Electron transfer theories semiconductors

In summary, at nanostructured tin-oxide semiconductor-aqueous solution interfaces, back ET to molecular dyes is well described by conventional Marcus-type electron-transfer theory. The mechanistic details of the reaction, however, are remarkably sensitive to the nature of the semiconductor-dye binding interactions. The mechanistic differences point, potentially, to differing design strategies for kinetic optimization of the corresponding liquid-junction solar cells. 

Zinc oxide seems to be a semiconductor with many of the properties necessary for a comparison with the electron transfer theory partially described in the preceding chapter. 

While the ability to treat capture cross sections theoretically is very primitive and the experimental data on capture cross sections are very limited this phenomenological parameter seems to be an appropriate meeting place for experiment and theory. More work in both of these areas is needed to characterize and understand the important role of surface states in electron transfer at semiconductor-electrolyte interfaces. 

Theory Gerischer has described a theory for excited-state electron transfer to semiconductors.90-92 The rate constant for interfacial electron transfer is proportional to the overlap of occupied donor levels of the excited state, fTdon( ), with unoccupied acceptor states in the semiconductor IXE) (Equation 12.6) ... 

The simple models of electron transfer at semiconductor interfaces, which have been used until recently, are now being extended and improved, and Wilson has provided an authoritative review of the theory, which includes some discussion of solar photoelectrochemical cells. Albery et have explored the transport and kinetics of minority carriers at illuminated semiconductor electrodes. The exact analytical solution of the problem is obtained in terms of confluent... 

It is instructive to first examine the historical evolution of this field. Early work in the fifties and sixties undoubtedly was motivated by application possibilities in electronics and came on the heels of discovery of the first transistor. Electron transfer theories were also rapidly evolving during this period, starting from homogeneous systems to heterogeneous metal-electrolyte interfaces leading, in turn, to semiconductor-electrolyte junctions. The 1973 oil embargo... 

During polarization, various electrode processes can occur such as electrochemical dissolution, O2 evolution and oxide formation during anodic polarization, and surface reduction and H2 formation during cathodic polarization. It must be emphasized that the theory derived above is not quantitatively applicable here because, in most processes, a strong interaction between semiconductor and electrolyte is involved, whereas the electron transfer theory is only valid for weak interactions, i.e., it is applicable only for redox processes. The other processes, electrochemical dissolution, etc., will be treated briefly before discussing pure electron transfer reactions (redox processes) because they present the basic behavior of semiconducting electrodes. 

The proposed model for the so-called sodium-potassium pump should be regarded as a first tentative attempt to stimulate the well-informed specialists in that field to investigate the details, i.e., the exact form of the sodium and potassium current-voltage curves at the inner and outer membrane surfaces to demonstrate the excitability (e.g. N, S or Z shaped) connected with changes in the conductance and ion fluxes with this model. To date, the latter is explained by the theory of Hodgkin and Huxley U1) which does not take into account the possibility of solid-state conduction and the fact that a fraction of Na+ in nerves is complexed as indicated by NMR-studies 124). As shown by Iljuschenko and Mirkin 106), the stationary-state approach also considers electron transfer reactions at semiconductors like those of ionselective membranes. It is hoped that this article may facilitate the translation of concepts from the domain of electrodes in corrosion research to membrane research. 

In classical kinetic theory the activity of a catalyst is explained by the reduction in the energy barrier of the intermediate, formed on the surface of the catalyst. The rate constant of the formation of that complex is written as k = k0 cxp(-AG/RT). Photocatalysts can also be used in order to selectively promote one of many possible parallel reactions. One example of photocatalysis is the photochemical synthesis in which a semiconductor surface mediates the photoinduced electron transfer. The surface of the semiconductor is restored to the initial state, provided it resists decomposition. Nanoparticles have been successfully used as photocatalysts, and the selectivity of these reactions can be further influenced by the applied electrical potential. Absorption chemistry and the current flow play an important role as well. The kinetics of photocatalysis are dominated by the Langmuir-Hinshelwood adsorption curve [4], where the surface coverage PHY = KC/( 1 + PC) (K is the adsorption coefficient and C the initial reactant concentration). Diffusion and mass transfer to and from the photocatalyst are important and are influenced by the substrate surface preparation. 

It is well known that the flotation of sulphides is an electrochemical process, and the adsorption of collectors on the surface of mineral results from the electrons transfer between the mineral surface and the oxidation-reduction composition in the pulp. According to the electrochemical principles and the semiconductor energy band theories, we know that this kind of electron transfer process is decided by electronic structure of the mineral surface and oxidation-reduction activity of the reagent. In this chapter, the flotation mechanism and electron transferring mechanism between a mineral and a reagent will be discussed in the light of the quantum chemistry calculation and the density fimction theory (DFT) as tools. 

Gao YQ, Gerogievskii Y, Marcus RA (2000) On the theory of electron transfer reactions at semiconductor/liquid interfaces. J Chem Phys 112 3358-3369... 

Boroda YG, Voth GA (1996) A theory of adiabatic electron transfer processes across the semiconductor-electrolyte interface. J Chem Phys 106 6168-6183... 

The basic theory of the kinetics of charge-transfer reactions is that the electron transfer is most probable when the energy levels of the initial and final states of the system coincide [5] following the Franck-Condon principle. Thus, the efficiency of the redox reaction processes is primarily controlled by the energy overlap between the quantum states in the energy bands of the semiconductor and the donor and acceptor levels of the reactants in the electrolyte (Fig. 1). In the ideal case, the anodic current density is given by the... 

There have been many attempts to relate bulk electronic properties of semiconductor oxides with their catalytic activity. The electronic theory of catalysis of metal oxides developed by Hauffe (1966), Wolkenstein (1960) and others (Krylov, 1970) is base d on the idea that chemisorption of gases like CO and N2O on semiconductor oxides is associated with electron-transfer, which results in a change in the electron transport properties of the solid oxide. For example, during CO oxidation on ZnO a correlation between change in charge-carrier concentration and reaction rate has been found (Cohn Prater, 1966). 

The advances made since 1970 start with the fact that the solid/solution interface can now be studied at an atomic level. Single-crystal surfaces turn out to manifest radically different properties, depending on the orientation exposed to the solution. Potentiodynamic techniques that were raw and quasi-empirical in 1970 are now sophisticated experimental methods. The theory of interfacial electron transfer has attracted the attention of physicists, who have taken the beginnings of quantum electrochemistry due to Gurney in 1932 and brought that early initiative to a 1990 level. Much else has happened, but one thing must be said here. Since 1972, the use of semiconductors as electrodes has come into much closer focus, and this has enormously extended the realm of systems that can be treated in electrochemical terms. 

The n-p Junction. Before beginning a discussion of electron transfer at interfaces between H-type semiconductor/solution interlaces, it is helpful to describe something of the theory of the famous n-p junction. This is not a part of electrode-process chemistry (which deals with electron-transfer reactions between electronically and ionically conducting phases), but it is the basis of so much modem technology (e.g., the transistor in computers) that an elementary version of events at the junction should be understood. Further, knowing about the n-p junction makes it easier to understand electrochemical interfaces involving semiconductors. 

A modification of this simple adsorption theory must be made if there are other surface levels present. If the surface concentration of these levels is very large compared to the concentration of ions to be adsorbed, one would expect the adsorption to more closely resemble that on a clean metal, as electron transfer between the various surface traps may predominate over transfer between the adsorbed ions and the bulk semiconductor. If the number of these traps is small compared to the amount of adsorption, one would expect the adsorption characteristics to resemble those for the theory discussed above. Intermediate cases are also possible. 

Most of the modern theories of the photoconductivity sensitization consider that local electron levels play the decisive role in filling up the energy deficit The photogeneration of the charge carriers from these local levels is an essential part of the energy transfer model. Regeneration of the ionized sensitizer molecule due to the use of the carriers on the local levels takes place in the electron transfer model. The existence of the local levels have now been proved for practically all sensitized photoconductors. The nature of these levels has to be established in any particular material. A photosensitivity of up to 1400 nm may be obtained for the known polymer semiconductors. There are a lot of sensitization models for different types of photoconductors and these will be examined in the corresponding sections. 

Figure 1 illustrates different modes of electron transfer between electrolyte states and carriers in the bands at the semiconductor surface. If the overlap between the electrolyte levels and the semiconductor bands is insufficient to allow direct, isoenergetic electron transfer, then an inelastic, energy-dissipating process mustnbe used to explain experimentally observed electron transfer. Duke has argued that a complete theory for electron transfer includes terms that allow direct, inelastic processes. The probability of such processes, however, has not been treated quantitatively. 

Theory (1) The effective energy barrier between the two harmonic oscillators, AE (oo IT), which determines the probability of electron transfer along the conjugated chain decreases with increasing temperature thus, conductivity is semiconductor-like. (2) The spin susceptibility is due only to the unpaired Ji-electrons from TTF (all the 7i-electrons on TCNQ are in the paired state). Thus, the susceptibility is weak. (3) The spin-paired n-electrons on TCNQ resonate between the two harmonic oscillator states at frequency, . Such oscillation can perturb the g-factor of (TTF)+. As the increases with the temperature rise, the perturbation becomes greater, and the g-factor deviates more from that of the pure (TTF)+. 

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