Bipolaron hopping model

We would expect here that the low carrier mobilities present in the disordered polyacetylene, estimated to be about 10 cm /Vsec, should put the Schottky barriers formed with it in the regime of the diffusion-limited current. We can reasonably take as a value for / the distance between hops estimated from the bipolaron hopping model, equation 11. This is estimated to be 3 nm, so that the inequality is only satisfied at values of Emax in excess of lO V/cm. We note that similar conclusions are made for the analysis of the behaviour of Schottky barriers formed with amorphous silicon/hydrogen alloys [56], though there are claims that the thermionic emission model is effective in this case, in spite of the low carrier mobilities [63]. 

The electronic band structure of a neutral polyacetylene is characterized by an empty band gap, like in other intrinsic semiconductors. Defect sites (solitons, polarons, bipolarons) can be regarded as electronic states within the band gap. The conduction in low-doped poly acetylene is attributed mainly to the transport of solitons within and between chains, as described by the intersoliton-hopping model (IHM) . Polarons and bipolarons are important charge carriers at higher doping levels and with polymers other than polyacetylene. 

At the end of the 80s, the first reports of carriers with a polaronic nature were measured with photo-induced absorption, optical conductivity and infrared reflexivity in LaCu04+x and NdCu04 y [46,47]. The advocate idea was that with the assistance of absorbed light, polarons gain the ability to hop from one localized site to another. The origin of the mid-infra red peak oscillations that register on these experiments was linked to polarons. This picture was supported by related theoretical studies of polarons and bipolarons [48]. It is important to emphasize that these carriers were successfully modeled by Holstein-Hubbard and Holstein t — J... 

Recently Zuppiroli and coworkers [117-119] proposed a polaron/bipolaron model involving correlated hopping and mutiphonon processes as an explanation for the exponential temperature dependence of conductivity. 

However, on the one hand, low ESR signals alone are a weak argument for the assumption of hole bipolarons. On the other hand, several experimental results are in contradiction of this model. For example, (a) the electrical conductivity of boron carbide is maximum at the minimum concentration of BnC icosahedra in the homogeneity range (b) polaron-type effects are restricted to one electron per icosahedron and no corresponding electron-phonon interaction with holes, in particular not with hole pairs in icosahedra, has been proved experimentally (c) the distortion of the icosahedra in boron carbide depends to only a small degree on electron-phonon interaction and (d) the electronic transport in boron-rich solids is due to classical band-type conduction and hopping processes side by side. Hence, the hole bipolaron theory for boron-rich solids can hardly be maintained. 

In conjugated polymers in which transport occurs via hopping between bound soliton-antisoliton pairs such as polarons and bipolarons, the Kivelson s model predicts that the thermopower increases weakly with temperature. At room temperature S 250 iVir . 

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