Valence band edge

Cadmium Sulfide Photoconductor. CdS photoconductive films are prepared by both evaporation of bulk CdS and settHng of fine CdS powder from aqueous or organic suspension foUowed by sintering (60,61). The evaporated CdS is deposited to a thickness from 100 to 600 nm on ceramic substates. The evaporated films are polycrystaUine and are heated to 250°C in oxygen at low pressure to increase photosensitivity. Copper or silver may be diffused into the films to lower the resistivity and reduce contact rectification and noise. The copper acceptor energy level is within 0.1 eV of the valence band edge. Sulfide vacancies produce donor levels and cadmium vacancies produce deep acceptor levels. 

In the case of negative bias, the Fermi level moves closer to the valence band edge. Consequently, the concentration of the majority of carriers (holes) at die insulator-semiconductor interface becomes laiger than in the bulk. This corresponds to the accumulation regime. When a positive bias is applied to die metal, the... 

Fig. 5.8 The energy levels of n-type M0S2 at the flat band potential relative to the positions of various redox couples in CH3CN/[n-Bu4N]C104 solution. The valence band edge of the semiconductor as revealed by accurate flat band potential measurement is at ca. +1.9 V vs. SCE implying that photooxrdations workable at Ti02 are thermodynamically possible at illuminated M0S2 as well. (Reproduced with permission from [137], Copyright 2010, American Chemical Society)...

For undoped a-Si H the (Tauc) energy gap is around 1.6-1.7 eV, and the density of states at the Fermi level is typically lO eV cm , less than one dangling bond defect per 10 Si atoms. The Fermi level in n-type doped a-Si H moves from midgap to approximately 0.15 eV from the conduction band edge, and in / -type material to approximately 0.3 eV from the valence band edge [32, 86]. 

Fig. 2-13. Schematic electron state density distribution curves in the valence and conduction bands of silicon cc = conduction band edge level Cv = valence band edge level c, = band gap (1.1 eV for silicon) CB = conduction band V6 = valence band.

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. 

In Eqns. 3-15 and 3-16, Og. and aj. are the unitary levels of the ion at the surface kink site and at the interior lattice site Ug and Ug are the unitary levels of the atom at the surface kink sit and at the interior lattice site Cy and ey are the levels of the valence band edge at the surface and in the interior, respectively. The ion levels of Ug. and ag. are dependent on the hole level but the atom levels of ttg and agj are constant and characteristic of individual semiconductors. 

Fig. S-41. Band edge levels and Fermi level of semiconductor electrode (A) band edge level pinning, (a) flat band electrode, (b) under cathodic polarization, (c) under anodic polarization (B) Fermi level pinning, (d) initial electrode, (e) under cathodic polarization, (f) imder anodic polarization, ep = Fermi level = conduction band edge level at an interface Ev = valence band edge level at an interface e = surface state level = potential across a compact layer.

Figures 8-16 and 8-17 show the state density ZXe) and the exchange reaction current io( ) as functions of electron energy level in two different cases of the transfer reaction of redox electrons in equilibrium. In one case in which the Fermi level of redox electrons cnxEDax) is close to the conduction band edge (Fig. 8-16), the conduction band mechanism predominates over the valence band mechanism in reaction equilibrium because the Fermi level of electrode ensa (= nREDOK)) at the interface, which is also dose to the conduction band edge, generates a higher concentration of interfadal electrons in the conduction band than interfadal holes in the valence band. In the other case in which the Fermi level of redox electrons is dose to the valence band edge (Fig. 8-17), the valence band mechanism predominates over the conduction band mechanism because the valence band holes cue much more concentrated than the conduction band electrons at the electrode interface.

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.

A further increase in anodic polarization lowers still further the Fermi level ersc)(ti) which gradually approaches the valence band edge Cy at the electrode interface as shown in Fig. 8-21. As the anodic polarization increases, the concentration of interfacial holes in the valence band increases, thus causing the anodic electron transfer to change from the conduction band mechanism to the valence band mechanism. 

Fig. 8-27. Polarization curves for transfer of redox electrons at n-type and p-type semiconductor electrodes solid curve near Egaxa = reaction with the Fermi level of redox electrons dose to the valence band edge dashed curve near F redok = reaction with the Fermi level of redox electrons dose to the conduction band edge dot-dash curve (FLP)= reaction in the state of Fermi level pinning.

The concentration of surface holes, p is given as a function of the Fermi level ej at the stuface, the valence band edge ty at the surface, and the effective state density of the valence band Ny ( Nc)in Eqn. 9-28 ... 

Equation 9-31 indicates that the electron level, er, of the intermediate radical is decisive in determining the ratio of the rates vjv. if the electron level of er is relatively close to the valence band edge Ey, the valence band mechanism, Eqn. 9-24d, will predominate whereas, if the electron level of er is relatively close to the conduction band edge e, the lone pair electron will be excited into the conduction band, and the conduction band mechanism, Eqn. 9-24c, will predominate. As the band gap of semiconductor electrode decreases, the conduction band increasingly participates. 

Electrons in the conduction band is predominemtly involved in the redox reaction when the electron level of adsorbed protons is close to the conduction band edge. On the other hand, holes in the valence band participate in the redox reaction when the electron level of adsorbed protons is close to the valence band edge. 

Fig. 10-3. Energy diagrams for an n-type semiconductor electrode (a) in the daik and (b) in a photoexdted state S = aqueous solution = conduction band edge level at an interface cy = valence band edge level at an interface = Fermi level of oxygen...

Fig. 10-13. Anodic transfer of pho-toexdted boles (minority charge carrier) at an n>type semiconductor electrode E( -e 9o/e) = electrode potential E% (= — c /e) = potential of the valence band edge B02 (= - = equilibrium...

For metal electrodes, the anodic 03Q n reaction proceeds at electrode potentials more anodic than the equilibrium potential Bo of the reaction as shown in Fig. 10-14. For n-type semiconductor electrodes, the anodic photoexdted oxygen reaction proceeds at electrode potentials where the potential E of the valence band edge (predsely, the potential pEp of the quasi-Fermi level of interfadal holes, pCp = — CpEp) is more anodic than the equilibrium oxygen potential Eq, even i/the observed electrode potential E is less anodic than the equilibrium oxygen potential E03. The anodic hole transfer of the o Qgen reaction, hence, occurs at photoexdted n-type semiconductor electrodes even in the range of potential less anodic than the equilibriiun potential Eq of the reaction as shown in Fig. 10-14. 

Fig. 11-11. Potential at a film/solution interface and potential dfp in a passive film as a fimction of anodic potential of a passive metal electrode in the stationary state the interface is in the state of band edge level pinning to the extent that the Fermi level e, is within the band gap, but the interface changes to the state of Fermi level pinning as e, coincides with the valence band edge Cy.

In the case of nickel electrodes on which the passive film is a p-f pe nickel oxide (NiO), the energy gap ( 0.2 eV) between the valence band edge and the Fermi level at the flat band potential is small so that the transpassivation potential Etp is relatively close to the flat band potential as in Fig. 11-13. 

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