Environmental Engineering Reference
In-Depth Information
Memming, 1996). These studies established the first models for the charge distribu-
tion, kinetics and energetic of charge transfer mainly across the semiconductor-liquid
interface. However, it was only in the seventies that the potential application of photo-
electrochemical systems for solar energy conversion and storage was truly recognized
(Fujishima and Honda, 19726). Given the enormous efforts devoted to understand-
ing the physics behind semiconductors, it might be expected that this is a mature
field. Nevertheless, most of this knowledge pertains to bulk and transport phenom-
ena and for the above mentioned applications; it is the surface (photo)chemistry
that governs the interfacial transfer and energy transduction, and here we are still
evolving our understanding (Archer and Nozik, 2008). Despite these difficulties,
the progress that has been made, mainly through the phenomenological understand-
ing of the processes occurring in the semiconductor surface, and more concretely at
the semiconductor-electrolyte interface, was indeed shown to be of great importance
(Butler, 1977; Gärtner, 1959; Henry et al., 1978; Reiss, 1978; Wilson, 1977). This
section targets a fundamental understanding of semiconductor physics, by describing
the different type of semiconductors and the main equations governing the charge car-
rier distribution. The semiconductor/electrolyte interface will be described in terms of
potential distribution. It is then described as an integrated phenomenological model for
photoelectrochemical cells for water-splitting. The continuity and transport-governing
equations are defined for the several mobile species involved in the phenomena
occurring in the different regions of the PEC cell (Andrade et al., 2010; Andrade
et al., 2011).
10.4.1 Semiconductor energy
Solid materials can be categorized as conductors, insulators or semiconductors,
depending on their ability to transport electrical current. A conductor carries elec-
trical current, whereas an insulator cannot carry current. Between these two materials
are the semiconductors. Electrons in semiconductors can have energies only within cer-
tain bands between the energy of the ground state, corresponding to electrons tightly
bound to the atomic nuclei of the material, and the free electron energy, which is the
energy required for an electron to escape. Between these two bands there is a bandgap
with energy
E
g
, which greatly determines the properties of the material (Andrade et al.,
2010; Andrade et al., 2011). The filled energy states that correspond to the valence
band are localized in the energy range below the gap and the empty energy states
corresponding to the conduction band are localized in the energy range above the gap
(Memming, 2001).
10.4.1.1 Intrinsic semiconductor
The Fermi-Dirac function
f
(
E
) gives the probability that a single-particle state of energy
E
would be occupied by an electron at thermodynamic equilibrium (at a constant
temperature with no external injection or generation of carriers). The Fermi-Dirac
distribution function, also called the Fermi function, is given by:
1
exp
E
−
E
F
kT
f
(
E
)
=
(10.4.1)
1
+
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