IEEE Solid-State Circuits Magazine - Summer 2017 - 32

The most important small-signal
parameter is without doubt the gate
transconductance Gm .

to be about equal to 1/VM for VD % VM.
In normalized form, we have

g ds
G ds
= n ·
G ds-max
v d IC
(m d IC + 1) 2 + 4IC - 1
.
=
IC· 6m d (m d IC + 1) + 2@
(19)

From (18), we can deduce that the
highest output conductance for a
given current is reached in WI and
is equal to G ds-max _ v d I D / (nU T ) . We
can then normalize the output conductance to G ds-max for the normalized output conductance to reach
unity in WI

U T , G ds U T = g ds
VM
ID
IC
(m d IC + 1) 2 + 4IC - 1
vd
·
.
=
n
IC· 6m d (m d IC + 1) + 2@

(18)

28-nm Bulk CMOS Processes

Gds/Gds-max

1
Symbols: Measurements
Lines: Theory

Parameter Extraction

Vs = 0 V
0.1 V = 1.1 V
G

0.01
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 9: Output conductance-to-current ratio G ds /G ds-max versus IC measured on minimum
and medium length transistors from a 28-nm bulk CMOS process.

n = ID /(Gm.UT) [-]

100

n = 1.22

10

1
10-10 10-9 10-8 10-7 10-6 10-5
ID [A]

10-4 10-3

Ispec = 13 µA

FIGURE 10: The extraction of the slope factor n and the specific current I spec .

32

SU M M E R 2 0 17

Equation (19) is plotted in Figure 9 and
compared to measurements made on
the same transistors than in Figure 7
and shows good agreement with the
measured data. Note that, unlike for
the transconductance, where we want
to get the highest transconductance
for a given current reached in WI, the
output conductance should be minimized for a given current. It will be
shown in Part 2 of this article that,
even though the output conductance
decreases in SI, the self-gain remains
actually maximum in WI and simply
equal to 1/v d .

IEEE SOLID-STATE CIRCUITS MAGAZINE

10-2

The four parameters n, I spec, VT 0, and
L sat required for fitting the simplified
model described in the section "The
Large-Signal dc Model" to measured
I D - VG data can be extracted from
measurements following the procedure described below. The extraction
starts from the I D - VG characteristic
measured on a wide and long transistor. After calculating (or measuring) the derivative G m , the slope
factor n is extracted from the plateau
reached by the I D / (G m U T ) curve in
WI as in Figure 10. The specific current for this particular device is
then obtained by the intersection
between the SI asymptote ? I D and
the slope factor horizontal line as
shown in Figure 10. For this particular long-channel device, this results
in n = 1.22 and I spec = 13 nA, from
which we can derive the specific current per square I spec4 by dividing by
the aspect ratio W/L.
The VS parameter m c is extracted
in Figure 11 from the normalized
G m nU T /I D characteristic of a wide
and short-channel transistor as the
IC corresponding to the intersection of the 1/IC asymptote with the
unity horizontal line after having
properly extracted the slope factor
n, which is usually affected by SCEs
( n = 1.48 in this case compared



Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2017

IEEE Solid-State Circuits Magazine - Summer 2017 - Cover1
IEEE Solid-State Circuits Magazine - Summer 2017 - Cover2
IEEE Solid-State Circuits Magazine - Summer 2017 - 1
IEEE Solid-State Circuits Magazine - Summer 2017 - 2
IEEE Solid-State Circuits Magazine - Summer 2017 - 3
IEEE Solid-State Circuits Magazine - Summer 2017 - 4
IEEE Solid-State Circuits Magazine - Summer 2017 - 5
IEEE Solid-State Circuits Magazine - Summer 2017 - 6
IEEE Solid-State Circuits Magazine - Summer 2017 - 7
IEEE Solid-State Circuits Magazine - Summer 2017 - 8
IEEE Solid-State Circuits Magazine - Summer 2017 - 9
IEEE Solid-State Circuits Magazine - Summer 2017 - 10
IEEE Solid-State Circuits Magazine - Summer 2017 - 11
IEEE Solid-State Circuits Magazine - Summer 2017 - 12
IEEE Solid-State Circuits Magazine - Summer 2017 - 13
IEEE Solid-State Circuits Magazine - Summer 2017 - 14
IEEE Solid-State Circuits Magazine - Summer 2017 - 15
IEEE Solid-State Circuits Magazine - Summer 2017 - 16
IEEE Solid-State Circuits Magazine - Summer 2017 - 17
IEEE Solid-State Circuits Magazine - Summer 2017 - 18
IEEE Solid-State Circuits Magazine - Summer 2017 - 19
IEEE Solid-State Circuits Magazine - Summer 2017 - 20
IEEE Solid-State Circuits Magazine - Summer 2017 - 21
IEEE Solid-State Circuits Magazine - Summer 2017 - 22
IEEE Solid-State Circuits Magazine - Summer 2017 - 23
IEEE Solid-State Circuits Magazine - Summer 2017 - 24
IEEE Solid-State Circuits Magazine - Summer 2017 - 25
IEEE Solid-State Circuits Magazine - Summer 2017 - 26
IEEE Solid-State Circuits Magazine - Summer 2017 - 27
IEEE Solid-State Circuits Magazine - Summer 2017 - 28
IEEE Solid-State Circuits Magazine - Summer 2017 - 29
IEEE Solid-State Circuits Magazine - Summer 2017 - 30
IEEE Solid-State Circuits Magazine - Summer 2017 - 31
IEEE Solid-State Circuits Magazine - Summer 2017 - 32
IEEE Solid-State Circuits Magazine - Summer 2017 - 33
IEEE Solid-State Circuits Magazine - Summer 2017 - 34
IEEE Solid-State Circuits Magazine - Summer 2017 - 35
IEEE Solid-State Circuits Magazine - Summer 2017 - 36
IEEE Solid-State Circuits Magazine - Summer 2017 - 37
IEEE Solid-State Circuits Magazine - Summer 2017 - 38
IEEE Solid-State Circuits Magazine - Summer 2017 - 39
IEEE Solid-State Circuits Magazine - Summer 2017 - 40
IEEE Solid-State Circuits Magazine - Summer 2017 - 41
IEEE Solid-State Circuits Magazine - Summer 2017 - 42
IEEE Solid-State Circuits Magazine - Summer 2017 - 43
IEEE Solid-State Circuits Magazine - Summer 2017 - 44
IEEE Solid-State Circuits Magazine - Summer 2017 - 45
IEEE Solid-State Circuits Magazine - Summer 2017 - 46
IEEE Solid-State Circuits Magazine - Summer 2017 - 47
IEEE Solid-State Circuits Magazine - Summer 2017 - 48
IEEE Solid-State Circuits Magazine - Summer 2017 - 49
IEEE Solid-State Circuits Magazine - Summer 2017 - 50
IEEE Solid-State Circuits Magazine - Summer 2017 - 51
IEEE Solid-State Circuits Magazine - Summer 2017 - 52
IEEE Solid-State Circuits Magazine - Summer 2017 - 53
IEEE Solid-State Circuits Magazine - Summer 2017 - 54
IEEE Solid-State Circuits Magazine - Summer 2017 - 55
IEEE Solid-State Circuits Magazine - Summer 2017 - 56
IEEE Solid-State Circuits Magazine - Summer 2017 - 57
IEEE Solid-State Circuits Magazine - Summer 2017 - 58
IEEE Solid-State Circuits Magazine - Summer 2017 - 59
IEEE Solid-State Circuits Magazine - Summer 2017 - 60
IEEE Solid-State Circuits Magazine - Summer 2017 - 61
IEEE Solid-State Circuits Magazine - Summer 2017 - 62
IEEE Solid-State Circuits Magazine - Summer 2017 - 63
IEEE Solid-State Circuits Magazine - Summer 2017 - 64
IEEE Solid-State Circuits Magazine - Summer 2017 - Cover3
IEEE Solid-State Circuits Magazine - Summer 2017 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2022
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2022
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2022
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2022
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
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2020
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2020
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2020
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2019
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2019
https://www.nxtbook.com/nxtbooks/ieee/mssc_2019summer
https://www.nxtbook.com/nxtbooks/ieee/mssc_2019winter
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018fall
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018summer
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018spring
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018winter
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2014
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2014
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2014
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2014
https://www.nxtbookmedia.com