Recombination in the space charge layer

Figure 20. Comparison of calculated current voltage profiles in the dark (curve d) and under illumination (curves a-c). Curve a is obtained from the basic Gartner model. Curve b considers surface recombination and curve c considers both surface recombination and recombination in the space-charge layer. These simulations are for an n-type semiconductor-electrolyte interface. (Reproduced with permission from Ref [230].)...

With the assumptions that (1) there is negligible recombination in the space charge layer and at the surface and all the carriers generated in the space charge layer are driven by the field to the surface, and (2) the electrode reactions are sufficiently fast, using Eq. (1.83) the contribution due to photogeneration in the depletion layer can be described by... 

Several techniques can be used to determine the flatband potential of a semiconductor. The most straightforward method is to measure the photocurrent onset potential, ( onset- At potentials positive of (/>fb a depletion layer forms that enables the separation of photogenerated electrons and holes, so one would expect a photocurrent. However, the actual potential that needs to be applied before a photocurrent is observed is often several tenths of a volt more positive than ( fb- This can be due to recombination in the space charge layer [45], hole trapping at surface defects [46], or hole accumulation at the surface due to poor charge transfer kinetics [43]. A more reliable method for determining ( fb is electrolyte electroreflectance (EER), with which changes in the surface free electron concentration can be accurately detected [47]. The most often used method, however, is Mott- chottky analysis. Here, the 1/ Csc is plotted as a function of the applied potential and the value of the flatband... 

Seeing this limitation, Jarrett proposed a revised model that allows for recombination in the space charge layer [8]. Jarrett considered the effects of low mobility on device efficiency by first examining the influence of mobility on the transit time, x the time required for minority carriers to cross the space charge layer. The transit time is calculated as... 

The schemes in Figs. 44 and 45 may serve to summarize the main results on photoinduced microwave conductivity in a semiconductor electrode (an n-type material is used as an example). Before a limiting photocurrent at positive potentials is reached, minority carriers tend to accumulate in the space charge layer [Fig. 44(a)], producing a PMC peak [Fig. 45(a)], the shape and height of which are controlled by interfacial rate constants. Near the flatband potential, where surface recombination... 

When a semiconductor electrode is at the flat band potential, photoexdted electrons and holes are soon annihilated by their recombination. In the presence of a space charge layer, however, the photoexdted electrons and holes are separated, vrith each moving in the opposite direction under an electric field in the space charge layer as shown in Fig. 10-4. 

In photoexcited n-type semiconductor electrodes, photoexcited electron-hole pairs recombine in the electrodes in addition to the transfer of holes or electrons across the electrode interface. The recombination of photoexcited holes with electrons in the space charge layer requires a cathodic electron flow from the electrode interior towards the electrode interface. The current associated with the recombination of cathodic holes, im, in n-type electrodes, at which the interfadal reaction is in equilibrium, has already been given by Eqn. 8-70. Assuming that Eqn. 8-70 applies not only to equilibrium but also to non-equilibrium transfer reactions involving interfadal holes, we obtain Eqn. 10-43 ... 

In general, the following equation is used, taking into account the electron-hole recombination at the surface and in the space charge layer,... 

In the model presented here, only recombination in the bulk of the semiconductor has been considered. It is well known from solid state junction (minority carrier devices) that also recombination within the space charge layer can taken place. In this case, a quality factor n, ranging between 1 and 2, is introduced. Then Eq. (45) has to be replaced by... 

A system in which only majority carriers (electrons in n-type) carry the current, is frequently called a majority carrier device . On the other hand, if the barrier height at a semiconductor-metal junction reaches values close to the bandgap then, in principle, an electron transfer via the valence band is also possible, as illustrated in Fig. 2.8a. In this case holes are injected under forward bias which diffuse towards the bulk of the semiconductor where they recombine with electrons ( minority carrier device ). It is further assumed that the quasi-Fermi levels are constant across the space charge region i.e. the recombination within the space charge layer is negligible. In addition Boltzmann equilibrium exists so that we have according to Eqs. (1.57) and (1.58)... 

In calculations of efficiency, Xt is to be compared with the carrier lifetime in the space charge layer, Tr. From a qualitative standpoint, if Xi > Tr, a sizable proportion of minority carriers generated inside space charge layer will recombine before making it to the semiconductor/electrolyte interface. Taking a quantitative approach, Jarrett solved the diffusion equation for an illuminated planar semiconductor/electrolyte interface and calculated incident photon-to-current efficiency (IPCE) for systems with varying xJxb. [8]. One series of calculations used as... 

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