Photoelectrochemical cells for hydrogen production from solar energy - Solar Energy Sciences and Engineering Applications - page 324

Table 10.4.1 Electron and hole densities in n-type and p-type semicon-
ductor materials at room temperature (Würfel, 2005).

n p E F

n i
n =

n i
N D

E F = E C − kT ln N C
N D

n-type n ≈ N D p =

n i n i

N A

E F = E V − kT ln N V
N A

p-type n = p ≈ N A

p =

Under room temperature and assuming that all donors and acceptors are com-
pletely ionized, the electron and the hole densities equal the donor and acceptor
densities, respectively: n

N A . Table 10.4.1 summarizes the equations
for obtaining electron and hole densities as well as their Fermi Level positions for an
n-type and a p-type semiconductor, with either shallow donors or shallow acceptors,
at room temperature.

= N D and p =

10.4.1.3 Potential distribution at the semiconductor-electrolyte
interface

A key feature of a semiconductor material in contact with a liquid solution is the
formation of a built-in electric-field or space-charge region in the semiconductor side
and a Helmholtz double-layer adjacent to the semiconductor, in the liquid side. The
space charge layer is an important concept in solar conversion systems since it is linked
to the efficient separation of photogenerated electrons and holes and by consequently
preventing the recombination phenomena (Würfel, 2005). Those layers arise when
a semiconductor is brought into contact with a second phase, both with different
initial chemical potentials. Charges are transferred between them until equilibrium
is established. The electrochemical potential of the liquid phase is determined by its
redox potential; on the other hand, the redox potential of the semiconductor material
is determined by the corresponding Fermi level.
Considering an n-type semiconductor, its Fermi level is typically higher than the
redox potential of the electrolyte solution. Consequently, the electrons will be trans-
ferred from the semiconductor to the electrolyte. The Fermi level in the semiconductor
moves “down'' and the process stops when the Fermi level equals the redox potential
in the electrolyte side. This movement is also followed by the conduction band edge,
giving rise to a band bending as illustrated in Figure 10.4.2a and described by Equation
10.4.14. Similarly, for a p-type semiconductor a depletion layer also occurs when the
region containing negative charges is depleted of holes since they are transferred to
the electrolyte media until Fermi level and redox potential equilibration. This nega-
tive layer will be compensated by the positive charges adsorbed on the solid electrode
surface in the electrolyte side - Figure 10.4.2b.
The potential distribution and the width of the space charge layer can be quan-
titatively described by the Poisson - Equation 10.4.11. This depends on the amount