Encyclopedia of Electrochemistry. Semiconductor Electrodes and Photoelectrochemistry
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The space charge region in the electrolyte, bounded on one side by the outer Helmholtz plane and decaying into the bulk of the electrolyte.
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This region is also called the Gouy diffuse layer. The electric charge needed for Fermi level equilibrium in the semiconductor phase originates from the donor impurities rather than from bonding electrons in the semiconductor lattice. Thus, the depletion layer that arises as a consequence within the semiconductor contains positive charges from these ionized donors. The Fermi level in the semiconductor, E F,n , moves down. This process stops when the Fermi level is the same on either side of the interface. The rather substantial difference in the density of states on either side dictates that E F,n moves further than the corresponding level, E F,redox , in the electrolyte [ 23 ].
The band-bending phenomenon is by no means unique to the semiconductor-electrolyte interface. Analogous electrostatic adjustments occur whenever two dissimilar phases are in contact. An important point of distinction from the corresponding situation involving a metal is that the charge, and thus the associated potential drop, is concentrated at the surface, penetrating at most a few angstroms into the interior. Stated differently, the high electrical conductivity of a metal cannot support an internal electric field. Thus, when a metal electrode comes into contact with an electrolyte, almost all of the potential drop at the interface occurs within the Helmholtz region in the electrolyte phase.
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On the other hand, the interfacial potential drop across a semiconductor-electrolyte junction is partitioned into V sc and V H , leading to a simple equivalent circuit model comprising two capacitors, C sc and C H , in series see Figure 3 [ 24 , 25 ]. Potential dependence of the capacitance components of the n-type semiconductor-electrolyte interface. The relative positions of the solution energy levels with respect to the semiconductor band edge positions at the interface can be represented by the total potential difference [ 26 ]:.
The potential difference, V sc , appears as a bending of the energy bands, as indicated in Figure 2 , and the total capacitance, C, in series see Figure 3 is given by:. The problematic factors in placing the semiconductor and solution energy levels on a common basis involve V H and V G.
In other words, theoretical predictions of the magnitude of V sc and how it changes as the redox couple is varied are hampered by a lack of knowledge of the magnitude of V H and V G. A degree of simplification is afforded by employing relatively concentrated electrolytes, such that V G can be ignored [ 27 ] see Figure 4 :. A simplified equivalent circuit for the semiconductor-electrolyte interface at equilibrium where the Gouy layer is neglected. As with metals, the Helmholtz layer is developed by adsorption of ions or molecules on the semiconductor surface, by oriented dipoles, or, especially in the case of oxides, by the formation of surface bonds between the solid surface and species in solution.
Information on band edge placement can be sought through differential capacitance measurements on the semiconductor-redox electrolyte interface [ 28 ]. From the capacitor in series model, we can see that the semiconductor space charge layer is usually the determining factor in the total capacitance of the interface. The capacitance of the Helmholtz layer depends only very little on potential. On the other hand, the space charge semiconductor capacitance depends strongly on the potential. The potential distribution in the space charge layer of a semiconductor can be found by solving the Poisson Equation for a given charge distribution [ 29 , 30 ].
For a semiconductor-electrolyte interface where the density of an electron donor, N D , is constant throughout the semiconductor, the potential, V x , at a distance, x, from the surface is given as follows [ 29 — 31 ]:. The values of V 0 and W are given by:.
Further reflection shows how the magnitude of W should depend on the semiconductor parameter N D , i. Nominal dimensions of W are in the 10—1, nm range. This may be compared with the corresponding Helmholtz layer width, typically 0. The space charge, Q s , per unit area is given by [ 32 ]:. Thus, the differential capacitance of the space charge layer, C sc , per unit area is given as follows:. Equation 54 can be applied to non-degenerate semiconductor systems. In the above discussion, the energy bands are pinned at the surface, and any variation of the electrode potential leads to a change in the band bending [ 33 — 35 ] see Figure 2b.
Investigations of many semiconductor electrodes have shown that the positions of the energy bands are independent of the doping. Therefore, the energy bands of n-type electrodes have the same position at the surface, as shown in Figure 1. As previously mentioned, in aqueous solutions, the potential across the Helmholtz double layer is entirely determined by the interaction of the semiconductor with the solvent.
If the energy band edges are pinned, they do not shift upon changing the redox system. Only a change in band bending occurs to maintain equal Fermi levels on both sides of the interface.
However, there are many cases where the energy bands are not pinned, but the Fermi level of the semiconductor is pinned [ 36 , 37 ]. The energy positions at the surface for several semiconductors in contact with aqueous solutions are given in Figure 5. In many cases, the flat-band potential V fb , and consequently the position of the energy bands, varies with the pH of the solution because of protonation and deprotonation of surface hydroxyl groups.
This effect is especially pronounced with oxide semiconductors, germanium and some III—V compounds. Position of energy bands of various semiconductors with respect to the electrochemical scale adopted from Ref. The capacitance of the semiconductor-electrolyte interface can be measured by use of a semiconductor electrode, in which the front side of the semiconductor is in contact with the electrolyte and the rear side is electrically connected to a metallic wire via an ohmic contact.
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The differential capacitance is measured by superimposing an AC voltage, with a small amplitude of about 10 mV and a frequency of a few Hz to 1 MHz, on the electrode potential [ 38 ]. For metallic electrodes, changing the applied potential shifts the Fermi level. The band edges in the interior of a semiconductor i.