Theoretical Aspects

With reference to Fig. 5, the so-called quasi-Fermi level formalism3,7,11,12 is useful for understanding the interfacial energetics at illuminated semiconductor-electrolyte interfaces. Thus, in the dark, at equilibrium:

Fig. 5. Diagrams for a semiconductor-electrolyte interface (a) at equilibrium and (b) under irradiation showing the quasi-Fermi levels for electrons and holes.

where Ef stands for the Fermi level energy and the subscripts n and p denote the two types of carriers, electrons and holes in the semiconductor respectively. This situation is schematized in Fig. 5a. Under illumination, at open-circuit, a non-equilibrium concentration of electronic carriers is created, and separate quasi-Fermi levels (Efn and Efp) are required to describe the electron and hole concentrations (Fig. 5b):

In Eqs. 4a and 4b, x is a position variable since the values of n, p, Efn and Efp are position dependent to varying degrees, Nc and Nv are the densities of states in the conduction and valence bands respectively, k is the Boltzmann constant and T is the absolute temperature. The splitting of the electron and hole quasi-Fermi levels under illumination (Fig. 5b) defines the magnitude of the photovoltage developed, A V (A Voc in the specific open-circuit case in Fig. 5b).

On the basis that the position of Efn at the semiconductor surface is dependent on the photon flux and that Efn has to lie above the HER redox level, a threshold in light intensity has been proposed217 for the sustained photoelectrolysis of water to occur. However, as discussed by other authors,218 no such threshold has been reported in the literature. It has been pointed out218 that the driving force for the photoinduced electron transfer process is related to the difference in standard potentials of the donor (say, an electron at the semiconductor CB edge) and the acceptor (say, protons in solution). This is independent of the carrier concentration and photon flux and thus a light intensity threshold for incipient product formation through photoelectrolysis should not occur.218

The experimental observations217 of an apparent light intensity threshold for the photocurrent onset have been rationalized218 on the basis that a critical photon flux must be exceeded to counteract the dark current of opposite polarity flowing through the cell. Thus, there appears to be confusion between alternate definitions of a light intensity threshold: a threshold for incipient product (say H2) formation and a threshold for product formation in a specific (e.g., standard) state.218

Other fundamental considerations for a solar photoelectrolysis system have been discussed.219-223 Theoretical formulations for photocurrents at p- and n-type semiconductor electrodes have been presented221 on the assumption that the rate-determining step is charge transfer across the interface. A theory for the light-induced evolution of H2 has been presented by the same group for semiconductor electrodes.222 The effect of an oxide layer of tunneling dimensions has been considered for photoelec-trochemical cells designed for fuel (e.g., H2) production.223 It is fair to say that these theoretical developments have occurred fairly early on in the evolution of this field (before 1985). The work in the subsequent two decades has largely focused on the discovery of new semiconductor materials for the photosplitting of water.

We consider these materials aspects in the next few Sections.

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