Central to the concept of Fermi level pinning by gap states is the charge neutrality level (CNL) concept, which can be roughly defined as follows. At zero temperature, the surface states are populated from the lowest energy states up to the Fermi level. If electrons are filled to a point short of the CNL, i.e. when the Fermi level is lower than the CNL, the very surface region, meaning the first few atomic planes of the surface, has a positive net charge. If the Fermi level is above the CNL, the surface has an excess of electrons and is negatively charged. Since the Fermi level is a constant throughout all regions of a semiconductor, the CNL allows a unique correspondence to be made between the band bending at the semiconductor surface and the population of surface states. To calculate the exact pinning position of the surface Fermi level, one can assume the density of surface states, D

Q

where f

For an intrinsic (meaning undoped) semiconductor with homogeneous surfaces,
the Fermi level should coincide with the CNL of the surface states.
For uniformly doped semiconductors, the surface Fermi level
position deviates slightly from the CNL to yield the necessary
surface net charge which balances the charge due to exposed
dopants in the space charge region:

e D_{GS} (
F^{o}_{B,n} +
f_{CNL} - E_{G} ) +
[ 2e_{s}
N_{D} ( F^{o}_{B,n}
-e V_{N} ) ]^{1/2} = 0

This equation can be used to solve for the Fermi level position
at the surface of a semiconductor.
Alternatively, one notes that F^{o}_{B,n}
can be obtained graphically, as shown in
this figure, by plotting both terms of the above equation on the
same graph. The graphical method is of some value as its results
can be more transparent than analytic expressions, especially
when the system gets more complex.
As shown by the above equation, even a relatively low density
of surface states, say 1x10^{13} cm^{-2} eV^{-1},
can quite effectively fixate the surface Fermi level to within 0.05eV
of the CNL independent of the doping type or the doping level of
a moderately doped (N_{D} < 1x10^{17}
cm^{-3}) semiconductor. The surface states are said to
pin the Fermi level near the CNL under these conditions.
Often, the density of surface states is thought to have peaks
at certain energetic positions, such as due to states associated
with defects or dangling bonds. With a non-uniform density
of surface states, the net charge due to surface states,
the first term of the above equation is replaced by an integral.
For a distribution of gap states with discrete peak(s),
as schematically illustrated in
this figure, the surface Fermi level can be pinned tightly
at the position of the peak. A review of the figures
makes it clear that only those gap states with energy above
the CNL, i.e. acceptors, affect the surface Fermi level position
on an uncharged, n-type semiconductor; and only gap states with
energy below the CNL (donors) can affect the Fermi level position
on a p-type semiconductor surface.

Perhaps because the net surface charge is the only relevant parameter
for the determination of surface Fermi level, the surface pinning
concept is clear and straightforward. An important aspect of
the surface states is the formation of the surface dipole, which
directly affect the electron affinity
of the semiconductor.
The magnitude of a surface dipole has to do with the entire spatial
distribution of charge. It is not difficult to imagine that
patches of the surface that have the same net charge desnity,
or even the same density of surface states distribution,
can turn out to have different surface dipoles.