The removing of the inversion-layer charge above the threshold voltage determines the amount of the charge which is transferred to the bulk. It is known from the studies of the charge transfer in the charge-coupled devices (CCD) that three mechanisms can be responsible for the lateral transport in such an MOS structure under the transient conditions:
is high [246][47][27].
where 
. Since the both standard assumptions
in the analytical MOS modeling that the perpendicular field is much larger than
the lateral field and the G.C.A. are expected to be valid, the following
relationship holds
The initial conditions and the boundary conditions at the middle of the channel are equivalent to those in solving the CCD discharging problem:
The 
is the 
-coordinate of the drain junction. Note that the carrier
concentration at the end of the channel does not vanish. It is given
approximately by its quasi-static value. The later changes with time as the
falls. The same holds for the boundary condition of 
at the
drain channel end.
The charge is removed from the channel by drift due to a field induced
by the gradient , like the mechanism 2). The
field almost linearly increases from the zero value at the channel center
to the maximal value at the channel end . With decreasing
the field 
increases. At very short 
this field can be quite large;
in the example with 
and 
shown in
Figure 3.15, the maximal ranges from 
to
for 
. Therefore, a non-linearity in the 
relation can influence the analysis at short fall times. After the 
is fallen below the 
, the charge is removed by both, drift and
diffusion (the process 1) in CCDs) at short and by diffusion alone at
long . Whether the drift is significant or not depends on the amount of
the . The diffusion mode of the operation has also been studied
in [259], by using an analytical-numerical model, while considering the
turn-off of pass MOSFETs. Our analysis has argued that the charge transferred
to the bulk depends strongly on the slope of the falling edge 
,
but not on 
and separately. For example, for 
device,
assuming 
, the 
varies from 
to 
when
is fixed and the 
is changed from
and 
to 
and 
.
The study suggests that the charge profile 
decays with time without
changing its shape. Therefore, an analytical solution to the problem may be
found by separating the variables 
and , in a form of product of two
independent functions of the individual variables. This should be done in
further work on this topic.
The switching terminal currents and the total net generation rates
in a long-channel MOSFET with are shown in
Figures 3.16. The parameter ranges from an extremely
short of 
to a long of 
. In the later case the turn-off of the
device is nearly quasi-static. Particularly interesting is the bulk electron
current 
which represents a parasitic effect in the measurements.
occurs
for all fall times. This finding is consistent with
Figure 3.14.
.
, as discussed above.
.
