Chemistry Reference
In-Depth Information
where is the empty state and the filled state. When the interaction with the solu-
tion can be neglected, the occupancy of the surface states is determined by the Fermi
level and the surface state capacitance can be expressed as
808
where is the surface electron concentration, the frequency of the potential or current
modulation, and and the rate constants for the forward reaction and reverse reac-
tion described by Eq. (1.39). At low frequency where
exhibits a
maximum as a function of potential
from which the density of surface states can be determined.
1.3.6. Fermi Level Pinning
The total charge on the solid side of the semiconductor/electrolyte interface
equals When surface states are present and their capacitance is significantly
larger than that of the space charge layer, that is, Fermi level pinning by the
surface states occurs.
270
Figure 1.9 illustrates the effect of dopant concentration and
surface state density on the magnitude of surface state charges and space charge layer
a surface state density on the order
of which is about 1% of the surface atomic density, can result in
When the Fermi level is pinned, the change of potential will mainly occur in the
Helmholtz layer rather than in the space charge layer as in the case without Fermi level
pinning.
As a consequence of Fermi level pinning, the Schottky barrier height
at the semiconductor/electrolyte interface becomes constant with respect to redox
couples of different
height value, has been found to occur at the
charges. It can be seen that for a doping of
values. Fermi level pinning, which results in a constant barrier
n
-Si/acetonitrile interface containing dif-
ferent redox couples.
486,935
1.3.7. Equivalent Circuit and Capacitance of Semiconductor/Electrolyte Interface
The electrical nature of the semiconductor/electrolyte interface region can be
described by an equivalent circuit of an array of resistors and capacitors arranged
according to the physical structure of the region. Figure 1.10 illustrates a typical equiv-
alent circuit of a semiconductor/electrolyte interface including the effect of the space
charge layer, Helmholtz layer, surface states, and electrolyte resistance. On application
of a voltage change of
dV
across the interface region, charge in the form of electrons,
holes, and ions will move in the corresponding layers, which can be characterized by
the capacitances of these layers.
The total potential change
is divided between the space charge layer and the
Helmholtz layer:
