Photoelectrochemical cells for hydrogen production from solar energy - Solar Energy Sciences and Engineering Applications - page 316

Figure 10.3.5 Schematic representation for an n-type semiconductor of: depletion layer zone and the
electrical double layer (Helmholtz layer).

separation that occurs across the interface: an excess of ions of opposite charge to that
on the electrode will be found at the electrolyte phase boundary. A simple way of
understanding the double layer behavior is to imagine that ions at each side of the
interface approach the electrode surface as closely as possible, originating two parallel
layers of equal and opposite charge, one on the electrode side and the other on the
electrolyte side - Figure 10.3.5. This double-layer will act as a charge storage (Bard
and Faulkner, 2001), i.e. a capacitor with an impedance response defined as follows:

1
jωC

Z C = (10.3.6)

In real cells, formed by nanoporous semiconductors, the double layer capacitor does
not behave ideally. Instead it acts like a constant phase element (CPE), a non-ideal
capacitance with a non-uniform distribution of current in the heterogeneous material.
In this case, the impedance of the double layer capacitance is defined as:

1
jωC n z

Z C = (10.3.7)

where n z (0 < n z < 1) is an empirical constant with no real physical meaning; for ideal
capacitors n z = 1 (Barsoukov and Macdonald, 2005).

For the case of a simple capacitor, the corresponding Nyquist plot is just a ver-
tical line coincident with the imaginary axis and thus with no real component -