By Yu. Ya. Gurevich, Yu V. Pleskov, Z. A. Rotenberg (auth.)
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Extra info for Photoelectrochemistry
28b). It can be seen from the derivation of Eq. 32) that the quantity Em == hw - hwo(O) - ecp equals (neglecting thermal effects) the maximum possible kinetic energy of emitted electrons for the given values of cp and w. 32), describes the voltammetric characteristics of the system in the near-threshold energy range for single- and multiphoton effects (in the latter case, w is replaced by nw). It is the basic relation for the analysis of photoemission phenomena in electrochemical systems. 5. 9) are fulfilled.
EF « I obtains. The order of magnitude of the final energy of electrons giving rise to the major part of the photoemission current at a light frequency w does not exceed hew - wo). Correspondingly, the initial energies of these electrons are contained in the energy "layer" extending to the thickness hew - wo) near the Fermi surface of the metal. 11) Taking into account that Wo is the threshold frequency, the sense of the term "threshold approximation" can be understood from Eq. 11): The frequency w should be sufficiently close to woo Then, the initial energies of emitted electrons are close to that of the Fermi surface of the metal, and the probability of photoexcitation can be assumed approximately to be the same for all electrons and equal to the probability of photoexcitation at the Fermi surface.
Since the Wronskian W[Cl' C2] == Cl(dc2/dx) - c2(dc 1/dx) is independent of x, normalization of this solution can be chosen so that W[Cl' C2] = 1. 8) The unknown constant included in C2 is determined from the boundary condition for x = O. 5) and the "reverse" current of solvated electrons, Ie, is given by Ie = e~e(dce/dx)lx=o, we obtain from Eqs. 9) Examples of results obtained using Eqs. 9) are discussed below. 47 Theory of Photodiffusion Currents Photo current in the Absence of External Fields In the simplest case, Sex) = const = Q2, where Q = (kACA(~e)1/2.
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