Let us define the entering in inversion at the oxide/semiconductor interface in
the standard way by , for
-type of semiconductor. Replacing
in A.5, taking advantage
of A.4 and
we derive
The potential may be written as
where
is the potential at the onset of inversion for the ideal band and MB statistics.
Band-gap narrowing and degeneration tend to cancel each other in
expression A.23. Like most quantities in our analysis,
is also only slightly influenced by the degeneration due to
FD statistics. For example, assuming
, the sum
contributes to
with only
at
and with
at
, both being less than the
small contribution of the electrical band-gap narrowing at this doping level.
In the preceding calculation we have accurately accounted for the temperature
dependence of
and
.