Charge carrier equilibria

The exchange of charge carriers in the molecular sphere at the zinc/electrolyte solution phase boundary corresponds to equal anodic and cathodic currents. These compensate each other in the case of equilibrium. 

To determine correlation between (t) and nd, therefore, to find out the type of dependence f let us consider the occupation kinetics for ASS levels by free charge carriers. The capturing of charge carriers occurring during transition of adsorption particles into the charged form will be considered, as usual, in adiabatic approximation, i.e. assuming that at any moment of time there is a quasi-equilibrium and the system of crystallites is characterized by immediate equilibrium values and L inside the conduction (valence) band. 

One can readily conclude from expression (1.119) - (1.126) that conditions in gaseous phase affect the values of equilibrium concentrations of all point defects and, therefore, the concentration of free charge carriers. 

Holes, which initiate the dissolution process, are minority charge carriers in n-type electrodes. The concentration of holes nh is very low in n-type Si under equilibrium conditions. The hole concentration can be increased by illumination or by... 

For n-type semiconductor electrodes in which a redox reaction of cathodic hole iiyection reaches its quasi-equilibrium state at the electrode interface, the recombination current of iiqected holes (minority charge carriers) with electrons (minority charge carriers), w, is given by Eqn. 8-70 [Reineke-Memming, 1992] ... 

Fig. 10-13. Anodic transfer of pho-toexdted boles (minority charge carrier) at an n>type semiconductor electrode E( -e 9o/e) = electrode potential E% (= — c /e) = potential of the valence band edge B02 (= - = equilibrium...

The potential, E, for the onset of the photoexdted reaction relative to the equilibrium electrode potential E of the same reaction can also be derived in a kinetics-based approach [Memming, 1987]. Here, we consider the transfer of anodic holes (minority charge carriers) at an n-type semiconductor electrode at which the hole transfer is in quasi-equilibrium then, the anodic reaction rate is controlled by the photogeneration and transport of holes in the n-type semiconductor electrode. The current of hole transport, has been given by Eqn. 8-71 as a function of polarization ( - ,) as shown in Eqn. 10-20 ... 

As suggested in Fig. 4.3 the charge carrier formation in step (a) may be compared to a dissociation leading to the following equilibrium... 

As shown in Fig. 3.6, for intrinsic (undoped) semiconductors the number of holes equals the number of electrons and the Fermi energy level > lies in the middle of the band gap. Impurity doped semiconductors in which the majority charge carriers are electrons and holes, respectively, are referred to as n-type and p-type semiconductors. For n-type semiconductors the Fermi level lies just below the conduction band, whereas for p-type semiconductors it lies just above the valence band. In an intrinsic semiconductor tbe equilibrium electron and bole concentrations, no and po respectively, in tbe conduction and valence bands are given by ... 

Fig. 4.12 Diagram illustrating space charge layer formation in microcrystalline and nanocrystalline particles in equilibrium in a semiconductor-electrolyte interface. The nanoparticles are almost completely depleted of charge carriers with negligibly small band bending.

However, one should be cautious about overinterpreting the field and temperature dependence of the mobility obtained from ToF measurements. For instance, in the analyses of the data in [86, 87], ToF signals have been considered that are dispersive. It is well known that data collected under dispersive transport conditions carry a weaker temperature dependence because the charge carriers have not yet reached quasi-equilibrium. This contributes to an apparent Arrhenius-type temperature dependence of p that might erroneously be accounted for by polaron effects. 

In fact, in their recent work, Mensfoort et al. [90] conclude that in polyfluorene copolymers hole transport is entirely dominated by disorder. This is supported by a strictly linear In p cx dependence covering a dynamic range of 15 decades with a temperature range from 150 to 315 K (Fig. 8). Based upon stationary space-charge-limited current measurement, where the charge carriers are in quasi equilibrium so that dispersion effects are absent, the authors determine a width a of the DOS for holes as large as 130 meV with negligible polaron contribution. 

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