Recombination of minority carriers

For n-type semiconductor electrodes in which a redox reaction of cathodic hole iiyection reaches its quasi-equilibrium state at the electrode interface, the recombination current of iiqected holes (minority charge carriers) with electrons (minority charge carriers), w, is given by Eqn. 8-70 [Reineke-Memming, 1992]  

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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. 

Consideration of the rates of arrival, charge transfer, trapping and recombination of minority carriers leads to expressions for the time dependent surface concentrations (cm-2) of free ps,(Tee and trapped pJ>trap holes ... 

One other problem which arises in dealing with deep space charge region is the part played by the barrier in limiting the recombination of minority carriers at the surface. In the papers of Bardeen and Brattain (6), Stevenson and Keyes (16),... 

Fig. 32. Injection and recombination of minority carriers for a n-type semiconductor electrode...

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. 

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... 

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.

Frequently it has been observed with n-type as well as with p-type electrodes in aqueous solutions that the onset potential of the pure photocurrent differs considerably from the flatband potential. The latter can be determined by capacity measurements in the dark as illustrated by the dashed line in the ij — Ub curve in Fig. 8 a. This effect is usually explained by recombination and trapping of minority carriers created by light excitation at the surface. It is obvious that these effects have a negative effect... 

Thus, nonequilibrium electrons and holes generated by light in a corroding semiconductor are consumed to accelerate the corresponding partial reactions. Simultaneous disappearance of these carriers in the course of photocorrosion is similar, from the formal point of view, to surface recombination. This gives every reason to speak about such processes as electrochemical recombination (Belyakov et ai, 1976). If the dark corrosion rate and equilibrium concentration of minority carriers are known, the rate of electrochemical recombination can be calculated. 

If neither of these goals can be realized, layered semiconductors may not become useful electrode material in either semiconductor liquid junction or Schottky junction devices. Fortunately, evidence is already being obtained that the negative effects due to steps can be at least temporarily and partially alleviated (35, 36). Future development of chemical methods to inhibit deflection of minority carriers to the edges of steps and to reduce the high recombination rates at steps may open the way for the use of polycrystalline layered chalcogenide semiconductors in solar cell devices. 

Recombination in the depletion layer can become important when the concentration of minority carriers at the interface exceeds the majority carrier concentration. Under illumination minority carrier buildup at the semiconductor-electrolyte interface can occur due to slow charge transfer. Thus surface inversion may occur and recombination in the depletion region can become the dominant mechanism accounting for loss in photocurrent. 

Mechanisms 1 and 2 are included in the model that is used here for comparison with experimental data. Interface recombination and dark current effects are not included however, the experimental data have been adjusted to exclude the effects of dark current. To include the additional bulk and depletion layer recombination losses, the diffusion equation for minority carriers is solved using boundary conditions relevant to the S-E junction (i.e., the photocurrent is linearly related to the concentration of minority carriers at the interface). Using this boundary condition and assuming quasi-equilibrium conditions (flat quasi-Fermi levels) ( 4 ) in the depletion region, the following current-voltage relationship is obtained. 

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