Minority carrier transfer junctions

This relation is identical to that derived for a pure solid state device which is determined by minority carrier transfer and recombination, such as a pn junction (see Section 2.3) or semiconductor-metal contact (see Section 2.2.3). The corresponding current-potential curves in the dark and under illumination are given by the solid lines in Fig. 7.16. Taking the complete Eq. (7.71), there may be a certain potential range where the recombination current determines the process until the current levels off to a constant jy. For very large jy values, the cathodic current can ultimately be diffusion-limited, which can be checked experimentally by using a rotating electrode. 

This relation is identical to that derived for a pure solid state device which is determined by minority carrier transfer and recombination, such as a p-n junction (see Section 2.3) or semiconductor-metal contact (see Section 2.2.3). The corresponding current-potential curves in the dark and under illumination are given... 

The photovoltage is esentially determined by the ratio of the photo- and saturation current. Since io oomrs as a pre-exponential factor in Eq. 1 it determines also the dark current. Actually this is the main reason that it limits the photovoltage via Eq. 2, The value of io depends on the mechanism of charge transfer at the interface under forward bias and is normally different for a pn-junction and a metal-semiconductor contact. In the first case electrons are injected into the p-region and holes into the n-region. These minority carriers recombine somewhere in the bulk as illustrated in Fig. 1 c. In such a minority carrier device the forward current is essentially determined... 

Hot carrier transfer is most likely expected for semiconductors having high carrier mobility, low minority carrier effective mass and of high doping density [167]. The first experiments were reported by Nozik and co-workers for p-GaP and p-InP liquid junctions [168, 166]. Especially InP was a good candidate, because of its high electron mobility. The authors used p-nitrobenzene (U edox = — 0-86 V (SCE)) as an electron acceptor, because the standard potential occurs 0.44 eV above the conduction band at the interface, as shown in Fig. 36. A photocurrent was observed at potentials negative of Ue = -I- 0.15 V. 

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)... 

The situation is quite different if minority carriers are involved. Then electrons and holes are not in equilibrium and their quasi-Fermi levels become different. In the case of an n-type semiconductor, f,p can be located above or below depending on the minority carrier process, i.e. on whether minority carriers are extracted from or injected into the semiconductor. However, quasi-Fermi levels have been qualitatively used in the theory of non-equilibrium processes in solid state devices, such as the excitation and recombination of electrons and holes (see Section 1.6), and also for the descriptions of charge transfer processes in p-n junctions (see Section 2.3). In this section a quantitative analysis of reactions at n- and p-type electrodes in terms of quasi-Fermi levels will be derived [19, 54]. 

Eq. (11.1) is also valid for pure solid state devices, such as semiconductor-metal contacts (Schottky junctions) and p-n junctions, as described in Chapter 2. The physics of the individual systems occurs only in y o- The main difference appears in the cathodic forward current which is essentially determined by /o. In this respect it must be asked whether the forward current is carried only by minority carriers (minority carrier device) or by majority carriers (majority carrier device). Using semiconductor-liquid junctions, both kinds of devices are possible. A minority carrier device is simply made by using a redox couple which has a standard potential close to the valence band of an n-type semiconductor so that holes can be transferred from the redox system into the valence band in the dark under cathodic polarization. In this case, the dark current is determined by hole injection and recombination (minority carrier device) and /o is given by Eq. (7.65), i.e. 

In the absence of surface recombination, all minority carriers that are collected by diffusion and migration in the semiconductor/electrolyte junction will eventually either transfer to redox species in the solution or react with the semiconductor itself leading to anodic or cathodic photodecomposition. Slow interfacial kinetics will result in the build up of photogenerated carriers at the interface, but unless photocurrent multiplication occurs, the saturation photocurrent will simply be determined by the light intensity, and the quantum efficiency will be unity. This means that the photocurrent contains no information about interfacial kinetics. In reality, most semiconductor/electrolyte interfaces are non-ideal, and a substantial fraction of the photogenerated electrons or holes do not take part in interfacial redox reactions because they recombine via surface states (see section 2.3.3). It is this competition between interfacial electron transfer and surface recombination that opens the way to obtain information about the rates of interfacial processes. 

Figures 2.1 and 2.2. The light-generated minority carriers diiFuse and drift towards the electrolyte interface where charge transfer to the respective species (oxidized electrons reduced holes) occurs. The majority carrier current results in injection of the opposite carrier (here electrons) at the counter electrode-electrolyte interface where the opposite redox reaction takes place. The semiconductor-electrolyte junction shown here is characterized by a photovoltage and a photocurrent, that is, the solar cell is operating at or near its maximum power which, in efficient devices, is rather close to the open circuit condition. This is indicated in the inset of Figure 2.12. Therefore, a residual band bending has been shown and the photovoltage under these conditions is given by the quasi-Fermi levels at the surface. Here, only the quasi-Fermi level for holes is shown because Hf( ) only marginally differs from Ef, the Fermi level without illumination.

Buried channel CCDs are fabricated using ion implantation to form a. p—n junction several thousand Angstroms below the surface. With a structure such as the one shown in Fig. 6.4, the potential minimum is not quite at the surface so that the minority carriers do not come into contact with surface states. This has a number of advantages associated with more complete charge transfer and lower noise. A relationship similar to (6.1) can be developed for buried channel CCDs [6.3]. 

The Gaertner model, used for solid state devices, can be used to determine minority carrier diffusion lengths and the flatband potential at semiconductor-electrolyte junctions [53]. With the advent of photoelectrochemical energy conversion in the 1970s, models have been developed that were specifically addressed to the semiconductor-electrolyte boundary [54-59], taking into account the specific situation at the reactive boundary by introducing the charge transfer rate and the surface recombination velocity as parameters. 

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