When MB statistics apply to both carrier types the relationship between the surface field and the surface potential has the well known form
Note that the last term is negligible. This equation directly follows
from A.11, when we remember that for MB statistics the normalized
Fermi integrals reduce to for an arbitrary order
. In common cases,
holds. In A.14,
the quantity
is the effective Fermi barrier
The effective intrinsic concentration is given by A.7 for
=0, because FD statistics is adopted for majorities.
This effective Fermi barrier differs from the Fermi barrier introduced
in 2.15 for the case of nonsymmetric band-gap narrowing, as
it follows from the relationship
valid for MB statistics. However, the differences between and
are not only small, but also of only academic importance,
since we do not dispose of any experimental technique to measure the individual
band shifts
and
separately from each other
at present.