3.4.1 Minority Carriers Remaining in the Channel



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3.4.1 Minority Carriers Remaining in the Channel

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:

The problem of discharging an MOSFET is more complicated than the discharging a CCD due to the presence of the junctions and a finite width of the falling edge of the gate pulse. The problem in an approximate one-dimensional form reads

 

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.

 



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Next: 3.4.2 Carriers Emitted from Up: 3.4 Geometric Current Component Previous: 3.4 Geometric Current Component



Martin Stiftinger
Sat Oct 15 22:05:10 MET 1994