Hole capture

Figure 3 shows different forms of chemisorption for a C02 molecule. In the weak form of chemisorption the C02 molecule is bound to the surface by two valency bonds, as shown in Fig. 3a. This is an example of adsorption on a Mott exciton which is a pair of free valencies of opposite sign (i.e., an electron-hole pair). This may be either a free exciton wandering about the crystal or a virtual exciton generated in the very act of adsorption. As seen from Fig. 3a, in the case of the C02 molecule the weak form of chemisorption is a valency-saturated and electrically neutral form. As a result of electron capture, this form is transformed into a strong acceptor form shown in Fig. 3b, while as a result of hole capture it becomes a strong donor form shown in Fig. 3c. Both these forms are ion-radical ones. It should, however, be noted that the ion-radicals formed in these two cases are quite different and, having entered into a reaction, may cause it to proceed in different directions.

Sometimes it is possible to dope crystals with impurities which act as electron or hole traps, but if powder e.s.r. spectra suffice, it is convenient to use specific solvents to encourage either specific electron-capture or hole-capture by dilute solutions of suitable compounds. 

Fig. 17. LHeT absorption of the Si-related LVMs in p+-GaAs Si after holes capture by (a) electron irradiation-induced effects and (b) deuterium-related neutralizing complexes. The spectral resolution is 0.1 cm1. J. Chevallier el al., Mat. Res. Soc. Symp. Proc. 104, 337 (1988). Materials Research Society. 

A.C. Morteani, A.S. Dhoot, J.S. Kim, C. Silva, N.C. Greenham, C. Murphy, E. Moons, and R.H. Friend, Barrier-free electron-hole capture in polymer blend heterojunction light-emitting diodes, Adv. Mater., 15 1708-1712, 2003. 

The donor electron level, cd, which may be derived in the same way that the orbital electron level in atoms is derived, is usually located close to the conduction band edge level, ec, in the band gap (ec - Ed = 0.041 eV for P in Si). Similarly, the acceptor level, Ea, is located close to the valence band edge level, ev, in the band gap (ea - Ev = 0.057 eV for B in Si). Figure 2-15 shows the energy diagram for donor and acceptor levels in semiconductors. The localized electron levels dose to the band edge may be called shallow levels, while the localized electron levels away from the band edges, assodated for instance with lattice defects, are called deep levels. Since the donor and acceptor levels are localized at impurity atoms and lattice defects, electrons and holes captured in these levels are not allowed to move in the crystal unless they are freed from these initial levels into the conduction and valence bands. 

Fig. 8-31. Transfer reacdons of redox electrons and holes via sin face states (1) exothermic election capture at surface states c d, (2) adiabatic transfer of electrons from surface states to oxidant particles, (3) exothermic hole capture at sui> face states, (4) adiabatic transfer of holes from surface states to reductant particles.

Equation 9—49 is the anodic transfer of surface cation into aqueous solution (cation dissolution) and Eqn. 9-60 is the anodic oxidation (hole capture) of surface anion producing molecules ofX2, i (e.g. gaseous oxygen molecules irom oxide ions). Electric neutrality requires that the rate of cation dissolution equals the rate of anion oxidation hence, the rate of the oxidative dissolution of semiconductor electrode can be represented by the anodic hole current for the oxidation of surface anions. 

Pig. 10-19. (a) Capture of photogenerated holes in surface states to form siuface ions and (b) anodic dissolution of surface ions to form hydrated ions on an n-type semiconductor electrode Oj = rate of hole capture in surface states oqx = rate of anodic dissolution of surface ions Cn = surface state level S, = surface atom of semiconductor electrode h(vs) = hole in the valence band h(n> = hole captured in smface states h(soH-) = hole in dissolved ions. 

Similarly, the flat band potential also shifts itself at photoexdted n-type semiconductor electrodes on which a transfer reaction involving anodic redox holes occurs via the surface state level e , if the rate of hole capture at the surface state is greater than the rate of hole transfer across the compact layer, as shown in Fig. 10-20(a). 

By its nature, the acceptor bond, like the donor bond, may be purely ionic or purely homopolar or, in the general case, a mixed one. As we shall see below, this depends on how the electron or the hole captured by the particle and participating in the bond is distributed between the adsorbed particle and the adsorption center. In other words, this depends on the type of localization of the electron or the hole, which in turn, is determined by the nature of the adsorbate and the adsorbent. 

The excess free carriers (and excitons) do not represent stable excited states of the solids. A fraction of them recombine directly after thermahzation either radiatively or by multiphonon emission. In most materials, nonradiative transitions to defect states in the gap are the dominant mode of decay. The lifetime of free carriers T = 1/avS is determined by the density a of recombination centers, their thermal velocity v, and the capture cross section S, and may span 10-10 s. Electrons, captured by states above the demarcation level, and holes, captured by states below the hole demarcation level, may get trapped. The condition for trapping is given when the occupied electron trap has a very small cross section for recombining with a free hole. The trapping process has, until recently, not been well understood. 

Another interpretation would be to suppose that the adsorbed sulfide ion forms a surface state that can be directly oxidized by a hole in the valence band. In this case the shift in current onset to lower voltages would be due to an increase in the charge transfer rate rather than the decrease in the recombination rate discussed in the preceeding paragraph. The corrosion suppression associated with the sulfide could then be partially attributed to the rapid kinetics of hole capture by these surface sulfide ions and partially due to reduction of oxidized corrosion sites by sulfide ions in solution. 

Case (L). It is logical to assume here that the further oxidation of an AB unit occurs through consecutive hole-capture steps, so that reaction (5) i... 

The results of this kinetic analysis have been included in Table I. It can be seen that, if both the anodic decomposition of the semiconductor and the anodic oxidation of the competing reactant would occur by irreversible hole-capture steps ((L)(H)(I) or (M)(H)(1)), as was hitherto generally accepted, the stabilization should be independent of light intensity, in contradiction with the results described above. The mechanism in which the reducing agent reacts by donating an electron to a localized surface hole ((L)(X)) leads to an expression in which s is a function of the variable (y/j) only. The three other mechanisms considered lead to the relationship of the type (18), in which s is a function of (y2/j). 

The stabilization of illuminated n-type III-V semiconductor electrodes through competing hole capture by reducing agents added to the aqueous solution has been studied as a function of concentration and of the light intensity. The main result concerns the observed light-intensity dependence. From a kinetic analysis of the stabilization process, it follows that two types of reaction mechanisms can be held responsible for the observed kinetics. 

The photoanodic dissolution of n-silicon in acidic fluoride media provides an example of the complexity of multistep photoelectrochemical reactions [33, 34]. The reaction requires the transfer of four electrons, but it is clear that not all of the steps involve photogenerated holes because the photocurrent quantum efficiency is between 2 and 4. The explanation of the high quantum efficiencies is that the initial hole capture step can be followed by a series of steps in which intermediates with low electron affinity inject electrons into the conduction band. These intermediates can be assigned nominal oxidation states as shown in the following scheme. 

Reaction (8.39d) is responsible for photocurrent doubling since it results in the two electron oxidation of formic acid to C02 for the absorption of only one photon. The electron injection step competes with the hole capture reaction, (8.39c), and as a result the photocurrent quantum efficiency depends on illumination intensity. At high intensities, the supply of photogenerated holes to the surface favours reaction (8.39c), and the quantum efficiency is I. At low light intensities, electron injection becomes predominant, and the quantum efficiency tends towards 2. 

Fig. 8.16. Reaction scheme for photoanodic dissolution of silicon in low intensity limit illustrating the competition between hole capture steps (rate constants k to k ) and electron injection steps (rate constants k to k,). The nominal valence states of the silicon intermediates are indicated. The final product Si(IV) is the soluble hexafluorosilicate species.

Assumption number 4 can be justified as follows. Electrons that survive to reach the electrode do so because their corresponding holes are no longer available for the recombination reaction. While the hole reaction responsible cannot be identified for certain, in light of the information presented in Sections 9.4.1.2 and 9.2.1, it is reasonable to assume that it involves rapid hole capture (on the 0.2-2 ns timescale) by either sulphur vacancies or surface S2- ions. At higher ODRE rotation speeds, the... 

Hole capture by a solute (S) is probably not sufficient to explain the Ps yield enhancement as recombination might well occur as easily between the electron and either M+ (the hole) or S+ (the trapped hole). An explanation to the phenomenon is probably that e+ cannot react with the electron once recombined with M+ whereas it can pick up an electron shallowly trapped by S+. The weakness of recombined S+/e pairs has been shown in some instances in pulse radiolysis experiments, where a delayed formation of e s has been observed from such a state [16]. The concentration range necessary for efficient enhancement of Ps formation is similar to that related to total inhibition, indicating that the processes involved occur on a very short time-... 

The study of the anodic dissolution of semiconductors has played an important role in clarifying the nature of faradaic processes occurring at semiconductor surfaces [112, 113]. In principle, anodic dissolution on such semiconductors as Ge, GaAs, and GaP might proceed either by hole capture from the VB or electron injection into the CB. For Ge, for example... 

In case (b), we may identify a surface state, T, which may be emptied by hole capture and filled by electron capture. If we suppose these two processes to be irreversible, i.e. that we have made a transition to Gerischer s recombination cases (b) or (c) and that the faradaic hole-capture route is via the reduced form of the redox couple R, then the equations describing the kinetics are... 

Recombination is evidently controlled by trapping into defect states, consistent with the other recombination measurements. The recombination transitions through defects with two gap states are illustrated in Fig. 8.24, with electrons and holes captured into either of the two states. This type of recombination is analyzed by the Shockley-Read-Hall approach which distinguishes between shallow traps, for which the carrier is usually thermally excited back to the band edge, and deep traps, at which the carriers recombine. A demarcation energy, which is usually close to the quasi-Fermi energy, separates the two types of states. The occupancy of the shallow states is determined by the quasi-equilibrium and that of the deep states by the recombination processes. No attempt is made here at a comprehensive analysis of the photoconductivity, which rapidly becomes complicated. Instead some approximate solutions are derived which illustrate the processes. 

For the dissolution of silicon in fluoride electrolytes where two electrons are transferred per silicon atom, it is generally assumed that the first step in the reaction sequence is hole capture ... 

For the case of pore formation in p-type silicon where the holes are the majority carriers, silicon dissolution occurs at much lower potentials than for n-type silicon. Both hole capture and electron injection have been suggested for the second elec-... 

Fig. 11. Energy-level diagram for the etching of n-type silicon in the dark. Holes are generated by tunneling of electrons from the valence band into the conduction band (i). The first electrochemical step is hole capture resulting in the formation of the intermediate X (ii). The second electrochemical step can occur through hole capture (ii), thermal excitation into the conduction band (iii), or tunneling into the conduction band (iv) [70].

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