a
`
`UL qv WOU 4 Upetel i
`a tiesTle eeueyWy ralob acS
`VeaTaoTe
`
`Robert F. Pierret
`
`ieeeieetireeee
`
`with Computer-Based Exercises
`
`\
`
`and Homework Problems
`
`
`
`HANWHA 1033
`
`

`

`SEMICONDUCTOR
`DEVICE
`FUNDAMENTALS
`
`Robert F. Pierret
`School of Electrical and Computer Engineering
`Purdue University
`
`Addison
`Wesley
`Longman
`
`Reading. Massachusetts • Menlo Park. California • New York
`Don Mills. Ontario • Wokingha m. England • Amsterdam • Bonn
`Sydney • Singapore • Tokyo • Madrid • San Juan • Milan • Paris
`
`

`

`Katherine Harutunian Associme .Editor
`Helen Wythe Senior Production Supervisor
`Hugh Crawford 1vlonuf11ct1tring Supervisor
`Barbara Atkinson Associate Cover Design Supervisor
`Peter Blaiwas Cover design
`Kenneth J. Wilson Text design
`Joyce Grandy Copyeditor
`Sandra Rigney Production Packaging Services
`G & S Typesetters, Inc. Composition
`Publishers' Design and Production Services, Inc.
`
`llfustrations
`
`Library of Congress Cataloging-in-Publication Data
`Pierret. Robert F.
`Semiconductor device fundamentals / Robert F. Pierre!.
`p.
`cm.
`Includes index.
`ISBN 0-20 l-54393- l
`I. Title.
`l. Semiconductors.
`TK787 I .85.P484 1996
`621.38l5'2-dc20
`
`95-17387
`CIP
`
`Many of the designations used by manufacturers and sellers to distinguish their products arc claimed
`as trademarks. Where those designations appear in th.is book, and Addison-Wesley was aware of a
`trademark claim. the designations have been printed in initial caps or all caps.
`
`MAIL.AB is a registered trademark of The Math Works, lnc ..
`24 Prime Park Way, Natick, MAO l 760-1500.
`Phone: (508) 653-1415. Fax: (508) 653-2997
`E-mail: info(i1rnathworks.com
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`Access the latest information about Addison-Wesley books from our Internet gopher site or our World
`Wide Web page:
`
`Copyright:
`
`1996 by Addison-Wesley Publishing Company, lne.
`
`Reprinted with corrections March, l 996
`
`All rights reserved. No part of this publication may be reproduced. stored in a retrieval system, or
`trnnsmittcd in any form or by any means, electronic. mechanical, photocopying, recording, or other(cid:173)
`wise, without the written permission of the publisher.
`
`Printed in the United States of America
`
`27 28 V092 16 15
`
`

`

`"The little voice inside never grows any older."
`
`Frank Pierret ( 1906- 1994)
`
`j
`1;
`
`...
`
`i -------------------::-~
`
`

`

`PREFACE
`
`Why another text on solid state devices? The author is aware of at least 14 undergraduate
`texts published on the subject during the past decade. Although several motivating factors
`could be cited, a very significant factor was the desire to write a book for the next millen(cid:173)
`nium (a Book 2000 so to speak) that successfully incorporates computer-assisted learning.
`In a recent survey, members of the Undergraduate Curriculum Committee in the School of
`Electrical and Computer Engineering at Purdue University listed integration of the com(cid:173)
`puter into the learning process as the number one priority. Nationally, university consor(cid:173)
`tiums have been formed which emphasize computer-assisted learning. In January 1992,
`distribution began of the Student Edition of MATLAB, essentially a copy of the original
`MATLAB manual bundled with a low-cost version of the math-tools software. Over 37,000
`copies of the book/software were sold in the first year! Texts and books on a variety of
`topics from several publishers are now available that make specific use of the MATLAB
`software. The direction is clear as we proceed into the second millennium: Computer(cid:173)
`assisted learning will become more and more prevalent. In dealing with solid state devices,
`the computer allows one to address more realistic problems, to more readily experiment
`with "what-if" scenarios, and to conveniently obtain a graphical output. An entire device
`characteristic can often be computer generated with less time and effort than a small set of
`manually calculated single-point values.
`It should be clarified that the present text is not a totally new entry in the field, but is
`derived in part from Volumes I-IV of the Addison-Wesley Modular Series on Solid State
`Devices. Lest there be a misunderstanding, the latest versions of the volumes in the Modu(cid:173)
`lar Series were not simply glued together. To the contrary, more than half of the material
`coverage in the four volumes was completely rewritten. Moreover, several supplemental
`sections and two additional chapters were added to the Volumes I-IV outline. The new text
`also contains computer-based text exercises and end-of-chapter problems, plus a number
`of other special features that are fully described in the General Introduction.
`In just about any engineering endeavor there are tradeoffs. Device design is replete
`with tradeoffs. Tradeoffs also enter into the design of a book. For example, a few topics
`can be covered in detail (depth) or lesser coverage can be given to several topics (breadth).
`Similarly one can emphasize the understanding of concepts or optimize the transmission of
`factual information. Volumes I-IV in the Modular Series are known for their pedantic
`depth of coverage emphasizing concepts. While retaining the same basic depth of coverage,
`four "read-only" chapters have been specifically added herein to broaden the coverage and
`enhance the transmission of factual information. In the read-only chapters the emphasis is
`more on describing the exciting world of modern-day devices. Compound semiconductor
`devices likewise receive increased coverage throughout the text. There is also a natural
`
`V
`
`

`

`Vi
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`tradeoff between the effort devoted to developing qualitative insight and the implementa(cid:173)
`tion of a quantitative analysis. Careful attention has been given to avoid slighting the de(cid:173)
`velopment of "intuition" in light of the greatly enhanced quantitative capabilities arising
`from the integrated use of the computer. Lastly, we have not attempted to be all-inclusive
`in the depth and breadth of coverage- many things are left for later (another course, other
`books). Hopefully, the proper tradeoffs have been achieved whereby the reader is reason(cid:173)
`ably knowledgeable about the subject matter and acceptably equipped to perform device
`analyses after completing the text.
`The present text is intended for undergraduate juniors or seniors who have had at least
`an introductory exposure to electric field theory. Chapters are grouped into three major
`divisions or "parts," with Part II being further subdivided into IIA and IIB. With some
`deletions, the material in each of the three parts is covered during a five-week segment of
`a one-semester, three-credit-hour, junior-senior course in Electrical and Computer Engi(cid:173)
`neering at Purdue University. A day-by-day course outline is supplied on the Instructor's
`Disk accompanying the Solutions Manual. If necessary to meet time constraints, read-only
`Chapters 4, 9, 13, and 19 could be deleted from the lecture schedule. (An instructor might
`preferably assign the chapters as independent readings and reward compliant students by
`including extra-credit examination questions covering the material.) Standard Chapters 12,
`14, and 15, except for the general field-effect introduction in Section 15.1, may also be
`omitted with little or no loss in continuity.
`Although a complete listing of special features is given in the General Introduction,
`instructors should take special note of the Problem Information Tables inserted prior to the
`end-of-chapter problems. These tables should prove useful in assigning problems and in
`dealing with homework graders. When faced with constructing a test, instructors may also
`be interested in examining the Review Problem Sets found in the mini-chapters (identified
`by a darkened thumb tab) at the end of the three book parts. The Review Problem Sets are
`derived from old "open-book" and "closed-book" tests. Concerning the computer-based
`exercises and problems, the use of either the student or professional version of MATLAB is
`recommended but not required. The in-text exercise solutions and the problem answers
`supplied to the instructor, however, do make use of MATLAB. Although it would be helpful,
`the user need not be familiar with the MATLAB program at the beginning of the book. The
`MATLAB problems in successive chapters make increasingly sophisticated use of the pro(cid:173)
`gram. In other words, the early exercises and homework problems provide a learning
`MATLAB by using MATLAB experience. It is critical, however, that the user complete a
`large percentage of the computer-based exercises and problems in the first three chapters.
`The exercises and problems found in later chapters not only assume a reasonably competent
`use of MATLAB, but also build upon the programs developed in the earlier chapters.
`The author gratefully acknowledges the assistance of associates, EE305 students, the
`respondents to an early marketing survey, the manuscript reviewers, and Addison-Wesley
`personnel in making Book 2000 a reality. Deserving of special thanks is Ali Keshavarzi for
`arranging the author's sabbatical at Intel Corporation and for providing photographs of
`equipment inside the Albuquerque fabrication facility. Prof. Mark Lundstrom at Purdue
`University was also most helpful in supplying key information and figures for several book
`sections. Of the undergraduate students asked to examine the manuscript for readability
`
`

`

`PREFACE
`
`vii
`
`and errors, Eric Bragg stands out as especially perceptive and helpful. The very conscien(cid:173)
`tious manuscript reviewers were Prof. Kenneth A. James, California State University, Long
`Beach_; Prof. Peter Lanyon, Worcester Polytechnic Institute; Prof. Gary S. May, Georgia
`Institute of Technology; Prof. Dieter K. Schroder, Arizona State University; and Prof. G. W.
`Stillman, University of Illinois at Urbana-Champaign. In recognition of a fruitful associa(cid:173)
`tion, a special thanks to Don Fowley, the former editor at Addison-Wesley who enticed the
`author into writing the book. Last but not least, editor Katherine Harutunian is to be cred(cid:173)
`ited with smoothly implementing the project, and executive assistant Anita Devine with
`cheerfully handling many of the early details.
`
`Prof Robert F. Pierret
`School of Electrical and Computer Engineering
`Purdue University
`
`:l(J
`\id
`
`;;;~ 1
`Jl ,)"1i
`{tl .J..
`
`

`

`CONTENTS
`
`General Introduction
`
`Part I Semiconductor Fundamentals
`
`Chapter 1 Semiconductors: A General Introduction
`
`1.1 General Material Properties
`1.1.1 Composition
`1.1.2 Purity
`1.1.3 Structure
`
`1.2 Crystal Structure
`1.2.1 The Unit Cell Concept
`1.2.2 Simple 3-D Unit Cells
`1.2.3 Semiconductor Lattices
`1.2.4 Miller Indices
`
`1.3 Crystal Growth
`1.3. l Obtaining Ultrapure Si
`1.3.2 Single-Crystal Formation
`
`1.4 Summary
`
`Problems
`
`Chapter 2 Carrier Modeling
`
`2.1 The Quantization Concept
`
`2.2 Semiconductor Models
`2.2.1 Bonding Model
`2.2.2 Energy Band Model
`2.2.3 Carriers
`2.2.4 Band Gap and Material Classification
`2.3 Carrier Properties
`2.3. l Charge
`2.3.2 Effective Mass
`2.3.3 Carrier Numbers in Intrinsic Material
`
`xxi
`
`3
`
`3
`3
`5
`6
`6
`7
`8
`9
`12
`16
`16
`17
`19
`19
`
`23
`
`23
`
`25
`26
`26
`29
`31
`32
`32
`32
`34
`
`ix
`
`

`

`X
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`2.3.4 Manipulation of Carrier Numbers-Doping
`2.3.5 Carrier-Related Terminology
`
`2.4 State and Carrier Distributions
`2.4.1 Density of States
`2.4.2 The Fermi Function
`2.4.3 Equilibrium Distribution of Carriers
`
`2.5 Equilibrium Carrier Concentrations
`2.5.1 Formulas for n and p
`2.5.2 Alternative Expressions for n and p
`2.5.3 ni and the np Product
`2.5.4 Charge Neutrality Relationship
`2.5.5 Carrier Concentration Calculations
`2.5.6 Determination of EF
`2.5.7 Carrier Concentration Temperature Dependence
`
`2.6 Summary and Concluding Comments
`
`Problems
`
`Chapter 3 Carrier Action
`
`3.1 Drift
`3. l. l Definition- Visualization
`3.1.2 Drift Current
`3 .1.3 Mobility
`3. I .4 Resistivity
`3. I .5 Band Bending
`
`3.2 Diffusion
`3.2. I Definition-Visualization
`3.2.2 Hot-Point Probe Measurement
`3.2.3 Diffusion and Total Currents
`Diffusion Currents
`Total Currents
`3.2.4 Relating Diffusion Coefficients/Mobilities
`Constancy of the Fermi Level
`Current Flow Under Equilibrium Conditions
`Einstein Relationship
`3.3 Recombination-Generation
`3.3.1 Definition- Visuali zation
`Band-to-Band Recombination
`
`35
`40
`
`40
`41
`42
`46
`
`49
`49
`52
`53
`57
`59
`61
`65
`67
`
`69
`
`75
`
`75
`75
`76
`79
`85
`89
`
`94
`94
`97
`98
`98
`99
`99
`99
`101
`101
`105
`105
`105
`
`

`

`R-G Center Recombination
`Auger Recombination
`Generation Processes
`3.3.2 Momentum Considerations
`3.3.3 R- G Statistics
`Photogeneration
`Indirect Thermal Recombination- Generation
`3.3.4 Minority Carrier Lifetimes
`General Information
`A Lifetime Measurement
`
`3.4 Equations of State
`3.4.1 Continuity Equations
`3.4.2 Minority Carrier Diffusion Equations
`3.4.3 Simplifications and Solutions
`3.4.4 Problem Solving
`Sample Problem No. I
`Sample Problem No. 2
`
`3.5 Supplemental Concepts
`3.5. l Diffusion Lengths
`3.5.2 Quasi-Fermi Levels
`
`3.6 Summary and Concluding Comments
`
`Problems
`
`Chapter 4 Basics of Device Fabrication
`
`4. l Fabrication Processes
`4.1.1 Oxidation
`4.1.2 Diffusion
`4.1.3 Ion Implantation
`4.1.4 Lithography
`4.1.5 Thin-Film Deposition
`Evaporation
`Sputtering
`Chemical Vapor Deposition (CVD)
`4.1.6 Epitaxy
`4.2 Device Fabrication Examples
`4.2.I pn Junction Diode Fabrication
`4.2.2 Computer CPU Process Flow
`4.3 Summary
`
`CONTENTS
`
`xi
`
`105
`107
`107
`107
`110
`110
`112
`116
`116
`116
`
`120
`121
`122
`124
`124
`124
`128
`
`131
`131
`132
`
`136
`
`138
`
`149
`
`149
`149
`152
`155
`159
`162
`162
`162
`164
`164
`
`165
`166
`166
`174
`
`

`

`Xii
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`Rl Part I Supplement and Review
`
`Alternative/Supplemental Reading List
`
`Figure Sources/Cited References
`
`Review List of Terms
`
`Part I-Review Problem Sets and Answers
`
`Part IIA pn Junction Diodes
`
`Chapter 5 pn Junction Electrostatics
`
`5.1 Preliminaries
`5. l. l Junction Terminology/[dealized Profiles
`5.1.2 Poisson's Equation
`5. l.3 Qualitative Solution
`5.1.4 The Built-in Potential ( Vb)
`5.1.5 The Depletion Approximation
`
`5.2 Quantitative Electrostatic Relationships
`5.2.1 Assumptions/Definitions
`5.2.2 Step Junction with VA = 0
`Solution for p
`Solution for cg
`Solution for V
`Solution for x0 and xP
`5.2.3 Step Junction with VA -:t:. 0
`5.2.4 Examination/Extrapolation of Results
`5.2.5 Linearly Graded Junctions
`
`5.3 Summary
`
`Problems
`
`Chapter 6 pn Junction Diode: 1-V Characteristics
`
`6.1 The Ideal Diode Equation
`6.1. l Qualitative Derivation
`6.1.2 Quantitative Solution Strategy
`General Considerations
`Quasineutral Region Considerations
`Depletion Region Considerations
`Boundary Conditions
`
`175
`
`175
`177
`
`178
`
`179
`
`193
`
`195
`
`195
`195
`197
`198
`203
`206
`
`209
`209
`210
`210
`210
`212
`213
`215
`219
`223
`
`226
`
`227
`
`235
`
`235
`235
`241
`241
`242
`243
`244
`
`

`

`"Game Plan" Summary
`6.1.3 Derivation Proper
`6.1.4 Examination of Results
`Ideal 1-V
`The Saturation Current
`Carrier Currents
`Carrier Concentrations
`6.2 Deviations from the Ideal
`6.2.1 Ideal Theory Versus Experiment
`6.2.2 Reverse-Bias Breakdown
`Avalanching
`Zener Process
`6.2.3 The R-G Current
`6.2.4 VA ➔ Vb; High-Current Phenomena
`Series Resistance
`High-Level Injection
`
`6.3 Special Considerations
`6.3.1 Charge Control Approach
`6.3.2 Narrow-Base Diode
`Current Derivation
`Limiting Cases/Punch-Through
`
`6.4 Summary and Concluding Comments
`
`Problems
`
`Chapter 7 pn Junction Diode: Small-Signal Admittance
`
`7.1 Introduction
`7.2 Reverse-Bias Junction Capacitance
`7.2. l General Information
`7.2.2 C-V Relationships
`7.2.3 Parameter Extraction/Profiling
`7.2.4 Reverse-Bias Conductance
`7.3 Forward-Bias Diffusion Admittance
`7.3.l General Information
`7.3.2 Admittance Relationships
`7.4 Summary
`Problems
`
`CONTENTS
`
`xiii
`
`246
`247
`249
`249
`250
`254
`255
`
`260
`260
`263
`264
`268
`270
`277
`278
`279
`
`281
`282
`284
`284
`286
`
`288
`
`289
`
`301
`
`301
`
`301
`301
`305
`309
`313
`
`315
`315
`318
`323
`324
`
`

`

`xiv
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`Chapter 8 pn Junction Diode: Transient Response
`
`8.1 Turn-Off Transient
`8.1. l Introduction
`8. l .2 Qualitative Analysis
`8.1.3 The Storage Delay Time
`Quantitative Analysis
`Measurement
`8. 1.4 General Information
`
`8.2 Turn-On Transient
`8.3 Summary
`
`Problems
`
`Chapter 9 Optoelectronic Diodes
`
`9.1 Introduction
`
`9.2 Photodiodes
`9.2.1 pn Junction Photodiodes
`9.2.2 p-i-n and Avalanche Photodiodes
`p-i-n Photodiodes
`Avalanche Photodiodes
`
`9.3 Solar Cells
`9.3.1 Solar Cell Basics
`9.3.2 Efficiency Considerations
`9.3.3 Solar Cell Technology
`
`9.4 LEDs
`9.4.1 General Overview
`9.4.2 Commercial LEDs
`9.4.3 LED Packaging and Photon Extraction
`
`Part 118 BJTs and Other Junction Devices
`
`Chapter IO BJT Fundamentals
`
`l 0.1 Terminology
`10.2 Fabrication
`I 0.3 Electrostatics
`I 0.4 Introductory Operational Considerations
`
`I 0.5 Performance Parameters
`Emitter Efficiency
`
`327
`
`327
`327
`329
`333
`333
`334
`338
`
`338
`343
`
`344
`
`347
`
`347
`
`349
`349
`352
`352
`355
`356
`356
`357
`360
`361
`361
`362
`366
`
`369
`
`371
`
`371
`374
`378
`380
`382
`382
`
`

`

`CONTENTS
`
`xv
`
`Base Transport Factor
`Common Base d.c. Current Gain
`Common Emitter d.c. Current Gain
`10.6 Summary
`Problems
`
`Chapter 11 BJT Static Characteristics
`11.1 Ideal Transistor Analysis
`11.1.1 Solution Strategy
`Basic Assumptions
`Notation
`Diffusion Equations/Boundary Conditions
`Computational Relationships
`11.1.2 General Solution (W Arbitrary)
`Emitter/Collector Region Solutions
`Base Region Solution
`Performance Parameters/Terminal Currents
`ll.1.3 Simplified Relationships (W ~ la)
`~p8 (x) in the Base
`Performance Parameters
`11.1.4 Ebers-Moll Equations and Model
`11.2 Deviations from the Ideal
`11.2.1 Ideal Theory/Experiment Comparison
`11.2.2 Base Width Modulation
`11 .2.3 Punch-Through
`11.2.4 Avalanche Multiplication and Breakdown
`Common Base
`Common Emitter
`11.2.5 Geometrical Effects
`Emitter Area ::f. Collector Area
`Series Resistances
`Current Crowding
`I I .2.6 Recombination-Generation Current
`11.2.7 Graded Base
`11.2.8 Figures of Merit
`11.3 Modern BJT Structures
`11.3.1 Polysilicon Emitter BJT
`11.3.2 Heterojunction Bipolar Transistor (HBT)
`
`383
`383
`384
`
`385
`
`385
`
`389
`
`389
`389
`389
`390
`390
`392
`393
`393
`394
`395
`397
`398
`398
`403
`
`407
`407
`410
`412
`414
`414
`414
`420
`420
`421
`421
`422
`423
`424
`426
`426
`429
`
`

`

`xvi
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`11.4 Summary
`
`Problems
`
`Chapter 12 BJT Dynamic Response Modeling
`
`I 2.1 Small-Signal Equivalent Circuits
`12.1. l Generalized Two-Port Model
`12.1.2 Hybrid-Pi Models
`
`12.2 Transient (Switching) Response
`12.2.1 Qualitative Observations
`12.2.2 Charge Control Relationships
`12.2.3 Quantitative Analysis
`Turn-on Transient
`Turn-off Transient
`12.2.4 Practical Considerations
`
`12.3 Summary
`
`Problems
`
`Chapter 13 PNPN Devices
`
`13.1 Silicon Controlled Rectifier (SCR)
`
`13.2 SCR Operational Theory
`
`13 .3 Practical Turn-on/Turn-off Considerations
`13 .3. l Circuit Operation
`13.3.2 Additional Triggering Mechanisms
`13.3.3 Shorted-Cathode Configuration
`13.3.4 dildt and dv/dt Effects
`13.3.5 Triggering Time
`13.3.6 Switching Advantages/Disadvantages
`
`13.4 Other PNPN Devices
`
`Chapter 14 MS Contacts and Schottky Diodes
`
`14. I Ideal MS Contacts
`14.2 Schottky Diode
`14.2. J Electrostatics
`Built-in Voltage
`p,~ , V
`Depletion Width
`14.2.2 l- V Characteristics
`14.2.3 a.c. Response
`
`432
`
`433
`
`443
`
`443
`443
`446
`449
`449
`452
`454
`454
`456
`457
`458
`459
`
`463
`
`463
`465
`470
`470
`471
`471
`472
`473
`473
`474
`
`477
`
`477
`
`483
`483
`483
`485
`486
`487
`493
`
`

`

`CONTENTS
`
`xvii
`
`14.2.4 Transient Response
`
`14.3 Practical Contact Considerations
`14.3.1 Rectifying Contacts
`14.3.2 Ohmic Contacts
`14.4 Summary
`Problems
`
`R2 Part II Supplement and Review
`
`Alternative/Supplemental Reading List
`Figure Sources/Cited References
`
`Review List of Terms
`Part II-Review Problem Sets and Answers
`
`Part Ill Field Effect Devices
`
`Chapter 15 Field Effect Introduction-The J-FET and MESFET
`
`15 .1 General Introduction
`15.2 J-FET
`15.2.1 Introduction
`15.2.2 Qualitative Theory of Operation
`15.2.3 Quantitative / 0 -V0 Relationships
`15.2.4 a.c. Response
`15.3 MESFET
`15.3. l General Information
`15.3.2 Short-Channel Considerations
`Variable Mobility Model
`Saturated Velocity Model
`Two-Region Model
`15.4 Summary
`Problems
`
`Chapter 16 MOS Fundamentals
`
`16.1 Ideal Structure Definition
`16.2 Electrostatics-Mostly Qualitative
`16.2.1 Visualization Aids
`Energy Band Diagram
`Block Charge Diagrams
`
`496
`497
`497
`498
`500
`501
`
`505
`
`505
`
`506
`507
`
`508
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`525
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`525
`530
`530
`531
`536
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`550
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`557
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`563
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`563
`565
`565
`565
`566
`
`

`

`xviii
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`16.2.2 Effect of an Applied Bias
`General Observations
`Specific Biasing Regions
`
`16.3 Electrostatics-Quantitative Formulation
`16.3. I Semiconductor Electrostatics
`Preparatory Considerations
`Delta-Depletion Solution
`16.3.2 Gate Voltage Relationship
`
`16.4 Capacitance-Voltage Characteristics
`16.4.1 Theory and Analysis
`Qualitative Theory
`Delta-Depletion Analysis
`16.4.2 Computations and Observations
`Exact Computations
`Practical Observations
`
`16.5 Summary and Concluding Comments
`Problems
`
`Chapter 17 MOSFETs-The Essentials
`
`17. I Qualitative Theory of Operation
`17.2 Quantitative / 0 -V O Relationships
`17 .2.1 Preliminary Considerations
`Threshold Voltage
`Effective Mobility
`17.2.2 Square-Law Theory
`17.2.3 Bulk-Charge Theory
`17.2.4 Charge-Sheet and Exact-Charge Theories
`17 .3 a.c. Response
`17.3.1 Small-Signal Equivalent Circuits
`17.3 .2 Cutoff Frequency
`17.3.3 Small-Signal Characteristics
`17.4 Summary
`Problems
`
`Chapter 18 Nonideal MOS
`
`18. l Metal-Semiconductor Workfunction Difference
`
`567
`567
`568
`
`571
`571
`571
`576
`580
`
`584
`584
`584
`590
`591
`591
`595
`599
`600
`
`611
`
`611
`
`617
`617
`617
`618
`620
`625
`628
`
`630
`630
`633
`634
`637
`638
`
`645
`
`645
`
`

`

`18.2 Oxide Charges
`18.2. l General Information
`18.2.2 Mobile Ions
`18.2.3 The Fixed Charge
`18.2.4 Interfacial Traps
`18.2.5 Induced Charges
`Radiation Effects
`Negative-Bias Instability
`18.2.6 Ll VO Summary
`18.3 MOSFET Threshold Considerations
`18.3.1 Vr Relationships
`18.3.2 Threshold, Terminology, and Technology
`18.3.3 Threshold Adjustment
`18.3.4 Back Biasing
`18.3.5 Threshold Summary
`
`Problems
`
`Chapter 19 Modern FET Structures
`
`19.1 Small Dimension Effects
`19.l.l Introduction
`19.1.2 Threshold Voltage Modification
`Short Channel
`Narrow Width
`19.1.3 Parasitic BJT Action
`19.1.4 Hot-Carrier Effects
`Oxide Charging
`Velocity Saturation
`Velocity Overshoot/Ballistic Transport
`
`19.2 Select Structure Survey
`19.2.1 MOSFET Structures
`LDD Transistors
`DMOS
`Buried-Channel MOSFET
`SiGe Devices
`SOI Structures
`19.2.2 MODFET (HEMT)
`
`Problems
`
`CONTENTS
`
`xix
`
`650
`650
`653
`658
`662
`668
`668
`669
`670
`
`674
`675
`676
`678
`680
`681
`
`684
`
`691
`
`691
`691
`694
`694
`697
`698
`700
`700
`700
`701
`702
`702
`702
`703
`704
`704
`705
`707
`710
`
`

`

`XX
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`R3 Part III Supplement and Review
`
`Alternative/Supplemental Reading List
`
`Figure Sources/Cited References
`
`Review List of Terms
`Part III-Review Problem Sets and Answers
`
`Appendices
`Appendix A Elements of Quantum Mechanics
`
`A. l The Quantization Concept
`A. I. I Blackbody Radiation
`A.1.2 The Bohr Atom
`A.1.3 Wave-Particle Duality
`
`A.2 Basic Formalism
`
`A.3 Electronic States in Atoms
`A.3.1 The Hydrogen Atom
`A.3.2 Multi-Electron Atoms
`
`Appendix B MOS Semiconductor Electrostatics-Exact Solution
`
`Definition of Parameters
`Exact Solution
`
`Appendix C MOS C-V Supplement
`
`Appendix D MOS 1-V Supplement
`
`Appendix E List of Symbols
`
`Appendix M MATLAB Program Script
`
`Exercise 10.2 (BJT _. Eband)
`Exercise 11.7 (BJT) and Exercise l 1. 10 (BJTplus)
`Exercise 16.5 (MOS _ CV)
`
`Index
`
`713
`
`713
`
`714
`
`717
`
`718
`
`733
`
`733
`
`733
`733
`735
`737
`
`739
`
`741
`741
`744
`
`749
`
`749
`750
`
`753
`
`755
`
`757
`
`771
`
`771
`774
`778
`
`781
`
`

`

`GENERAL INTRODUCTION
`
`Coincident with the writing of this book, there has been considerable media discussion
`about the "Information Superhighway." The envisioned highway itself, the physical link
`between points supporting the information traffic, is fiber optic cable. Relative to the topic
`of this book, the on and off ramps, which insert and extract the information from the high(cid:173)
`way, are semiconductor (solid state) devices. Traffic control, the information processing
`and the conversion to and from the human interface, is performed by computers. The cen(cid:173)
`tral processing unit (CPU), memory, and other major components inside the computer are
`again semiconductor devices. In the modern world, semiconductor devices are incorporated
`in just about every major system from automobiles to washing machines.
`Although roughly a half-century old, the field of study associated with semiconductor
`devices continues to be dynamic and exciting. New and improved devices are being devel(cid:173)
`oped at an almost maddening pace. While the device count in complex integrated circuits
`increases through the millions and the side-length of chips is measured in centimeters, the
`individual devices are literally being shrunk to atomic dimensions. Moreover, semiconduc(cid:173)
`tor properties desired for a given device structure but not available in nature are being
`produced artificially; in essence, the semiconductor properties themselves are now being
`engineered to fit device specifications.
`This book should be viewed as a gateway to what the reader will hopefully agree is the
`fascinating realm of semiconductor devices. It was written for junior- or senior-level stu(cid:173)
`dents who have at least an introductory exposure to electric field theory. The coverage
`includes a representative sampling of information about a wide variety of devices. Primary
`emphasis, however, is placed on developing a fundamental understanding of the internal
`workings of the more basic device structures. As detailed below, this book contains a num(cid:173)
`ber of unique features to assist the reader in learning the material. Alerted at an early stage
`to their existence, the reader can plan to take full advantage of the cited features.
`
`• Computer-Based Exercises and End-of Chapter ( Homework) Problems. The majority
`of chapters contain one or more MATLAB-based exercises requiring the use of a com(cid:173)
`puter. MATLAB is a math-tools software program that has been adapted to run on most
`computer platforms. A low-cost student edition of MATLAB, which can be used to run
`all of the files associated with this book, is available in both IBM-compatible and Mac(cid:173)
`intosh versions. The MATLAB program scripts yielding exercise answers are listed in the
`text and are available in electronic form as detailed below. Computer-based problems,
`identified by a bullet(•) before the problem number, make up approximately 25% of the
`
`xxi
`
`

`

`xxii
`
`SEMICONDUCTOR DEVICE FUNDAMENTALS
`
`problem total. Although other math-tools programs could be employed, the use of
`MATLAB is recommended in answering computer-based problems. Because computer(cid:173)
`based exercises and problems in the early chapters are specifically designed to progres(cid:173)
`sively enhance MATLAB-use proficiency, the user need not be familiar with the MATLAB
`program at the beginning of the book. It is very important, however, to complete a large
`percentage of the computer-based exercises and problems in the first three chapters. The
`exercises and problems found in later chapters not only assume a reasonably competent
`use of MATLAB, but also build upon the programs developed in the earlier chapters.
`
`• Computer Program Files. Program files of the MATLAB scripts associated with com(cid:173)
`puter-based exercises are available via the Internet (ftp. ma thworks. com in the di(cid:173)
`rectory pub/books/pierret) or on a floppy disk distributed free of charge by
`Math Works, Inc . A pull-out card is provided herein for obtaining the free program disk
`which is formatted for use with either an IBM-compatible or Macintosh computer. Each
`floppy disk contains two sets of "m-files" to be used respectively with the pre-4.0 (stu(cid:173)
`dent 1st edition) or post-4.0 (student 2nd edition) versions of MATLAB. The listings in
`the text are specifically derived from the Macintosh post-4.0 version, but they are iden(cid:173)
`tical to the corresponding IBM-compatible version except for the occasional appearance
`of a Greek letter.
`
`• Supplement and Review Mini-Chapters. The book is divided into three parts. At the end
`of each part is a Supplement and Review mini-chapter. The mini-chapters, identified by
`a darkened thumb tab, contain an alternative/supplemental reading list and information
`table, reference citations for the preceding chapters, an extensive review-list of terms,
`and review problem sets with answers. The review problem sets are derived from
`"closed-book" and "open-book" examinations.
`
`• Read-Only Chapters. Chapters 4, 9, 13, and I 9 have been classified as "read-only."
`Chapters with the read-only designation contain mostly qualitative information of a sup(cid:173)
`plemental nature. Two of the chapters survey some of the latest device structures. In(cid:173)
`tended to be fun-reading , the read-only chapters are strategically placed to provide a
`change of pace. The chapters contain only a small number of equations, no exercises,
`and few, if any, end-of-chapter problems. In a course format, the chapters could be
`skipped with little loss in continuity or preferably assigned as independent readings.
`
`• Problem Information Tables. A compact table containing information about the end-of(cid:173)
`chapter problems in a given chapter is inserted just before the problems. The information
`provided is (i) the text section or subsection after which the problem can be completed,
`(ii) the estimated problem difficulty on a scale of I (easy or straightforward) to 5 (very
`difficult or extremely time consuming), (iii) suggested credit or point weighting, and
`(iv) a short problem description. A bullet before the problem number identifies a com(cid:173)
`puter-based problem. An asterisk indicates computer usage for part of the problem.
`• Equation Summaries. The very basic carrier modeling equations in Chapter 2 and the
`carrier action equations in Chapter 3, equations referenced throughout the text, are or(cid:173)
`ganized and repeated in Tables 2.4 and 3.3, respectively. These tables would be ideal as
`"crib sheets" for closed-book examinations covering the material in Part I of the text.
`
`

`

`GENERAL INTRODUCTION
`
`xxiii
`
`• Measurements and Data. Contrary to the impression sometimes left by the sketches and
`idealized plots often found in introductory texts, device characteristics are real, seldom
`perfect, and are routinely recorded in measurement laboratories. Herein a sampling of
`measurement details and results, derived from an undergraduate EE laboratory adminis(cid:173)
`tered by the author, is included in an attempt to convey the proper sense of reality. For
`added details on the described measurements, and for a description of additional mea(cid:173)
`surements, the reader is referred to R. F. Pierret, Semiconductor Measurements Labora(cid:173)
`tory Operations Manual, Supplement A in the Modular Series on Solid State Devices,
`Addison-Wesley Publishing Company, Reading MA, © 1991.
`
`• Alternative Treatment. Section 2.1 provides the minimum required treatment on the
`topic of energy quantization in atomic systems. Appendix A, which contains a more in(cid:173)
`depth introduction to the quantization concept and related topics, has been included for
`those desiring supplemental information. Section 2.1 may be totally replaced by Appen(cid:173)
`dix A with no loss in continuity.
`
`

`

`
`
`PART I
`PART I
`
`SEMICONDUCTOR
`SEMICONDUCTOR
`FUNDAMENTALS
`FUNDAMENTALS
`
`----------------;
`
`

`

`1 Semiconductors:
`A General Introduction
`
`1.1 GENERAL MATERIAL PROPERTIES
`
`The vast majority of all solid state devices on the market today are fabricated from a class
`of materials known as semiconductors. It is therefore appropriate that we begin the discus(cid:173)
`sion by examining the general nature of semiconducting materials.
`
`1.1.1 Composition
`
`Table l. l lists the atomic compositions of semiconductors that are likely to be encountered
`in the device literature. As noted, the semiconductor family of materials includes the ele(cid:1