Current-voltage relation

Studies of double carrier injection and transport in insulators and semiconductors (the so called bipolar current problem) date all the way back to the 1950s. A solution that relates to the operation of OLEDs was provided recently by Scott et al. [142], who extended the work of Parmenter and Ruppel [143] to include Lange-vin recombination. In order to obtain an analytic solution, diffusion was ignored and the electron and hole mobilities were taken to be electric field-independent. The current-voltage relation was derived and expressed in terms of two independent boundary conditions, the relative electron contributions to the current at the anode, jJfVj, and at the cathode, JKplJ. 

The above mechanistic aspect of electron transport in electroactive polymer films has been an active and chemically rich research topic (13-18) in polymer coated electrodes. We have called (19) the process "redox conduction", since it is a non-ohmic form of electrical conductivity that is intrinsically different from that in metals or semiconductors. Some of the special characteristics of redox conductivity are non-linear current-voltage relations and a narrow band of conductivity centered around electrode potentials that yield the necessary mixture of oxidized and reduced states of the redox sites in the polymer (mixed valent form). Electron hopping in redox conductivity is obviously also peculiar to polymers whose sites comprise spatially localized electronic states. 

For an interface described by a constant Helmholtz potential electron exchange between the semiconductor and redox electrolyte solution. The result is that dV = d(psc, and for a non-equilibrium system one can obtain the current-voltage relation ... 

Under non-equilibrium conditions, the current-voltage relation can be described as... 

Figure 17-6 Observed current-voltage relation for electrolysis of 0.2 M CuS04 in 1 M HCIO4 under N2, using the apparatus in Figure 17-5.

In contrast to such asymmetrical cells, in a symmetrical polarization cell (cells 4 and 6) variation of the voltage is not of great worth, as this only affects the magnitude of the P0 variation around the mean value. (The corresponding current voltage relations are discussed in Ref.242 243). Nonetheless a mean value of [Pg.90]

Fig. 4.7 Typical current-voltage relation for a voltage-dependent resistor.

Additional information with respect to the mechanism of the grain boundary resistance can be obtained from temperature- and voltage-dependent impedance measurements. The grain boundary semicircle varies, for example, considerably with the applied dc bias (Fig. 39a). The current-voltage relations calculated from such bias-dependent impedance measurements are thus non-linear. In the logarithmic plot (Fig. 39b) it can be seen that the low bias regime exhibits a non-linearity factor a (= d og(I/A)/d og(U/ V)) of almost one (ohmic behavior), while at a bias value of about 0.35 V this factor changes to a x 2. 

The current-voltage relation is obtained by integrating the field F(x ) over the thickness d of the sample... 

Figure 13. Current-voltage relations for synthetic PHBus/polyP ( ) and E. coli PHB/polyP channel complexes (A). The conductance of the channel for Ca2+ in symmetric solutions, under the experimental conditions described in Figure 12, is 101 6 pS for the synthetic channels and 104 12 pS for the E. coli channels. The data points represent mean values of 10 observations.28...

It is interesting to compare these values with the result of another method, the analysis of current-voltage relation for space-charge-limited currents. Such a study on a-sexithienyl [229] has given an effective mobility p, 2 x 10 2 cm2/V s, limited by traps 0.28 eV above the top of the valence band. Thus the trap-free microscopic mobility is likely to be at least two orders of magnitude larger, a typical value for a molecular crystal. 

Figure 25 Current-voltage relation [log /j versus V] of an Al ftww-PA Au Schottky diode. (From Ref. 245.)...

Figure 29 (a) Current-voltage relation (b) light intensity-injected current relation for a MEH-PPV diode. (From Ref. 298.)... 

A considerable amount of work has been done on the deposition of H2 gas at cathodes and on O2 gas at anodes. The reduction of H+ ions at a metal cathode to form H2 gas is no less complex than the process of catalytic hydrogenation. The current-voltage relation is very sensitive to trace impurities in the solution and also to the metal used and its conditioning. The data obtained with smooth Pt and Pd electrodes has been interpreted as due to a slow recombination of sorbed H atoms, while on Hg the mechanism has been presented as a slow H atom transfer from HaO near the surface to the metal electrode. 

This relation is identical to that derived for a pn-junction (see e.g. [89]) (solid curve in Fig. 14). It also looks similar to the current-voltage relation derived for a majority carrier transfer, as given by Eq. (42), both relations differ only by the pre-exponential factor. The first case, i.e. limitation by surface kinetics (Eq. (44)), is difficult to realize, because the majority carrier transfer becomes dominant for redox systems, the standard potential of which is located in the middle of the gap. 

Nonlinear corrections Nonlinear corrections in current-voltage relations are only relevant in the proximity of y pC. Well below jpc the resistance 9ts = L/cre s of the saturated state determines the membrane performance. Above ypc the residual conductivity of dehydrated domains determines the performance. 

The first and third parentheses on the right hand side of Eq. (86) represent the electrodes and electrolyte contact resistances and the second term represent the bulk resistance of the electrolyte. Substitution of Eqs. (78-86) into (85) gives the following current-voltage relation, or polarization equation, for PEMFC... 

The provocative idea Donovan and Wilson (DW) (3,A) introduced into the discussion is that even for times tfree chain motion prevails the transport velocity is still field-saturated because of formation of an acustic polaron which becomes bigger as it moves in an electric field (5). A transition between defect controlled to free chain motion will therefore not be revealed by a change in the current voltage relation measured in course of a transient photoconductivity experiment. We briefly recall the experiment (3,4) that led to the above conclusion ... 

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