Chemistry Reference
In-Depth Information
the surface, equilibrium is not established and a deep depletion layer is formed as shown
by the dashed line in Fig. 1.8.
1.3.4. Helmholtz Double Layer
The potential drop in the Helmholtz layer is defined as
where is the potential at the solid surface and is the potential at the ohp.
The charge on the solution side of the Helmholtz layer originates from the accu-
mulation of ions at the ohp, whereas on the solid side it can arise in three forms: an
accumulation of free charge, free charge trapped from the solid onto surface states, and
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For nondegenerated semiconductors, is primarily determined by
adsorption/desorption processes between the surface and the electrolyte. The contribu-
tion from electron transfer between the surface and the bulk of the semiconductor is
negligible. This is because the amount of charge captured by the surface associated with
this transfer is on the order of or less which is very small in
comparison with the amount of charge (on the order of associated with the
adsorption/desorption processes on the surface. Thus, for non heavily doped semicon-
ductor the applied potential variation can be considered to drop entirely in the space
charge layer and the Mott-Schottky equation can be used for determination of the flat-
band potential. The contribution to the Helmholtz layer by charge transfer becomes
more important for degenerated semiconductors, which can accommodate more charge
in the bands near the surface.
When the charge on the solid surface is determined by the specific adsorption of
adsorbed ions.
and
which is the case for many semiconductors,
is determined by the reaction
where
is the adsorbed
on the surface. At equilibrium the concentration of
can
be expressed as
where
is a constant. Assuming the double layer capacitance, is independent of
we obtain
A
Equations (1.31) and (1.32) indicate that
which changes linearly with
will
vary slowly compared with
which changes exponentially with
As an
approximation we have
which shows that the Helmholtz potential varies by 60 mV per pH unit.
