Physics

for

Computer

Science

Students

Springer Science+Business Media, LLC

Narciso Garcia Arthur Damask Steven Schwarz

Pbysics for Computer Science Students

Springer

Witb Empbasis on Atomic and Semiconductor Pbysics

Second Edition

with 487 illustrations

N arciso Garcia (deceased) Arthur Damask (emeritus) Steven Schwarz Department of Physics Queens College Flushing, NY 11367 USA

Library ofCongress Cataloging-in-Publication Data Garcia, Narcis<>

Physics for computer science students : with emphasis on atomic and semiconductor physics / Narciso Garcia, Arthur Damask, Steven Schwarz. - 2nd ed.

p. cm. Originally published: New York: Wtley, 1986. Includes bibliographica1 references and index. ISBN 978-1-4612-7217-5 ISBN 978-1-4612-1616-2 (eBook) DOI 10.1007/978-1-4612-1616-2 1. Physics. 2. Computer science. 1. Damask, A.C. II. Schwarz,

Steven, 1953- III. Title. QC21.2.G32 1997 530'.024'6213-dc21

Printed on acid-free paper.

© 1991, 1998 Springer Seienee+Business Media New York Originally published by Springer-Verlag New York, Ine. in 1998 Softeover reprint ofthe hardeover 2nd edition 1998 A1l rights reserved. This work mav not be translated or copied in whole or in pact without the written permission of the publisher, Springer Science+Business Media, LLC, except for brief excerpts in connection with reviews or scholarly ana1ysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especia11y identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may according1y be used freely by anyone.

Production rnanaged by Robert Wex1er; manufacturing supervised by J acqui Ashri. Typeset in 1BX by The Bartlett Press, Inc., Marietta, GA.

9 8 765 432 1

ISBN 978-1-4612-7217-5

The primary goal of this second edition is to provide expanded coverage of key

issues and recent developments in semiconductor technology. Since the first edition

appeared in 1985, the proportion of MOS-based integrated circuits has increased

dramatically, the use of compound semiconductor devices in optical communications

has mushroomed, and the production of increasingly dense DRAM's has driven

the evolution of the personal computer. These topics are now addressed in the

text. The present edition expands Chapter 26 to include intuitive descriptions of

junction breakdown, Schottky barriers and ohmic contacts, MOSFET operation,

bipolar/MOS tradeoffs, solar cells, CCD imaging arrays, light emitting diodes, and

semiconductor lasers. Discussions of the CMOS inverter and the DRAM cell are

incorporated in Chapter 27. These additions are supported by new material, in

Chapters 23, 24, and 25, on carrier mobility, compound semiconductors, direct

and indirect gaps, diffusion and drift, and carrier generation and recombination.

The discussion of fabrication and trends in Chapter 28 has also been updated. Ten

problems have been added to the later chapters. The various additions constitute

approximately 20 pages of new text, and illuminate many of the physical concepts

presented in the earlier chapters. The additions have been incorporated into the second

semester course (covering Chapters 17 to 28) at Queens College, where students have

responded favorably to the broader coverage of semiconductor applications. While

the emphasis in the added material is on semiconductor device physics, the intentions

of the book as a whole remain unchanged, i.e., to provide a broad and effective

one-year introduction to classical and modern physics, to foster retention and the

development of physical intuition and analytical skills by connecting fundamental

concepts to technological issues of interest to computer science students, and to give

these students access to much of the literature on computer hardware developments. The second edition deletes little material from the first edition. Small but significant revisions may be noted in the discussions of phase and group velocity (Section 19.6), the tight-binding approximation (Section 24.4), and hole motion (Section 24.7), and numerous minor corrections are incorporated. Homework problems requiring computer programming have been slightly revised under the assumption that students will have access to a personal computer with some graphics capability.

Narciso Garcia

Arthur Damask

Steven Schwarz Queens College

Flushing, NY

Priface to

tbe Second

Edition

This text is the product of several years' effort to develop a course to fill a specific

educational gap. It is our belief that computer science students should know how

a computer works, particularly in light of rapidly changing technologies. The text

was designed for computer science students who have a calculus background but

have not necessarily taken prior physics courses. However, it is clearly not limited to

these students. Anyone who has had first-year physics can start with Chapter 17. This

includes all science and engineering students who would like a survey course of the

ideas, theories, and experiments that made our modern electronics age possible.

This textbook is meant to be used in a two-semester sequence. Chapters 1

through 16 can be covered during the first semester, and Chapters 17 through 28 in

the second semester. At Queens College, where preliminary drafts have been used,

the material is presented in three lecture periods (50 minutes each) and one recitation

period per week, 15 weeks per semester. The lecture and recitation are complemented

by a two-hour laboratory period per week for the first semester and a two-hour

laboratory period biweekly for the second semester.

Computer Science students are usually required to take one year of physics;

therefore, we examined conventional first-year physics courses with care so as to

delete topics not relevant to the physics of semiconductors and logic circuits (such as

Bernoulli's equation or nuclear decay rates). To achieve this contraction with some

precision, we developed the second semester, Chapters 17-28, and taught these

chapters for two years before writing Chapters 1-16 for the first semester.

The first-semester chapters include the First Principles of physics. The student

normally develops the concepts of sliding and colliding blocks because these can be

readily visualized and the principles understood from common experience. These

concepts are later applied to electrons and holes, which are not readily visualized; hence the early foundation permits the understanding of more complex conceptual models.

The second part of this textbook begins with a presentation of some of the phenomena that led to the breakdown of classical physics and the advent of the

quantum in blackbody radiation, photoelectric effect, electromagnetic spectrum of atoms, and so forth (Chapters 17 and 18). After laying down the fundamental

principles of wave mechanics, de Broglie's hypothesis, and the Uncertainty Principle,

we introduce the student to the Schrodinger theory of quantum physics. This theory

is applied to the simple example of the infinite potential well (Chapters 19 and 20). An

outline of the solution of the Schrodinger equation (i.e., the three quantum numbers

n, I, ml) and some of the features of the wavefunctions are presented in Chapter 2l.

After investigating the need for the electron spin, we use these results, together with

Pauli's exclusion principle, to determine the electron configurations and some of the

properties of multi-electron atoms.

The student is then ready to study the electrical properties of solids. A brief

discussion of the crystal structure and bonding mechanisms (Chapter 22) precedes the

Priface to

tbe First

Edition

viii • PREFACE TO THE FIRST EDITION

presentation of the classical and quantum free electron theories and their successes and

shortcomings (Chapter 23). In order to explain the large differences in the electrical

properties of solids as well as the peculiar properties of semiconductors, the existence

of allowed and forbidden energy bands is investigated (Chapter 24). In this chapter,

we introduce the concepts of the electron effective mass and of holes. Intrinsic and

doped semiconductors, their electron and hole densities, and their electrical properties

are discussed in Chapter 25.

It is now a rather simple matter for the student to understand the behavior

and the characteristics of semiconductor devices: diodes, bipolar transistors, field

effect transistors, etc. Semiconductor devices are the subject of Chapter 26. The text

concludes with two chapters unique to this physics textbook. In Chapter 27, we show

how diodes and transistors can be used to construct the logic circuits (gates) that

constitute the fundamental building blocks of the computer. Chapter 28 is a layman'S

introduction to some of the techniques used in the fabrication of integrated circuits.

The laboratory experiments for the first semester are standard in any physics

department, and thus we do not feel that is is necessary to include them in this book.

The seven experiments in the second semester have been designed to illustrate impor­

tant measurements; they are not standard in most physics courses. The equipment

needed for these experiments is not generally available in quantity in physics depart­

ments but can be ordered from standard suppliers or constructed in school shops. For

this reason the seven laboratory experiments are described in the instructor's manual

that complements this textbook. Although some of the topics and the level of treatment of Chapters 20-27 may

appear to be potentially formidable for a first course in physics, in practice they have

proved not to be so. We have tried to soften the impact of mathematical complexities

with intuitive physical arguments. For example, the existence of energy bands in

solids is first introduced by outlining the solution of the Schr6dinger equation for

an electron moving in the periodic potential of the ions. The student is shown that

the imposition of the boundary conditions leads to a transcendental equation for

the dispersion relation whose numerical solution leads in turn to the existence of

forbidden and allowed energy bands. (Students are encouraged to use their computer

programming skills to solve this equation.) This presentation is followed by an

alternative approach that relies on simple intuitive arguments; here, the mathematics

is kept to a minimum. The student is shown how, when two atoms are brought

together to form a molecule, two separate energy levels are formed from each level

of the individual atom. This is then extended to a situation where a large number of

atoms come together to form a solid. It is thus relatively simple to show that each

atomic level becomes a band of very closely spaced energy levels.

PREFACE TO THE FIRST EDITION II lX

By blending mathematical and physical arguments, we believe we have achieved

a thorough presentation of the concepts of solid state physics while staying within

the reach of students with an intermediate background in mathematics.

Narciso Garcia

Arthur Damask

Queens College

Flushing, NY

The course for which this text was developed was conceived by Professor Joseph

Klarfeld of the Physics Department and Professor Jacob Rootenberg, Chairman of the

Computer Science Department of Queens College. Many useful suggestions on style,

pace, and content were made by Professor Arthur Paskin of the Physics Department,

who taught the course for several trial semesters. Topics requiring fuller explanation

and wording requiring greater clarity were pointed out by Jay Damask, a high school

junior with a knowledge of elementary calculus.

We appreciate the thorough work and many suggestions of the reviewers of this

book: Professor Joseph 1. Budnick-University of Connecticut, CT, Professor William

Faissler-Northeastern University, MA, Professor David B. Fenner-University of

Santa Clara, CA, Professor H. L. Helfer-The University of Rochester, NY, Professor

Marvin D. Kemple-Purdue University, IN, and Professor Lawrence A. Mink­

Arkansas State University, AR. The manuscript was typed and prepared for the

publisher by Mrs. Marion Gaffga of Spring Hill, Florida. Mrs. Shirley Allen and Mrs.

Susan Wasserman of Queens College contributed to the typing.

In the preparation of the second edition, the authors gratefully acknowledge

Professors Azriel Genack and Alexander Lisyansky at Queens College, and Professors

Miriam Rafailovich and Jonathan Sokolov at the State University of New York at

Stony Brook, for their careful review of the manuscript. Professor Narciso Garcia

passed away as the revisions to this text neared completion. Professor Garcia was a

very popular and dedicated teacher, with a clear, good-natured lecturing style that

we hope is fully reflected in this new edition. He was also a talented researcher, who

contributed to many significant publications in the field of electromagnetic wave

propagation in disordered media. This edition is dedicated to his memory.

A.D.

S.A. S.

Acknowl-

edgments

Preface to the Second Edition v

Preface to the First Edition vii

Acknowledgments xi

I Physical Quantities 1

I.I Introduction 2 1.2 Quantities and Units 3 1.3 Powers of 10 5 1.4 Accuracy of Numbers 6

Problems 7

Vectors 9 2.1 Introduction 10 2.2 Vector Components 10 2.3 Unit Vectors 14 2.4 Dot Product IS 2.5 Cross Product 16

Problems 18

Uniformly Accelerated Motion 21 3.1 Introduction 22 3.2 Speed and Velocity 22 3.3 Acceleration 24 3.4 3.5

Linear Motion Projectile Motion Problems 34

25 30

Newton's Laws 37 4.1 Introduction 38 4.2 Newton's Laws 38 4.3 Mass 41 4.4 Weight 42 4.5 Applications of Newton's Laws 4.6 Friction 48

Problems 50

43

Contents

XlV • CONTENTS

Work, Energy, and Power 55 5.1 Introduction 56 5.2 Work 56 5.3 Potential Energy 58 5.4 Work Done by a Variable Force 59 5.5 Kinetic Energy 60 5.6 Energy Conservation 61 5.7 Power 64

Problems 65

Momentum and Collisions 69 6.1 Introduction 70 6.2 Center of Mass 70 6.3 Motion of the Center of Mass 6.4 Momentum and its Conservation 6.5 Collisions 77

Problems 80

Rotational Motion 83 7.1 Introduction 84 7.2 Measurement of Rotation 84 7.3 Rotational Motion 85 7.4 7.5 7.6 7.7

Equations of Rotational Motion Radial Acceleration 90 Centripetal Force 9 I Orbital Motion and Gravitation Problems 95

73 74

88

93

Rotational Dynamics 99 8.1 Introduction 100 8.2 Moment ofInertia and Torque 100

8.3 Rotational Kinetic Energy 103 8.4 Power 107 8.5 Angular Momentum 108 8.6 Conservation of Angular Momentum

Problems III IIO

Kinetic Theory of Gases and the Concept of Temperature 115 9. I Introduction I 16 9.2 Molecular Weight I 16

CONTENTS .. xv

9.3 Thermometers II7 9.4 Ideal Gas Law and Absolute Temperature II8 9.5 Kinetic Theory of Gas Pressure 121 9.6 Kinetic Theory of Temperature 123 9.7 Measurement of Heat 125 9.8 Specific Heats of Gases 126 9.9 Work Done by a Gas 127 9.10 First Law of Thermodynamics 128 Supplement 9-1: Maxwell-Boltzmann Statistical Distribution 129

Problems 132

I Oscillatory Motion 135

10.1 Introduction 136 10.2 Characterization of Springs 136 10.3 Frequency and Period 137 10.4 Amplitude and Phase Angle 138 10.5 Oscillation of a Spring 138 10.6 Energy of Oscillation 144

Problems 146

I I Wave Motion 149 11.1 Introduction ISO 11.2 Wavelength, Velocity, Frequency, and Amplitude ISO 11.3 Traveling Waves in a String 151 11.4 Energy Transfer of a Wave ISS

Problems 158

I Interference of Waves 161

12.1 Introduction 162 12.2 The Superposition Principle 162 12.3 Interference from Two Sources 163 12.4 Double Slit Interference of Light 166 12.5 Single Slit Diffraction 170 12.6 Resolving Power In 12.7 X-Ray Diffraction by Crystals: Bragg Scattering 174 12.8 Standing Waves 177

Problems 178

I Electrostatics 181 13.1 Inttoduction 182 13.2 Attraction and Repulsion of Charges 182

XVI " CONTENTS

I

I

13.3 Coulomb's Law 183 13.4 Charge of an Electron 187 13.5 Superposition Principle 187

Problems 189

The Electric Field and the Electric Potential 14.1 Introduction 192 14.2 The Electric Field 192 14.3 Electrical Potential Energy 195 14.4 Electric Potential 198 14.5 The Electron Volt 201 14.6 Electromotive Force 201 14.7 Capacitance 202

Problems 203

Electric Current 207

15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9

Introduction 208 Motion of Charges in an Electric Field 208 Electric Current 209 Resistance and Resistivity 212 Resistances in Series and Parallel 214 Kirchhoff's Rules 218 Ammeters and Voltmeters 223 Power Dissipation by Resistors 225 Charging a Capacitor-RC Circuits 226 Problems 229

16 Magnetic Fields and Electromagnetic Waves 16.1 Introduction 234 16.2 Magnetic Fields 234 16.3 Force on Current-Carrying Wires 235 16.4 Torque on a Current Loop 236 16.5 Magnetic Dipole Moment 238 16.6 Force on a Moving Charge 240 16.7 The Hall Effect 241 16.8 Electromagnetic Waves: The Nature of Light 243

Problems 245

I The Beginning of the Quantum Story 249

17.1 Introduction 250

191

233

I

I

17.2 17.3

Blackbody Radiation The Photoelectric Effect

251 253

17.4 Further Evidence for the Photon Theory 259 Supplement 17-1: Momentum of the Photon 266

Problems 266

Atomic Models Introduction 270 The Rutherford Model

269

270 18.1 18.2 18.3 18.4

The Spectrum Of Hydrogen The Bohr Atom 275

273

18.5 The Franck-Hertz Experiment 281 Problems 283

Fundamental Principles of Quantum Mechanics 19.1 Introduction 288 19.2 De Broglie's Hypothesis and Its Experimental Verification 288 19.3 Nature of the Wave 291 19.4 The Uncertainty Principle 294 19.5 Physical Origin of the Uncertainty Principle 296 19.6 Matter Waves and the UncertaintyPrinciple 297 19.7 Velocity of the Wave Packet: Group Velocity 300 19.8 The Principle of Complementarity 302

Problems 302

CONTENTS .. XVll

287

An Introduction to the Methods of Quantum Mechanics 305 20.1 Introduction 306 20.2 The Schrodinger Theory of Quantum Mechanics 306 20.3 Application of the Schrodinger Theory 3 19

Problems 326

I Quantum Mechanics of Atoms 329 21.1 Introduction 330 21.2 Outline of the Solution of the Schrodinger Equation for the H Atom 331 21.3 Physical Significance of the Results 333 21.4 Space Quantization: The Experiments 334 21.5 The Spin 339 21.6 Some Features of the Atomic Wavefunctions 341 21.7 The Periodic Table 344

Problems 353

XVll1 m CONTENTS

Crystal Structures and Bonding in Solids 355 22.1 Introduction 356 22.2 Crystal Structures 356 22.3 Crystal Bonding 359

Problems 366

Free Electron Theories of Solids 369 23.1 Introduction 370 23.2 Classical Free Electron (CFE) Model 371 23.3 Quantum-Mechanical Free Electron Model (QMFE) 378 Supplement 23-1: The Wiedemann-Franz Law 395 Supplement 23-2: Fermi-Dirac Statistics 398

Problems 400

Band Theory of Solids 403 24.1 Introduction 404 24.2 Bloch's Theorem 405 24.3 The Kronig-Penney Model 406 24.4 Tight-Binding Approximation 415 24.5 Conductors, Insulators, and Semiconductors 423 24.6 Effective Mass 426 24.7 Holes 43 I

Problems 434

Semiconductors 437 25.1 Introduction 438 25.2 Intrinsic Semiconductors 438 25.3 Extrinsic or Impurity Semiconductors 446 25.4 Carrier Transport in Semiconductors 454 25.5 Photoconductivity 458 25.6 Compound Semiconductors 460

Problems 46 I

Semiconductor Devices 465 26.1 Introduction 466 26.2 Metal-Metal Junction: The Contact Potential 466 26.3 The Semiconductor Diode 468 26.4 The Bipolar Junction Transistor (BJT) 480 26.5 FieldcEffect Transistors (FET) 489

CONTENTS II XiX

26.6 Optoelectronic Devices 496 Problems 500

Some Basic Logic Circuits of Computers 505 27.1 Introduction 506 27.2 Rudiments of Boolean Algebra 506 27.3 Electronic Logic Circuits 509 27.4 Semiconductor Gates 512 27.5 NAND and NOR Gates 517 27.6 Other Gates: RTL, TTL, and CMOS 517 27.7 Memory Circuits 522 27.8 Clock Circuits 524

Problems 526

The Technology of Manufacturing Integrated Circuits 529 28.1 28.2 28.3 28.4 28.5 28.6

Introduction 530 Semiconductor Purification: Zone Refining Single-Crystal Growth 532 The Processes ofIe Production 534 Electronic Component Fabrication on a Chip Conclusion 543 Problems 544

Index 547

Photo Credits 555

530

539