For an abrupt PN junction with a step doping on the high concentration side, the deep depletion approximation results in similar equations to (4.6) and (4.7) for the value of the doping concentration on the low side:
and
where 
is the distance from the junction and 
is the reverse
junction depletion capacitance per unit area.
CV profiling can only yield the doping on one side of the junction. For this
reason, the profile of the high concentration side should be determined
using direct measurement techniques such as secondary ion mass spectroscopy
(SIMS) or incremental spreading resistance (SRP). Both methods
provide reasonable accuracy for this type of profile measurements. The
logarithm of the measured concentration is then fitted by a B-spline
function using least-squares approximation.
An initial guess for the low side doping profile is calculated by performing
the analytical extraction using (4.9) and
(4.10). The analytical profile is defined from the junction location
to 
the extent of the depletion region corresponding to the maximum
reverse junction applied. For convenience, it is extended uniformly by adding
a knot at the silicon surface. The coefficient of this knot
is not included in the optimization since the doping at this position is
compensated by the doping of the high concentration side. The same algorithm
as described in Section 4.5.1 can be used to automatically determine the
B-spline partition during the inverse modeling extraction.
