Localized tail states

If the maximum width of the energy due to disorder is finite, fV, the width of the localized tail states is also finite. If this disorder energy is much higher than the bandwidth, the entire band gets localized. Semiconducting glasses are often transparent because the tail states have a finite width and are localized. Also, the valence band tail states may not overlap with the conduction band tail states. 

Photoluminescence observed in amorphous chalcogenides (see chapter 11 for a discussion on photoluminescence) can also be understood on the basis of the presence of defect states. Photo-excitation of electrons occurs from states in the valence band to the states in conduction band. The electron energy thermalises and electron recombination with holes takes place in one of the deep-lying localized tail states which causes the... 

Which shows that as L is increased the localized tail states dominate the partition sum until only the ground state remains when Ei — Eg,)L >> 1. 

It should be emphasized that the subtle dependence on the volume of the system is a direct consequence of replica symmetry breaking. In fact, as shown in Fig. 4 the replica symmetric solution does not correctly describe the size of the polymer chain, since it fails to capture the dominance of localized tail states. 

In this chapter we have demonstrated the rich behavior of polymer chains embedded in a quenched random environment. As a starting point, we considered the problem of a Gaussian chain free to move in a random potential with short-ranged correlations. We derived the equilibrium conformation of the chain using a replica variational ansatz, and highlighted the crucial role of the system s volume. A mapping was established to that of a quantum particle in a random potential, and the phenomenon of localization was explained in terms of the dominance of localized tail states of the Schrodinger equation. 

We also gave a physical interpretation of the 1-step replica-symmetry-breaking solution, and elucidated the connection with the statistics of localized tail states. Our coucusions support the heuristic arrguments of Cates ajid Ball, but it starts with the microscopic model. 

The temperature dependence of the total conductivity of As2Te3 is shown in Figure 5.27 for two frequencies. These measurements by Rockstad (1972) show that the a.c. conductivity of the small band gap materials may be composed of three contributions. The low temperature part is proportional to T as described by Eq. (5.33). If this portion is extrapolated to higher T and added to the d.c. conductivity, one obtains less than the total a.c. conductivity. The additional component 02 is also proportional to but rises more rapidly with T than Eq. (5.33). Rockstad (1971, 1972) attributes 02 to hopping conduction in localized tail states. The insert in Figure 5.27 shows that 02 is thermally activated. The slope is always smaller... 

In a-C H, the tail states are dominated by n electrons, which results, as pointed out by Robertson [99, 100], in an enhanced localization as compared to a-Si H, giving rise to higher band tail density of states and also to higher defect density in the midgap. 

As shown in Fig. 2- 3, localized electron levels arise (A and C in the figure) near the band edges at relatively high state densities tailing into the band gap these are called diffuse band tail states. Further, localized electron levels may occur due to dangling bonds and impurities (B in the figure) in the band gap, which are called gap states. 

It is prerequisite to define localized, diabatic state wave fimctions, representing specific Lewis resonance configurations, in a VB-like method. Although this can in principle be done using an orbital localization technique, the difficulty is that these localization methods not only include orthorgonalization tails, but also include delocalization tails, which make contribution to the electronic delocalization effect and are not appropriate to describe diabatic potential energy surfaces. We have proposed to construct the locahzed diabatic state, or Lewis resonance structure, using a strictly block-localized wave function (BLW) method, which was developed recently for the study of electronic delocalization within a molecule.(28-3 1)... 

Fig. 10.1 Two overlapping bands with localized tails. A transition in a liquid can take place when the overlap is sufficiently large that states at EF become delocalized, the...

The recombination process comprises two sequential steps, as illustrated in Fig. 8.1. An excited electron or hole first loses energy by many transitions within the band, in which the energy decrements are small but frequent. This process is referred to as thermalization. The thermalization rate decreases as an electron moves into the localized band tail states and the density of available states is lower. Eventually the electron completes the recombination by making a transition to a hole with the release of a large energy. Recombination lifetimes are generally much longer than the thermalization times, so that the two processes usually occur on distinctly different time scales. 

Non-radiative transitions invariably involve the conversion of excitation energy into phonons. Thermalization involves many inelastic transitions between states in the band or band tails. Three mechanisms of thermalization apply to a-Si H. Carriers in extended states lose energy by the emission of single phonons as they scatter from one state to another. Transitions between localized states occur either by direct tunneling or by the multiple trapping mechanism in which the carrier is excited to the mobility edge and recaptured by a different tail state. 

Examples of the low temperature luminescence spectra are shown in Fig. 8.12. The luminescence intensity is highest in samples with the lowest defect density and so we concentrate on this material. The role of the defects is discussed in Section 8.4. The luminescence spectrum is featureless and broad, with a peak at 1.3-1.4 eV and a half width of 0.25-0.3 eV. It is generally accepted that the transition is between conduction and valence band tail states, with three main reasons for the assignment. First, the energy is in the correct range for the band tails, as the spectrum lies at the foot of the Urbach tail (Fig. 8.12(6)). Second, the luminescence intensity is highest when the defect density is lowest, so that the luminescence cannot be a transition to a defect. Third, the long recombination decay time indicates that the carriers are in localized rather than extended states (see Section 8.3.3). 

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