Electron models charged-particle state

Appendix A The Lorentz Condition Appendix B Electron Model of Present Theory B.l. General Equations of the Equilibrium State The Charged-Particle State... 

The new states can either be interpreted in the band picture as polarons and/or bipolarons which occur due to electron-phonon coupling after ionization (see below) (electron-electron interaction is neglected) or as the new HOMO and LUMO states in charged particles if localized molecular orbitals are assumed (electron-electron correlation is taken into account, electron-phonon coupling neglected). Both models will be discussed in parallel in the following subsections. However, in general discussions the band stmeture terms will be used as they are more common in literature. 

Parker [55] studied the IN properties of MEH-PPV sandwiched between various low-and high work-function materials. He proposed a model for such photodiodes, where the charge carriers are transported in a rigid band model. Electrons and holes can tunnel into or leave the polymer when the applied field tilts the polymer bands so that the tunnel barriers can be overcome. It must be noted that a rigid band model is only appropriate for very low intrinsic carrier concentrations in MEH-PPV. Capacitance-voltage measurements for these devices indicated an upper limit for the dark carrier concentration of 1014 cm"3. Further measurements of the built in fields of MEH-PPV sandwiched between metal electrodes are in agreement with the results found by Parker. Electro absorption measurements [56, 57] showed that various metals did not introduce interface states in the single-particle gap of the polymer that pins the Schottky contact. Of course this does not imply that the metal and the polymer do not interact [58, 59] but these interactions do not pin the Schottky barrier. 

Orientational disorder and packing irregularities in terms of a modified Anderson-Hubbard Hamiltonian [63,64] will lead to a distribution of the on-site Coulomb interaction as well as of the interaction of electrons on different (at least neighboring) sites as it was explicitly pointed out by Cuevas et al. [65]. Compared to the Coulomb-gap model of Efros and Sklovskii [66], they took into account three different states of charge of the mesoscopic particles, i.e. neutral, positively and negatively charged. The VRH behavior, which dominates the electrical properties at low temperatures, can conclusively be explained with this model. 

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