiconductor by using its dielectric constant and carrier effective mass, which leads to ... 

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