In the following, the charge-pumping threshold voltage 
and the
charge-pumping flat-band potential 
are compared with the device
threshold and flat-band voltages.
From the one-dimensional Poisson equation one derives for 
-channel devices
with 
. 
is the device flat-band potential. The critical
concentration 
depends on the top-level duration 
according
to 3.64. The device threshold voltage 
follows
from 3.102 assuming 
. The charge-pumping
flat-band potential can be derived in an analogous way
The critical hole concentration 
is given by 3.65.
The calculated versus top level duration and 
versus bottom level duration are shown in Figure 3.8.
The bulk doping 
is a parameter. The charge-pumping threshold and
flat-band voltage differ significantly from the device voltages for the very
short and long duration of the top and bottom levels, while they are close to
the device voltages for medium time intervals.
The dependence of and on the frequency of the gate
signal 
may be exploited to measure the capture cross-sections
separately for electrons and holes. The derivation
follows from 3.102. It depends on the ratio 
and the bulk doping . The concentration results as the
solution of a simple transcendental equation. By measuring the characteristic
one is able to obtain and consequently,
. In an analogous way, the derivation of the
characteristics 
can be used to extract the critical hole
concentration and finally, the capture cross-section
. Note that both cross-sections can be measured in the
same device by the same experiment. The bulk doping profile, assumed here as
uniform with concentration , must be measured separately. This technique
is proposed for long-channel devices. Further experimental and theoretical
work is necessary to evaluate the feasibility of this technique to be applied
in practice, in particular to examine its sensitivity and the influence of
errors in the determination of .
