275
Compact MOSFET Models for RF Applications
impractical when the device channel length is small because the short channel effects in the subtransistors may be activated. As an example, it is found
that the results of modeling a 200 μm long MOSFET device in strong inversion (saturation) is completely different from modeling two 100 μm long
MOSFETs in series.
It has been found that for RF applications the NQS model is necessary to
fit the measured high-frequency characteristics of devices with even short
channel length where the operation frequency is above 1 GHz [39,40]. Thus,
NQS model is desirable in some mixed signal IC (integrated circuit) and RF
applications. Therefore, a compact model that accounts for the NQS effect
is highly desirable. Some NQS models based on solving the current continuity equation have been proposed [41–43]. They are complex and require
long simulation time, making them unattractive for use in circuit simulation.
In this chapter, an NQS model based on the Elmore-equivalent resistancecapacitance (RC) circuit is described [35]. It uses a physical relaxation time
approach to account for the finite channel charging time. This NQS model
applicable for both the large signal transient and small signal AC analysis is
discussed in the next section.
7.3.1 Modeling NQS Effect in MOSFETs
Typically, the channel of a MOSFET is analogous to a bias-dependent
RC-distributed transmission line [44]. In QS approach, the gate capacitors are
lumped with the intrinsic source and drain nodes [35]. This ignores the fact
that the charge build-up in the center portion of the channel does not follow
a change in V g as readily as it does at the source or drain edge of the channel. Breaking the transistor into N devices in series offers a good approximation for the RC network but has the disadvantages discussed in Section 7.3.
A physical and efficient approach to model the NQS effect would be to formulate an estimate for the delay time through the channel RC network, and
incorporate this time constant into the model equations.
One of the most widely used methods to approximate the RC delay was
proposed by Elmore [45], considering the mean, or the first moment, of the
impulse response. Utilizing Elmore’s approach, the RC distributed channel
can be approximated by a simple RC equivalent circuit that retains the lowest frequency pole of the original RC network. The new equivalent circuit
is shown in Figure 7.5. The Elmore resistance (R Elmore ) in strong inversion is
calculated from the channel resistance and is given by [35].
R
L
E W Q
L
E W C V V
Elmore
eff
LM
eff i
eff
LM
eff ox
g s
t h
=
=
−
(
)
µ
µ
(7.39)
Compact MOSFET Models for RF Applications
impractical when the device channel length is small because the short channel effects in the subtransistors may be activated. As an example, it is found
that the results of modeling a 200 μm long MOSFET device in strong inversion (saturation) is completely different from modeling two 100 μm long
MOSFETs in series.
It has been found that for RF applications the NQS model is necessary to
fit the measured high-frequency characteristics of devices with even short
channel length where the operation frequency is above 1 GHz [39,40]. Thus,
NQS model is desirable in some mixed signal IC (integrated circuit) and RF
applications. Therefore, a compact model that accounts for the NQS effect
is highly desirable. Some NQS models based on solving the current continuity equation have been proposed [41–43]. They are complex and require
long simulation time, making them unattractive for use in circuit simulation.
In this chapter, an NQS model based on the Elmore-equivalent resistancecapacitance (RC) circuit is described [35]. It uses a physical relaxation time
approach to account for the finite channel charging time. This NQS model
applicable for both the large signal transient and small signal AC analysis is
discussed in the next section.
7.3.1 Modeling NQS Effect in MOSFETs
Typically, the channel of a MOSFET is analogous to a bias-dependent
RC-distributed transmission line [44]. In QS approach, the gate capacitors are
lumped with the intrinsic source and drain nodes [35]. This ignores the fact
that the charge build-up in the center portion of the channel does not follow
a change in V g as readily as it does at the source or drain edge of the channel. Breaking the transistor into N devices in series offers a good approximation for the RC network but has the disadvantages discussed in Section 7.3.
A physical and efficient approach to model the NQS effect would be to formulate an estimate for the delay time through the channel RC network, and
incorporate this time constant into the model equations.
One of the most widely used methods to approximate the RC delay was
proposed by Elmore [45], considering the mean, or the first moment, of the
impulse response. Utilizing Elmore’s approach, the RC distributed channel
can be approximated by a simple RC equivalent circuit that retains the lowest frequency pole of the original RC network. The new equivalent circuit
is shown in Figure 7.5. The Elmore resistance (R Elmore ) in strong inversion is
calculated from the channel resistance and is given by [35].
R
L
E W Q
L
E W C V V
Elmore
eff
LM
eff i
eff
LM
eff ox
g s
t h
=
=
−
(
)
µ
µ
(7.39)