Electron trapping modelling

Concerning the nature of electronic traps for this class of ladder polymers, we would like to recall the experimental facts. On comparing the results of LPPP to those of poly(para-phenylene vinylene) (PPV) [38] it must be noted that the appearance of the maximum current at 167 K, for heating rates between 0.06 K/s and 0.25 K/s, can be attributed to monomolecular kinetics with non-retrapping traps [26]. In PPV the density of trap states is evaluated on the basis of a multiple trapping model [38], leading to a trap density which is comparable to the density of monomer units and very low mobilities of 10-8 cm2 V-1 s l. These values for PPV have to be compared to trap densities of 0.0002 and 0.00003 traps per monomer unit in the LPPP. As a consequence of the low trap densities, high mobility values of 0.1 cm2 V-1 s-1 for the LPPPs are obtained [39]. 

Figure 1. The tunneling of a single electron (SE) between two metal electrodes through an intermediate island (quantum dot) can be blocked of the electrostatic energy of a single excess electron trapped on the central island. In case of non-symmetric tunneling barriers (e.g. tunneling junction on the left, and ideal (infinite-resistance) capacitor on the right), this device model describes a SE box .

Schiller and Vass (1975) attempted a theoretical correlation between free-ion yield and electron mobility in a trapping model, and thereby further correlation with V. In this model, electrons are trapped due to local energy fluctuations with a probability... 

Baird and Rehfeld (1987) have analyzed the thermodynamics of electron transport in the two-state trapping model. According to these authors, the effective mobility, ignoring the mobility in the trapped state, is given by... 

Thermodynamics of Electron Trapping and Solvation in the Quasi-ballistic Model... 

Mozumder (1996) has discussed the thermodynamics of electron trapping and solvation, as well as that of reversible attachment-detachment reactions, within the context of the quasi-ballistic model of electron transport. In this model, as in the usual trapping model, the electron reacts with the solute mostly in the quasi-free state, in which it has an overwhelmingly high rate of reaction, even though it resides mostly in the trapped state (Allen and Holroyd, 1974 Allen et ah, 1975 Mozumder, 1995b). Overall equilibrium for the reversible reaction with a solute A is then represented as... 

FIGURE 10.5 Standard free energy change, in various liquid hydrocarbons, versus temperature upon electron trapping from the quasi-free state according to the quasi-ballistic model. Reproduced from Mozumder, (1996), with the permission of Am. Chem. Soc. ... 

Leading theoreticians were, however, attracted to the phenomenon and soon suggested models for F centers. In 1930 Frenkel suggested that an F center was an electron trapped in a distorted region of crystal structure, an idea that was incorrect in this instance but led directly to development of the concepts of excitons and... 

It is, however, not clear at present whether such a model can be applied to metal solutions. It is worth mentioning again at this point that the specific conductivity of a saturated solution of lithium in methyl-amine (10) (concentration 5.5M) has been found to be 28 ohm l cm."-1, which is two orders of magnitude lower than that for a corresponding saturated metal-ammonia solution. This experimental result seems to indicate that the overlap between electron trapping centers may not be... 

Model for Electron Trapping in the Frozen Alkali Hydroxide Solutions. Since the line A and the associated 585 mm absorption band in 7-irradiated alkaline ice are not caused by either solvated electrons as such, or their reaction products, we are necessarily led to believe that they are to be attributed to trapped electrons. Any electropositive center can, in principle, be considered capable of functioning as an electron trap. (In this discussion any electron deficient center is considered electropositive.)... 

From the preceding discussion it may be concluded that the main resonance line at g — 2.0006 in irradiated frozen alkali hydroxide solutions is attributable to the radiation-produced electron trapped around a hydrated O- radical ion. Insofar as the latter is an electron vacancy created by the reaction of the radiation produced holes with the OH ions, the trapped electron may be considered to be analogous to an F center formed in alkali halide crystals, where, however, the electron vacancies exist even prior to irradiation. The term trapped electron (symbolized T ) has been used throughout the present paper. This model will be... 

The bipolar single-trap model assumes that both electrons and holes share identical trap centers. Since sequential trappings of the electrons and holes by the identical centers mean the neutralization of the electric charge, the effective space-charge field will depend on the relative power (i.e., the mobilities) of electron and hole transports. The expressions for the writing and erasing diffraction efficiency are [100] ... 

A first test of this model was performed with pressure experiments on InP Yb3+. Here the Yb3+ ion introduces an electron trap to the semiconductor host. The pressure-induced shift of the 2F5/2 -> 2Ft/2 intra 4f shell transitions amounts to 0.96 meV/GPa up to 4 GPa (Stapor et al., 1991), while the bandgap energy of InP increases by 85 meV/GPa (Trommer et al., 1980). 

The electron affinities of adsorbed silver clusters, calculated using Eq. (27), are shown in Table XI. These values indicate that electron-trapping ability of Ag and Ag3 is greater than that of AgBr with the reverse true for Ag2 and Ag4. With inareasing Ag cluster size, EA increases, as expected for isolated Ag clusters and shown in Fig. 7, so that at sufficient size, EA is greater for the cluster than the AgBr model. When this is true, electrons added to the crystal become localized at the Ag cluster where Ag+ reduction takes place. 

Fig. 3.25. Experimental and theoretical J-V characteristics of theAko electron only device at higher temperatures. The solid lines are fits of the theoretical prediction to trap model where the current obeys the power law J = V H, while the symbols are the experimental data. From these measurements characteristic temperature (7c) of 2300 K can be derived [54].

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