Localized carriers

It is not overly difficult to include the effects of interconversion of hydrogen among its charge states if these are equilibrated with the local carrier concentrations and if we continue to neglect complex formation and assume that the spatial scale of the diffusion-migration phenomena is large... 

An IR study of electro-oxidized PS showed a decrease in the OH signal and an increase in the SiO signal with anodization time. This can be interpreted as oxide formation on the PS surface and a removal of electrolyte from the pores. Furthermore a correlation in intensity of localized carrier IR absorption and luminescence indicates that localized states are involved in the red EL [Du4]. 

In an exact calculation of the distribution of the electrostatic potential, the carrier densities and their currents, (4.81)-(4.87) are solved simultaneously, bearing in mind that only the sum of the diffusion and drift currents has physical significance. Due to the complexity of the above relations and in particular due to the coupling of electron and hole concentrations by Poisson s equation, analytical solutions exist only for a few, very specific conditions. Generally, the determination of local carrier concentrations, current densities, recombination rates, etc., requires extensive numerical procedures. This is especially true if they vary with time, but even in the steady state context. 

Peak photocurrents excited In a polymer of bis ( -toluene-sulfonate) of 2,4-hexadlyne-l,6-dlol (PTS) by N2-laser pulses vary superquadratically with electric field. The ratio ip(E)/((i(E), where ()i denotes the carrier generation efficiency, increases linearly with field. This indicates that on a 10 ns scale the carrier drift velocity is a linear function of E. Information on carrier transport kinetics in the time domain of barrier controlled motion is inferred from the rise time of photocurrents excited by rectangular pulses of A88 nm light. The intensity dependence of the rate constant for carrier relaxation indicates efficient interaction between barrier-localized carriers and chain excitons promoting barrier crossing. 

Therefore, by fitting simple Gaussian functions to the features of the spectrum, i.e. the carrier states, the upper Hubbard band and the main absorption edge intensity, the local carrier concentration can be quantified to an accuracy of 5% [11.17]. 

This local carrier energy change results in significant OFET current changes, as shown, for example, in pentacene [17,18] and poly(hexylthiophene) [19] OFETs. While the voltage applied to most OFETs in published accounts... 

The film thickness is d. By multiplying these surface charges by the local carrier mobility n and E = — 50/5r, the local component of the field in the direction of the wave velocity, one obtains two surface currents. Since 6 and E are proportional to 0, these surface currents are second order in 0 and have finite time averages... 

McNeill et al. [113,114] studied the near-field photoluminescence of thin-fihn MEH-PPV induced by a voltage bias applied between the near-field probe and the substrate. The goal was to investigate the field-induced modulation of the local carrier density. The injected carriers recombined giving rise to photoluminescence measured by the NSOM probe. The images under applied bias showed a domain structure similar to those reported by other groups. This indicates that the inhomogeneous polymer structure affects the process both with and without an electric-field-induced carrier injection. 

The shortest possible mean free path is one lattice constant (a) in the limit where X a, the transport is better described as due to hopping of localized carriers, rather than scattering of free carriers. If we consider the hopping limit (mean free path of about one carbon-carbon distance), cm, then T-10 seconds, and p 0.2 cm /V-s. 

However, the low frequency electrical response is not dominated by localized carriers for samples A-D near the IMT. Figure 15.22b shows e((o) for samples A-D. In addition to the dielectric response of localized electrons at 1 eV, a third zero crossing of s co) termed Wp is evident in the far-IR. For energies lower than Wp, s co) remains negative as expected for free carriers. If the carriers are free electrons, then their frequency response is described by the Drude model. At sufficiently high frequencies (t 1/w), the Drude dielectric function is given by... 

A typical fit of the localization-modified Drude model is shown in Figure 15.27 for sample E. To ensure that causality is satisfied, the parameters were chosen (Table 15.5) to describe both values obtained for the localized carrier scattering time Tj are comparable with the values obtained from the Drude fits to [Pg.635]

The microwave frequency dielectric constant ( mw) is a key probe of the delocalization of charge carriers. For delocalized Drude electrons at frequencies less than their plasma frequency, the real part of the dielectric function s a>) is negative due to the inertia of the free electron in an alternating current field [40,103,130,164]. For a localized carrier, the charges can stay in phase with the field and s to) is positive at low frequencies. Thus, the sign of the microwave dielectric constant serves as a sensitive probe of the presence of free electrons and provides independent verification of the IR results. 

The zero crossing (Wpi) at higher energy (1-3 eV) is attributed to the majority of carriers that are localized with short mean free times (t 10 s). For conducting polymers whose dielectric response is dominated by only localized carriers, s (o) is positive in the far-IR and (Zdc, has a strong temperature dependence, and becomes insulating at low T. 

The frequency response of si for PAN-CSA prepared from chloroform and subsequently briefly exposed to m-cresol vapor (crpc 20S/cm) [193] (Fig. 46.26) is characteristic of localized electrons. si is positive at all optical frequencies the scattering due to disorder in these materials has broadened and washed out the dielectric zero crossings. Lorentzian dispersion due to a localized polaron [146] is evident in bi around 12,000 cm (1.5 eV) and for this material increases positively with decreasing wavenumber in the far IR, characteristic of a material with a small residual band gap or localized carriers. Lower conductivity PAN-HCl [193] (ctdc 10 S/cm) materials show even less dispersion with wavenumber. si for these materials is also positive over the whole range and shows only a modest... 

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