Phonon-induced delocalization

The temperature dependence of E, is more difficult to evaluate. The Boltzmann factor in Eq. (7.4) increases the contribution to the conduction from higher energy states as the temperature increases. This gives a negative value to y, with a magnitude which depends on how rapidly o( ) increases with energy. There is another contribution Yt if the shape of o( ) is temperature-dependent. Section 7.4.3 describes a model in which Yt is positive because of phonon-induced delocalization of states below the mobility edge. 

Fig. 7.20. The model of conduction near a mobility edge at elevated temperature, showing the phonon-induced delocalization which enhances the conductivity near E. (Fenz et at. 1985).

When the electron-phonon interaction is included, there may be a phonon-induced delocalization which further broadens the mobility edge and allows conductivity to occur below Ef,. However, sufficiently strong electron-phonon coupling results in polaron formation in the band tails which suppresses the conductivity in the localized states and restores the discontinuous change in a. ... 

PEDOT PSS, 20-24, 20-45-20-46, 20-49 substituted PEDOTs, 20-25 PEDOT/PSS nanowires, 16-5 Peierls instability, 17-3 Pentacene, 2-2, 2-15, 2-16, 2-17, 2-18 Percolation models, 16-2 Percolation transition, 15-12 Pemigraniline, 7-25 Perturbation, 19-3, 19-11, 19-14 Phase diagram, 17-11-17-12, 17-15, 17-24-17-27 Phenyl-fused EDOT, 13-15-13-16 Phonon scattering, 15-13, 15-30 Phonon-assisted tunneling, 16-4 Phonon-induced delocalization, 15-8, 15-12—15-13, 15-41, 15-51, 15-69 Phosphonic add, 9-18, 9-19... 

Phonon Induced Delocalization in disordered solids, localization can result when a wavefunction interferes with itself due to elastic scattering and forms a standing wave. Phonon scattering can destroy this interference effect and cause the wavefunctions to be more extended. 

In delocalized bands, the charge transport is limited by the scattering of the carriers by lattice vibrations (phonons). Therefore, an increase in the temperature, which induces an increase in the density of phonons, leads to a decrease in the mobility. 

Therefore the lack of an observable bleach can only be explained by the cancellation of all contributions to the pump-probe signal, which is the case for a perfect harmonic state. It can be shown that the anharmonicity of a vibrational exciton is a direct measure of its degree of delocalization [5]. Thus, we conclude that the free exciton state is almost perfectly delocalized at 90 K. As temperature increases, a bleach signal starts to be observed, pointing to a non-complete cancellation of the different contributions of the total pump-probe signal. Apparently, thermally induced disorder (Anderson localization) starts to localize the free exciton. The anharmonicity of the self-trapped state (1650 cm 1), on the other hand, originates from nonlinear interaction between the amide I mode and the phonon system of the crystal. It... 

---