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Compact Models for Integrated Circuit Design
In the case of short channel MOSFETs, the terminal charges and capacitances cannot be calculated just by substituting V ds = V dsat . However, for
short channel devices, where velocity saturation and channel length
modulation (CLM) become important, charge near the saturation consists
of two components. One is the charge near the source region where the
gradual channel approximation can be applied and the other is the charge
near the pinch-off region at the drain-end where carrier velocity saturates.
This two-section model creates a discontinuity in the capacitances from the
linear to saturation regions, similar to the case of drain current modeling.
Therefore, often the charge in the pinch-off is ignored for short channel
modeling.
The effect of including velocity saturation in the charge expressions is a
reduction in the amount of charge from its long channel value, which intuitively makes sense because carriers are velocity saturated. Although the
effect of S/D resistance is not taken into account it is possible to include its
effect externally.
In weak inversion, Q I , and hence Q S and Q D , are assumed zero, similar to
the long channel case. This means that Q G = −Q B in weak inversion. For short
channel devices, the bulk charge Q B is still given by Equation 6.24, however,
the long channel body factor γ is replaced by an effective value of γ, to account
for the reduction in the bulk charge density due to short channel and narrow
width effects as discussed in Chapter 5.
6.3.4 Short Channel Capacitance Model
The expressions for the terminal charges for short channel devices given
in Section 6.3.3 are used to calculate the corresponding capacitances using
the procedure discussed for the long channel devices. The mathematics is
basic, however involved. Thus, we will not derive the final expressions for the
capacitances.
It is difficult to accurately measure the capacitances for short channel
MOSFETs unlike the long channel devices. This is attributed to very
small value of capacitances (~1 × 10 −18 F) and the difficulty in separating the
small transient currents due to the capacitances associated with the source
and drain terminals by the large steady-state current (I ds ) in small devices.
Thus, most reported data on short channel capacitances are on the gate
capacitances C GS , C GD , and C GB .
The measured capacitances include the overlap capacitances, and as such,
they do not entirely describe intrinsic capacitances. This is particularly true
for short channel devices with lightly doped drain (LDD) regions. However,
no such bias-dependent overlap is generally observed in short channel conventional S/D pn-junctions. The bias dependence of the overlap capacitance
is due to the modulation of the lightly doped regions (n-region for nMOSFETs and p-region for pMOSFETs).
Compact Models for Integrated Circuit Design
In the case of short channel MOSFETs, the terminal charges and capacitances cannot be calculated just by substituting V ds = V dsat . However, for
short channel devices, where velocity saturation and channel length
modulation (CLM) become important, charge near the saturation consists
of two components. One is the charge near the source region where the
gradual channel approximation can be applied and the other is the charge
near the pinch-off region at the drain-end where carrier velocity saturates.
This two-section model creates a discontinuity in the capacitances from the
linear to saturation regions, similar to the case of drain current modeling.
Therefore, often the charge in the pinch-off is ignored for short channel
modeling.
The effect of including velocity saturation in the charge expressions is a
reduction in the amount of charge from its long channel value, which intuitively makes sense because carriers are velocity saturated. Although the
effect of S/D resistance is not taken into account it is possible to include its
effect externally.
In weak inversion, Q I , and hence Q S and Q D , are assumed zero, similar to
the long channel case. This means that Q G = −Q B in weak inversion. For short
channel devices, the bulk charge Q B is still given by Equation 6.24, however,
the long channel body factor γ is replaced by an effective value of γ, to account
for the reduction in the bulk charge density due to short channel and narrow
width effects as discussed in Chapter 5.
6.3.4 Short Channel Capacitance Model
The expressions for the terminal charges for short channel devices given
in Section 6.3.3 are used to calculate the corresponding capacitances using
the procedure discussed for the long channel devices. The mathematics is
basic, however involved. Thus, we will not derive the final expressions for the
capacitances.
It is difficult to accurately measure the capacitances for short channel
MOSFETs unlike the long channel devices. This is attributed to very
small value of capacitances (~1 × 10 −18 F) and the difficulty in separating the
small transient currents due to the capacitances associated with the source
and drain terminals by the large steady-state current (I ds ) in small devices.
Thus, most reported data on short channel capacitances are on the gate
capacitances C GS , C GD , and C GB .
The measured capacitances include the overlap capacitances, and as such,
they do not entirely describe intrinsic capacitances. This is particularly true
for short channel devices with lightly doped drain (LDD) regions. However,
no such bias-dependent overlap is generally observed in short channel conventional S/D pn-junctions. The bias dependence of the overlap capacitance
is due to the modulation of the lightly doped regions (n-region for nMOSFETs and p-region for pMOSFETs).