IEEE Solid-State Circuits Magazine - Fall 2017 - 73

Christian Enz, Francesco Chicco, and Alessandro Pezzotta

Nanoscale
MOSFET Modeling
Part 2: Using the inversion coefficient
as the primary design parameter

T

his article illustrates the use of the inversion coefficient (IC) as the main design parameter to explore the
various tradeoffs faced in the design of analog circuits.
We start with showing that the same transconductance,
gain-bandwidth (GBW) product, or input-referred thermal noise resistance of a common-source (CS) amplifier can be achieved
with lower current by shifting the IC toward moderate inversion (MI) at
the cost of a slight increase of the transistor aspect ratio and area. In such
case the self-loading gate capacitance cannot be ignored, and accounting
for it introduces a minimum bias current at an IC that lies in the middle of
the MI to achieve a given GBW.
Various figures-of-merit (FoMs) are then introduced starting with the
current or transconductance efficiency G m /I D. It is shown that G m /I D is
maximum in weak inversion (WI) and that because of velocity saturation
(VS) more current is required in strong inversion (SI) to reach the same
transconductance than when VS is absent. The transit frequency Ft is then
derived as a function of the IC, and it is shown that it reaches a maximum
Ftpeak in SI that is inversely proportional to the VS parameter m c . It is also
shown that Ftpeak does not scale as 1/L and only depends on the ratio of
the oxide capacitance per unit area to the total extrinsic gate capacitance
per unit width. Finally the product G m /I D ·Ft FoM is introduced. The latter reaches a maximum in MI, offering a good tradeoff among gain, noise,
and current consumption. All the presented FoMs can be expressed versus
the IC using simple analytical expressions requiring only four parameters.
They are favorably compared to measurements of short-channel devices
from 40- and 28-nm bulk CMOS technologies and with the BSIM6 compact
model for the 40-nm device, illustrating the effectiveness of using the IC in
the design of analog circuits.

Introduction
The design of analog circuits is the art of finding the right tradeoff
between conflicting constraints or specifications such as power, noise,
IMAGE LICENSED BY GRAPHIC STOCK

Digital Object Identifier 10.1109/MSSC.2017.2745838
Date of publication: 16 November 2017

1943-0582/17©2017IEEE

IEEE SOLID-STATE CIRCUITS MAGAZINE

FA L L 2 0 17

73



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

IEEE Solid-State Circuits Magazine - Fall 2017 - Cover1
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