Charge transport band model

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. 

Fig. 8.8 Model of charge transport and band structure of macroscopic polycrystalline (A) and (B) nano crystalline metal oxide semiconductors (a) in their initial state and (b) after exposure to reducing gas (adapted from Franke et al., 2006)...

The conductivity is a solid-state phenomenon, and, as pointed out already, conductivity is not a single chain phenomenon. The band-gap description of a conjugated chain is a one-dimensional model. Additionally, considerably interchain charge transport is necessary to describe a metal-like behavior in the highly doped three-dimensional sample and further transfer mechanisms across the polymer chains have to be discussed. What one actually needs to know in explaining conductivity of organic polymers is how the charge transport proceeds... 

An expression for the internal space-charge field can be obtained through the Kukhtarev model [38] that was developed to describe photorefractivity in most inorganic materials. In this model, the photorefractive material is described by a band model. As for a traditional semiconductor, the material consists of a conduction and a valence bands separated by a band gap as shown in Fig. 13. The model describes the transport of single carrier species and the band gap of the material contains localized energy levels that can be excited optically promoting either holes in the valence band (VB) or electrons in the conduction band (CB). In the model that we adopt here, we assume that the dopant is a donor with an energy level located in the band gap with concentration N. Furthermore, the crystal contains Nj acceptors with that are all ionized and that have accepted a... 

The simplest model of charge transport in delocalized bands is the Drude model, which assumes the carriers are free to move under the inhuence of an applied electric held, but subject to collisional damping forces. Note that the scattering centers are not the nuclei of the background material, but rather phonons (lattice vibrahons) or impurities. A statistical equahon for estimahng the mean drift velocity of the carriers in the direction of the electric held may be written as... 

The electron transfer model presented here recalls the process of charge transport in semiconductors that is, a conduction band is populated by a thermalized electron, which then moves freely through the semiconductor via wavelike k states. While the possibility of semiconductorlike electron transfer in biological systems was first raised many years ago by DeVault and Chance [93], it has never been found experimentally in fact, there was reasonable skepticism that nature would choose such a mechanism in natural biological systems [84]. The density matrix method allows one to construct a model in which the conditions for such a process can be clarified and investigated in a detailed way. 

What is the origin of the charge transport phenomena and what do these experimental observations tell us about the material We show that the Mott-CFO model can answer these questions at least to first order, with the additional assumption that the density of localized band-tail states falls off exponentially away from the mobility edges. In this picture, the time-dependent charge transport is dominated by the statistical process associated with the progressive thermalization of electrons (or holes) into the band-tail states. We confine the discussion to electrons and assume that it can be generalized to holes trivially. 

---