IEEE Solid-State Circuits Magazine - Fall 2017 - 79

Figure 10, fom rf shows a peaking
behavior [13] that makes it useful
for locating the optimum IC, which
is due to the asymptotic behavior of
two quantities that it incorporates
[7], [14]. This maximum is located
approximately at IC , 1/m 4c /3. What
is even more interesting is that this
peak lies at the higher end of the MI
region for the contemporary CMOS
technologies and moves deeper into
the MI region with decreasing channel lengths, as shown in the bottom
plot of Figures 11 and 12. It is worth
noting that the peaking behavior of
this FoM is caused by the degradation of G m and G m /I D in SI due to
VS [14]. In the absence of VS, in SI,
G m (consequently Ft ) and G m /I D
are respectively proportional to
I D and 1/ I D , implying that the
FoM would simply saturate in this
region as shown by the blue dashed

10
λC = 0
1

∝

IC

1/

IC

IC

∝
0.1

∝

fomrf = gms/id · ft

λC = 1/3

0.01
0.01

0.1

1

10

100

1

1

1

λC

) 4/3

λC

2

(λC

Inversion Coefficient IC

FIGURE 10: The normalized FoM fom rf (on a log scale) as a function of IC , along with
the WI and SI asymptotes. The peak of the FoM lies at the intersection of IC and 1/ ^ m 2c IC h
asymptotes.

1

10

ft

1

gms/id

W = 108 µm
L = 40 nm
n = 1.48
0.1 Ispecsq = 650 nA
Ispec = 2.1 mA
Lsat = 19.5 nm
λc = 0.4875
0.01

W = 108 µm
L = 31 nm
n = 1.46
0.1 Ispecsq = 870 nA
Ispec = 3.9 mA
Lsat = 20.2 nm
λc = 0.6516
0.01
10

ft sat = 1/λc = 2.05

1

Ft spec = 128.4 GHz

0.1

ft

gms/id

1

CGeW = 640 pF/m

0.001

0.1

∝

IC
C

∝I

CGeW = 670 pF/m

1
∝

0.1
2

1/λc = 4.21

0.01

C
∝I

fomrf

fomrf

0.1
1/λc = 2.05
4/3

0.01

0.1
1
Inversion Coefficient IC

Measurements

BSIM6

10

1/

IC

1/λc = 1.53
2
1/λc = 2.36

0.01

4/3

1/λc = 2.61
0.001
0.001

IC
1/
IC

Ft spec = 226.6 GHz

0.001

1

∝

ft sat = 1/λc = 1.5

0.01

0.01

∝1

1/λc = 1.77
100

Theory

FIGURE 11: g ms /i d , ft , and fom rf versus IC for a 40-nm device [12].

0.001
0.001

0.01

0.1
1
Inversion Coefficient IC
Measurements

10

100

Theory

FIGURE 12: g ms /i d , ft and fom rf versus IC for a 30-nm device [12].

IEEE SOLID-STATE CIRCUITS MAGAZINE

FA L L 2 0 17

79



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

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