Operation and Modeling of
The MOS
Transistor
Operation and Modeling of
The MOS
Transistor
Second Edition
Yannis Tsividis
Columbia University
New York Oxford
OXFORD UNIVERSITY PRESS
PREFACE
This book provides a unified treatment of the many phenomena encountered in the operation of modern MOS transistors, and shows how such phenomena can be modeled
analytically. The book is mainly written for use in a senior or first-year graduate
course. It is felt that electrical engineering students have much to gain from a course
devated to the subject. The MOS transistor is the dominant VLSI device. A course devoted to it is, of course, invaluable to those planning a career in device physics and
modeling. For such people, the standard courses on semiconductor devices usually
cover too many different devices to do justice to any one af them, and do not present
the intricacies and tradeoffs involved in a detailed modeling effort. The value of a
course devoted to the MOS transistor is also extremely high for those who want to use
the device to design state-of-the-art circuits. Integrated circuit designers have the opportunity to suit devices to circuit needs, and they can do this most intelligently if they
really understand the workings of the devices. One can, of course, design systems by
using predesigned circuit building blocks as black boxes, if truly high performance is
not important. But when state-of-the-art performance is a must, one has to consider
device details. In addition, a deep knowledge of device operation and modeling is
needed for understanding the computer simlilator models a designer is working with,
and for identifying their limitations. Many circuit designers in the industry spend endless hours trying to interpret strange circuit simulation results, not realizing that these
are largely due to modeling inadequacies. Without adequate device understanding,
valuable time and effort is bound to be wasted on overdesign, brute-force approaches,
and design iterations. This author believes that no IC designer's education is complete
without detailed exposure to MOS transistor operation and modeling.
In the dozen years that have passed since the publication of the first edition of
this book there have been significant advances in the understanding and modeling of
the MOS transistor. In addition, the requiren~entsfor modeling this device on the pari
of the circuit design community are now much more demanding. For example, the
push for low-voltage and micropower operation has made necessary careful modeling
of the device below strong inversion, and the push for ever smaller dimensions has
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PREFACE
revealed phenomena previously ignored. In addition, the advent of "mixed-signal"
circuits, which combine analog and digital functions on the same chip, makes it necessary to use models that are good enough for analog work. These developments
have pointed to the need for a major revision of this book, However, the basic philosophy of the first edition has been retained. Several aspects of this philosophy are
summarized below.
The book starts with basic concepts. Readers should be able to follow even if they
had no prior exposure to the device. The discussions of these concepts are often
from a perspective different from the one usually taken, thus making them interesting reading even to those with prior exposure.
Every effort has been made to give the subject a careful treatment. The reader may
at times get the feeling that the author is "splitting hairs." The author would rather
be accused of this than fudge. The MOS transistor is a device so complex that,
once one has decided to fudge, things grow out of hand very quickly, and one ends
up with a hodgepodge of careless derivations, conflicting models, and a lot of
patchwork. This has been avoided at all costs. Also, the reason for hair-splitting at
some points can only be appreciated further along in the book, where those "too
fine" details can be seen to make a lot of difference. The use of one name for several quantities, common in some of the literature, is carefully avoided. For example, at least four distinct quantities encountered in MOS transistor work are described by using the single name "threshold voltage." Although the reader is
amply warned of this practice, the practice itself is avoided in this book.
The emphasis is on principles. At the same time. to illustrate these principles, relevant models are extensively derived and discussed. Thus, physics and modeling
are discussed in paralie1 throughout the book.
Analytical results are derived in a logical manner after carefully stating the assumptions made. Empirical modeling is avoided as much as possible. However,
there are phenomena for which the only analytical results available are empirical
or serniempirical. Such results are presented for completeness after pointing out
the necessary hand-waving behind them.
This book is not a survey. In fact, a conscious effort has been made to avoid making it one. A well-connected set of topics has been chosen, and most of these are
discussed in significant detail. Nevertheless. for completeness certain other topics
are mentioned, albeit briefly. In such cases. some representative results are shown
without proof, so that the reader can know what to expect if he or she consults the
references provided.
A great deal of emphasis is placed on providing intuition for the various phenomena discussed. It is rather hopeless to attempt working with a device as complex as
the MOS transistor relying only on analytical relations. The emphasis on intuition
has made lengthy discussions necessary.
The pace is unhurried. The author believes that this actually makes i t possible to
study the material faster. Thus, whereas the treatment of a given topic may be [ong
in terms of number of pages, it actually should take less time to comprehend it, because of both the detailed derivations and the intuitive discussions. At times, the
reader may get the feeling of dc'ja vu, since some points are repeated more than
once to make sure they are not missed, especially if the reading of the topics is
done out of sequence. In generai, the book is written in the style in which the author would Iike to have any new subject presented to him. He would very much
llke to see the new subject "beaten to death:' presented with several points of view
to increase perspective and with a significant amount of repetition. The author has
been in the past grateful for treatments of this type and never felt offended by this
style. If the reader happens to be "faster" than the author in this respect, he or she
can easily skip some of the discussions.
Almost all chapters in this book, and almost all sections within each chapter,
have been extensively revised. Many sections have been rewritten, and new ones have
been added. One chapter is entirely new. A list of chapters follows, along with an explanation of their features and of what is new in them in this edition.
Chapter I: Semiconductors, Junctions, and MOSFET Overview
All preliminary materid necessary for the understanding of MOS structures is given
here. This material is important to the newcomer, but part of it should also make interesting reading for those with some previous exposure to basics. This includes the material
on contact potentials, which is used to advantage in the following chapter. The chapter
concludes with an overview of the MOS transistor. This section is new to this edition. It
provides a framework for the rest of the book, and makes it clear why particular details
of the two- and three-terminai MOS structures are studied in the following two chapters.
Chapter 2: The Two-Terminal MOS Structure
Here the reader will find a treatment of the MOS structure with gate and substrate
terminals only. Concepts not directly related to the presence of the source and drain
in the MOS transistor are treated here. The regions of weak, moderate, and strong inversion are all introduced in this chapter. Potentials are used throughout rather than
energy bands. This is not only common in current literature but also helps provide
rigorous straightforward derivations. Consider, for example, the well-known term
,@
,
appearing in the expression for the flat-band voltage. In energy band treatments
it is often not clear where in the MOS structure this potential actually resides. In this
book, it is made evident that # M S is nothing but a contact potential, and the places
where it resides are made obvious. Also, its presence in the flat-band voltage expression is rigorously justified through Kirchhoff's voltage law. The material on weak
and moderate inversion has been improved and expanded in this edition.
Chapter 3: The Three-Teminal MOS Structure
Here one more terminal is added to the structure of Chap. 2, to connect the inversion
layer to the external world. MOS transistor concepts that are not directly related to
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current flow are presented in this chapter. This includes the important "substrate effect," which is amply treated. The section on limits of regions of inversion has been
streamlined and shortened. On the other hand, an entirely new section, "A 'V,, Control' Point of View," has been added, to lay the foundation for the discussion of certain recent models covered in Chap. 4.
Chapter 4: The Four-Terminal MOS Transistor
The four-terminal MOS transistor is obtained in this chapter by adding one terminal
to the structure of Chap. 3. This device is now very easy to understand, on the basis
of the concepts already presented for the two- and three-terminal structures. This is
the central chapter in the book. Several models are presented in detail. The first of
them is the complete charge sheet model, including drift and diffusion currents, valid
in all regions of operation. Thanks to a simplified derivation, this material is brief but
thorough. This is followed by new material on simplified charge sheet models, including both symmetric and source-referenced versions.
The above models form the basis for deriving several popular strong- and
weak-inversion models, which are covered in detail. A considerable part of this material is new to this edition, and has been included to reflect recent trends. Some of this
material can be shpped without loss of continuity, and this is indicated at the appropriate points. The various models are extensively related and/or compared to each
other, and the way they can all be derived from one master model (the complete
charge sheet model) is pointed out. A new section on interpolation models has been
added. Sections on effective mobility (expanded), temperature effects, etc., are also
included. The tradeoffs between accuracy and simplicity are pointed out throughout
the chapter.
Chapter 5: MOS Transistors with Ion-Implanted Channeis
This chapter was Chap. 6 in the first edition. It now precedes the chapter on small dimension effects. This change was made because all modern devices, small or large,
have ion-implanted channels; also, having been exposed to this material, the reader
can understand better certain small-dimension effects discussed in the following
chapter. Nevertheless, Chaps. 5 and 6 have been revised in such a way that they can
be covered in either order, in order to accommodate the need of instructors who prefer the original order.
This chapter. arguably the most tersely written one in the first edition, has been
extensively revised. it has now been written so that specific sections correspond more
closely to actual devices (enhancement nMOS, depletion nMOS. surface- or buriedchannel PMOS), and a much smoother development is given. The revision also
makes it possible. if desired, for an instructor to cover only the parts which discuss
the effects of ion implantation on threshold voltage, and to skip the detailed development of other aspects of I-V characteristics. In certain settings, this may be necessary
because of time limitations.
Chapter 6: Small-Dirnensiun Effects
This chapter has been revised and expanded by a n expert in device miniaturization,
Prof. D. A. Antoniadis of MIT. The new title reflects the fact that the effects of
miniaturization in all three dimensions (including Lrery thin oxide effects) are discussed. Among the new topics in this edition are reverse short-channel and narrowchannel effects and hot carrier effects. Although space does not allow for a detailed
exposition of all small-dimension effects, the reader is made aware of their existence,
and a qualitative discussion is given. This includes such effects as poly gate deple-
tion, nonzero inversion layer thickness, quantum mechanical threshold increase, and
insulator tunneling.
Chapter 7: The MOS Tramistor in Dynnnric Operation-Large-Signal Modeling
This chapter is largely devoted to charge modeling. The concept of quasi-static operation is carefully introduced, and general techniques for charge evaluation are presented, illustrated by charge computations for one representative model. Non-quasistatic analysis is then introduced. Since this chapter was considered by instructors
and reviewers to be one of the most successful ones in the first edition, its basic structure was retained. Some material was added cln general charge modeling independent
of inversion regions, and on transient response in non-quasi-static operation.
Chapter 8: Small-Signal Modeling for Lorv and Medirrm Frequencies
The principles behind small-signal modeling are presented. The discussion is limited
to quasi-static behavior. A useful small-signal model is developed for operation at
low and medium frequencies. Major changes in this chapter include a detailed discussion of the effects of substrate current, notably on output conductance, a discussion
of single-piece expressions for small-signal parameters valid in all regions of inversion, an expanded discussion of small-dimension effects, and an expanded discussion
of extrinsic capacitance modeling. Noise is then discussed. including an expanded
description of flicker noise and of the effects of small device dimensions on noise.
Chapter 9: High- Frequencv Small-Signal Models
In this chapter, two kinds of small-signal models are developed. First, complete
quasi-static models are introduced, which differ from the models of Chap. 8 in that
they include transcapacitors. The nature of these somewhat controversial elements is
carefully discussed. Techniques are given for the rigorous development of cquivalentcircuit topologies from a complete quasi-static description. Then, non-quasi-static
models are introduced through a careful development of the transistor's "transmission
line" equations, and a useful y-parameter model is derived for high-frequency applications. It is shown that each level of modeIing reduces to the next lower one if the
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frequency is sufficiently reduced. In this edition, the section on non-quasi-static modeling has been revised to Include a more extensive explanation for the presence of inductance in intrinsic small-signal models. A new section on high-frequency noise,
emphasizing induced gate noise, has been added. Another new section deals with
considerations for radio-frequency (RF) modeling, including the effects of gate resistance and discussing the two common figures of merit for high-frequency performance, the transition frequency and the maximum frequency of osciIlation.
Chapter 10: MOSFET Modeling fbr. Circuit Simulation
This chapter is entirely new in the second edition. and replaces the one on fabrication. Having been exposed to the many phenomena in the MOS transistor and to the
modeling of such phenomena, the reader will find in this chapter an exposition of the
many issues and considerations involved In putting all these together to make an extensive model suitable for circuit simulation. Discussed here are the various types of
models, the ways that models of particular phenomena are combined, parameter extraction. desirable properties for simulator models, common pitfalls in modeling, and
many benchnlark tests for models, which have recently been included in an IEEE
standard. This chapter, it is hoped, will provide a starting point for readers who intend to work in modeling, and will save them tirne and effort by clearly warning of
common errors. it is also meant to provide a background for circuit designers, allowlng them to understand the limitations of the models they are using, and ro better
communicate their needs to nodel ling experts.
The book concludes with 13 appendixes containing an introduction to energy
band concepts, the basic laws of electrostatics as well as several general but complicated results which, it was felt, would distract if put in the main text, For the
same reason, some material in the main text was put in fine print or in footnotes or,
as already mentioned, was described in the statements of some homework problems, Such material includes certain fine details. alternative points of view, etc. To
avoid distraction, the reader may prefer to skip fine-print footnotes and appendixes
during a first reading; the main text is self-contained. This material can always be
consulted at a later time, because its connection with specific points in the text is
obvious.
References to the technical literature were extensively updated and expanded.
In most cases, a reference was selected for inclusion because it is technically important, or is widely mentioned in the literature, or has historical significance, or is part
of controversy that has not yet been resolved.
A change from the first edition has to do with units. The consistent system of
units used in that edition has been abandoned, as it failed to work we11 in most settings. Thus, in the present edition common units have been adopted [e.g., ,& for oxide
thickness and crn2/(V.s) for mobility]. In some instances, the value of a quantity is
given in such units, with the !due in different units given after that in parentheses;
for example, a field intcns~tyis given as "3 x 104 V/cm (or 3 V/,um)," sjnce the latter
form relates directly to typical 1 alues of voltages and channel lengths.