Semiconductor particles, valence band holes

After their generation according to reaction (1) both conduction band electrons and valence band holes are migrating to the surface of the semiconductor particle. The transit time t needed by these charge carriers to reach the surface of the particle is given by Equation (a)... 

Crystals exhibit excitonic effects near the band edges, in which the Coulomb interaction between an electron and a valence band hole results in absorption which does not follow the one-particle joint density of states in Eq. (3.25). Excitons produce an absorption peak just below the band gap energy and modify the absorption at higher energies. There is no exciton absorption peak observable in any amorphous semiconductor, because it is broadened out by the disorder. The Coulomb interaction is present in a-Si H, but its significance in the optical absorption is unclear. 

Figure 12.15. Simplified scheme of light absorption by a semiconductor particle and subsequent redox reaction on the surface, vb. Valence band cb, conduction band X and A, adsorbed species. Note that in this scheme, the y axis is at the same time energy and distance. Valence band holes and conduction band electrons can oxidize and/or reduce, respectively, molecules adsorbed on the surface directly ...

Cobalt(II) 4,4, 4",4" -tetrasulfophthalocyanine, covalently linked to the surface of titanium dioxide particles, Ti02-CoTSP, was shown [207] to be an effective photocatalyst for the oxidation of sulfur (IV) to sulfur (VI) in aqueous suspensions. Upon bandgap illumination of the semiconductor, conduction-band electrons and valence-band holes are separated the electrons are channeled to the bound CoTSP complex resulting in the reduction of dioxygen, while the holes react with adsorbed S(IV) to produce S(VI) in the form of sulfate. 

On the basis of the above discussion, in its most simple description photocatalysis implies a catalysed process preceded by absorption of a photon by a material acting as the catalyst. Where the photocatalyst is a semiconductor nanoparticulate system, e.g. TiOi, which is the material treated in most detail in this chapter, absorption of photons of energy greater than 3.2 eV (for anatase 3.0 eV for the rutile polymorph) leads to formation of conduction-band electrons and valence-band holes, which subsequently diffnse to the particle surface in competition with bnlk recombination. 

In the absence of suitable electron and hole scavengers adsorbed to the surface of a semiconductor particle, recombination occurs within 1 ns. However, when appropriate scavengers are present, the valence-band holes, hv+b, (E = 2.3 V oxidation potential function as powerful oxidants while the conduction-band electrons, e b, (E = 0.0 V reduction potential function as moderately powerful reductants. 

The weak-coupling limit takes as its starting point the conventional semiconductor noninteracting band picture, introduced in Chapter 3. The ground state is an occupied valence-band and an empty conduction-band. A bound conduction band electron and valence band hole move through the lattice as an effective-particle. In this section we derive the effective-particle model, discuss its solutions and compare them to essentially exact calculations on the same Hamiltonian (Barford et al. 2002b). We develop this theory for a linear, dimerized chain. 

In a semiconductor, conduction occurs through the movement of electrons excited to the conduction band and through the movement of holes in the valence band. Holes are positively charged particles that represent the absence of electrons. The dynamical equations of an electron in a crystal in an applied electric field can be rewritten to resemble the equations of motion of a free electron in an electric field. To compensate for the effects of the crystal, the mass of the electron is replaced with an effective mass, m. The effective mass can be negative, representing a hole. A hole with a negative effective mass behaves in the same way as a positive charge and moves in the opposite direction as an electron in an electric field. Both electrons and holes contribute to the current flow. 

Where b is Planck s constant and m and are the effective masses of the electron and hole which may be larger or smaller than the rest mass of the electron. The effective mass reflects the strength of the interaction between the electron or hole and the periodic lattice and potentials within the crystal stmcture. In an ideal covalent semiconductor, electrons in the conduction band and holes in the valence band may be considered as quasi-free particles. The carriers have high drift mobilities in the range of 10 to 10 cm /(V-s) at room temperature. As shown in Table 4, this is the case for both metallic oxides and covalent semiconductors at room temperature. 

The description of the properties of this region is based on the solution of the Poisson equation (Eqs 4.3.2 and 4.3.3). For an intrinsic semiconductor where the only charge carriers are electrons and holes present in the conductivity or valence band, respectively, the result is given directly by Eq. (4.3.11) with the electrolyte concentration c replaced by the ratio n°/NA, where n is the concentration of electrons in 1 cm3 of the semiconductor in a region without an electric field (in solid-state physics, concentrations are expressed in terms of the number of particles per unit volume). 

According to the electronic theory, a particle chemisorbed on the surface of a semiconductor has a definite affinity for a free electron or, depending on its nature, for a free hole in the lattice. In the first case the chemisorbed particle is presented in the energy spectrum of the lattice as an acceptor and in the second as a donor surface local level situated in the forbidden zone between the valency band and the conduction band. In the general case, one and the same particle may possess an affinity both for an electron and a hole. In this case two alternative local levels, an acceptor and a donor, will correspond to it. 

The electronic properties of silicon are essential in the understanding of silicon as an electrode material in an electrochemical cell. As in the case of electrolytes, where we have to consider different charged particles with different mobilities, two kinds of charge carriers - electrons and holes - are present in a semiconductor. The energy gap between the conduction band (CB) and the valence band (VB) in silicon is 1.11 eV at RT, which limits the upper operation temperature for silicon devices to about 200 °C. The band gap is indirect this means the transfer of an electron from the top of the VB to the bottom of the CB changes its energy and its momentum. 

In addition to redox reactions due to the direct transfer of electrons and holes via the conduction and valence bands, the transfer of redox electrons and holes via the surface states may also proceed at semiconductor electrodes on which surface states exist as shown in Fig. 8-31. Such transfer of redox electrons or holes involves the transition of electrons or holes between the conduction or valence band and the surface states, which can be either an exothermic or endothermic process occurring between two different energy levels. This transition of electrons or holes is followed by the transfer of electrons or holes across the interface of electrodes, which is an adiabatic process taking place at the same electron level between the surface states and the redox particles. 

Fig. 10-21. Quasi-Fermi levels of holes in transfer reaction of anodic holes, from the valence band (a) of a photoexcited n-type electrode and (b) of a dark p-type electrode of the same semiconductor, to redox particles pCp, = quasi-Fermi level of interfacial holes in a photoexcited n-type electrode where pCp, is lower than the Fermi level cp and in a dark n-type electrode where pCp, equals the Fermi level sp.

The equation can also be illustrated in Figure 9.1. When a semiconductor such as Ti02 absorbs photons, the valence band electrons are excited to the conduction band. For this to occur, the energy of a photon must match or exceed the band-gap energy of the semiconductor. This excitation results in the formation of an electronic vacancy or positive hole at the valence band edge. A positive hole is a highly localized electron vacancy in the lattice of the irradiated Ti02 particle. This hole can initiate further interfacial electron transfer with the surface bound anions. 

If photons of sufficient energy are incident on a semiconductor, excess electrons and holes are created in the semiconductor conduction and valence bands respectively. Further, if the semiconductor is fabricated to contain one or more p-n junctions, the chemical potential of the excess carriers can be converted into a flow of charges resulting in an electric current. This current can then be used to power the direct electrolysis of water. Alternatively, the excess charge carriers can migrate to the semiconductor surface where they initiate chemical reactions and produce H2 and/or 02 in the surrounding medium either in a PEC or in a suspension of semiconductor particles. 

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