Chemistry Reference
In-Depth Information
At the surface where
the factor
is negligible for a reasonable value
of
From Gauss's law we have
is the total charge in the space charge layer per unit electrode surface area
and is the point in the semiconductor where the field is zero. Since the capacitance
of the space charge layer
where
differentiating Eq. (1.23) with respect to
an
expression for
is obtained:
Equation (1.24) is the much-used Mott-Schottky equation, which relates the space charge
capacity to the surface barrier potential
Two important parameters can be determined
by plotting
versus
the flatband potential
at
(where
and the
density of charge in the space charge layer, that is, the doping concentration
1.3.3. Accumulation Layer and Inversion Layer
In the case of an accumulation layer, for example, when electrons are injected
into (instead of extracted from) an
n
-type sample, or holes are injected into (instead of
extracted from) on a
-type sample, the surface charge region has an excess of the
majority carriers. For
n
-type materials, according to Eq. (1.16),
p
where the first term represents the contribution of electrons in the conduction band and
the second represents the contribution of immobile positive ions. An accumulation layer
can be formed, for example, on an
n
-type material by applying a sufficiently large neg-
ative voltage on the semiconductor relative to the solution. If the band bending is such
that the Fermi energy moves into the band, a “degenerate surface” is formed, which
marks the transition from semiconducting behavior to metallic behavior. The thickness
of an accumulation layer is typically on the order of 100 Å. Such a layer as thin as
3 Å has been found at
n-
Si in acetonitrile.
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Under a depletion condition, an inversion layer is formed when near the surface
the minority carriers accumulate and are in equilibrium with those in the bulk (that is,
the consumption rate of the carriers in the electrochemical reactions is low). When an
inversion layer occurs, the density of minority carriers near the surface may exceed that
of the bulk majority carriers. Under such a condition, when
n
(
x
)
<p
(
x
) within the space
charge layer equation, the Poisson equation [Eq. (1.16)] becomes
where the first term represents the immobile ions and the second term represents the
density of minority carriers, which becomes comparable to the first term at relatively
