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Transcript
1
Subthreshold FinFET for Low Power Circuit
Operation
Anupama Bowonder, Pratik Patel, University of California, Berkeley

Abstract— FinFET subthreshold operation will be
analyzed for low power applications. With current
technology scaling, FinFETs seem like the most likely
replacement for bulk CMOS in the near future. Further
since they have near 60mV/dec swing, they are more ideal
for subthreshold operation than bulk CMOS.
Subthreshold FinFET SRAM operation is studied to
determine the limit of subthreshold voltage scaling since
supply voltage scaling is limited by SRAM functionality.
Finally the role of process variations on FinFET SRAM
operation in the subthreshold regime is also studied.
MOTIVATION FOR SUBTHRESHOLD OPERATION
Steady scaling down of CMOS has enabled realization of
very high performance VLSI circuits. However for several
applications, such high speeds are not required. Medical
equipments such as hearing aids and pace-makers and wireless
devices such as cellular phones and PDAs, for example require
extremely low power consumption [1], [6]. It is for such
applications that subthreshold operation of circuits provides
highly reduced power consumption in return for a speed
penalty. Subthreshold circuits are the most effective to achieve
low power because they reduce both dynamic power and static
power consumption. In addition to the quadratic decrease in
dynamic power consumption, decreased VDD also decreases
DIBL and hence decreases the transistor leakage currents,
which may at one point even, exceed the active power
consumption and dominate the total power consumption of a
transistor. Thus for battery driven wireless devices
subthreshold operation is ideal as reduced leakage power helps
enhance battery life [7].
ENERGY MINIMIZATION IN SUBTHRESHOLD DESIGN
The total energy dissipated in a circuit operating in
subthreshold is broken into active energy and leakage energy.
The active or switching component is the energy consumed in
charging the output capacitance to VDD and is given as
Fig. 1. Minimum energy point and constant energy and performance lines
for 16-b and 1024-pt FFT. [1]
2
Eactive  NCVDD
Note that the activity factor is given by α and the total number
of clock cycles is given as N. On the other hand, the
component due to leakage arises from source to drain diffusion
currents when the gate of the transistor is “off”, i.e. VGS = 0 V.
This current is drawn statically from the supply during logic
computation and is modeled as
Vgs Vth
Eleakage  VDD I S e
nVT
(1  e
 Vds
)Tdelay
VT
For a fixed threshold voltage, scaling supply voltage VDD into
the subthreshold range results in substantial total energy
reduction for both active and leakage energy, although at a
significant penalty in performance. Wang, et. al have simulated
constant energy and performance contours within VDD and Vt
space for a 0.18µm process 16-b 1024-pt FFT as shown in Fig.
1. This figure confirms that for constant Vt, reduction in
overall energy follows from reduction in supply voltage.
However, further reduction in VDD results in increased energy
consumption because delay increases exponentially with
decreasing supply voltage, thereby increasing the total leakage
energy component. This implies that the absolute minimum
supply voltage for correct functionality does not necessarily
coincide with the minimum voltage for energy. [1]
For fixed VDD, increasing the threshold voltage decreases
the leakage energy since the off-current reduces exponentially,
while the delay increases only moderately in a quadratic
fashion. When Vt approaches the supply voltage, however, the
2
Fig. 3. Double-Gate Cgate vs. VGS characteristic for various gate length [2]
Fig. 2. PMOS sizing constraints on subthreshold inverter for minimum sized
NMOS for 0.18um process. [1]
leakage energy begins to increase because the impact on delay
becomes significant. This results in a minimum energy point
with respect to threshold voltage Vt. In general, for a given
design there exists an optimal (VDD, Vt) pair for which total
energy consumption is minimized. Although typically the
penalty paid in terms of performance for operating at this
minima is severe. By backing off from the absolute lowest
energy slightly, the gains in performance can be substantial. In
Fig 1., for example, increasing energy by 1.5X results in a
performance improvement of 100X. [1]
Fig. 4. Double-Gate ION and S vs. Lgate (VDD = 0.2 V)[2]
SIZING CONSIDERATION IN SUBTHRESHOLD DESIGN
When scaling the supply voltages into the subthreshold
regime, proper transistor sizing and process variation control
become critical for ensuring correct circuit operation.
Reduction in ION/IOFF ratio and unwanted leakage paths have to
be taken into account when designing logic circuits at the
lower limit of VDD. For the case of the subthreshold inverter
with minimum sized NMOS pull down, supply voltage
reduction places upper and lower limits on the sizing of the
PMOS pull up device for proper functionality. For the case
with a ‘0’ input at the gate, the PMOS must pull up the output
node to VDD by overpowering the IOFF idle current of the
NMOS device. If the device is not sized strong enough, the
output will not rise to the top rail, resulting in reduced noise
margins. With process variations the worse case is the fast
NMOS/slow PMOS (FS) corner because the pull down has the
largest leakage current and the pull up has the smallest drive
current. Similarly for the case with a ‘1’ input, the minimum
sized NMOS must discharge the output to 0 V, while
overpowering the PMOS leakage current with worst case slow
NMOS/fast PMOS. Wang, et. al have performed sizing
analysis on the subthreshold inverter in 0.18µm process
technology as shown in Fig. 2, where the minimum and
maximum PMOS width Wp for proper logic swing is plotted as
a function of supply voltage. With continued voltage scaling
Wp is seen to increase substantially, imposing a significant
area penalty when operating at the minimum allowable limit.
Fig. 5. Double-Gate Inverter Delay vs. Lgate. [2]
DEVICE DESIGN FOR SUBTHRESHOLD OPERATION
In subthreshold CMOS circuit operation since Ion is Ioff scaled
by 1/S, for a fixed Ioff, the ideal device for subthreshold
operation needs to have near ideal 60mV/dec swing [2]. Prior
studies analyzed the use of devices such as DTMOS in the
subthreshold regime, since DTMOS has near ideal
subthreshold slope [5]. DTMOS, is a device where the body of
a planar MOSFET is tied to the gate of the MOSFET. Thus
when Vg=0V, the leakage and S of the device are exactly the
same as those of a regular MOSFET, but when Vg>0, then Vt
decreases as the source body junction gets forward biased.
3
This leads to increased performance due to increased on
current for the same off current as a regular MOSFET. The
subthreshold DTMOS circuits exhibited lower delay due to
increased Ion, higher power consumption due to the forward
biased junction and lower power delay product. Also the delay
of subthreshold DTMOS as a function of fan-out was found to
be almost constant unlike regular CMOS. [5]
In our study, we will analyze FinFETs in subthrsehold
operation, since FinFETs and double gate devices are devices
which achieve near ideal swing because of enhanced back gate
control, thus making these devices the perfect candidates for
subthreshold operation. In addition, as transistor scaling
continues, FinFETs are seen as the mostly likely replacement
to bulk CMOS in the near future.
IMPACT OF FINFET PROCESS VARIATION ON
SUBTHRESHOLD OPERATION
While FinFETs are more easily scaled down to 20nm gate
lengths and below due to improved subthreshold swing,
building such devices pose several problems. The fabrication
process for double gate devices being more complicated than
that for planar devices, the chances of non-uniformity across a
wafer during fabrication are increased. These increased
process variations could adversely affect the electrical
characteristics of FinFETs since these variations introduce
variations in the Vt of the device and in subthreshold operation
Ion is exponentially dependant on Vt. Process variations in
double gate fabrication can be induced by various factors, such
as body thickness variation, tox variation and gate length
variation. Studies of sensitivity of FinFETs to process
variations have already been performed. We intend to use the
knowledge from these studies to further aid our analysis of
how process variations affect subthreshold FinFET operation
of logic circuits and SRAM circuits. Since FinFETs have
completely depleted bodies and use work function tuning to
tune Vt, they are inherently immune to Vt variations due to
random dopant fluctuations. In order to get swings close to the
ideal 60mV/dec, the silicon body has to be extremely thin.
Tsi< 0.5Leff - 6Tox. Variations in body thickness affect not only
the Vt of the device but also leakage due to DIBL, and the
subthreshold slope of the device. Thinner body thicknesses
help improve S and increase Vt due to enhanced back gate
control. It has been shown that 1nm variations in body
thickness can result in an order of magnitude difference in off
currents and 100uA difference in on currents. In order to keep
variation of electrical parameters to a minimum the 3sigma
variation of body thickness needs to be less than 1nm for a
device with 20nm body thickness [3]. Thus we can see that
body thickness variation could affect subthreshold circuit
operation adversely by affecting S (thus affecting Ion/Ioff),
leakage currents and Vt (thus affecting subthreshold Ion).
The nature of the Fin etch would determine the roughness of
the fin surfaces and thus determine the variations in Tox of a
device. However unlike planar MOS devices which rely on
thinner oxide thickness to improve S, FinFETs use the back
gate to control the short channel effects. Further the drain
current of FinFETs in subthreshold is independent of Tox as
seen from the equation below.
I DS  
W
L
2
Vg Vth
Vds

 kT  mkt q
  e
(1  e kT / q )
 q 
Thus to first order it would be ok to consider that Tox
variations in FinFETs don’t really affect subthreshold circuit
operation.
Kim, et. al have shown that for reliable subthreshold
operation, under the same Ioff condition, a longer channel
length device should be used instead of the minimum gate
length (Lg) device. To first order delay can be modeled by
CgV/Ion. The study shows that in subthreshold, Cg is almost
independent of Lg, since the main component of Cg is the gate
overlap capacitance and fringing gate capacitance, both of
which are not dependent on Lg. (Fig. 3) [2]
As seen in Fig. 4 Ion however depends on Lg if Ioff is fixed
across all gate lengths as then Ion depends only on S of the
device and for shorter channel lengths the S being worse, Ion
gets worse and hence increases delay. Thus from Fig. 5 we
can see that immunity to variations in length in the
subthreshold regime can be obtained by using, longer channel
length devices for a small penalty in area and increased gate
capacitance [2].
Thus variations introduced by dopant fluctuations, length
variations and tox variations can easily be dealt with in the
subthreshold regime by using work function tuning, and longer
channel devices with no significant penalty in variations in
electrical parameters of the FinFET. Body thickness variation
is the only process induced variation which is difficult to
control and thus affects subthreshold operation of FinFETs.
IMPACT OF FINFET WIDTH QUANTIZATION ON
SUBTHRESHOLD OPERATION
Apart from process induced variations brought about by the
inherently difficult process of fabricating a FinFET, another
inherent drawback of FinFETs is width quantization. Unlike
planar CMOS, FinFETs can only have integer widths, as the
required width is obtained by placing several fins in parallel.
This makes designing circuits difficult, as it eliminates the use
of non integer Wp/Wn for proper circuit functioning.
Soeleman, et. al have shown that the delay minimum as a
function of Wp/Wn for a planar CMOS inverter is much
shallower in subthreshold operation and hence a much wider
range of Wp/Wn can be accommodated to achieve minimum
delay in subthreshold operation [5]. If the minimum is shallow
then it would mean that for any Wp/Wn other than the
optimum value the delay penalty would be large and in the
case of FinFETs if the optimum Wp/Wn happened to be a non
integer value then the delay penalty would be inevitable. A
shallow minimum however, would ensure that no such penalty
occurs. This if true for FinFETs, could prove to be very useful
for subthreshold FinFET operation.
4
performance (SNM). This study uses built-in feedback to
improve cell read margin, while simultaneously consuming
low standby leakage power. [4]
SRAM DATA RETENTION VOLTAGE (DRV)
Defined as the minimum supply voltage required to retain data,
an SRAM cell DRV can be determined from the following
relationship. [7]
Fig. 6. SRAM DRV vs. transistor width scaling. [7]
V1
V2
Fig. 7. Deterioration of inverter VTC as function of VDD. [7]
SUBTHRESHOLD SCALING LIMITATIONS IMPOSED BY SRAM
FUNCTIONALITY
Scaling VDD to voltages below the threshold voltage of a
transistor however presents many challenges, several of which
have been studied in the recent past. It is clear from studies
that it is ultra low voltage SRAM operation that ultimately
limits the VLSI system voltage scaling [7]. Subthreshold logic
gates function normally except for degraded speed. However
SRAM read stability, static noise margin and data retention
voltage are all degraded with lowering VDD. Further in
subthreshold operation Ion is just Ioff scaled by 1/S, thus
degraded Ion/Ioff becomes a problem, especially in the case of
bitlines of memory where several drains of NMOS transistors
are connected to the drain of a single PMOS transistor(for
charging the bitline up to VDD) [6]. Thus design of
subthreshold memory circuits will require the knowledge of
the maximum fan-out that ensures proper circuit functioning
such as charging up of the bitline
In many chip designs, SRAM arrays occupy a large fraction
of the chip area. Scaling of memory density needs to track
scaling of logic circuits, however this implies dealing with
increased transistor leakage and process induced parameter
variations. Scaling VDD is the easiest way to reduce leakage,
however a low VDD coupled with process variations severely
degrades SNM of an SRAM cell. Guo, et. al shows the
possible use of FinFETs in both 6T and 4T SRAM cells.
FinFETs with their inherently lower leakage and smaller
footprint help aid memory scaling, where bulk CMOS cannot.
Also FinFETs provide the possibility of using back gate
biasing to dynamically adjust threshold voltage to help tune

leftinverter
V1
V2
, when VDD  DRV
rightinverter
As the VDD is scaled down to DRV, the VTCs of the
inverters of the SRAM cell degrade until finally at supply
voltage equal to DRV the noise margin of the cell degrades to
zero. (Fig. 7) If VDD is reduced below this voltage then the
inverters flip and lose the capability to preserve the stored
data. [7]
Quin, et. al have shown that the DRV of an SRAM cell can
be determined by solving subthreshold VTC equations of the
two inverters of the SRAM cell. [7]
This paper also explores the effect of transistor sizing of the
various transistors in the SRAM to tune DRV. It is shown that
appropriate sizing of the PMOS devices can be used
effectively to tune DRV of the cell as seen in Fig. 6. [7]
OUR PROPOSAL
In our study we will simulate the subthreshold FinFET inverter
and compare energy, delay and energy-delay across a range of
supply voltages to 45 nm CMOS inverter to determine the
advantages FinFETs may offer. From this analysis we will
determine the ideal supply voltage we intend to use for all our
subthreshold simulations in regards to energy/performance
tradeoff. We will then determine tpo and gamma of a FinFET
inverter and further determine the ideal fan-out for the
obtained gamma.
Next it will be interesting to see if in subthreshold the delay
as a function of Wp/Wn does indeed have a shallow minimum.
This will be very important if and when work function tuning
is not available to make the PMOS and NMOS drive strengths
equal. If a range of Wp/Wn provide a minimum delay then
width quantization will not prove to be a problem in
subthreshold operation. Further we will study the relationship
between delay and gate length in subthreshold to see if a
length trade off can be made to reduce delay. Transistors with
longer gate length should exhibit increased Ion and thus
reduced delay because of improved S. In addition it will also
be interesting to compare the energy-delay of FinFET logic
gates such as a two input NAND, NOR etc to regular bulk
CMOS logic gates in the subthreshold regime.
For the bulk of our study we hope to understand the
tradeoffs that need to be made to make 6T and 4T FinFET
SRAMs functional and as high performance as possible in the
5
Fig. 8. Schematic of 6T SRAM Cell. [4]
Fig. 9. Hold/Write Margin vs. VDD. [4]
subthreshold regime. We will study the design tradeoffs that
need to be made to achieve a high hold stability, read stability
and good write margin.
Hold Stability: This can be quantified by the cell static noise
margin in standby mode. The PMOS load transistor needs to
compensate for the leakage of all the NMOS transistors
connected to the storage node Vl (Fig. 8) [4]. This will be
challenging in subthreshold due to the degraded Ion/Ioff ratio.
Perhaps longer channel devices will be preferred, in spite of
the area tradeoff as longer channel FinFETs have better S and
thus better Ion for a fixed Ioff than short channel FinFETs. We
intend to study if upsizing the PMOS transistors can be used to
improve hold stability, while also decreasing DRV as
explained earlier in the paper.
Read Stability: This can be quantified by the cell SNM
during a read access. During a read operation, the node Vr
rises above 0 depending on the resistive divider between the
access transistor AXR and the pull down transistor NR. To
ensure read stability the ratio of the W/L of these two
transistors needs to be carefully set to ensure Vr does not flip
the bit in the other inverter(formed by NL and PL) of the
SRAM cell [4]. In our study we intend to vary the widths of
the transistors in each inverter of the SRAM to determine,
what area tradeoff can be made to achieve high read stability.
Write Margin: A successful write operation is performed if
the voltage divider pulls Vl below the trip point of the inverter
formed by NR and PR. Write margin can usually be improved
by keeping the PMOS device at minimum size and upsizing
the access transistor [4]. We need to determine the ideal
PMOS device sizing to ensure that neither hold stability nor
write margin are compromised.
Designing a cell with good read stability, write margin and
hold stability by playing only with transistor sizing will prove
challenging. The role of back gate biasing in the FinFET to
dynamically control Vt will be studied to determine if the cell
beta ratio can be adjusted dynamically. By connecting the back
gate of the access transistor to the storage node, the strength of
the access transistor can be selectively degraded. If the storage
node is at 0, the access transistor FinFET has degraded drive
strength or in other words increased beta ratio during the read
cycle. The tradeoff made here though is reduced write margin
because of the degraded drive current of the back-gated
FinFET access transistor. [4]
Since prior work (Fig. 9) indicates that lowering Vdd,
increases write margin without a significant hit to hold margin,
it will be interesting to determine if subthreshold SRAM
design inherently allows for large write margin [4]. This large
write margin without having to upsize the access transistor
would then imply no degradation of cell read margin induced
by the large access transistor.
Subthreshold FinFET operation however is challenging
because not only do we need to work the sizing of the various
transistors to design a stable cell, but we also have to deal with
inherent process variations and their impact on Vt and further
the electrical parameters of the transistors. We intend to study
the effect of process variations as best as we can through
simulations.
Though from simulations of SRAM cells at various supply
voltages we can determine the minimum Vdd for data retention
or DRV, ultimately the minimum DRV that can be used will
also depend on process variations. Having determined from
our study of past work that the body thickness variation is the
most significant effect of process variation, we intend to study
how random body thickness variations of the transistors in an
SRAM cell, will affect the mean SNM and DRV. In order to
study these we will use a random generator to generate random
variations in the body thicknesses of the devices in the SRAM
cell. These variations in body thickness will translate to
random variations in Vt and hence variations in on current in
the subthreshold regime if all transistors have a fixed Ioff. We
will then simulate these SRAM cells with these random
variations and plot the SNM distribution density function and
DRV distribution function as a function of body thickness to
determine the mean DRV and SNM and also the or 3sigma
variation in DRV and SNM. [4],[7]
.
REFERENCES
[1]
A. Wang, and A. Chandrakasan, “A 180-mVSubthreshold FET
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6
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[6]
[7]
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