ee
`eee:=.—
`iSSSsi:eS:ee
`. .SoeeresSeeoe_ceeeeesoeenee:=
`ce:SSoe——..
`Seesee=
`
`=:=See
`
`ae
`
`eaennens
`
`eeee
`ae
`
`a
`
`oe
`
`oe
`
`Ne = ee Oe
`
`ee ==
`
`ReeeeSe
`
`INTEL 1011
`
`1
`
`

`

`
`
`2
`
`

`

`Selected List of Symbols
`Certain symbols used only locally within a section, or whose meaning is clear from
`the context, are not includediin this list.
`Section
`Description Section .
`
`Symbol
`
`Description
`
`
`
`Depletion region capacitance
`per-unit area
`Body-drain intrinsic
`capacitance
`Body-sourceintrinsic
`capacitance
`Gate-body intrinsic
`. capacitance
`Gate-body capacitance per
`unit area
`Gate-drain intrinsic
`capacitance
`Gate-source intrinsic
`capacitance
`Inversion layer capacitance
`per unit area
`Interface traps capacitance
`per unit area
`pn junction capacitance
`pn junction capacitance per
`unit area
`Difference between C,dg
`and Cyq
`Difference between Cy,
`and Cy4
`Differerice between Cp,
`and Coy
`Total oxide intrinsic
`capacitance
`Oxide capacitance per
`unit area
`
`4.1, 7.2
`
`16,66,
`12
`6.6
`
`43, 6.6
`
`454.
`45.1
`43
`
`43
`
`2.6
`
`’ Drain current
`
`Drain-to-body current
`Drain-to-source current
`(channel current)
`Value ofIpg at the onset of
`saturation
`Nonsaturation Ip,
`Component of Ip, due to drift
`Componentof Ipg due to
`diffusion
`Gate current
`* Value of Ipg at upperlimit
`of weak inversion
`
`—
`
`Value of Ing at upperlimit of .
`weak inversion, normalized
`
`oltzmann’s constant
`
`Depletion region depth
`Electric field
`
`“Critical” field in velocity
`saturation formulation ~
`
`Longitudinal electric field
`Transverse electric field
`Body-drain small-signal
`conductance
`Gate small-signal
`transconductance
`Body small-signal
`transconductance
`
`Output small-signal
`conductance
`Source-drain. small-signal
`conductance
`Source small-signal
`conductance
`
`Body: current
`
`-
`
`Effective’channel length
`Length of pinchoff region.
`Acceptor concentration
`Donorconcentration
`1., Free electron concentration
`2. The quantity (div,,/dVgp
`Intrinsic carrier concentration
`Hole concentration
`Depletion region charge
`Depletion region charge
`per unit area
`Effective depletion region
`charge
`Inversion layer charge
`Inversion layer charge
`per unit area
`Value of Q; at drain end of
`channel
`~ Value of Q; at source end of
`~ channel
`Gate charge
`Gate charge per unit area
`- Effective interface charge
`Magnitude of electronic. charge
`Drain-associated inversion
`layer charge
`
`:
`
`3
`
`

`

`Description Section
`
`Symbol
`Section
`Description
`Symbol
`Distance in direction
`Source-associated inversion
`y
`perpendicular to the surface
`layer charge
`Gate transadmittance
`Absolute temperature
`Body transadmittance
`Oxide thickness
`Effective channel width
`Characteristic voltage in first-
`Coefficient of first-order term
`order channellength
`‘ modulation formula
`in expansion for -Oj/C;,
`Value of a for expansion |
`Body voltage
`around the source potential
`Channel-body voltage
`Bodyeffect coefficient
`Drain voltage
`Symbol denoting a changein
`Drain-source voltage
`the quantity following it
`Value of Vpg at onset of
`Difference between the actual
`saturation .
`strong-inversion surface
`Flat band voltage
`potential and its classical
`Gate voltage
`value of 2d
`_
`Gate-source voltage
`Permittivity of free space
`Value of Voc, or of Vas,at
`Permittivity of SiO,
`onset of strong inversion °
`Permittivity of silicon
`Value of Vaz at onset of
`Degree of nonsaturation —
`strong inversion
`Effective surface mobility
`Value of Vizp for two-
`terminal structure
`Value of Vgc, or of Vag, at
`onset of weak inversion
`Value of Vga at onset of weak
`inversion
`Valueof V,» for two-terminal
`structure
`
`frequency
`
`73
`1.2
`2.2
`
`6.2
`72
`3.2
`7.2
`
`.
`
`Value of Vgc, or of Vg, at
`onset of moderate inversion
`Value of Vg, at onset of
`moderate inversion
`Value of Vy, for two-terminal
`structure
`' Pinchoff voltage
`Value of channel-body voltage
`at the boundary between
`strong and moderate
`inversion, for a given Voz
`Source voltage
`Source-body voltage
`Extrapolated threshold voltage
`in terms of Vgc or Veg
`Effective V;
`Extrapolated threshold voltage
`in terms of Vez
`Value of Vz, for two-terminal
`structure
`
`Value of channel-body voltage
`at the boundary between
`weak inversion and
`depletion, for a given Vgg
`Drift velocity ©
`Distance along the channel
`
`Yin
`Ymb
`Ww
`a@
`
`ay.
`
`y
`A
`
`Ad
`
`Bulk mobility
`Transit time
`Built-in potential pn junction
`_ Fermipotential
`Contact potential of body
`material to gate material
`(“work function difference”
`potential)
`Thermal voltage, kT/q
`Moderate inversion region
`width in terms of surface
`potential
`Moderate inversion region
`width in terms of surface
`potential for two-terminal
`MOSstructure
`Surface potential of two-
`terminal MOSstructure in
`strong inversion
`Oxide potential
`- Surface potential
`Surface potential in the
`absence of inversion layer,
`for a given Voz
`Value of surface potential
`at drain end of channel
`Value of surface potential
`at source end of channel
`Characteristic angular
`frequency
`Intrinsic transition angular
`
`4
`
`

`

`
`
`Thermalvoltage, #; = KT/q, at 300 K
`
`0.0259 V .
`
`-
`
`Values for some useful quantities
`
`Magnitudeofelectronic charge, g
`1.602 x 10-9 C
`
`s
`
`Permittivity of silicon,e,
`
`1.04 x 10-12 F/yem
`
`Permittivity ofsilicon dioxide, ¢,,
`
`3.45 x 10-8 F/em —
`
`2g€.
`
`5.79 x 10716 F.V12 . cmt?
`
`5
`
`

`

`Operation and Modeling of
`The MOS
`Transistor
`
`
`
`6
`
`

`

`Operation and Modeling of
`
`_|The MOS
`Transistor
`
`Second Edition
`
`Yannis Tsividis
`Columbia University
`
`WGB |
`
`raw
`
`He McGraw-Hill
`
`-
`
`Boston Burr Ridge, JL Dubuque, IA Madison, WI New York San Francisco
`St. Louis Bangkok Bogoté Caracas Lisbon London Madrid
`Mexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto
`
`
`
`7
`
`

`

`4
`
`N
`WCB/McGraw-Hilt~22
`A Division ofTheMcGrawHillCompanies
`OPERATION AND MODELING OF THE MOS TRANSISTOR
`
`Jf
`
`see
`My4 | ‘)}
`oS
`l 4 4
`
`http://www.mbhe.com
`
`Tsividis, Yannis.
`Operation and modeling of the MOStransistor / Yannis Tsividis.—
`2nd ed.
`p.
`cm.
`Includes index.
`ISBN 0-07-065523-—5
`.2. Metal
`1. Metal oxide semiconductors—-Mathematical models.
`oxide semiconductorfield-effect transistors—Mathematical models.
`I. Title.
`TK7871.99.M44T77
`621.3815'284—dc21
`
`Copyright © 1999 by The McGraw-Hill Companies,Inc. All rights reserved. Previous edition
`© 1987. Printed in the United States of America. Except as permitted under the United States
`Copyright Act of 1976,no partof this publication may be reproducedordistributed in any form or
`by any means,or stored in a database or retrieval system, without the prior written permission of
`the publisher.
`
`This bookis.printed on acid-free paper.
`
`1234567890DOC/DOC 9321098
`
`ISBN 0-07-065523-5
`
`Vice president and editorial director: Kevin T. Kane
`Publisher: Thomas Casson
`Executive editor: Elizabeth A. Jones
`Developmental editor: Bradley K. Kosirog
`Marketing manager: John T. Wannemacher
`Project manager: Christina Thornton-Villagomez
`Production supervisor: Lori Koetters
`Art director: Francis Owens
`Cover designer: Brad Thomas
`Supplement coordinator: Carol Loreth
`Compositor: Shepherd, Inc.
`Typeface: 10.5/12 Times Roman
`Printer: R. R. Donnelley & Sons Company
`
`Library of Congress Cataloging-in-Publication Data
`
`1999
`
`98-23682
`
`8
`
`

`

`_ In memory of J. E. Lilienfeld—
`aman ahead of his time.
`
`
`
`ousedition
`ited States
`
`{in any form or
`permission of
`
`98~-23682
`
`
`
`9
`
`

`

`
`ABOUT THE AUTHOR
`
`University.
`
`Yannis Tsividis received the B.S. degree from the University of Minnesota, Min-
`neapolis, in 1972, and the M.S. and Ph.D. degrees from the University of California,
`Berkeley, in 1973 and 1976, respectively.
`His involvement with MOStransistors began in the early seventies as part of his
`industrial and doctoral work. In 1975, to prove the feasibility of MOS technology for
`analog and mixed-signal integrated circuits, he designed and built a fully integrated
`MOSoperational amplifier and demonstrated its use in a PCM codec. Since that
`time, his work has focused on device and circuit issues in the merging of analog and
`digital circuits.on the samechip.
`Dr. Tsividis is Charles Batchelor Professor of Electrical Engineering at Colum-
`bia University in New York. He has,also taught, as part of regular or visiting appoint-
`ments, at the University of California, Berkeley, the Massachusetts Institute of Tech-
`nology, and the National Technical University of Athens. He has worked for
`Motorola Semiconductor and for AT&T Bell Laboratories.
`In addition to this book, he has written Mixed Analog-DigitalDevices and
`Technology (McGraw-Hill, 1996) and has edited several other books. He is the au-
`thor/coauthor of 10 patents.
`Dr. Tsividis is a Fellow of the IEEE. Heis the recipient of the 1984 IEEE
`W. R. G. Baker Best Paper Award and the 1986 European Solid-State Circuits Con-
`ference Best Paper Award. Heis corecipient of the 1987 Darlington Best Paper
`Award andrecipient of the 1998 Guillemin-Cauer Best Paper Award of the IEEE Cir-
`cuits and Systems Society. He has received the Great Teacher Award at Columbia
`
`10
`
`

`

`
`
`
`
`
`
`
`
`
`
`PREFACE
`
`
`
`
`
`
`
`
`
`
`noesota, Min-
`' of California,
`
`'$ as part of his
`technology for
`ully integrated
`iec. Since that
`of analog and
`
`ring at Colum-
`siting appoint-
`titute of Tech-
`is worked for
`
`| Devices and
`He is the au-
`
`re 1984 JEEE
`Circuits Con-
`om Best Paper
`the IEEE Cir-
`1 at Columbia
`
`This book provides a unified treatment of the many phenomena encounteredin the op-
`eration of modern MOStransistors, 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
`devoted to the subject. The MOStransistor is the dominant VLSI device. A course de-
`voted 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 of them, and do not present
`the intricacies and tradeoffs involved in a detailed modeling effort. The value of a
`course devoted to the MOStransistoris also extremely high for those who wantto use
`the device to design state-of-the-art circuits. Integrated. circuit designers have the op-
`portunity to suit devices to circuit needs, arid they can do this mostintelligently 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 performanceis
`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 simulator models a designer is working with,
`and for identifying their limitations. Many circuit designers in the industry spend end-
`less hours trying tointerpret 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 MOStransistor operation and modeling.
`In the dozen years that have passed since the publication ofthe first edition of
`this book there have been significant advances in the understanding and modeling of
`the MOStransistor. In addition, the requirements for modeling this device on the part
`of the circuit design community are now much more demanding. For example, the
`push for low-voltage and micropower operation has made necessarycareful modeling
`of the device below strong inversion, and the push for ever smaller dimensions has
`
`_
`
`
`
`vii
`
`11
`
`

`

`viii.
`
`PREFACE
`
`revealed phenomenapreviously ignored. In addition, the advent of “mixed-signal”
`circuits, which combine analog anddigital functions on the same chip, makesit nec-
`essary 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 philos-
`ophy of the first edition has been retained. Several aspects of this philosophy are
`summarized below.
`
`cause of both the detailed derivations and the intuitive discussions. At times, the
`
`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 inter-
`esting 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 authoris “splitting hairs.’ The author would rather:
`be accused of this than fudge. The MOStransistor 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 atall 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 makea lot of difference. The use of one namefor sev-
`eral quantities, common in some ofthe literature, is carefully avoided. For exam-
`ple, at least four distinct quantities encountered in MOStransistor work are de-
`scribed by using the single name “threshold voltage.” Although the reader is
`amply warnedofthis practice, the practice itself is avoided in this book.
`The emphasis is on principles. At the same time, to illustrate these principles, rele-
`vant models are extensively derived and discussed. Thus, physics and modeling
`are discussed in parallel throughout the book.
`Analytical results are derived in a logical manner after carefully stating the as-
`sumptions made. Empirical modeling is avoided aS much as possible. However,
`there are phenomena for which theonly analytical results available are empirical
`or semiempirical. 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 mak-
`ing it one. A well-connected set of topics has been chosen, and mostofthese 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 whatto expect if he or she consults the
`references provided.
`A great deal of emphasis is placed on providing intuition for the various phenom-
`ena discussed.It is rather hopeless to attempt working with a device as complex as
`the MOStransistor relying only on analytical relations. The emphasis on intuition
`has madelengthy discussions necessary.
`The pace is unhurried. The author believes that this actually makes it possible to
`study the material faster. Thus, whereasthe treatmentofa given topic may be long
`in terms of numberofpages,it actually should takeless time to comprehendit, be-
`
`12
`
`

`

`
`
`PREFACE
`
`3X
`
`“mixed-signal”
`, makesit nec-
`developments
`ie basic philos-
`dhilosophy are
`
`ow even if they
`cepts are often
`ng them inter-
`
`“he reader may
`w would rather
`complex that,
`7, and one ends
`3, and a lot of
`1air-splitting at
`iere those “too
`:namefor sev-
`led. For exam-
`t work are de-
`t the reader is
`0k.
`rinciples, rele-
`and modeling
`
`stating the as-
`ible. However,
`> are empirical
`‘t pointing out
`
`to avoid mak-
`ist of these are
`in other topics
`ults are shown
`1e consults the
`
`rious phenom-
`as complex as
`sis on intuition
`
`reader may get the feeling of déja 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 general, the book is written in the style in which the au-
`thor would like to have any new subject presented to him. He would very much
`like to see the new subject “beaten to death,” presented with several points of view
`to increase perspective and with a significant amountof repetition. The author has
`been in the past grateful for treatments of this type and neverfelt offended by this
`style. If the reader happensto be “faster” than the authorin 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.ex-
`planation of their features and of whatis new in them in this edition.
`
`Chapter 1: Semiconductors, Junctions, and MOSFET Overview
`All preliminary material necessary for the understanding of MOSstructuresis given
`here. This material is important to the newcomer, butpart of it should also make interest-
`ing 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 MOStransistor. This section is newto this edition.It
`provides a framework for the rest of the book, and makes it clear why particular details
`of the two- and three-terminal MOSstructures 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 MOStransistorare treated here. The regions of weak, moderate, and strong in-
`version 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
`ys appearing in the expression for the flat-band voltage. In energy band treatments
`it is often not clear where in the MOSstructure this potential actually resides, In this
`book, it is made evident that dy, is nothing but a contact potential, and the places
`where it resides are made obvious. Also, its presence in the flat-band voltage expres-
`sion is rigorously justified through Kirchhoff’s voltage law. The material on weak
`and moderate inversion has been improved and expandedin this edition.
`
`Chapter 3: The Three-Terminal MOS Structure
`
`Here one more terminal is added to the structure of Chap.-2, to connect the inversion
`
`
`
`3 it possible to
`ic may be long
`prehend it, be-
`, At times, the
`
`layer to the external world. MOStransistor concepts that are not directly related to
`
`13
`
`

`

`X
`
`PREFACE
`
`The four-terminal MOStransistor 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. Thefirst 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, in-
`cluding 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 mate-
`rial is new to this edition, and has been included to reflect recent trends. Someofthis
`material can be skipped without loss of continuity, and this is indicated at the appro-
`priate 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.
`:
`
`because of time limitations.
`
`current flow are presented in this chapter. This includes the important “substrate ef-
`fect,’ 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 ‘Ve, Con-
`trol’ Point of View,” has been addéd, to lay the foundation for the discussion of cer-
`tain recent models covered in Chap.4.
`
`Chapter 4: The Four-Terminal MOS Transistor
`
`Chapter 5: MOS Transistors with Ion-Implanted Channels
`This chapter was Chap.6 in thefirst edition. It now precedes the chapter on small di-
`mension effects. This change was made becauseall modern devices, small orlarge,
`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 pre-
`fer 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 buried-
`channel 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 develop-
`ment of other aspects of J-V characteristics. In certain settings, this may be necessary
`
`14
`
`

`

`
`
`Chapter 6: Small-Dimension Effects
`
`PREFACE Xi
`
`This chapter has been revisedand expanded by an 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 very thin oxide effects) are dis-
`cussed. Among the new topics in this edition are reverse short-channel and narrow-
`channel effects and hot carrier effects. Although space does not allow for a detailed
`exposition of all small-dimension effects, the reader is made aware oftheir 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 Transistor in Dynamic Operation—Large-Signal Modeling
`This chapter is largely devoted to charge modeling. The concept of quasi-static oper-
`ation is carefully introduced, and general techniques for charge evaluation are pre-
`sented, illustrated by charge computations for one representative model. Non-quasi-
`static analysis is then introduced. Since this chapter was considered by instructors
`and reviewers to be one of the most successful ones in thefirst edition, its basic struc-
`ture was retained. Some material was added on general charge modeling independent
`of inversion regions, and on transient response in non-quasi-static operation.
`
`Chapter 8: Small-Signal Modeling for Low and Medium Frequencies
`The principles behind small-signal modeling are presented. The discussion isJimited
`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 discus-
`sion 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 inver-
`sion, 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-Frequency 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 equivalent-
`circuit topologies from a complete quasi-static description. Then, non-quasi-static
`models are introduced through a careful development ofthe transistor’s “transmission
`line” equations, and a useful y-parameter model is derived for high-frequency appli-
`cations. It is shown that each level of modeling reduces to the next lower one if the
`
`t “substrate ef-
`rsion has been
`, “A ‘Vop Con-
`cussion of cer-
`
`g one terminal
`d, on the basis
`ictures. This is
`il. The first of
`currents, valid
`rial is brief but
`set models, in-
`
`ar strong- and
`rt of this mate-
`s. Some ofthis
`d at the appro-
`apared to each
`(the complete
`odels has been
`3, Etc., are also
`out throughout
`
`ier on smalldi-
`small or large,
`rial, the reader
`the following
`y that they can
`\ctors who pre-
`
`lition, has been
`respond more
`ace- or buried-
`> revision also
`which discuss
`tailed develop-
`
`
`
`ty be necessary
`
`15
`
`

`

`xii|PREFACE
`
`frequency is sufficiently reduced. In this edition, the section on non-quasi-static mo
`eling has been revised to include a more extensive explanation for the presence of in
`ductance in intrinsic small-signal models. A new section on high-frequency nois
`emphasizing induced gate noise, has been added. Another new section deals wit
`considerations for radio-frequency (RF) modeling, including the effects of gate resi
`tance and discussing the two commonfigures of merit for high-frequency perfo
`mance,the transition frequency and the maximum frequency ofoscillation.
`
`form relates directly to typical values of voltages and channel lengths.
`
`Chapter 10: MOSFET Modeling for Circuit Simulation
`This chapter is entirely new in the second edition, and replaces the one on fabrica
`tion. Having been exposed to the many phenomenain the MOStransistor and to th
`modeling of such phenomena,the reader will find in this chapter an exposition of th
`many issues and considerations involved in putting all. these together to make an ex
`tensive model suitable for circuit simulation. Discussed here are the various types o
`models, the ways that models of particular phenomena are combined, parameter ex
`traction, desirable properties for simulator models, commonpitfalls in modeling, an
`many benchmark tests for models, which have recently been included in an IEE
`standard. This chapter, it is hoped, will provide a starting point for readers who in
`tend to work in modeling, and will save them time and effort by clearly warning o
`common errors.It is also meant to provide a backgroundfor circuit designers, allow
`ing them to understand the limitations of the models they are using, and to better|
`communicate their needs to modeling 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 com- |
`plicated results which, it was felt, would distractif put in the main text. For the
`same reason, some material in the main text wasput in fine print or in footnotes or.
`as already mentioned, was described in the statements of some homework prob- |
`lems. Such material includescertain 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 becauseit is technically impor
`tant, or is widely mentionedin the literature, or has historical significance, oris par
`of controversy that has notyet been resolved.
`vO
`A change from the first edition has to do with units. The consistent system. 0
`units used in that edition has been abandoned, as it failed to work well in most set- |
`tings. Thus, in the present edition common units have been adopted [e.g., A for oxide |
`thickness and cm?/(V-s) for mobility]. In some instances, the value of a quantity is
`given in such units, with the value in different units given after that in parentheses
`for example,a field intensity is given as “3 x 10+ V/cm (or 3 V/m),” since the latter {
`
`:
`
`16
`
`

`

`
`
`PREFACE XH
`
`
`
`
`
`
`
`
`
`
`The subject of this book is definitely among those that ‘are best digested by
`doing. The homework problems should help to give a feeling for the kind of work
`involved in modeling. Most of the homework problemsfall in one of the following
`categories:
`
`1. They sketch additional modeling ideas not in the main text and encourage the
`reader to try them out.
`2. They compare several models introduced in the text.
`3. They ask for computations and plots to help provide a quantitative feeling and in-
`vestigate various properties.
`4. They ask for detailed derivations which were sketched in the main text, but which
`were not shownin detail in order to avoid distraction from the main points.
`
`Students can be encouraged to write subroutines for the calculation of various
`quantities as they go along andto save them forlater use. In this way, they will grad-
`ually build a library of useful subroutines that can be helpful not only in new home-
`work assignments but also in a final project if one is assigned. It has been the au-
`thor’s experience that project work is invaluable, and the more extensive the project,
`the greater the benefits. The project can take the form of the implementation of mod-
`els on the computer. Here it is not enough to just copy a model from the book into a
`computer program. One must worry about choosing the right models, appropriately
`combining them to form general models, ensuring continuity of calculated quantities
`with respect to all given parameters, etc. Some examples of projects follow.
`
`uasi-static mod-
`: presence of in-
`requency noise,
`‘tion deals with
`tts of gate resis-
`squency perfor-
`ation.
`
`one on fabrica-
`sistor and to the
`Xposition of the
`to make an ex-
`various types of
`|, parameter ex-
`1 modeling, and
`Jed in an IEEE
`readers whoin-
`arly warning of
`esigners, allow-
`g, and to better
`
`iction to energy
`sneral but com-
`in text. For the
`in footnotes or,
`omework prob-
`af view, etc. To
`and appendixes
`ican always be
`ts in the text is
`
`| and expanded.
`hnically impor-
`cance, or is part
`
`
`
`
`e Write a computer program to evaluate the drain current of a device on a uniform
`substrate, including short- and narrow-channel effects. The current should be contin-
`uous with respect to any input parameter (voltage, geometric dimensions,etc.), and
`so should be the derivatives of the current with respect to eachterminal voltage.
`@ Develop a computationally efficient technique for the evaluation of drain current in a
`long-channel device, valid in weak, moderate, and strong inversion. This will neces-
`sitate the developmentof efficient numerical techniques, because the general charge
`sheet approach, if unmodified, will lead to complex computations. Again, continuity
`of the currentand its derivatives with respect to all parameters should be ensured.
`e Develop a program for modeling ion-implanted devices in strong inversion, again
`ensuring continuity,
`e Develop a program for the modeling of low- and medium-frequency small-signal
`parameters in strong inversion, paying special attention to the small-signal output
`conductance in the saturation region. All small-signal parameters should be con-
`istent system of
`tinuous with respect to all input parameters.
`‘ell in most set-
`@ Develop a program for the evaluation of all charges and small-signal capacitances.
`1g. A for oxide
`All these quantities should be continuous with respect to any input parameter.
`of a quantity is
`® Develop a program for the extraction of parameter values to be used with a given
`in parentheses;
`model. The inputto this program is assumed to consist of measured quantities.
`’ since the latter
`
`17
`
`

`

`XIV PREFACE
`
`In addition, certain long homework problems can easily be expanded into pro-
`jects. In all cases, the value of the project, and the challenge in it, can be enhancedif
`the results are compared to measurements, obtained either in the lab or from the tech-
`nicalliterature (the references provided should be very helpful in the latter case). De-
`pending on the magnitude of effort foreseen, students can work separately or in
`teams.
`The first edition of this book has been used for senior or graduate courses at
`many universities and in industrial short courses. For a one-semester course, a large
`number of possibilities exist in regard to the topics selected for coverage. Thus, for
`example, a course emphasizing general principles would cover Chaps. 1 through3,
`Chap.4 including a careful