Generation and transport of holes

The overvoltage for ihe generation and transport of holes, ii p, ac, is the difTerence between the quasi-Fermi level of interfacial holes and the Fermi level enso of electrons in the electrode interior as defined in Eqn. 10-29  

For p-type electrodes in the dark and in the photoexdted state, the concentration of majority charge carriers (holes) is sufficiently great that the Fermi level eptso of the electrode interior nearly equals the quasi-Fermi level of interfacial holes hence, the overvoltage Up sc for the generation and transport of holes in the space charge layer is zero even as the transfer of anodic holes progresses as expressed in Eqn. 10-30  

For n-type electrodes in the dark, the transfer of anodic holes reduces the concentration of interfacial holes (minority carriers) so that the quasi-Fermi level pEfj of interfacial holes is raised beyond the Fermi level efcso (pej ertso) of the electrode interior, hence, a positive overvoltage Up sc emerges due to the diffusion of holes in the electrode as shown in Eqn. 10-31  

This negative overvoltage in the anodic hole transfer reaction may better be called the undervoltage or the inverse overvoltage (the negative overvoltage in the anodic reaction) rather than the usual overvoltage which is positive in the 

The energy equivalent to the inverse overvoltage corresponds to the gain of energy due to the absorption of photons in n-type semiconductor electrodes. 

---

The transfer of anodic holes is associated with the following three processes the generation and transport of holes in the electrode the hole transfer across the compact layer and the diffusion of redox particles in aqueous solution. The total overvoltage, T], is the sum of the three overvoltages np sc for the generation and transport of holes in the electrode, ria for the transfer of holes across the electrode interface, and ii4ur for the diffusion of redox particles in the solution as defined in Eqn. 10-27 ... 

Since the overvoltage iip,sc for the generation and transport of holes is a negative quantity, the total overvoltage becomes negative when the magnitude of Ti p, sc exceeds t) h the condition usually occims with photoexcited n-type electrodes. This provides the basis for the fact that the potential for the onset of anodic hole transfer at photoexcited n-type electrodes is more cathodic (n ative) than the potential for the onset of anodic hole transfer at p-type electrodes of the same semiconductor or at metal electrodes. 

Fig. 10-22. Overvoltages in an anodic hole transfer (a) at a photoexcited n-type electrode and (b) at a p-type electrode of the same semiconductor iih = overvoltage for hole transfer across an interface = inverse overvoltage due to generation and transport of photoexcited holes in an n>type electrode.

Fig. 10-28. Polarization curves for cell reactions of photoelectrolytic decomposition of water at a photoezcited n-type anode and at a metal cathode solid curve M = cathodic polarization curve of hydrogen evolution at metal cathode solid curve n-SC = anodic polarization curve of oxygen evolution at photoezcited n-type anode (Fermi level versus current curve) dashed curve p-SC = quasi-Fermi level of interfadal holes as a ftmction of anodic reaction current at photoezcited n-type anode (anodic polarization curve r re-sented by interfacial hole level) = electrode potential of two operating electrodes in a photoelectrolytic cell p. sc = inverse overvoltage of generation and transport ofphotoezcited holes in an n-type anode.

As shown in Eqn. 10-46, the difference in the polarized potential at constant anodic current, between the photoexcited n-type and the dark p-type anodes of the same semiconductor, represents the inverse overvoltage iip sc for the generation and transport of photo-excited holes. 

Like the performance of chemical reactors, in which the transport and reactions of chemical species govern the outcome, the performance of electronic devices is determined by the transport, generation, and recombination of carriers. The main difference is that electronic devices involve charged species and electric fields, which are present only in specialized chemical reactors such as plasma reactors and electrochemical systems. Furthermore, electronic devices involve only two species, electrons and holes, whereas 10-100 species are encountered commonly in chemical reactors. In the same manner that species continuity balances are used to predict the performance of chemical reactors, continuity balances for electrons and holes may be used to simulate electronic devices. The basic continuity equation for electrons has the form... 

Latent image fonnation involves the creation of free electron-hole pairs by the absorption of an image exposure and the displacement of these carriers by a field. Experimental techniques for characterizing these phenomena are of considerable importance to xerography. This section reviews experimental methods for measuring parameters that describe charge generation and transport phenomena. 

In materials where the photogeneration involves the surface-enhanced dissociation of an exciton, as is generally the case for the phthalocanines, the photogeneration efficiency defined by Kanemitsu and Imamura represents the fraction of photons that create exitons that diffuse to the interface between the generation and transport layers. The injection efficiency then represents the fraction of pairs that dissociate into free electrons and free holes. The field dependence of the photogeneration efficiency was described by the Onsager theory. A primary quantum yield of 0.50 was reported. Values of the thermalization distance and the injection efficiency were not cited. 

Scott et al. (1990) reported that the activation energy for the hole mobility in DEH doped polymers is less in polymers that form charge-transfer complexes. It was also shown that the residual potential is related to the energy differences between the highest occupied molecular orbitals of the generation and transport materials. The effects of the different polymers on hole mobilities are discussed in Chapter 8. Endo et al. (1994) has shown that polymer effects on the mobility are also related to the photoreceptor sensitivity. 

With the Monte Carlo method, the sample is taken to be a cubic lattice consisting of 70 x 70 x 70 sites with intersite distance of 0.6 nm. By applying a periodic boundary condition, an effective sample size up to 8000 sites (equivalent to 4.8-p.m long) can be generated in the field direction (37,39). Carrier transport is simulated by a random walk in the test system under the action of a bias field. The simulation results successfully explain many of the experimental findings, notably the field and temperature dependence of hole mobilities (37,39). 

---