Chemistry Reference
In-Depth Information
where is the bulk minority carrier density and is the increased carrier density due
to light excitation. This equation indicates that large photovoltages are already obtained
at rather low intensities of light, because the carrier density created by light excitation
can easily exceed the minority carrier density. Since
is a constant for a given
material and
is proportional to the light intensity
the above equation can be
reduced to
where
b
is a positive constant. The same expression as Eq. (1.95) can be derived for
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It can be seen that is always negative because when an
n
-type semi-
conductor is illuminated, the band bending decreases. At relatively low intensities
of illumination, i.e.,
the absolute value of the photopotential increases
linearly with increasing
whereas at high intensities, i.e.,
the change is
logarithmic.
When the photoeffect is limited mainly by the bulk recombination process, i.e.,
the diffusion of the minority carriers, the photopotential can be quantitatively related
to the minority diffusion coefficient,
and the diffusion length,
at a photocurrent
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of
:
When the redox species in the solution do not interact with the semiconductor
surface and the band edge at the surface is fixed with respect to the redox potential,
the changes in the redox potential in the solutions will result in identical
change in the photovoltage on an illuminated electrode. The presence of a redox
couple with more negative than for
n
-type material or more positive than
for
p
type results in an interface with no photovoltage. For
more positive than
for
n
type or more negative than
for
p
type, the photoeffects are also expected to
be minimal. Only for
situated within the band gap can a large photovoltage be
expected.
For a semiconductor that is at equilibrium with a redox couple in the solution,
the band bending is determined by the redox potential. The maximum attainable pho-
tovoltage is the size of band bending, which is ideally related to the barrier height,
Under an equilibrium condition, generally does not
move into the valence band to form an inversion layer and thus the maximum band
bending cannot exceed that is, about the band gap.
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Thus, theoretically, the
maximum attainable photovoltage is close to the band gap when the redox potential is
near the valence band edge at the surface.
As a semiconductor/electrolyte interface for photoenergy conversion, the objec-
tive is to position close to for
n
-type material for photoanodes, or close to
for
p
type for photocathodes to achieve the largest band bending in the dark and thus
the maximum photovoltages. The maximum open-circuit photovoltage is equal to the
amount of band bending or the barrier height, which can be given as
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