Recombination in the space charge

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... 

Here, the ratio of the photocurrent, photo to the incident photon flux, 70, (corrected for reflection) is the photocurrent conversion efficiency, Since eqn. (3) takes no account of recombination in the space-charge region or at the interface, it represents an upper limit to the photocurrent conversion efficiency. Several treatments of recombination have been discussed in the literature [7], but they lie outside the scope of the present chapter. 

Figure 20. Schematic representation of p-type semiconductor/electrolyte interface under illumination. Semiconductor side is divided into space charge region (SCR) and field free region (FFR) at x = W. Numbers in the figure represent the following steps (1) Excitation of an electron from the valence band to the conduction band, leaving a hole in the valence band. (2) Recombination in the bulk. (3) Recombination in the space charge region. (4) Electron transfer from the conduction band to an oxidized state. (5) Electron capture by a surface state. (6) Electron transfer from the surface state to the oxidized state (electron transfer via surface state). (7) Hole capture by the surface state (surface recombination via surface state). There is also a possibility of direct recombination of a conduction band electron with a valence band hole, although this step is not shown in the figure.

Guibaly et al.154-156 took into account not only charge transfer kinetics and surface recombination but also the recombination in the space charge region and the effect of separation between the quasi-Fermi level of minority carrier and that of majority carrier. 

So far only the recombination in the bulk and at the surface of the semiconductor are considered and the recombination in the space charge region is neglected. The assumption is valid only if the transit time of the photogenerated minority carriers across the depletion region is less than the minority carrier lifetime.151 167... 

P. Panayotatos and H. C. Card, Recombination in the space-charge region of Schottky barrier solar cells, Solid State Electron. 23 (1980) 41-47. 

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... 

It should be emphasized that the previous models only describe the current due to minority carriers. Under near-flatband conditions, the majority carriers start to contribute to the overall current. This can be recognized by an increase in the dark current, and under those conditions (2.64) and (2.65) are no longer useful. Another implicit assumption is the absence of mass transport hmitations in the electrolyte, but this is rarely an issue in photoelectrochemistry due to the high electrolyte concentrations and modest efficiencies reported thus far. Finally, it should be realized that the models described above cannot accormt for recombination at the semiconductor/electrolyte interface. Wilson pubhshed an extension of G tner s original model that included interfacial recombination effects [56]. Although this somewhat complicated model is not often used because it does not account for the dark current and recombination in the space charge, it is of value for metal oxides that show extensive surface recombination. 

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... 

Here, it is assumed that the applied field fully drops over the n-type side of the junction. Eq. (21) is only valid if electron-hole pairs do not recombine in the space-charge region, or at the surface. For practical devices this assumption usually does not hold, but to avoid complications we shall not consider these types of electron-hole pair recombination here. 

To simplify the analysis, recombination in the space charge region is ignored, and surface electron-hole recombination is formulated in terms of the surface concentration of majority carriers present in the dark. Consider an n-type semiconductor electrode with a space charge region. If the diffusion length of holes, Lp, is much smaller than W, the flux of holes, Jp, into the surface under steady-state conditions is given by [cf. Equation (18.12)] ... 

It was shown in 1957 that while normally a = 1, the recombination in the space charge region can lead to a = 2. We shall therefore, without further enquiry, study (3.4) in the generalised form (3.4a)... 

Choo. Carrier generation-recombination in the space charge region of an asymmetrical p-n junction... 

Recombination in the space charge region dramatically increases the voltage needed to achieve a given level of current injection. It can be shown that the exponent in the diode equation is modified to yield ... 

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