Polaronic transport

During the polaron transport therefore, this polaron formation energy behaves as an additional barrier for hopping. Thus the polaronic conductivity, due to the carriers which are excited above the mobility edge, is given by. 

Good examples of small polaron transport are the glasses containing transition metal ions in two valence states such as (V, V ), (Fe, Fe ), (Cu, Cu ) and (Mo , Mo ). In all of them, when the electron jumps from the lower valent ion to the higher valent ion, the lattice distortion also moves along with the electron. Mott derived an expression for the polaronic d.c. electrical conductivity of glasses containing transition metal ions. 

fields the behaviour of conductivity of amorphous semiconductors as a function of co follows the same universal behaviour as 

The loss tangent is simply, tan5 = The real part of the a.c. 

For g(x) to be proportional to 1/x, it requires the relaxation time to be an exponential function of some random variable such that x = xq exp ( ), where itself has a flat distribution. It means that ( ) = constant, and rt(x) = n ). (d /dx) oc x. If a, the polarisability, is also a function of then it can lead to a sub-linear frequency dependence of a (co). The functional form given for the variation of x can arise from two different relaxation mechanisms. The first is a classical barrier hopping, in which two energetically favourable sites like in a double well potential are separated by a barrier fV and = W/kT. The second mechanism is a phonon assisted quantum tunneling through a barrier, which separates two equilibrium positions, in which case = 2aR, where a is the localization length and R is the separation between the sites. In the first case, by treating JV as independent of R, it has been shown (Poliak and Pike, 1972) that 

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Hopping Models Hole-Resting-Site and Phonon-Assisted Polaron Transport... 

Many other time parameters actually enter - if the molecule is conducting through a polaron type mechanism (that is, if the gap has become small enough that polarization changes in geometry actually occur as the electron is transmitted), then one worries about the time associated with polaron formation and polaron transport. Other times that could enter would include frequencies of excitation, if photo processes are being thought of, and various times associated with polaron theory. This is a poorly developed part of the area of molecular transport, but one that is conceptually important. 

Fishchuk II, Kadashchuk A, Bassler H, Nespurek S (2003) Nondispersive polaron transport in disordered organic solids. Phys Rev B 67 224303... 

Another mechanism that has been proposed is that the carriers move as small polarons20. A small polaron is a carrier that is self trapped in a well created by the lattice distortion. This lattice distortion is formed when a carrier stays sufficiently long in a position to polarize the medium around it. The applied field can lower the polaron barrier in a PF fashion and increase the mobility. The polaron transport model is attractive in that the mobilities in this mechanism are not critically dependent on the sample preparation. 

Fig. 4 The photoinduced infrared conductivity solid line) in the insulator precursor of LSCO. The dotted line indicates a simulation based on the small polaron transport theory [4]...

The mid-IR peak has been explained due to the small polaron formation since the early days of the cuprate research. A support for this assignment is the photoinduced conductivity measurement [4] the photoinduced conductivity in LSCO (Fig. 4) shows a very similar peak to the mid-IR peak of the optical conductivity in the V = 0.02 sample. It is also qualitatively explained by the small polaron transport theory [4]. However, this mid-IR peak assignment contradicts the assignment that the Drude-like peak is due to the coherent motion of holes since the former assumes that the hole-lattice interaction is so strong that doped holes become small polarons, while the latter does opposite. Therefore, if we assign that the mid-IR peak is due to small polaron formation, we have to abandon the assignment that the Drude-like peak is due to the coherent motion of doped-holes. 

Photoinduced optical studies show that positive (P+) and negative (P ) polaron levels exist inside the n-n bandgap of EB associated with benzenoid and quinoid levels, respectively.17 They are believed to play an important role in charge injection and transport. We propose the following mechanism for the SCALE device operation. Under low bias voltages, electrons and holes can be injected from the electrodes into the quinoid and benzenoid levels of EB and form negative and positive polarons, respectively. These polarons transport to the EB/PPy interfaces via... 

Similarly the temperature dependence of a has been derived as a oc 7, where a = 1 - 5 In (l/(toTo)). In the case of small polarons there is a strong local polarization and an associated polaron formation energy, Wp. Due to the strongly localized nature of the distortions, there may not be any overlap between small polarons and the corresponding activation energy is simply Wn Wp/2, which is independent of the inter-site separation R. The small polaron transport is therefore characterized by a modified s value, which is given by. 

In this section, after a brief introduction of the OFET operation principles, we outline the main signatures of the intrinsic polaronic transport observed in the experiments with single-crystal OFETs. We compare them to the results of TOF and space-charge limited current (SCLC) experiments that probe charge transport in the bulk. 

Because of the small size of polarons in molecular crystals, the conduction channel in organic transistors extends in the transverse direction for only a few molecular layers [20-22]. For the same reason, polarons interact strongly with chemical impurities and structural defects. As a result, polaronic transport in organic OFETs is very sensitive to the morphology of the semiconductor surface and to the presence... 

Increasing the purity of organic crystals and reducing the contact resistance in OFETs is another challenging direction of future experimental work, which will help to extend the temperature range where the intrinsic polaronic transport can be studied. The development of more advanced techniques for purification of molecular materials will enable the expansion of the intrinsic transport regime to much lower temperatures, where the effects of quantum statistics and polaron-polaron interactions should become experimentally accessible. 

Calhoun, M.E., Hsieh, C., and Podzorov, V., Effect of shallow traps on polaron transport at the surface of organic semiconductors, cond mat/0610851. 

Good examples of small polaron transport are the glasses... 

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