Semiconductor particles, valence band

FIGURE 22.2 Electron energy levels for a standard pair of hydrated redox particles and for an intrinsic semiconductor ered = the most probable electron level of oxidant, eox = the most probable electron level of reductant, 8p(redox) = standard Fermi level of redox electrons, 8p = Fermi level of an intrinsic semiconductor, v = valence band edge level, and c = conduction band edge level. 

A number of electronic and photochemical processes occur following band gap excitation of a semiconductor. Figure 5 illustrates a sequence of photochemical and photophysical events and the possible redox reactions which might occur at the surface of the SC particle in contact with a solution. Absorption of light energy greater than or equal to the band gap of the semiconductor results in a shift of electrons from the valence band (VB) to... 

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. 

In most metals the electron behaves as a particle having approximately the same mass as the electron in free space. In the Group IV semiconductors, dris is usually not the case, and the effective mass of electrons can be substantially different from that of the electron in free space. The electronic sUmcture of Si and Ge utilizes hybrid orbitals for all of the valence elecU ons and all electron spins are paired within this structure. Electrons may be drermally separated from the elecU on population in dris bond structure, which is given the name the valence band, and become conduction elecU ons, creating at dre same time... 

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. 

Figure 8-11 shows as a function of electron energy e the electron state density Dgdit) in semiconductor electrodes, and the electron state density Z e) in metal electrodes. Both Dsd.t) and AKe) are in the state of electron transfer equilibrium with the state density Z>bei)ox(c) of hydrated redox particles the Fermi level is equilibrated between the redox particles and the electrode. For metal electrodes the electron state density Ai(e) is high at the Fermi level, and most of the electron transfer current occurs at the Fermi level enio. For semiconductor electrodes the Fermi level enao is located in the band gap where no electron level is available for the electron transfer (I>sc(ef(so) = 0) and, hence, no electron transfer current can occur at the Fermi level erso. Electron transfer is allowed to occur only within the conduction and valence bands where the state density of electrons is high (Dsc(e) > 0). 

Fig. 8-17. Electron state density in a semiconductor electrode and in hydrated redox particles, rate constant of electron tunneling, and exchange redox current in equilibrium with a redox electron transfer reaction for which the Fermi level is dose to the valence band edge.

TABLE 8-1. Preference for the conduction band mechanism (CB) and the valence band mechanism (VB) in outer sphere electron transfer reactions of hydrated redox particles at semiconductor electrodes (SC) Eo = standard redox potential referred to NHE c, = band gap of semiconductors. [From Memming, 1983.]... 

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 last section revealed that semiconductor band gaps for nanostructures vary with the size of the structure. The wavelength of light emitted when an electron in the conductance band returns to the valence band will therefore also vary. Thus, different colour fluorescence emission can be obtained from different-sized particles of the same substance (e.g., different sized quantum dots of CdSe irradiated with UV emit different colours of light). To produce fluorescence, light of greater photon energy than the band gap is shone onto the nanocrystal. An electron is excited to a... 

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. 

Lanthanides doped into nanocrystalline semiconductors have been the subject of numerous investigations in the past decades. If the size of a semiconductor particle is smaller than the Bohr radius of the excitons, the so-called quantum confinement occurs. As a result, the band gap of the semiconductor increases and discrete energy levels occur at the edges of the valence and conduction bands (Bol et al., 2002 Bras, 1986). These quantum size effects have stimulated extensive interest in both basic and applied research. 

The colloidal or powder particle can be composed of either insulating, semiconductive, or conductive molecules. While only semiconductor particles are likely to be photoactive per se (by virtue of the energy gap between the filled valence band and the vacant conduction band), photoactivity of adsorbates can be mediated at the surface of other solids [18] which are often used themselves, or in conjunction with an irradiated semiconductor, as catalytic sites for alteration of kinetics of dark reactions initiated by photoexcitation. 

Band gap photochemical excitation of a semiconductor particle promotes an electron from the valence band to the conduction band, thus forming an electron-hole pair. Under illumination, the bands shift from their dark equilibrium positions to ones closer to the flat band condition, Scheme 9. Here the chemical potential of the electrons becomes different from that of the holes and a photovoltage develops. The concentration of free carriers, and hence of the number of available redox equivalents, will depend linearly on the incident light intensity. The free energy of these charge carriers will be related to... 

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