Chemistry Reference
In-Depth Information
to generate electrode reactions, the exponential region occurs only at sufficiently high
illumination intensities such that the availability of holes is no longer the rate-limiting
step. Under such a condition, the Tafel slope of
n
-Si is similar to that of other silicon
materials.
Phenomenologically, the occurrence of the 60 mV/decade Tafel slope can be
attributed either to a rate-limiting process involving charge transfer in the Helmholtz
layer or to one involving carrier supply in the space charge layer. If it is in the Helmholtz
layer, the Tafel is 60 mV/decade, assuming the charge transfer coef-
ficient is 0.5 and the number of charges per dissolved silicon atom is 2. If it is in the
space charge layer, it also gives 60 mV/decade since
V/
log
i
for the current involving
carrier supply in the space charge layer is
kT/
2.3
q.
The slope will not be 60 mV/decade
if the rate determining process involves both layers.
Deviation of 60 mV/decade can be seen in Table 5.3 under different condi-
tions. In addition to the potential distribution in the two double layers, there are
two other possible causes for the deviations. The first is possible potential drops
in other parts of the electrical circuit, e.g., in the electrolyte and semiconductor.
The second possibility is the change of effective surface area due to the forma-
tion of a porous silicon layer during the course of
i-V
curve measurement.
2
In
addition, if the reaction is controlled by a process involving the Helmholtz layer,
the apparent Tafel slope may be smaller than the 60 mV/decade as would be ex-
pected from the formula, because the effective dissolution valence
is not a constant with respect to potential but varies from 2 to 3 in the exponential
region.
5.8.2. Potential Distribution
The impedance data on
p
-Si and
n
-Si at different doping concentrations sug-
gest that the distribution of the applied potential depends on silicon material as well
as potential range. Table 5.4 is a summary of the potential distribution of different
materials in the three potential regions, from OCP to the potential of onset current,
the exponential region, and the region above the passivation potential. While the
distribution of the potential below depends on doping type and concentration,
the applied potential is principally dropped in the oxide film at potentials higher
than for all materials. There is a transition zone between the regions, where
the potential drop changes from predominantly in one layer to predominantly in
another.
