Conduction band potential

In order for injection of an electron from the excited state of the dye species into the conduction band of a semiconductor (as described by Equation (2.39)) to occur, the oxidation potential of the dye excited state (A+ / A ) must be more negative than the conduction band potential of the semiconductor. Conversely, photoinduced hole injection from the excited dye into the semiconductor valence band (Equation (2.40)) requires the excited-state reduction potential of the sensitizer (A /A-) to be more positive than the valence band potential. 

Below we discuss the photochemical processes in the systems containing suspension of mesoporous Ti02 and Ni2+. Anatase conduction band potential at pH 7 amounts to -0.53 V versus NHE [11] thus, photoreduction ofNi2+ (E°(Ni27Ni° = -0.23 V [40]) is thermodynamically favorable up to the practically total conversion of Ni2+ into Ni° (E°(Nr7Ni°) = -0.40 V at 99% degree of Ni2+ photoreduction... 

Fe(ni)/Fe(II), Ag(I)/Ag(0), and Hg(II)/Hg(0). Figure 1 reports the reduction potential of different metals compared with both the valence band potential and the conduction band potential. All metals located above the conduction band can theoretically be reduced (Chen and Ray, 2001). 

Since it is a stable molecule, one wants to supply additional energy to convert the linear structure to bent form, i.e., CO2 to C02-. Because of the high LUMO level of carbon dioxide, the transfer of one electron to free CO2 is thermodynamically unfavourable, requires a very negative redox potential up to the order of -1.9V vs Normal Hydrogen Electrode (NHE). In photocatalytic route, no semiconductor possesses the conduction band potential required for CO2 activation, there is a need to supply additional overvoltage which will lead to another energy dilemma. 

Fig. 9.1 Illustration of polaron size. The periodic potential, V(x), is plotted with the range of conduction band potentials (energies) depicted in gray. The wavefunctions, ij/, of a small (solid line), intermediate (dashed line), and large (dotted line) polaron are plotted as a function of a single spatial dimension, x. Illustration is based on [5]...

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. 

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

Electrons excited into the conduction band tend to stay in the conduction band, returning only slowly to the valence band. The corresponding missing electrons in the valence band are called holes. Holes tend to remain in the valence band. The conduction band electrons can estabUsh an equihbrium at a defined chemical potential, and electrons in the valence band can have an equiUbrium at a second, different chemical potential. Chemical potential can be regarded as a sort of available voltage from that subsystem. Instead of having one single chemical potential, ie, a Fermi level, for all the electrons in the material, the possibiUty exists for two separate quasi-Fermi levels in the same crystal. 

Solar cells the difference between conduction and valence band chemical potentials is the available output voltage of a solar cell. Light creates the chemical potential difference simply by boosting a population of electrons from the valence band into the conduction band (see Photovoltaic cells Solar energy). 

Lasers (qv) levels just above the valence band chemical potential are essentially (2) empty and unfilled, but levels just below the conduction band chemical potential are filled, permitting a population inversion. Filled levels above, empty levels below, is the principle by which lasers operate (see also... 

Fig. 3. The lattice-matched double heterostmcture, where the waves shown in the conduction band and the valence band are wave functions, L (Ar), representing probabiUty density distributions of carriers confined by the barriers. The chemical bonds, shown as short horizontal stripes at the AlAs—GaAs interfaces, match up almost perfectly. The wave functions, sandwiched in by the 2.2 eV potential barrier of AlAs, never see the defective bonds of an external surface. When the GaAs layer is made so narrow that a single wave barely fits into the allotted space, the potential well is called a quantum well.

Electron-tunneling Model. Several models based on quantum mechanics have been introduced. One describes how an electron of the conducting band tunnels to the leaving atom, or vice versa. The probability of tunneling depends on the ionization potential of the sputtered element, the velocity of the atom (time available for the tunneling process) and on the work function of the metal (adiabatic surface ionization, Schroeer model [3.46]). 

The usual way to visualize a junction is to draw an eneigy diagram that shows the bottom of the conduction band Er and the top of the valence band Ev as a function of distance. The so-called band curvature that appears at both sides of the junction interface reveals a variation in the potential with a distance in the direction perpendicular to the junction surface. The formation of an MS barrier is depicted in Figure 14-1. 

Figure 9-21. EL process in PLEDs. VB... valence band LB. ..conducting band V... potential M,M2... Mclal electrodes, U... bias voltage Z X2 —Interface luyers tK...bandgap P and Pr... positive and negative polarons /. Fermi energy, and 0... work I unclion.

Figure 13-4. Encigy level diagnim of a single-layer OLED, where the organic malerial is depicted as a fully depleted semiconductor. The valence band Ey corresponds to the HOMO and the conduction band Ec corresponds to the LUMO. Tile Fermi levels of the two metal electrodes are marked as Et-. Upon contact a built-in potential is established and needs to be compensated for, before the device will begin to operating.

Voltammograms of a polythiophene film showing reasonably reversible electrochemistry of both types are shown in Fig. 2.M The formal potentials (average of the anodic and cathodic peak potentials) for p- and n-doping can provide useful estimates of the energies of the polymer s valence and conduction bands and its band gap35... 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

Figure 5.20. Left Schematic of an O2 conducting solid electrolyte cell with fixed P02 and PO2 values at the porous working (W) and reference (R ) electrodes without (top) and with (bottom) ion backspillover on the gas exposed electrodes surfaces, showing also the range of spatial constancy of the electrochemical potential, PQ2-, of O2. Right Corresponding spatial variation in the electrochemical potential of electrons, ]Ie(= Ef) UWR is fixed in both cases to the value (RT/4F)ln( P02 /pc>2 ) also shown in the relative position of the valence band, Ev, and of the bottom of the conduction band, Ec, in the solid electrolyte (SE) numerical values correspond to 8 mol% Y203-stabilized-Zr02, pc>2=10 6 bar, po2=l bar and T=673 K.32 Reproduced by permission of The Electrochemical Society.

The deposition takes place from HTeOs and cadmium-EDTA complex solutions at a potential whereat, whilst Te is deposited from HTeOs under a diffusion-limited condition, the Cd-EDTA complex ion is not reduced to metallic Cd. The first step is the dark deposition of one monolayer of elemental Te on the p-Si substrate (Fig. 4.11a, i). After completion of this step, as specified by measuring the charge passed, the electrode is illuminated by light with energy higher than the band gap energy of silicon for a limited time. Then conduction band electrons are... 

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