Mid-gap states

Fig. 5. A schematic band structure and molecular orbital diagram for a conjugated polymer containing no mid-gap states.

In a band structure model, the partial oxidation or reduction of an extended r-system is described as creating new electronic states in the original band gap (mid-gap states), a process which is, of course, closely related to the creation of charge carriers.140... 

Fig. n.lO. Unpassivated and Zn-passivated CdS eigenvalue spectra for 46 A nanocrystals. Passivation removes the mid-gap states as shown in the inset to the two panels. The zero of energy corresponds to the Fermi energy for bulk CdS. Adapted from [75]. 

In the SSH model, both neutral and charged solitons will show an absorption peak at half the energy gap between HOMO and LUMO. Experimentally, both charged solitons and neutral solitons are claimed to be photogenerated and they show absorption features which are distinct and at two different frequencies [174, 175]. This feature is believed to be due to electron-electron interactions. It is by now well established that electron correlations remove the notion of a mid-gap state in the neutral odd-polyene compounds this is demonstrated by the fact that in undistorted finite polyenes, the optical gap of both odd and even polyenes plotted as inverse chain length, fall on the same straight line in the PPP and the Hubbard models [176] and extrapolate to the same infinite chain value. In the dimerized case, while the odd and even chains extrapolate differently [177], the optical gap in the infinite chain limit are quite close in value. However, in the SSH model, the odd and even car-... 

The quantum confined nature of carriers in these systems strongly manifests itself in the optical properties of these materials. To fully realise the possibilities offered by these materials, it is crucial to not just understand the underlying physics but also to be able to accurately predict the material behaviour over a broad range of conditions. The central theme of quantum confinement, that is, the evolution of physical properties with size, determines not just the basic photophysics, but also provides the opportunities for addressing a wide range of applications. Experimentally, the onset of quantum confined regime is most easy to detect in the absorption and fluorescence spectra. Both techniques further provide rich information on other aspects of the electronic properties of these finite sized solids, including aspects such as mid gap states, traps, etc. 

The sp -bonded zeolite type structures are obtained from natural silica frameworks by substituting the silicon atoms with carbon and removal of oxygen. We demonstrate that considering n-type doping such structures [46-48] behave very much like diamond. A mid-gap state occurs after a substantial relaxation of the impurity which is localized on a nearby carbon atom. 

Fig. 4.3. The mid-gap state and associated soliton distortions for an odd-site chain.

These geometric properties of the chain are also associated with mid-gap states (Pople and Walmsley 1962). To see this, consider the energy spectrum of an even-site chain. There are N/2 states in each of the valence and conduction bands. As a result of particle-hole symmetry, every valence band state with energy e" = e maps into a conduction band state with energy = —e. Thus, the energy spectrum is symmetric about e = 0, as shown in Fig. 3.4. Now, for an odd-site chain there are N — l)/2 states in each of the valence and conduction bands, and one localized gap state. As a consequence of particle-hole symmetry the localized state lies at e = 0. This mid-gap state is occupied by one electron, and is associated with the soliton, as shown in Fig. 4.3. 

Fig. 4.4. The normalized, staggered bond dimerization, of the ground state of an odd-site chain obtained by iterating eqn (4.21). The wavefunction of the mid-gap state, is also shown.

Also shown in Fig. 4.4 is the single-particle wavefunction, of the mid-gap state, which is localized at the soliton. In the continuum limit, a,... 

Fig. 4.9. The occupancy of the mid-gap states (left) by a doped particle, and the associated polaronic distortion of the chain (right).

Figure 4.11 shows the probability density of the Wannier orbitals associated with the mid-gap states. Although the relative separation of Wannier orbitals is small with an extrinsic dimerization of = 0.1, the fact that there are two... 

Figure 4.11 shows the probability density of the Wannier orbitals associated with the mid-gap states. Although the relative separation of Wannier orbitals is small with an extrinsic dimerization of = 0.1, the fact that there are two distinct Wannier orbitals implies that the argument employed in Section 4.6 -concerning the different characters of the 1 B and 1 B+ states after electron-lattice relaxation - is a general one. Thus, the 1 B state is comprised of spinless electron-hole pairs, while the l B state is comprised of two spin-1/2 objects. These become confined in the presence of extrinsic dimerization. We would therefore expect that, as before, the different character of the PB and 1 S+ states will be evident by the different type of geometrical distortions when electron-electron interactions are included. 

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