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Compact Models for Integrated Circuit Design
7.3 NQS Effect
In Chapter 6, the charge and C–V models are derived based on the QS
approximation; that is, the inversion charge responds to the changes in the
applied signal instantaneously. However, the QS approximation breaks
down when signal changes occur on a timescale comparable to the device
transit time.
As very-large-scale-integrated (VLSI) circuits become more performancedriven, it is sometimes necessary to predict the device performance for
operation near the device transit time. However, as discussed in Chapter 5,
most models available in SPICE use the QS approximation [33]. In a QS
model, the channel charge is assumed to be a unique function of the
instantaneous biases; that is, the charge has to respond to change in voltages with infinite speed. Thus, the finite charging time of the carriers in
the inversion layer is ignored. In reality, the carriers in the channel do
not respond to the signal immediately; thus, the channel charge is not a
unique function of the instantaneous terminal voltages (QS) but a function of the history of the voltages (NQS). This problem may become pronounced in the RF applications, or when V gs is close to V th , or when long
channel devices coexist with deep submicron devices as in many mixed
signal circuits. In these circuits, the input signals may have rise or fall
times comparable to or even smaller than the channel transit time. For
long channel devices, the channel transit time is approximately inversely
proportional to (V gs − V th ) and directly proportional to L 2 . Since the carriers
in these devices cannot follow the changes of the applied signal, the QS
models may give inaccurate or anomalous simulation results that cannot
be used to guide circuit design. Two-dimensional (2D) numerical simulation results show that the most common QS model that uses 40/60 drain/
source charge partitioning [34] results in an unrealistic large drain current
spike during a fast turn-on [35].
Besides affecting the accuracy of simulation, the nonphysical results can
also cause oscillation and convergence problems in the numerical iterations
in circuit CAD. It is common among circuit designers to circumvent the convergence problem by using a 0/100 drain/source charge partitioning ratio
[36], which attributes all transient charges to the source side. However, the
numerical device simulation results show that this nonphysical solution
merely shifts the current-spike problem to the source current; thus it only
works when the source is grounded.
Moreover, none of these QS models can be used to accurately predict the
high-frequency transadmittance of a MOSFET as pointed out by Tsividis
and Masetti [37]. It is a common practice in high- frequency circuit designs
to break a long channel MOSFET into N equal parts in series (N-lumped
model) due to the lack of NQS models. The accuracy increases with N,
at the expense of simulation time [38]. However, this method becomes
Compact Models for Integrated Circuit Design
7.3 NQS Effect
In Chapter 6, the charge and C–V models are derived based on the QS
approximation; that is, the inversion charge responds to the changes in the
applied signal instantaneously. However, the QS approximation breaks
down when signal changes occur on a timescale comparable to the device
transit time.
As very-large-scale-integrated (VLSI) circuits become more performancedriven, it is sometimes necessary to predict the device performance for
operation near the device transit time. However, as discussed in Chapter 5,
most models available in SPICE use the QS approximation [33]. In a QS
model, the channel charge is assumed to be a unique function of the
instantaneous biases; that is, the charge has to respond to change in voltages with infinite speed. Thus, the finite charging time of the carriers in
the inversion layer is ignored. In reality, the carriers in the channel do
not respond to the signal immediately; thus, the channel charge is not a
unique function of the instantaneous terminal voltages (QS) but a function of the history of the voltages (NQS). This problem may become pronounced in the RF applications, or when V gs is close to V th , or when long
channel devices coexist with deep submicron devices as in many mixed
signal circuits. In these circuits, the input signals may have rise or fall
times comparable to or even smaller than the channel transit time. For
long channel devices, the channel transit time is approximately inversely
proportional to (V gs − V th ) and directly proportional to L 2 . Since the carriers
in these devices cannot follow the changes of the applied signal, the QS
models may give inaccurate or anomalous simulation results that cannot
be used to guide circuit design. Two-dimensional (2D) numerical simulation results show that the most common QS model that uses 40/60 drain/
source charge partitioning [34] results in an unrealistic large drain current
spike during a fast turn-on [35].
Besides affecting the accuracy of simulation, the nonphysical results can
also cause oscillation and convergence problems in the numerical iterations
in circuit CAD. It is common among circuit designers to circumvent the convergence problem by using a 0/100 drain/source charge partitioning ratio
[36], which attributes all transient charges to the source side. However, the
numerical device simulation results show that this nonphysical solution
merely shifts the current-spike problem to the source current; thus it only
works when the source is grounded.
Moreover, none of these QS models can be used to accurately predict the
high-frequency transadmittance of a MOSFET as pointed out by Tsividis
and Masetti [37]. It is a common practice in high- frequency circuit designs
to break a long channel MOSFET into N equal parts in series (N-lumped
model) due to the lack of NQS models. The accuracy increases with N,
at the expense of simulation time [38]. However, this method becomes