Electron-scattering mechanisms

It is worthwhile at this point, therefore, to examine in more detail some of the electron scattering mechanisms which govern the various signals involved and to show how detector geometries may be optimized for maximum sensitivity. 

The reflectance, dielectric functions, and refractive indices, together with calculations based on the Drude theory, for the common metal aluminum are shown in Fig. 9.11. Aluminum is described well by the Drude theory except for the weak structure near 1.5 eV, which is caused by bound electrons. The parameters we have chosen to fit the reflectance data, hu>p = 15 eV and hy = 0.6 eV, are appreciably different from those used by Ehrenreich et al. (1963), hup = 12.7 eV and hy = 0.13 eV, to fit the low-energy (hu < 0.2 eV) reflectance of aluminum. This is probably caused by the effects of band transitions and the difference in electron scattering mechanisms at higher energies. The parameters we use reflect our interest in applying the Drude theory in the neighborhood of the plasma frequency. 

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. 

Fig. 102. Schematic shape of the temperature dependence of tc[, and K for a metal when electron-impurity interaction is the main electron scattering mechanism, k,.

However if there is an electronic scattering mechanism present which leads in t(small term aalEp in order to obtain a nonvanishing thermoelectric power. For example the giant thermopowers of Kondo systems are due to that effect. As will be demonstrated below there are also anomalies in the thermopower due to CEF-splitting. 

There are three different electron scattering mechanisms that can lead to excitation (or annihilation) of surface vibrations and are discussed in the following. The dipole scattering is usually the dominating mechanism for electron detection in the specular reflection geometry in which the highest count rate can be achieved. 

MetaUic behavior is observed for those soHds that have partially filled bands (Fig. lb), that is, for materials that have their Fermi level within a band. Since the energy bands are delocalized throughout the crystal, electrons in partially filled bands are free to move in the presence of an electric field, and large conductivity results. Conduction in metals shows a decrease in conductivity at higher temperatures, since scattering mechanisms (lattice phonons, etc) are frozen out at lower temperatures, but become more important as the temperature is raised. 

A type of molecular resonance scattering can also occur from the formation of short-lived negative ions due to electron capture by molecules on surfrices. While this is frequently observed for molecules in the gas phase, it is not so important for chemisorbed molecules on metal surfaces because of extremely rapid quenching (electron transfer to the substrate) of the negative ion. Observations have been made for this scattering mechanism in several chemisorbed systems and in phys-isorbed layers, with the effects usually observed as smaU deviations of the cross section for inelastic scattering from that predicted from dipole scattering theory. 

The theory discussed in this paper treats the biased superlattices as onedimensional systems in a single particle envelope approximation in which the electrons and holes act independently. Scattering mechanisms, which cause a loss of coherence, have not yet been included in the formalism. Loss of coherence represents a significant obstacle to quantum control in... 

Hall and drift mobilities have been measured in mixtures of n-pentane and NP by Itoh et al., (1991) between 20 and 150°C. They found both mobilities to decrease with the addition of n-pentane to the extent that the Hall mobility in a 30% solution was reduced by a factor of about 5 relative to pure NR However the Hall ratio remained in the range 0.9 to 1.5. This indicates that, up to 30% n-pentane solution in NP, the incipient traps are not strong enough to bind an electron permanently. However, they are effective in providing additional scattering mechanism for electrons in the conducting state. 

The term III scattering (equation 8) is the weakest in the three scattering mechanisms, as shown by two derivative terms (M ) in the electronic transition integrals. Clearly, for a dipole forbidden transition (M° = 0) the only non-zero term is term III. The term in scattering results in binary overtone and combination transitions of vibronically active modes. It is noted that no fundamental transition survives. 

For many nonpolar liquids, the electron drift mobility is less than 10 cm /Vs, too low to be accounted for in terms of a scattering mechanism. In these liquids, electrons are trapped as discussed in Sec. 4. Considerable evidence now supports the idea of a two-state model in which equilibrium exists between the trapped and quasi-free states ... 

Note that because of the different scattering mechanisms, the bond lengths determined by X-ray and neutron studies will be different. The neutron determination will give the true distance between the nuclei, whereas the X-ray values are distorted by the size of the electron cloud and so are shorter. 

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