Photoelectrochemical cells for hydrogen production from solar energy - Solar Energy Sciences and Engineering Applications - page 332

The η ohmic term decribes the ohmic loss through the electrode area A and may be
written in terms of an ohmic resistance, R ohmic (Nozik, 1978):

η ohmic = J cell AR ohmic (10.4.38)

The left term in Equation 10.4.38 represents the net photon energy necessary to gener-
ate an electron-hole pair in the semiconductor and that has to equal the electrochemical
work described by the right hand of the same equation.

10.4.2.2 Metal-liquid interface

In a PEC cell for water-splitting electrons return from the external circuit to the counter-
electrode in order to reduce water into hydrogen. This reaction occurs in the surface of
a metal electrode, typically a platinum wire. The interface electrolyte metal electrode
can be treated as an electrochemical half-cell and described using the well-known
Butler-Volmer equation:

j 0 C R
C 0 R

exp βzeη c
kT

exp −

C P
C 0 P

( 1 − β) zeη c

kT

j = − (10.4.39)

where η is the overvoltage, z is the number of electrons transferred in the electro-
chemical reaction, C R and C P are the surface concentrations of the reactants and
products, j 0 is the exchange current density (Aruchamy et al., 1982). Basically, Butler-
Volmer equation states that the current produced by an electrochemical reaction
increases exponentially with the activation overvoltage. Taken as an example the
electrolyte/platinum interface in a PEC cell system for water-splitting, Equation 10.4.38
becomes:

j 0 n H 2 O ( b )
n re H 2 O ( b )

exp βzqη Pt
k B T

exp −

n H 2 ( b ) n OH − ( b )
n re H 2 ( b )( n re OH − ) 2 ( b )

(1 − β ) zqη Pt

k B T

j = − (10.4.40)

The overpotential may be regarded as the extra voltage needed to reduce the energy
barrier of the rate-determining step to a value such that the electrode reaction proceeds
at a desired rate. Thus, this equation tells us that if we want more current we have to
pay a price in terms of voltage lost - overvoltage.

10.4.2.3 PEC cell photoresponse

The photoresponse of the PEC cell will be determined by the behavior of photogener-
ated electron-hole pairs and thus the physical properties of the semiconductor. Thus,
the photocurrent flowing through the interface, under illumination, was derived by
Gärtner, for an n-type semiconductor, as follows:

eI 0 1

exp( − βW )

j G = j 0 + − (10.4.41)

1 + βL p

where I 0 , is the incident photon flux, β is the absorption coefficient (assuming
monochromatic illumination), W is the depletion layer width, L p is the hole diffu-
sion length and j 0 is the exchange current density. The Gärtners's model assumes that