Recombination surface

Detailed treatments of surface recombination have been given elsewhere [39, 40]. From the point of view of photoelectrochemical kinetics, surface 

The rate of recombination depends on the density of surface states and their occupation with electrons. In the case of an n-type semiconductor, the competition between electron transfer involving the reduced component of a redox couple and surface recombination can be described by the simplified reaction scheme 

Here X is a surface state that is occupied by an electron and is therefore able to capture a hole. Xf is the vacant state created that is now able to accept an electron from the conduction band. The surface concentration of X will depend on the total surface density of surface states and their electron occupancy. The rate constants for hole and electron capture, (3p and f can be defined as the products of the thermal velocities, vp and v and the capture cross sections ap and tr of X and X+. 

The scheme in equation (8.11) is not complete, because a hole that has been trapped at a surface state can also react with the reduced component of a redox couple. This can be written in terms of X+ as 

In principle, all of the steps in equation (8.11) must be reversible in order to satisfy the equilibrium condition in the dark. However, it is often convenient to regard them as irreversible under illumination in order to simplify the description of electron transfer kinetics. 

This equation differs from Eq. (1.55) insofar as we have introduced the carrier densities at the surface, namely and We further assume that during light excitation, quasi-equilibrium exists for the distribution of electrons and holes in the space charge layer, i.e. the surface densities of electrons and holes at the surface are related to the bulk densities, Wb and via the Boltzmann factor. We have then 

This assumption does not include the condition that equilibrium is achieved between electrons and holes (UsPs  

The electron and hole densities are changed from their thermal equilibrium 6n and 6p when electron-hole pairs are created by light excitation. In the bulk, these deviations must be equal to preserve electrical neutrality. Therefore we may write 

The definition of s = 7 /6n is useful because j is a quantity which is independent of 6n and consequently of the light intensity. According to Eq. (2.47), s must pass a maxi- 

In the case of doped semiconductors, the assumption no or 6n po is almost impossible to fulfill for minority carriers under experimental conditions. An increase of the light intensity then leads to a decrease of the surface recombination velocity along the branch determined by the minority carrier density (for details see ref. [5]). 

one obtains the so-called surface recombination velocity (dimension, cms ) 

In order to understand Wilson s treatment in detail, the nature of surface recombination must be considered in more detail. 

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 

The nett surface capture rate ovNt can be estimated by assuming a corresponds to atomic dimensions a 10 16cm2 if v 107cms andiVt 1013cm 2, we have avNt K cms 1, which is a substantial rate constant. 

The expression (364) can be simplified writing t,, = l/iVtCp and t 9 = 1/ Nt C and considering the situation in which we have an n-type semiconductor in which nf n3ps, we find 

For a simple ease where the surface reeombination involves monoenergetic surfaee states the basie processes are illustrated in Fig. 1.23. represents the flux due to capture of eleetrons from the eonduction band, Jc2 the emission of eleetrons into the conduction band, 7vi the capture of holes from the valenee band, and Jy2 the emission of holes into the valence band. The recombination rates of electrons, R , and of holes, / p,s can then be expressed as 

At equilibrium 7 = J. and7vi = Jy2, the reeombination rates are zero. Equation (1.98) can be further expressed as 

FIGURE 1.23. The elemental steps involved in surface recombination via surface states, (a) Flux of capture of electrons, J, and holes, 7, (b) Flux of emission of electrons, 7,2. and holes, 7,2. 

The recombination velocity, which characterizes the recombination process, may vary over a wide range, from 1 to lO cm/s, at room temperature. Surface recombination centers that can be described by the one discrete recombination center model have been found to exist in different sihcon/electrolyte systems. ° The states that can exchange charge carriers with only one of the bands are traps for electrons or holes. Surface states that contribute to the interface capacitance but do not act as the 

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Nonradiative surface recombination is a loss mechanism of great importance for some materials (e.g., GaAs). This effect, however, can be minimized by increasing the electron-beam energy in order to produce a greater electron penetration range. 

A method for quantification of the CL, the so-called MAS corrections, in analogy with the ZAP correction method for X rays (see the article on EPMA), has been proposed to account for the effects of the excess carrier concentration, absorption and surface recombination. In addition, a total internal reflection correction should also be included in the analysis, which leads to the MARS set of corrections. This method can be used for further quantification efforts that also should involve Monte Carlo calculations of the generation of excess carriers. 

Figure 12. Energy diagram of a semiconductor/electrolyte interface showing photogeneration and loss mechanisms (via surface recombination and interfacial charge transfer for minority charge carriers). The surface concentration of minority...

In the depletion region for a band bending U - Ujb> 100 mV, where a reasonably low surface recombination velocity is found, the PMC signal can consequently be approached by... 

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).

Experimental evidence with very different semiconductors has shown that at semiconductor interfaces where limited surface recombination and a modest interfacial charge-transfer rate for charge carriers generate a peak... 

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. 

Therefore, no experimental knowledge is available on interfacial reaction mechanisms under such conditions. These now become accessible via PMC measurements. As theory shows [Fig. 13(b)], the PMC signals in the accumulation region are controlled by potential-dependent surface recombination and charge-transferrates, as well as by the bulk lifetime of charge carriers. 

Surface recombination processes of charge carriers are mechanisms that cannot easily be separated from real semiconductor interfaces. Only a few semiconductor surfaces can be passivated to such an extent as to permit suppression of surface recombination (e.g., Si with optimized oxide or nitride layers). A pronounced dip is typically seen between the potential-dependent PMC curve in the accumulation region and the photocurrent potential curve (e.g., Fig. 29). This dip may be partially caused by a surface... 

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... 

With electrochemically studied semiconductor samples, the evaluation of t [relation (39)] would be more straightforward. AU could be increased in a well-defined way, so that the suppression of surface recombination could be expected. Provided the Debye length of the material is known, the interfacial charge-transfer rate and the surface recombination... 

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. 

Intensity-modulated photocurrent spectroscopy has been used in combination with microwave reflectivity measurements to investigate hydrogen evolution at a p-type silicon45 and an n-type silicon.46 The measurement of amplitude and phase under harmonic generation of excess carriers, performed by Otaredian47 on silicon wafers in an attempt to separate bulk and surface recombination, should also be mentioned here. 

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.

Surface recombination, at semi conductors, 490 Surface reconstruction of gold, 83 and work of Kolb, 86 Surface tension and determination of the potential of zero charge, 32 Surface tension methods, and the potential of zero charge, 32 Surfaces,... 

Another major computational effort is in the area of metals and their chemistry, which comprises the subject of this manuscript. The studies are directed towards both catalysis and the development of improved materials, such as stronger matrix composites. The materials and gas phase work have some overlap. For example, surface recombination affects the heating on the AOTV heat shield and on the walls of the scramjet. In addition, desorption of these molecules from the walls of the scramjet could impact the chemistry in the flow. 

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