Electron mobility localized states

In the above expression, a is the inter-site distance, N(Ec) is the DOS at the mobility edge, J is the overlap integral (which determines E), z is the coordination number and z is the average number of closed three site paths around a given site. The above formulation suggest that the Hall mobility is temperature independent. Assuming that z z, a 3 A and J = BUz 1 eV, pw is about lO cm V s which may be compared with electron mobilities from conductivity studies of about 10 cm V s. xh for hopping electrons in localized states turns out to be even smaller. 

We have supposed that the states are localized from E to E. and extended outside it. Anderson (1958) has shown that electrons in localized states cannot diffuse at T = 0°K. At finite temperatures they presumably can contribute to the conductivity only by phonon assisted hopping. We therefore expect a fall in (E) near E or E. of at least several orders of magnitude, as shown in Figure 3.3b. The energies E and E. are therefore mobility edges (Cohen (1969)). Evaluation of Eq. (3.4) with n (E) and (E)... 

A celebrated derivation of the temperature dependence of the mobility within the hopping model was made by Miller and Abrahams 22. They first evaluated the hopping rate y,y, that is the probability that an electron at site i jumps to site j. Their evaluation was made in the case of a lightly doped semiconductor at a very low temperature. The localized states are shallow impurity levels their energy stands in a narrow range, so that even at low temperatures, an electron at one site can easily find a phonon to jump to the nearest site. The hopping rate is given by... 

Considering the case of electronic transport at a specific energy, the carrier mobility is envisaged as decreasing rather sharply in the vicinity of the boundary between extended and localized states. Consequently, this dividing energy has been termed a mobility edge. ... 

The concept of a mobility edge has proved useful in the description of the nondegenerate gas of electrons in the conduction band of non-crystalline semiconductors. Here recent theoretical work (see Dersch and Thomas 1985, Dersch et al. 1987, Mott 1988, Overhof and Thomas 1989) has emphasized that, since even at zero temperature an electron can jump downwards with the emission of a phonon, the localized states always have a finite lifetime x and so are broadened with width AE fi/x. This allows non-activated hopping from one such state to another, the states are delocalized by phonons. In this book we discuss only degenerate electron gases here neither the Fermi energy at T=0 nor the mobility edge is broadened by interaction with phonons or by electron-electron interaction this will be shown in Chapter 2. 

Localized states in the bulk of a semiconductor that have energies within the bandgap are known to capture mobile carriers from the conduction and valence bands.— The bulk reaction rate is determined by the product of the carrier density, density of empty states, the thermal velocity of the carriers and the cross-section for carrier capture. These same concepts are applied to reactions at semic ijiductor surfaces that have localized energy levels within the bandgap.— In that case the electron flux to the surface, F, reacting with a surface state is given by... 

As the prospective systems for spintronics, two-dimensional semiconducting electron structures where electrons are localized in the -direction and free in the lateral ones, are assumed. High mobilities of electrons (n > I (P cm2/(Vs)) achievable there make the electron transport easy. In order to discuss the possible effects of SO coupling we will consider three types of structures shown in Fig.l. In these structures, the electron states are extended along... 

The purpose of performing calculations of physical properties parallel to experimental studies is twofold. First, since calculations by necessity involve approximations, the results have to be compared with experimental data in order to test the validity of these approximations. If the comparison turns out to be favourable, the second step in the evaluation of the theoretical data is to make predictions of physical properties that are inaccessible to experimental investigations. This second step can result in new understanding of material properties and make it possible to tune these properties for specific purposes. In the context of this book, theoretical calculations are aimed at understanding of the basic interfacial chemistry of metal-conjugated polymer interfaces. This understanding should be related to structural properties such as stability of the interface and adhesion of the metallic overlayer to the polymer surface. Problems related to the electronic properties of the interface are also addressed. Such properties include, for instance, the formation of localized interfacial states, charge transfer between the metal and the polymer, and electron mobility across the interface. 

In addition to creating the distinction between extended and localized states, the disorder also influences the mobility of the electrons and holes above the mobility edges. The carrier mobility is reduced by scattering, which increases with the degree of disorder. Under conditions of weak scattering, the mobility is. 

---