Surface recombination rate

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).

Interesting results have also been obtained with light-induced oscillations of silicon in contact with ammonium fluoride solutions. The quantum efficiency was found to oscillate complementarity with the PMC signal. The calculated surface recombination rate also oscillated comple-mentarily with the charge transfer rate.27,28 The explanation was a periodically oscillating silicon oxide surface layer. Because of a periodically changing space charge layer, the situation turned out to be nevertheless relatively complicated. 

Another way to determine the sensitivity factor consists in determining the difference between the PMC minimum (flatband potential) and the PMC maximum in the accumulation region (the infinite and negligible surface recombination rate). This difference can be calculated to be17... 

Fig. 16.3 Quantum yield (QY) for electron and hole transfer to solution redox acceptors/donors as a function of the reduced variables y (related to the surface properties of the catalyst, i.e., ratio between interfacial electron transfer rate and surface recombination rate) and w (related to the ratio between surface migration currents of hole and electrons to the rate of bulk recombination), according to the proposed kinetic model [23],...

It thus appears that even on metal-free SrTi03 conduction-band electrons are the primary reductants. Since similar reaction rates occur on pre-reduced and stoichiometric crystals with disparate depletion layer widths, the electrons do not tunnel through the depletion layer. With no Pt to provide an outlet for electrons at potentials far positive of the flatband potential, strong illumination would flatten the bands almost completely and allow electrons to reach the semiconductor surface. The presence of both electrons and holes at the surface could lead to unique chemistry as well as high surface recombination rates. 

Another way of disappearance of nonequilibrium charge carriers is their recombination at the particle surface (radiative with the rate constant ks>r, and nonradiative with the rate constant ks>n). Of basic importance is the question of whether the surface recombination sites are the sites of the quencher adsorption. In other words, is the quencher adsorption able to result in disappearance of the surface recombination sites. With positive answer, the expression for the surface recombination rate should be written as (k + ks,n)-S-(l - 0a)-e-h, where S is the particle surface area, and 0a is the surface fraction occupied by the quencher (electron acceptor). Otherwise, the latter multiplier (1 - 0J should be excluded. Further we will consider the both cases (1 and 2), compare them with experimental data and choose the case providing a better description of the phenomena observed. 

Figure 90 Injection-limited current j (normalized to jo) vs. applied electric field Fo for (a) l = 0.01, and (b) 0.5 nm, and different surface recombination rates tir(0)/is (as given in the figure). The tunneling constant for the surface recombination o<2 = 10 nm-1, other parameters as in Fig. 87. After Ref. 408. Copyright 1994 Wiley-VCH, with permission.

We saw that the bulk recombination rate was given by eqn. (351) where Cn and Cp are the trap capture rate constants (s 1) and nlr and ptr are defined above. At the surface, the relevant parameter of interest is the surface recombination rate, S, the number of recombining electron-hole pairs per unit area per second, which can be expressed [2] by... 

These equations predict that the effective surface recombination rate, st, decreases as fin0 increases e.g. as the light intensity increases, st should decrease, which corresponds to the Gerischer case (a)- (c) transition, above. 

Fig. 66. Maximum surface recombination rate for Ge as a function of electron concentration n". The intrinsic value nt is marked.

The microwave conductivity is proportional to the number of free electronic charge carriers multiplied by their respective mobilities (the contribution of ions and dipoles can be neglected in a first approximation.). The microwave sensitivity constant S must be obtained by calibration. The potential-dependent photoinduced microwave conductivity (PMC) of a semiconductor resulting from illumination has been calculated analytically as a function of the interfacial charge-transfer and surface recombination rates (Schlichthorl and Tributsch, 1992). The starting point is the general set of equations of the form... 

An O-atom production rate of about 200 torr/sec. by dissociative electron impact is thus indicated, and all other production terms are negligible by comparison. Surface recombination of O-atoms is kinetically similar to that of H-atoms except for a lower diffusion coefficient and molecular velocity by a factor of three. Thus, the effective first order surface recombination rate constant is 6 X 104 y sec. 1 for small y and 5 X 103 sec."1 for y approaching unity. 

Increase and decrease of surface recombination rates of electrons with holes by chemical modifications... 

Separation of Charge Transfer and Surface Recombination Rate... 

Si amounts to approximately 1 ML. Under accumulation conditions. Si oxidation by hole injection processes is difficult because of the large concentration of conduction band electrons in an accumulation layer that leads an increased surface recombination rate. Hole injection into occupied surface states would only be possible if the reaction rate of an oxidized surface defect with the surrounding water were faster than the recombination via conduction band electrons which is unlikely. It is therefore concluded that oxide formation is hkely to have occurred by the procedure where the sample was scanned from open circuit potential (about -0 V) to the peak C2 thus allowing for oxidation under transient depletion conditions. 

S is the distance between the semiconductor surface and the reaction plane at OHP, and Np(x = 0) is the number of photoexcited minority carriers per unit volume in the surface region of the semiconductor which arrive from the interior of the semiconductor to this region. f E, hv) is the Fermi distribution of photoexcited minority carrier. This quantity, Np x = 0), depends on the intensity, energy, and absorption coefficient of incident light, diffusion length of electron in the semiconductor, and its band gap, etc. Furthermore, it depends on the charge transfer phenomena and the surface recombination rate at the interface. The surface recombination rate constant depends on the induced density of surface states due to adsorbed anions at the electrodesolution interface. The recombination rate constant can be expressed as... 

Surface recombination rate constant, Kr, at the interface is one of the most important factors that influence the overall rate, and this quantity depends mainly on the density of surface states, Dss E) and can be determined quantum mechanically, using the Anderson Hamiltonian formalism/ In this expression (76), cTc is the recombination cross section. The value of cTc can be obtained using the scattering theory. Sp E) is the velocity of photoexcited electron, and f E) represents the distribution of surface states which one may consider to be of Gaussian type of distribution, centered at the midgap energy. 

Measuring the surface recombination rate S from the variation of EBIC with increasing electron energy and depth of carrier formation... 

In the present work, the above continuum will be described by means of dimensionless boundary condition parameters, r and r, for positive and negative mobile charge species, respeclively. These parameters may be related to thermally activated heterogeneous rate constants or to surface recombination rates. Although they may sometimes be complex and frequency-dependent in ac situations, such possibilities will not be further considered herein. When r = 0 for a given positive species at a given electrode, the contact is completely blocking for this species. 

It has been shown S5>56>63>64 that when the dimensionless quantities r and/or r are neither zero nor infinite, they may be related to hlterogeneous reaction rate constants, 5. The result is E (D./il)r, where i = p or n. Since is associated with an electrode reaction, it cannot depend on il. Thus, both r and r must be proportional to when they are neither zero nor infinite and are associated with thermally activated reaction rates or surface recombination rates. 

An expression for the quantum efficiency of photoconductors, taking into accoimt reflection coefficients from both the firont and the back side of detector, as well as surface recombination rates on both sides (interference effects are neglected), is [10]... 

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