IEEE Solid-State Circuits Magazine - Summer 2017 - 31

This article presents the simplified EKV
transistor model in saturation since, except
for switches, most transistors in CMOS analog
circuits are biased in saturation.

10

28-nm Bulk CMOS Processes

1

gds

Symbols: Measurements
Lines: Theory
0.1 Vs = 0 V
VG = 1.1 V
0.01
0.001
0.0001
0.0001

0.001

0.01

0.1

1

10

100

IC
n = 1.51, λd = 0.24, σd = 0.067
n = 1.27, λd = 0, σd = 0.025
W = 3 µm, L = 30 nm
W = 3 µm, L = 80 nm

FIGURE 7: Normalized output conductance g ds versus IC measured on minimum and
medium length transistors from a 28-nm bulk CMOS process.

28-nm and 40-nm Bulk CMOS Processes
1

Gm.n.UT /ID

The expression in (17), which is continuous from WI to SI and includes
the effect of VS, is plotted in Figure 2.
The figure shows that G m nU T /I D is
maximum in WI and decreases as
1/ IC in SI for long-channel devices
in which VS is absent (dashed blue
curve). Note that the specific current
has been defined from the G m nU T /I D
versus I D characteristic of a longchannel transistor as the current
at which the WI and SI asymptotes
cross. This is why these two asymptotes cross at IC = 1 when G m nU T /I D
is plotted versus IC as in Figure 2.
As shown in Figure 4, for shortchannel devices subject to VS, the
drain current in SI becomes a linear
function of the gate voltage, independent of the transistor length. Hence,
the transconductance becomes independent of the current and length.
Since G m becomes independent of I D ,
and hence of IC , the G m nU T /I D curve
scales like 1/ (m c IC) in SI (red curve)
instead of 1/ IC when VS is absent. In
essence, the effect of VS is to degrade
the transconductance efficiency in SI,
meaning that more current is required to obtain the same transconductance than without VS. Nevertheless,
irrespective of the channel length,
G m nU T /I D remains invariant (i.e.
g ms /IC = 1) in WI, since short-channel
effects (SCEs), including VS, have the
same effect on G m than on I D simply
because G m is proportional to I D in
WI. As shown in Figure 2, the inversion
coefficient for which the SI asymptote
of a short-channel device crosses the
horizontal unity line is equal to 1/m c .
As discussed in the next section, this
is how the parameter m c is extracted
from measurements on a short-channel device.
The normalized transconductance efficiency given by (17) is compared
to measurements in Figure 8 for the
same devices as shown in Figures 4
and 6. Despite that the normalized
G m nU T /I D only requires one parameter (m c or L sat), the model fits very
well to the data over more than five
decades of IC .
In a similar way, we can define the
G ds /I D ratio, which from (11) turns out

Symbols: Measurements
Lines: Theory
0.1

0.01
0.0001

0.001

0.01

0.1
IC

1

10

Vs = 0 V, VD = 1 V, n = 1.48, λc = 0.71
Vs = 0 V, VD = 1.1 V, n = 1.51, λc = 0.95
Vs = 0 V, VD = 1.1 V, n = 1.48, λc = 0.48
W = 108 µm, L = 30 nm
W = 3 µm, L = 30 nm
W = 108 µm, L = 40 nm
FIGURE 8: Normalized transconductance efficiency g ms /IC versus IC measured on minimum
length transistors from a 40-nm and two different 28-nm bulk CMOS processes.

IEEE SOLID-STATE CIRCUITS MAGAZINE

SU M M E R 2 0 17

31



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https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2023
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https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2022
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https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2020
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https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2020
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