Mobility edges

Normally the defect density is low, and electronic transport is considered to occur predominantly at the mobility edges. For electron transport one can write the following expression for the conductivity a ... 

Fig. 2-33. Electron energy and state density in amorphous semiconductors A and C = diffuse band tail states B = gap states, cmc = mobility edge level for electrons MV = mobility edge level for holes ...

Electrons in the diffuse band tail states migrate in accord with the hopping mechanism rather than the band mechanism. The energy gap between the mobility edge Cue for electrons and the mobility edge mv for holes is called the mobility gap, Emt, instead of the band gap, C(. 

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. ... 

Disordered systems localization, the Anderson transition and the mobility edge... 

If the Anderson criterion is not satisfied then, as first pointed out by Mott (1966), since states are likely to become localized in the tail of a band, there exists a critical energy Ec (the mobility edge )f separating localized from non-localized states (Fig. 1.21). The simplest definition of Ec in terms of the behaviour of the conductivity a(E) is as follows ... 

Fig. 1.21 Density of states in an Anderson band, with the two mobility edges Ec and E c.

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. 

Economou et al. (1985) and Soukoulis et al. (1985, 1986, 1987) have used somewhat similar methods to calculate both the density of states, the mobility edge and the conductivity as a function of energy for the case of diagonal disorder their work is limited to disorder parameters V0 less than one-fifth of the bandwidth B, and is therefore relevant to the band tail... 

Fig. 5.7 Suggested position of the mobility edge Ee as a function of field H, as suggested by Shapiro (1984). If the mobility edge lies at A in the absence of a field, increasing the field...

In liquids, if F crosses the mobility edge c, no discontinuity in the Knight shift is expected, because the timescale of the nuclear resonance is long compared with the time in which atomic movement will change the positions of the localized states. If Warren s interpretation of his measurements on liquid tellurium alloys is accepted, there is certainly no discontinuity in K when this happens. 

We note that at the consolute point the conductivity is still metallic, the appearance of an activation energy e2 occurring for somewhat lower concentrations. The reason for this, in our view, is as follows. The consolute point should occur approximately at the same concentration as the kink in the free-energy curve of Fig. 4.2, namely that at which the concentration n of carriers is of order given by n1/3aH 0.2. Above the consolute point there is no sudden disappearance of the electron gas as the concentration decreases its entropy stabilizes it, so metallic behaviour extends to lower concentrations, until Anderson localization sets in. Conduction, then, is due to excited electrons at the mobility edge, as discussed above. 

Fig. 4.19, The tunnelling luminescence kinetics for the Ej-, Tb3+ pairs in Na20 3Si02-Tb3+ glass. The ultraviolet excitation was at 120 K with further short thermal excitation of electrons above the mobility edge (curve 1) and prolonged heating up to 70 K below the excitation...

Azbel, M.Ya. and Platzman, P.M. (1981). Evidence for a positron mobility edge in gaseous helium. Solid State Cornmun. 39 679-681. 

Canter, K.F., Fishbein, M., Fox, R.A., Gyasi, K. and Steinman, J.F. (1980). Is there a positron mobility edge in gaseous helium Solid State Commun. 34 773-776. 

Farazdel, A. (1986). Confirmation of the positron mobility edge in gaseous helium by Monte Carlo simulation. Phys. Rev. Lett. 57 2664-2666. 

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