Photoelectrochemical cells for hydrogen production from solar energy - Solar Energy Sciences and Engineering Applications - page 320

the referred analogue and all have determined consistent values of flat-band potential,
in the range of 0.4-0.6 V RHE , and of donor density, 10 17 cm − 3 for undoped struc-
tures and 10 21 cm − 3 for doped materials (Sivula et al., 2011). Nevertheless, several
discrepancies were identified for oxide semiconductors electrodes from the typical
Mott-Schottky behavior: the near and far flat-band potential, ascribed to localized
interface states and to deep donor levels, respectively. To account for this, more com-
plete models were developed considering these intrabandgap states - Figure 10.3.9b
(Leduc and Ahmed, 1988; Horowitz, 1983; Goodman, 1963).
Considering an n-type semiconductor under forward bias, there are two main
charge transfer routes involving surface states: trapping electrons from the conduction
band or holes from the valence band, acting as a recombination center. Thus, the
electron transfer from the conduction band to the redox system occurs via two steps:
electron trapping in the surface states and posterior tunneling to the redox system.
The corresponding equivalent electrical analogue is presented in Figure 10.3.9c. This
analysis has also been extensively used for determining the injection of minority carriers
and subsequent recombination with majority carriers via surface states (Gomes and
Vanmaekelbergh, 1996). The physical meaning of the simple elements depends upon
the details of the entire mechanism.
More recently, the electrical analogue presented in Figure 10.3.9d was proposed to
describe the impedance response of a nanostructured hematite photoanode prepared by
atomic pressure chemical vapor deposition (APCVD) (Le Formal et al., 2011). In this
model the element R S is the series resistance, which includes the sheet resistance of the
TCO glass substrate and the external contacts resistance of the cell (e.g. wire connec-
tions). Then, two RC elements in series are considered representing the semiconductor
bulk and the surface phenomena, respectively (Le Formal et al., 2011). Accordingly,
and bearing in mind that the electronic processes in bulk are generally faster than the
charge transfer processes or diffusion of ions in solution, the low-frequency response
was assigned to the semiconductor-electrolyte charge transfer resistance, R CT , together
with the C H (Sivula et al., 2011; Le Formal et al., 2011). The faster electronic pro-
cesses occur in the semiconductor (high-frequency range, 0.1 Hz to 100 Hz); they are
ascribed to the resistance on the depletion layer, R SC , and the space charge capacitance,
C SC , similarly to the simple RC circuit shown in Figure 10.3.9a. Moreover, this RC
element is the combination of different resistances and capacitances related to trans-
port in the semiconductor layer, charge diffusion in the space charge layer and surface
trap charging by electrons and holes (Le Formal et al., 2011).
10.4 FUNDAMENTALS IN ELECTROCHEMISTRY APPLIEDTO
PHOTOELECTROCHEMICAL CELLS
Edmond Becquerel, in 1839, discovered the photoelectric effect while he was experi-
menting with an electrolytic cell made up of two metal electrodes (Becquerel, 1839).
This phenomenon was not completely understood until 1954, when Brattain and
Garret demonstrated how electrochemical reactions occurring at germanium electrodes
can be influenced by changing the germanium semiconducting properties and also by
light excitation (Archer and Nozik, 2008). This pioneer work was followed up by
several other investigations on semiconductors between 1954 and 1970 (Nozik and