It is assumed that three processes occur at the bottom level 
: hole
capture, hole emission and electron emission. The electron capture vanishes
when the bottom level is low so that 
.
With benefit of
, one obtains
. The traps above the Fermi level capture
holes with a much larger probability than they emit the holes. The
hole emission can be considered as vanishing in this interval.
For the levels above 
the hole emission can be
neglected during .
The lower boundary of the energy interval which is active in charge
pumping is given by
The Fermi level governs the lower boundary when
which corresponds to the cases when 
is lower than the
charge-pumping flat-band potential 
.
The hole capture is faster than the electron emission for all energy
levels below 
and vice versa.
An interesting relationship holds:
.
If the gate bottom level drives the interface into strong
accumulation, 
holds and it follows
that 
. In the later case the electron
emission is negligible during the capture of holes at the bottom
level.
The traps above the level 
are emptied during
by the electron emission. The emission is very fast for all traps,
except for the traps around the level . As a
consequence, the traps above this level are not available for hole
capturing during , when the hole capture has a low probability.
Regarding c) and d) the upper boundary of the energy
interval available for the hole capture is determined by
According to the preceding discussion, at the end of the bottom level
are filled,
are emptied by the electron
emission (they do not contribute to 
) and
and are
emptied to a some degree by the capture of holes from the valence band.
The hole capture obeys an exponential law with the time constant
. The number of holes captured during is
directly related to the charge-pumping current.
