Drift mobility process

A survey is given of the theoretical and experimental studies of electron-ion recombination in condensed matter as classified into geminate and bulk recombination processes. Because the recombination processes are closely related with the magnitudes of the electron drift mobility, which is largely dependent on molecular media of condensed matter, each recombination process is discussed by further classifying it to the recombination in low- and high-mobility media. 

To show this connection, consider an ion-pair as above (Sect. 2.1). Not only may the ion-pair diffuse and drift in the presence of an electric field arising from the mutual coulomb interaction, but also charge-dipole, charge-induced dipole, potential of mean force and an external electric field may all be included in the potential energy term, U. Both the diffusion coefficient and drift mobility may be position-dependent and a long-range transfer process, Z(r), may lead to recombination of the ion-pair. Equation (141) for the ion-pair density distribution becomes... 

There are several techniques for measuring the mobility in a-Si H, most notably the time-of-flight method. All the techniques measure the average motion of the carriers over a time longer than that taken to trap a carrier in the band tail states, so that the drift mobility is always measured, rather than the free carrier mobility. The drift mobility depends on the distribution of traps and the free mobility can only be extracted if the density of states distribution is known. Chapter 3 describes how the time-of-flight experiment is used to determine the shape of the band tail through the analysis of the dispersive transport process. 

Most practical polymer-based electrophotographic photoreceptor systems now in use are in fact solid solutions of an active species in a binder host polymer 11). This system concept embodies the notion of full chemical control of the transport process. Thus, the concentration of dopant molecules directly controls the drift mobility, which is in turn controlled by the overlap of wave functions between active sites. The host polymer binder is then specialized for its mechanical and adhesive properties. Understanding the key features of small-molecule transport provides guidelines for the optimization of injected-carrier range. The key point is to understand how chemically induced traps arise in such systems and how molecularly doped materials containing various contaminants in substantial quantities can still efficiently transport charge. (Even part-per-million concentrations of con-... 

By treating surface recombination as a hopping process in the image charge potential, Scott and Malliaras [140] have derived a very simple equation that describes the injected current as a function of electric field, temperature, and measurable parameters of the organic, namely the dielectric constant, the site density, and the drift mobility. The current has the usual form of thermionic emission, but with an effective Richardson constant that is several orders of magnitude lower than that in inorganic semiconductors. The results of the model are in... 

Further information on the transport processes in a-Si H and on the influence of doping can be obtained, e.g., from measurements of the drift mobility (Allan et al., 1977 Moore, 1977), of the photoconductivity (Rehm et al., 1977 Anderson and Spear, 1977), as well as of the magnetic field dependence of the photo- and dark conductivity (Weller et al., 1981). In this chapter, however, we shall confine ourselves mainly to results of conductivity and thermopower measurements. Some results from Hall effect and photoconductivity studies are also discussed. 

Measurements of the Hall mobility of electrons in nonpolar liquids are few in number, but those that have been made provide information about the transport processes that is not available from drift measurements alone. The Hall mobility, nn, is obtained by measuring the deflection of electrons by a magnetic field while they are drifting in an electric field. Since the deflection occurs only while the electrons are quasi-free, nn is a measure of qf. Measurements of nu that have been done are for liquids of high drift mobility. The results for liquid argon [165] and xenon [166] show that is approximately equal to near the respective triple points. The results for TMS indicate that the ratio is close to unity... 

From this estimation it is apparent that the process of geminate recombination occurs in the case of n-hexane in the time domain of picoseconds. Although at high electric fields the drift mobility does not remain constant (see Section 3.1), Equation 66 can be considered a good approximation for low-mobility liquids. 

We now have a compendium of key equations for the probability of FPT, mean FPT, and probability of successful escape through a particular exit for a general stochastic process obeying Equation 6.84. The drift coefficient A (x) depends on the free energy landscape where the particle is undergoing drift-diffusion process (Equations 6.60 and 6.64). The diffusion coefficient B(x) of the particle is taken to be uniform in most of the cases and it can in principle be position-dependent (Equation 6.61). By inputting the details of the free energy landscape for a specific system, the experimentally relevant quantities associated with the mobility of particles can be calculated from the above formulas. 

In Chap. 4, Debarshi Basu and Ananth Dodabalapur drift velocity and drift mobility measurements in organic field effect transistors. A method is introduced which is based on the time-of-fiight of an electron swarm injected into the channel by a voltage pulse. The method also grants an improved understanding of the injection process, the basic working mechanism of an organic transistor, and the nature of trap distributions. 

If there are no reactions, the conservation of the total quantity of each species dictates that the time dependence of is given by minus the divergence of the flux ps vs), where (vs) is the drift velocity of the species s. The latter is proportional to the average force acting locally on species s, which is the thermodynamic force, equal to minus the gradient of the thermodynamic potential. In the local coupling approximation the mobility appears as a proportionality constant M. For spontaneous processes near equilibrium it is important that a noise term T] t) is retained [146]. Thus dynamic equations of the form... 

The working electrode must be fitted in its holder, tight enough to prevent mobile phase from leaking into the space between the working electrode and its fitting. In practice this process appears to be a major source of noise and drift and is very difficult to overcome. 

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