Polaron, drift

To investigate polaron motion we started on the stack, at t=0, a polaron obtained by solution of Eqs. 1-5 with A=0. To apply a constant electric field we took A=Aot. The field is then -AqIc. Aq was chosen to give a moderate field, 5x10 V/cm. For this field numerical integration of the equations of motion gave a polaron drifting smoothly, maintaining its shape, when the stack consisted of the same base pair repeated (Fig. 6). 

Polaron Drift Interchain Hopping Molecular Crystals... 

Both the optical and the acoustic order parameters are used in the analysis of time evolution of the polaron drift. 

While experimental evidence for polaronic relaxation is extensive, other experiments render the polaron models problematic (i) the use of the Arrhenius relation to describe the temperature dependence of the mobility (see above) leads to pre-factor mobilities well in excess of unity, and (ii) the polaron models cannot account for the dispersive transport observed at low temperatures. In high fields the electrons moving along the fully conjugated segments of PPV may reach drift velocities well above the sound velocity in PPV.124 In this case, the lattice relaxation cannot follow the carriers, and they move as bare particles, not carrying a lattice polarization cloud with them. In the other limit, creation of an orderly system free of structural defects, like that proposed by recently developed self-assembly techniques, may lead to polaron destabilization and inorganic semiconductor-type transport of the h+,s and e s in the HOMO and LUMO bands, respectively. 

Let us calculate the correction to the proton polaron direct current density conditioned by light-induced transitions between the sites. This photocurrent calculation is analogous to that of the correction to the drift activation current carried out in the previous subsection [the analogy lies in the fact that operator (276) is similar to the correction to the Hamiltonian if the electric field is taken into account, with the correction being nondiagonal on the operator of the coordinate see expression (236)]. 

The challenging information of this contribution is that in the short time limit a PTS crystal behaves like a conventional semiconductor as far as carrier transport is concerned. Clearly, more work is required, notably, quantitative assessments. However, for reasons of conclstency, the drift velocities measured at highest fields employed in this study cannot exceed those measured earlier (4). This yields a mobility of order 10 cm (Vs)"l, A similar estimates results from the schubweg travelled by a carrier before immobilized by a large barrier. It has to be shorter than the distance travelled between localization events (-10 pm). The conclusion is that carrier motion is polaronic as described by Cade and Mova-ghar (27). 

Fig. 29 Fit to experimental current-voltage data circles) using electric field-dependent polaron pair dissociation, drift, and diffusion broken line) and additionally including space-charge and recombination solid line), a The high-field part (Vo- a > 10°) of the log-log I-V curve allows the determination of charge distance in the polaron pair, b The same data shown on a linear scale. (Reprinted with permission from [59], 2005, American Physical Society)...

Once electrons and holes have been injected into the polymer, they must encounter each other and recombine radiatively to give off light. In this context, the low mobility of the charge carriers (polarons) in semiconducting polymers is helpful since the slow drift of the charge carriers across the thickness of the semiconducting polymer will allow enough time for the carriers to meet and recombine radiatively. 

To understand the transition to supersonic velocities we also make use of a description of the lattice in terms of both optical and acoustic order parameters. Here, we study a strictly ID model that is a direct map of the fPA structure. However, as far as the properties of the drifting polaron are concerned, the model is more general and quantitatively describes these properties in other polymeric systems, e.g., poly(paraphenylene vinylene) or polythiophene. In the ID model, the displacement of the lattice sites entering Equation 2.14 and Equation 2.16 is described by a single variable u . In the description of the geometry of conjugated polymers, fPA in particular, it is common to study a smoothed atomic displacement order parameter. This optical order parameter is given by... 

With an electric field applied to the polymer chain, the self-localized polaron starts to drift along the chain. After a short acceleration phase the velocity becomes constant and the excess energy is dissipated by creation of lattice vibrations. Since the description of the lattice is classical in our model, the energy is dissipated continuously. 

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