Recombination minority carrier

Relaxations in photoprocesses, which may be due to surface recombination, minority carrier diffusion, or capacitive discharges, are typically measured as transients of photocurrents or photoprocesses. An analysis of such processes in the time domain encounters some inherent problems. 

It is evident from Eq. (94) that the maximum photovoltage depends critically on the exchange current Jo- In the case of pn-junctions, jo is determined by the injection and recombination (minority carrier device). Whereas in Schottky-type of cells jo can be derived from the thermionic emission model (majority carrier device). The analysis of solid state systems has shown that jo is always smaller for minority carrier devices [20,21]. Using semiconductor-liquid junctions, both types of cells can be realized. If in both processes, oxidation and reduction, minority carrier devices are involved, then jo is given by Eq. (37a), similarly as... 

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. 

Recombination. Minority carriers can recombine with majority carriers during the transit time, leading to a loss of charge Ag in time. In a simple approach, recombination is expressed as... 

There are many ways of increasing tlie equilibrium carrier population of a semiconductor. Most often tliis is done by generating electron-hole pairs as, for instance, in tlie process of absorjition of a photon witli h E. Under reasonable levels of illumination and doping, tlie generation of electron-hole pairs affects primarily the minority carrier density. However, tlie excess population of minority carriers is not stable it gradually disappears tlirough a variety of recombination processes in which an electron in tlie CB fills a hole in a VB. The excess energy E is released as a photon or phonons. The foniier case corresponds to a radiative recombination process, tlie latter to a non-radiative one. The radiative processes only rarely involve direct recombination across tlie gap. Usually, tliis type of process is assisted by shallow defects (impurities). Non-radiative recombination involves a defect-related deep level at which a carrier is trapped first, and a second transition is needed to complete tlie process. 

Radiative recombination of minority carriers is tlie most likely process in direct gap semiconductors. Since tlie carriers at tlie CB minimum and tlie VB maximum have tlie same momentum, very fast recombination can occur. The radiative recombination lifetimes in direct semiconductors are tlius very short, of tlie order of tlie ns. The presence of deep-level defects opens up a non-radiative recombination patli and furtlier shortens tlie carrier lifetime. 

The situation is very different in indirect gap materials where phonons must be involved to conserve momentum. Radiative recombination is inefficient, resulting in long lifetimes. The minority carrier lifetimes in Si reach many ms, again in tire absence of defects. It should be noted tliat long minority carrier lifetimes imply long diffusion lengtlis. Minority carrier lifetime can be used as a convenient quality benchmark of a semiconductor. 

Light is generated in semiconductors in the process of radiative recombination. In a direct semiconductor, minority carrier population created by injection in a forward biased p-n junction can recombine radiatively, generating photons with energy about equal to E. The recombination process is spontaneous, individual electron-hole recombination events are random and not related to each other. This process is the basis of LEDs [36]. 

The equihbtium lever relation, np = can be regarded from a chemical kinetics perspective as the result of a balance between the generation and recombination of electrons and holes (21). In extrinsic semiconductors recombination is assisted by chemical defects, such as transition metals, which introduce new energy levels in the energy gap. The recombination rate in extrinsic semiconductors is limited by the lifetime of minority carriers which, according to the equihbtium lever relation, have much lower concentrations than majority carriers. Thus, for a -type semiconductor where electrons are the minority carrier, the recombination rate is /S n/z. An = n — is the increase of the electron concentration over its value in thermal equihbtium, and... 

When electrons are injected as minority carriers into a -type semiconductor they may diffuse, drift, or disappear. That is, their electrical behavior is determined by diffusion in concentration gradients, drift in electric fields (potential gradients), or disappearance through recombination with majority carrier holes. Thus, the transport behavior of minority carriers can be described by a continuity equation. To derive the p—n junction equation, steady-state is assumed, so that = 0, and a neutral region outside the depletion region is assumed, so that the electric field is zero. Under these circumstances,... 

The recombination rate Ptlx, which is defined as the number of generated exci-tons in A/ divided by the number of generated excitons in At plus the number of minority carriers passing through the device in At, for an unbalanced LED (where j(x) jp(x) 3> j (x) and pp pH) is given by the following equation ... 

This means that the PMC signal will, apart from the generation rate of minority carriers and a proportionality constant, be determined by the interfacial charge transfer rate constant kr and the interfacial charge recombination rate sr... 

There is an additional simple relation between the surface concentration Aps of photogenerated minority carriers and the charge recombination and charge transfer rates sr and kr to be considered ... 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

Figure 13. Numerically calculated PMC potential curves from transport equations (14)—(17) without simplifications for different interfacial reaction rate constants for minority carriers (holes in n-type semiconductor) (a) PMC peak in depletion region. Bulk lifetime 10" s, combined interfacial rate constants (sr = sr + kr) inserted in drawing. Dark points, calculation from analytical formula (18). (b) PMC peak in accumulation region. Bulk lifetime 10 5s. The combined interfacial charge-transfer and recombination rate ranges from 10 (1), 100 (2), 103 (3), 3 x 103 (4), 104 (5), 3 x 104 (6) to 106 (7) cm s"1. The flatband potential is indicated.

Figure 14. PMC potential dependence, calculated from analytical formula (18) for different interfacial rate constants for minority carriers S = 1 cm, minority carrier flux toward interface I,- 1 cm-2s 1, a= 780enr1, L = 0.01 cm, 0=11.65 cmV, Ld = 2x 0"3cm), (a) sr = 0 and different charge-transfer rates (inserted in the figures in cm s 1), (b) Constant charge-transfer rate and different surface recombination rates (indicated in the figure).

As outlined at the beginning of this chapter, combined photocurrent and microwave conductivity measurements supply the information needed to determine three relevant potential-dependent quantities the surface concentration of excess minority carriers (Aps), the interfacial recombination rate (sr), and the interfacial charge-transfer rate ( r). By inserting the... 

Other situations may also occur that allow a simple determination of the sensitivity factor. When, for example, a sufficiently negative electrode potential forces all minority carriers to drift into the interior of the semiconductor electrode, where they recombine subject to the bulk lifetime Tfr we will see a limiting PMC signal (given a sufficiently thick electrode). Knowing the photonflux /0 (corrected for reflection), we may expect the following formula to hold ... 

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... 

Figure 44. Energy scheme showing essential phenomena for photoinduced microwave conductivity mechanisms (a) Accumulation of minority carriers near the onset of photocurrents in the depletion region, (b) Drift of minority carriers into the interior of an accumulation region, thus escaping surface recombination.

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