Carrier Transport Phenomena

When an electric field of strength if is applied across a crystal, electrons and holes are forced to move in the material. The corresponding current density is given by 

Accordingly, the mobility decreases with temperature. The mobility influenced by scattering of electrons (or holes) at ionized impurities can be described [2, 7] by 

The carrier diffusion coefficient, D, for electrons and Dp for holes, is another important parameter associated with mobility. It is given by 

It should be emphasized that a carrier transport can only be described by Ohm s law (Eq. 1.35) if sufficient empty energy levels exist in the corresponding energy band and a minimum carrier density is present in the material. On the other hand, in the case of an intrinsic high bandgap semiconductor, the carrier density may be negligible so that only those carriers carry the current which are injected into the crystal via one contact. In this case we have a space charge limited current which is proportional to (Child s law). 

The most common method for measuring the conductivity is the four-point probe technique [10]. Here a small current 1 is passed through the outer two probes and the voltage V is measured between the inner two probes (s is the distance between two probes). When such a measurement is performed with a semiconductor disk of diameter 2r and a thickness w, the resistivity is given by 

At extremely high impurity concentrations, the Fermi level may pass the band edge. In this case, the semiconductor becomes degenerated, and most of the relations derived above are no longer applicable. The semiconductor then shows a metal-like behavior. 

The mobility is a material constant. Values for some typical semiconductors are given in Appendix A.5. Electron and hole mobilities are typically in the range between 1 and 1000 cm V s These values are many orders of magnitude higher than the mobility of molecules and ions in solution ( 10 -10 cm s ). The presence of acoustic phonons and ionized impurities leads to carrier scattering which can significantly affect the mobility. The mobility p- ( or p ), determined by interaction with acoustic phonons, as shown in [2, 7], is given by 

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Abstract. Pentacene organic field effect transistors (OFETs) electrical and structural properties have already been analysed from the point of view of different gate dielectric and growth conditions utilization. The AFM and micro Raman investigations show that the first organic monolayer at the pentacene/dielectric interface are essential determinants of carrier transport phenomena and achievable drain current of pentacene OFETs. 

Several models can explain the carrier transport in organic semiconductors. However, none of them can be independently employed to explain the carrier transport phenomena and the mechanism at the same time. Among the theoretical models, the most often used models are the band transport model (Warta and Karl, 1985 Pemstich et al., 2008 Karl et al., 1991), polaron transport model (Holstein, 1959 Emin and Holstein, 1969 Marcus, 1960), hopping transport model (Vissenberg and Matters, 1998), and multiple trapping and release model (Horowitz et al., 1995 Le Comber and Spear, 1970). 

SUinsh, E.A., Shlihta, G.A., Juigis, A.J. A model description of charge carrier transport phenomena in organic molecular crystals. 1. Polyacene crystals. Chem. Phys. 138, 347-363 (1989)... 

Jaroslaw Jung received his MSc degree in physics in 1987 from the University of Lodz and in electronics in 1990 from the Technical University of Lodz. He earned the PhD inChemistry from the Technical University of Lodz in 2001. Currently, he works in the Technical University of Lodz in the Department of Molecular Physics. His fields of interest cover research of organic semiconductors and construction of equipments for measurement of photoconduction in oi anic semiconductors. He was involved in the realization of many projects concerning investigation of the photogeneration and chaise carrier transport phenomena in the organic semiconductors and application of such materials in optoelectronic devices. 

The transport phenomenon for any spray material released In the air Is foremost a function of the particle size and size distribution of the released spray. The particle density plays a minor role, the settling rate from Stokes law for example varies as the square root of the density. Further, the density differences between liquids commonly used for pesticides Is very little, varying only slightly from water at density of 1 gm/ml. Other formulation physical factors of surface tension, viscosity and viscoelasticity play significant roles In the atomization process. These are altered by the addition of petroleum and vegetable oil as solvents and carriers as well as a host of adjuvants In varying... 

The transport phenomenon occurs when the displacement of the carriers through different media ( process components ) and the passage from one medium to another are realized by a random commutation process ( connection process ). 

An alternative interpretation of the phenomenon of metal-support interactions induced by doping of semiconductive carriers with aliovalent cations is based on the theory of electrochemical promotion or the NEMCA effect. According to this interpretation, the charge carriers transported from the carrier to the metal particles are oxygen ions, which diffuse to the surface of the metal particles, thus altering the surface work function and, subsequently, chemisorptive and catalytic parameters. Work is currently in progress to elucidate the mechanism of induction of metal-support interactions by carrier doping. 

Figure 9.4 illustrates the effects of feed pressure on C02 flux and permeability. As illustrated in this figure, C02 flux increased rapidly with the feed pressure first and then approached a constant value. This can be explained with the carrier saturation phenomenon, which is a characteristic of facilitated transport membranes. As described by Ho and Dalrymple,51 when the partial pressure of C02 is equal to or higher than a critical C02 partial pressure, p[c, the carrier saturation occurs, in which the concentration of C02-carrier reaction product attains its maximum value, CAB, max, and becomes a constant. In other words, further increase in the partial pressure of C02 will not increase the concentration of C02-carrier reaction product. This can be expressed as follows ... 

Hall effect is another important transport phenomenon and has been extensively studied in amorphous semiconductors. The Hall effect studies also assumed importance because of an anomaly observed between the sign of the charge carriers indicated by Hall coefficient and S in amorphous semiconductors. The Hall coefficient Rh is given by. 

This model allows us to describe the evolution of the polyaniline radioelectrical properties for different doping levels. What is interesting in this approach is that physical parameters are taken into account. Moreover, Structural characteristics, such as coherence length, can be recovered. Finally, the calculations we carried out confirm that charge carriers are localised over some benzene rings, the three-dimensional aspect of the transport phenomenon occurs after only about 10 periods. 

Three processes that are of major importance in the phenomenon of photoconductivity are carrier generation, carrier recombination, and carrier transport. These will be discussed in that order, as they relate to homomolecular polycyclic aromatic hydrocarbon (PAH) crystals. It is surprising that the mechanisms of carrier generation and carrier transport in well-characterized crystalline compounds are still subjects for heated dispute. 

The peak width, is larger by 3 5 times and spin density is smaller by 2 4 orders of magnitude than those of iodine-doped polyacetylene [22]. Such a large peak width suggests that the unpaired electrons in the substituted polyacetylene tend to be more localized, probably due to an increase of non-planarity of the polyene chain. From the view point of electrical transport phenomenon, it can be argued that the present polymers have lower mobility and lower concentration of carriers. This may account for the lower electrical conductivity of the substituted polyacetylenes including the present PCH and BP polymers. 

Widdas s quantitative model of the simple carrier was able to explain a number of earlier observations and to make predictions about what would be observed in more complex experiments on membrane transport. Thus it was a highly productive scientific insight. One of the earlier, apparently anomalous, results that the theory explained was the dramatic fall of membrane permeability found for solutes which were rapidly transported as solute concentration was increased. For example, in the human red blood cell, Wilbrandt and colleagues had previously measured a permeability constant for glucose which was 1000 times higher in dilute solutions of glucose than it was in a concentrated solution. This phenomenon, subsequently called saturation kinetics, is formally equivalent to the fall, as substrate concentration increases, in the proportion of substrate converted to product by a limited amount of an enzyme. 

Further demonstrations of this sort of counterflow phenomenon for many different substrates in virtually every type of cell have been used as functional hallmarks of carrier-mediated transport. Experimental demonstration of this effect precludes transport being mediated either by simple diffusion or by fixed pores in the membrane. In reviewing 20 years of experimental work related to the carrier hypothesis, LeFevre (1975) lists a number of key functional properties of carrier mediated transport, all of which have stood the test of the subsequent 20 years. These include saturation of transport with increased substrate concentration and associated phenomena such as competition between similar substrates, high rates of unidirectional transport, and countertransport. Also covered are flux coupling (including trans effects and cotransport), chemical specificity, inhibition by protein-specific reagents, hormonal regulation, and a steep dependence of the rate of transport on temperature (included only to bemoan its common inclusion in textbooks ). 

The phenomenon of ambipolar conduction is not limited to chemical potential gradients only, and may occur in systems with several driving forces (e.g., chemical-potential and temperature gradients in combination with external electrical field). However, this phenomenon is always related to conjugate transport of several charge carriers. 

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