7.2.5 The variable depletion layer charge model
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Next: 7.3 Threshold voltage calculation
and threshold voltage adjustment
7.2.5 The variable depletion layer model
Required background: Threshold
voltage calculation
The variable depletion layer model includes the fact that the
voltage in the channel between the source and drain varies, which
causes the depletion layer width between the channel and the
substrate to vary as well. This in turn affects the inversion
layer charge which is still given by:
(vt0)
where we now acknowledge the implicit dependence of the threshold
voltage on the charge in the depletion region, or:
(mf21)
where the voltage VC is the difference between
the voltage within the channel and the source voltage. We can now
apply the linear model to a small section at a distance x
from the source
and with a thickness dx. The voltage at that point equals
VC + VS while the voltage across
that section equals dVC. This results in the following
expression for the drain current, ID:
(mf22a)
Both sides of the equation can be integrated from the source to the
drain with x varying from 0 to the gate length, L, and
VC varying from 0 to the drain-source voltage,
VDS.
(mf22b)
Integration along the channel yields the following drain current:
(mf22)
The current-voltage characteristics as obtained with the above
equation are shown in the figure below, together with those obtained
with the quadratic model. Again it was assumed that the drain
current saturates at its maximum value, since a positive inversion
layer charge can not contribute to the drain current. The drain
voltage at which saturation occurs is given by:
(mf23)
mosfetc0.xls - fetcomp0.gif
Fig.7.2.2 Comparison of the quadratic model (red curves) and the
variable depletion layer model (green curves)
The figure shows a clear difference between the two models: the
quadratic model yields a larger drain current compared to the more
accurate variable depletion layer charge model. However, because of
its simplicity, the quadratic model is widely used. Fitting parameters
are often used instead of the actual device parameters in order to
more closely describe the measured characteristics.
A more complete comparison between the two models is also available.
Next: 7.3 Threshold voltage calculation
and threshold voltage adjustment
7.2.4
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© Bart J. Van Zeghbroeck, 1996, 1997