Electronic Devices and Circuit Theory PDF

SEVENTH EDITION ELECTRONIC DEVICES AND CIRCUIT THEORY ROBERT BOYLESTAD LOUIS NASHELSKY PRENTICE HALL Upper Saddle River, New Jersey Columbus, Ohio  Contents PREFACE...

SEVENTH EDITION ELECTRONIC DEVICES AND CIRCUIT THEORY ROBERT BOYLESTAD LOUIS NASHELSKY PRENTICE HALL Upper Saddle River, New Jersey Columbus, Ohio  Contents PREFACE xiii ACKNOWLEDGMENTS xvii 1 SEMICONDUCTOR DIODES 1 1.1 Introduction 1 1.2 Ideal Diode 1 1.3 Semiconductor Materials 3 1.4 Energy Levels 6 1.5 Extrinsic Materials—n- and p-Type 7 1.6 Semiconductor Diode 10 1.7 Resistance Levels 17 1.8 Diode Equivalent Circuits 24 1.9 Diode Specification Sheets 27 1.10 Transition and Diffusion Capacitance 31 1.11 Reverse Recovery Time 32 1.12 Semiconductor Diode Notation 32 1.13 Diode Testing 33 1.14 Zener Diodes 35 1.15 Light-Emitting Diodes (LEDs) 38 1.16 Diode Arrays—Integrated Circuits 42 1.17 PSpice Windows 43 2 DIODE APPLICATIONS 51 2.1 Introduction 51 2.2 Load-Line Analysis 52 2.3 Diode Approximations 57 v  2.4 Series Diode Configurations with DC Inputs 59 2.5 Parallel and Series-Parallel Configurations 64 2.6 AND/OR Gates 67 2.7 Sinusoidal Inputs; Half-Wave Rectification 69 2.8 Full-Wave Rectification 72 2.9 Clippers 76 2.10 Clampers 83 2.11 Zener Diodes 87 2.12 Voltage-Multiplier Circuits 94 2.13 PSpice Windows 97 3 BIPOLAR JUNCTION TRANSISTORS 112 3.1 Introduction 112 3.2 Transistor Construction 113 3.3 Transistor Operation 113 3.4 Common-Base Configuration 115 3.5 Transistor Amplifying Action 119 3.6 Common-Emitter Configuration 120 3.7 Common-Collector Configuration 127 3.8 Limits of Operation 128 3.9 Transistor Specification Sheet 130 3.10 Transistor Testing 134 3.11 Transistor Casing and Terminal Identification 136 3.12 PSpice Windows 138 4 DC BIASING—BJTS 143 4.1 Introduction 143 4.2 Operating Point 144 4.3 Fixed-Bias Circuit 146 4.4 Emitter-Stabilized Bias Circuit 153 4.5 Voltage-Divider Bias 157 4.6 DC Bias with Voltage Feedback 165 4.7 Miscellaneous Bias Configurations 168 4.8 Design Operations 174 4.9 Transistor Switching Networks 180 4.10 Troubleshooting Techniques 185 4.11 PNP Transistors 188 4.12 Bias Stabilization 190 4.13 PSpice Windows 199 5 FIELD-EFFECT TRANSISTORS 211 5.1 Introduction 211 5.2 Construction and Characteristics of JFETs 212 5.3 Transfer Characteristics 219 vi Contents 5.4 Specification Sheets (JFETs) 223 5.5 Instrumentation 226 5.6 Important Relationships 227 5.7 Depletion-Type MOSFET 228 5.8 Enhancement-Type MOSFET 234 5.9 MOSFET Handling 242 5.10 VMOS 243 5.11 CMOS 244 5.12 Summary Table 246 5.13 PSpice Windows 247 6 FET BIASING 253 6.1 Introduction 253 6.2 Fixed-Bias Configuration 254 6.3 Self-Bias Configuration 258 6.4 Voltage-Divider Biasing 264 6.5 Depletion-Type MOSFETs 270 6.6 Enhancement-Type MOSFETs 274 6.7 Summary Table 280 6.8 Combination Networks 282 6.9 Design 285 6.10 Troubleshooting 287 6.11 P-Channel FETs 288 6.12 Universal JFET Bias Curve 291 6.13 PSpice Windows 294 7 BJT TRANSISTOR MODELING 305 7.1 Introduction 305 7.2 Amplification in the AC Domain 305 7.3 BJT Transistor Modeling 306 7.4 The Important Parameters: Zi, Zo, Av, Ai 308 7.5 The re Transistor Model 314 7.6 The Hybrid Equivalent Model 321 7.7 Graphical Determination of the h-parameters 327 7.8 Variations of Transistor Parameters 331 8 BJT SMALL-SIGNAL ANALYSIS 338 8.1 Introduction 338 8.3 Common-Emitter Fixed-Bias Configuration 338 8.3 Voltage-Divider Bias 342 8.4 CE Emitter-Bias Configuration 345 8.3 Emitter-Follower Configuration 352 8.6 Common-Base Configuration 358 Contents vii  8.7 Collector Feedback Configuration 360 8.8 Collector DC Feedback Configuration 366 8.9 Approximate Hybrid Equivalent Circuit 369 8.10 Complete Hybrid Equivalent Model 375 8.11 Summary Table 382 8.12 Troubleshooting 382 8.13 PSpice Windows 385 9 FET SMALL-SIGNAL ANALYSIS 401 9.1 Introduction 401 9.2 FET Small-Signal Model 402 9.3 JFET Fixed-Bias Configuration 410 9.4 JFET Self-Bias Configuration 412 9.5 JFET Voltage-Divider Configuration 418 9.6 JFET Source-Follower (Common-Drain) Configuration 419 9.7 JFET Common-Gate Configuration 422 9.8 Depletion-Type MOSFETs 426 9.9 Enhancement-Type MOSFETs 428 9.10 E-MOSFET Drain-Feedback Configuration 429 9.11 E-MOSFET Voltage-Divider Configuration 432 9.12 Designing FET Amplifier Networks 433 9.13 Summary Table 436 9.14 Troubleshooting 439 9.15 PSpice Windows 439 10 SYSTEMS APPROACH— EFFECTS OF Rs AND RL 452 10.1 Introduction 452 10.2 Two-Port Systems 452 10.3 Effect of a Load Impedance (RL) 454 10.4 Effect of a Source Impedance (Rs) 459 10.5 Combined Effect of Rs and RL 461 10.6 BJT CE Networks 463 10.7 BJT Emitter-Follower Networks 468 10.8 BJT CB Networks 471 10.9 FET Networks 473 10.10 Summary Table 476 10.11 Cascaded Systems 480 10.12 PSpice Windows 481 11 BJT AND JFET FREQUENCY RESPONSE 493 11.1 Introduction 493 11.2 Logarithms 493 11.3 Decibels 497 viii Contents 11.4 General Frequency Considerations 500 11.5 Low-Frequency Analysis—Bode Plot 503 11.6 Low-Frequency Response—BJT Amplifier 508 11.7 Low-Frequency Response—FET Amplifier 516 11.8 Miller Effect Capacitance 520 11.9 High-Frequency Response—BJT Amplifier 523 11.10 High-Frequency Response—FET Amplifier 530 11.11 Multistage Frequency Effects 534 11.12 Square-Wave Testing 536 11.13 PSpice Windows 538 12 COMPOUND CONFIGURATIONS 544 12.1 Introduction 544 12.2 Cascade Connection 544 12.3 Cascode Connection 549 12.4 Darlington Connection 550 12.5 Feedback Pair 555 12.6 CMOS Circuit 559 12.7 Current Source Circuits 561 12.8 Current Mirror Circuits 563 12.9 Differential Amplifier Circuit 566 12.10 BIFET, BIMOS, and CMOS Differential Amplifier Circuits 574 12.11 PSpice Windows 575 13 DISCRETE AND IC MANUFACTURING TECHNIQUES 588 13.1 Introduction 588 13.2 Semiconductor Materials, Si, Ge, and GaAs 588 13.3 Discrete Diodes 590 13.4 Transistor Fabrication 592 13.5 Integrated Circuits 593 13.6 Monolithic Integrated Circuit 595 13.7 The Production Cycle 597 13.8 Thin-Film and Thick-Film Integrated Circuits 607 13.9 Hybrid Integrated Circuits 608 14 OPERATIONAL AMPLIFIERS 609 14.1 Introduction 609 14.2 Differential and Common-Mode Operation 611 14.3 Op-Amp Basics 615 14.4 Practical Op-Amp Circuits 619 14.5 Op-Amp Specifications—DC Offset Parameters 625 14.6 Op-Amp Specifications—Frequency Parameters 628 14.7 Op-Amp Unit Specifications 632 14.8 PSpice Windows 638 Contents ix  15 OP-AMP APPLICATIONS 648 15.1 Constant-Gain Multiplier 648 15.2 Voltage Summing 652 15.3 Voltage Buffer 655 15.4 Controller Sources 656 15.5 Instrumentation Circuits 658 15.6 Active Filters 662 15.7 PSpice Windows 666 16 POWER AMPLIFIERS 679 16.1 Introduction—Definitions and Amplifier Types 679 16.2 Series-Fed Class A Amplifier 681 16.3 Transformer-Coupled Class A Amplifier 686 16.4 Class B Amplifier Operation 693 16.5 Class B Amplifier Circuits 697 16.6 Amplifier Distortion 704 16.7 Power Transistor Heat Sinking 708 16.8 Class C and Class D Amplifiers 712 16.9 PSpice Windows 714 17 LINEAR-DIGITAL ICs 721 17.1 Introduction 721 17.2 Comparator Unit Operation 721 17.3 Digital-Analog Converters 728 17.4 Timer IC Unit Operation 732 17.5 Voltage-Controlled Oscillator 735 17.6 Phase-Locked Loop 738 17.7 Interfacing Circuitry 742 17.8 PSpice Windows 745 18 FEEDBACK AND OSCILLATOR CIRCUITS 751 18.1 Feedback Concepts 751 18.2 Feedback Connection Types 752 18.3 Practical Feedback Circuits 758 18.4 Feedback Amplifier—Phase and Frequency Considerations 765 18.5 Oscillator Operation 767 18.6 Phase-Shift Oscillator 769 18.7 Wien Bridge Oscillator 772 18.8 Tuned Oscillator Circuit 773 18.9 Crystal Oscillator 776 18.10 Unijunction Oscillator 780 x Contents 19 POWER SUPPLIES (VOLTAGE REGULATORS) 783 19.1 Introduction 783 19.2 General Filter Considerations 783 19.3 Capacitor Filter 786 19.4 RC Filter 789 19.5 Discrete Transistor Voltage Regulation 792 19.6 IC Voltage Regulators 799 19.7 PSpice Windows 804 20 20.1 OTHER TWO-TERMINAL DEVICES Introduction 810 810 20.2 Schottky Barrier (Hot-Carrier) Diodes 810 20.3 Varactor (Varicap) Diodes 814 20.4 Power Diodes 818 20.5 Tunnel Diodes 819 20.6 Photodiodes 824 20.7 Photoconductive Cells 827 20.8 IR Emitters 829 20.9 Liquid-Crystal Displays 831 20.10 Solar Cells 833 20.11 Thermistors 837 21 pnpn AND OTHER DEVICES 842 21.1 Introduction 842 21.2 Silicon-Controlled Rectifier 842 21.3 Basic Silicon-Controlled Rectifier Operation 842 21.4 SCR Characteristics and Ratings 845 21.5 SCR Construction and Terminal Identification 847 21.6 SCR Applications 848 21.7 Silicon-Controlled Switch 852 21.8 Gate Turn-Off Switch 854 21.9 Light-Activated SCR 855 21.10 Shockley Diode 858 21.11 DIAC 858 21.12 TRIAC 860 21.13 Unijunction Transistor 861 21.14 Phototransistors 871 21.15 Opto-Isolators 873 21.16 Programmable Unijunction Transistor 875 Contents xi  22 OSCILLOSCOPE AND OTHER MEASURING INSTRUMENTS 884 22.1 Introduction 884 22.2 Cathode Ray Tube—Theory and Construction 884 22.3 Cathode Ray Oscilloscope Operation 885 22.4 Voltage Sweep Operation 886 22.5 Synchronization and Triggering 889 22.6 Multitrace Operation 893 22.7 Measurement Using Calibrated CRO Scales 893 22.8 Special CRO Features 898 22.9 Signal Generators 899 APPENDIX A: HYBRID PARAMETERS— CONVERSION EQUATIONS (EXACT AND APPROXIMATE) 902 APPENDIX B: RIPPLE FACTOR AND VOLTAGE CALCULATIONS 904 APPENDIX C: CHARTS AND TABLES 911 APPENDIX D: SOLUTIONS TO SELECTED ODD-NUMBERED PROBLEMS 913 INDEX 919 xii Contents  Acknowledgments Our sincerest appreciation must be extended to the instructors who have used the text and sent in comments, corrections, and suggestions. We also want to thank Rex David- son, Production Editor at Prentice Hall, for keeping together the many detailed as- pects of production. Our sincerest thanks to Dave Garza, Senior Editor, and Linda Ludewig, Editor, at Prentice Hall for their editorial support of the Seventh Edition of this text. We wish to thank those individuals who have shared their suggestions and evalua- tions of this text throughout its many editions. The comments from these individu- als have enabled us to present Electronic Devices and Circuit Theory in this Seventh Edition: Ernest Lee Abbott Napa College, Napa, CA Phillip D. Anderson Muskegon Community College, Muskegon, MI Al Anthony EG&G VACTEC Inc. A. Duane Bailey Southern Alberta Institute of Technology, Calgary, Alberta, CANADA Joe Baker University of Southern California, Los Angeles, CA Jerrold Barrosse Penn State–Ogontz Ambrose Barry University of North Carolina–Charlotte Arthur Birch Hartford State Technical College, Hartford, CT Scott Bisland SEMATECH, Austin, TX Edward Bloch The Perkin-Elmer Corporation Gary C. Bocksch Charles S. Mott Community College, Flint, MI Jeffrey Bowe Bunker Hill Community College, Charlestown, MA Alfred D. Buerosse Waukesha County Technical College, Pewaukee, WI Lila Caggiano MicroSim Corporation Mauro J. Caputi Hofstra University Robert Casiano International Rectifier Corporation Alan H. Czarapata Montgomery College, Rockville, MD Mohammad Dabbas ITT Technical Institute John Darlington Humber College, Ontario, CANADA Lucius B. Day Metropolitan State College, Denver, CO Mike Durren Indiana Vocational Technical College, South Bend, IN Dr. Stephen Evanson Bradford University, UK George Fredericks Northeast State Technical Community College, Blountville, TN F. D. Fuller Humber College, Ontario, CANADA xvii  Phil Golden DeVry Institute of Technology, Irving, TX Joseph Grabinski Hartford State Technical College, Hartfold, CT Thomas K. Grady Western Washington University, Bellingham, WA William Hill ITT Technical Institute Albert L. Ickstadt San Diego Mesa College, San Diego, CA Jeng-Nan Juang Mercer University, Macon, GA Karen Karger Tektronix Inc. Kenneth E. Kent DeKalb Technical Institute, Clarkston, GA Donald E. King ITT Technical Institute, Youngstown, OH Charles Lewis APPLIED MATERIALS, INC. Donna Liverman Texas Instruments Inc. William Mack Harrisburg Area Community College Robert Martin Northern Virginia Community College George T. Mason Indiana Vocational Technical College, South Bend, IN William Maxwell Nashville State Technical Institute Abraham Michelen Hudson Valley Community College John MacDougall University of Western Ontario, London, Ontario, CANADA Donald E. McMillan Southwest State University, Marshall, MN Thomas E. Newman L. H. Bates Vocational-Technical Institute, Tacoma, WA Byron Paul Bismarck State College Dr. Robert Payne University of Glamorgan, Wales, UK Dr. Robert A. Powell Oakland Community College E. F. Rockafellow Southern-Alberta Institute of Technology, Calgary, Alberta, CANADA Saeed A. Shaikh Miami-Dade Community College, Miami, FL Dr. Noel Shammas School of Engineering, Beaconside, UK Ken Simpson Stark State College of Technology Eric Sung Computronics Technology Inc. Donald P. Szymanski Owens Technical College, Toledo, OH Parker M. Tabor Greenville Technical College, Greenville, SC Peter Tampas Michigan Technological University, Houghton, MI Chuck Tinney University of Utah Katherine L. Usik Mohawk College of Applied Art & Technology, Hamilton, Ontario, CANADA Domingo Uy Hampton University, Hampton, VA Richard J. Walters DeVry Technical Institute, Woodbridge, NJ Larry J. Wheeler PSE&G Nuclear Julian Wilson Southern College of Technology, Marietta, GA Syd R. Wilson Motorola Inc. Jean Younes ITT Technical Institute, Troy, MI Charles E. Yunghans Western Washington University, Bellingham, WA Ulrich E. Zeisler Salt Lake Community College, Salt Lake City, UT xviii Acknowledgments  p n CHAPTER Semiconductor Diodes 1 1.1 INTRODUCTION It is now some 50 years since the first transistor was introduced on December 23, 1947. For those of us who experienced the change from glass envelope tubes to the solid-state era, it still seems like a few short years ago. The first edition of this text contained heavy coverage of tubes, with succeeding editions involving the important decision of how much coverage should be dedicated to tubes and how much to semi- conductor devices. It no longer seems valid to mention tubes at all or to compare the advantages of one over the other—we are firmly in the solid-state era. The miniaturization that has resulted leaves us to wonder about its limits. Com- plete systems now appear on wafers thousands of times smaller than the single ele- ment of earlier networks. New designs and systems surface weekly. The engineer be- comes more and more limited in his or her knowledge of the broad range of advances— it is difficult enough simply to stay abreast of the changes in one area of research or development. We have also reached a point at which the primary purpose of the con- tainer is simply to provide some means of handling the device or system and to pro- vide a mechanism for attachment to the remainder of the network. Miniaturization appears to be limited by three factors (each of which will be addressed in this text): the quality of the semiconductor material itself, the network design technique, and the limits of the manufacturing and processing equipment. 1.2 IDEAL DIODE The first electronic device to be introduced is called the diode. It is the simplest of semiconductor devices but plays a very vital role in electronic systems, having char- acteristics that closely match those of a simple switch. It will appear in a range of ap- plications, extending from the simple to the very complex. In addition to the details of its construction and characteristics, the very important data and graphs to be found on specification sheets will also be covered to ensure an understanding of the termi- nology employed and to demonstrate the wealth of information typically available from manufacturers. The term ideal will be used frequently in this text as new devices are introduced. It refers to any device or system that has ideal characteristics—perfect in every way. It provides a basis for comparison, and it reveals where improvements can still be made. The ideal diode is a two-terminal device having the symbol and characteris- Figure 1.1 Ideal diode: (a) tics shown in Figs. 1.1a and b, respectively. symbol; (b) characteristics. 1  p n Ideally, a diode will conduct current in the direction defined by the arrow in the symbol and act like an open circuit to any attempt to establish current in the oppo- site direction. In essence: The characteristics of an ideal diode are those of a switch that can conduct current in only one direction. In the description of the elements to follow, it is critical that the various letter symbols, voltage polarities, and current directions be defined. If the polarity of the applied voltage is consistent with that shown in Fig. 1.1a, the portion of the charac- teristics to be considered in Fig. 1.1b is to the right of the vertical axis. If a reverse voltage is applied, the characteristics to the left are pertinent. If the current through the diode has the direction indicated in Fig. 1.1a, the portion of the characteristics to be considered is above the horizontal axis, while a reversal in direction would require the use of the characteristics below the axis. For the majority of the device charac- teristics that appear in this book, the ordinate (or “y” axis) will be the current axis, while the abscissa (or “x” axis) will be the voltage axis. One of the important parameters for the diode is the resistance at the point or re- gion of operation. If we consider the conduction region defined by the direction of ID and polarity of VD in Fig. 1.1a (upper-right quadrant of Fig. 1.1b), we will find that the value of the forward resistance, RF, as defined by Ohm’s law is VF 0V RF      0  (short circuit) IF 2, 3, mA,... , or any positive value where VF is the forward voltage across the diode and IF is the forward current through the diode. The ideal diode, therefore, is a short circuit for the region of conduction. Consider the region of negatively applied potential (third quadrant) of Fig. 1.1b, VR 5, 20, or any reverse-bias potential RR         (open-circuit) IR 0 mA where VR is reverse voltage across the diode and IR is reverse current in the diode. The ideal diode, therefore, is an open circuit in the region of nonconduction. In review, the conditions depicted in Fig. 1.2 are applicable. VD Short circuit + – ID I D (limited by circuit) (a) 0 VD VD Open circuit – + ID = 0 (b) Figure 1.2 (a) Conduction and (b) nonconduction states of the ideal diode as determined by the applied bias. In general, it is relatively simple to determine whether a diode is in the region of conduction or nonconduction simply by noting the direction of the current ID estab- lished by an applied voltage. For conventional flow (opposite to that of electron flow), if the resultant diode current has the same direction as the arrowhead of the diode symbol, the diode is operating in the conducting region as depicted in Fig. 1.3a. If 2 Chapter 1 Semiconductor Diodes  p n the resulting current has the opposite direction, as shown in Fig. 1.3b, the open- circuit equivalent is appropriate. ID ID Figure 1.3 (a) Conduction and (b) nonconduction states of (a) the ideal diode as determined by the direction of conventional current established by the ID = 0 network. ID (b) As indicated earlier, the primary purpose of this section is to introduce the char- acteristics of an ideal device for comparison with the characteristics of the commer- cial variety. As we progress through the next few sections, keep the following ques- tions in mind: How close will the forward or “on” resistance of a practical diode compare with the desired 0- level? Is the reverse-bias resistance sufficiently large to permit an open-circuit ap- proximation? 1.3 SEMICONDUCTOR MATERIALS The label semiconductor itself provides a hint as to its characteristics. The prefix semi- is normally applied to a range of levels midway between two limits. The term conductor is applied to any material that will support a generous flow of charge when a voltage source of limited magnitude is applied across its terminals. An insulator is a material that offers a very low level of conductivity under pressure from an applied voltage source. A semiconductor, therefore, is a material that has a conductivity level some- where between the extremes of an insulator and a conductor. Inversely related to the conductivity of a material is its resistance to the flow of charge, or current. That is, the higher the conductivity level, the lower the resistance level. In tables, the term resistivity (, Greek letter rho) is often used when compar- ing the resistance levels of materials. In metric units, the resistivity of a material is measured in -cm or -m. The units of -cm are derived from the substitution of the units for each quantity of Fig. 1.4 into the following equation (derived from the basic resistance equation R  l/A): RA ()(cm2)      ⇒ -cm (1.1) l cm In fact, if the area of Fig. 1.4 is 1 cm2 and the length 1 cm, the magnitude of the resistance of the cube of Fig. 1.4 is equal to the magnitude of the resistivity of the material as demonstrated below: Figure 1.4 Defining the metric units of resistivity. l (1 cm) R        ohms A (1 cm2) This fact will be helpful to remember as we compare resistivity levels in the discus- sions to follow. In Table 1.1, typical resistivity values are provided for three broad categories of materials. Although you may be familiar with the electrical properties of copper and 1.3 Semiconductor Materials 3  p n TABLE 1.1 Typical Resistivity Values Conductor Semiconductor Insulator   106 -cm   50 -cm (germanium)   1012 -cm (copper)   50  103 -cm (silicon) (mica) mica from your past studies, the characteristics of the semiconductor materials of ger- manium (Ge) and silicon (Si) may be relatively new. As you will find in the chapters to follow, they are certainly not the only two semiconductor materials. They are, how- ever, the two materials that have received the broadest range of interest in the devel- opment of semiconductor devices. In recent years the shift has been steadily toward silicon and away from germanium, but germanium is still in modest production. Note in Table 1.1 the extreme range between the conductor and insulating mate- rials for the 1-cm length (1-cm2 area) of the material. Eighteen places separate the placement of the decimal point for one number from the other. Ge and Si have re- ceived the attention they have for a number of reasons. One very important consid- eration is the fact that they can be manufactured to a very high purity level. In fact, recent advances have reduced impurity levels in the pure material to 1 part in 10 bil- lion (110,000,000,000). One might ask if these low impurity levels are really nec- essary. They certainly are if you consider that the addition of one part impurity (of the proper type) per million in a wafer of silicon material can change that material from a relatively poor conductor to a good conductor of electricity. We are obviously dealing with a whole new spectrum of comparison levels when we deal with the semi- conductor medium. The ability to change the characteristics of the material signifi- cantly through this process, known as “doping,” is yet another reason why Ge and Si have received such wide attention. Further reasons include the fact that their charac- teristics can be altered significantly through the application of heat or light—an im- portant consideration in the development of heat- and light-sensitive devices. Some of the unique qualities of Ge and Si noted above are due to their atomic structure. The atoms of both materials form a very definite pattern that is periodic in nature (i.e., continually repeats itself). One complete pattern is called a crystal and the periodic arrangement of the atoms a lattice. For Ge and Si the crystal has the three-dimensional diamond structure of Fig. 1.5. Any material composed solely of re- peating crystal structures of the same kind is called a single-crystal structure. For semiconductor materials of practical application in the electronics field, this single- crystal feature exists, and, in addition, the periodicity of the structure does not change significantly with the addition of impurities in the doping process. Let us now examine the structure of the atom itself and note how it might affect the electrical characteristics of the material. As you are aware, the atom is composed of three basic particles: the electron, the proton, and the neutron. In the atomic lat- tice, the neutrons and protons form the nucleus, while the electrons revolve around the nucleus in a fixed orbit. The Bohr models of the two most commonly used semi- Figure 1.5 Ge and Si conductors, germanium and silicon, are shown in Fig. 1.6. single-crystal structure. As indicated by Fig. 1.6a, the germanium atom has 32 orbiting electrons, while silicon has 14 orbiting electrons. In each case, there are 4 electrons in the outermost (valence) shell. The potential (ionization potential) required to remove any one of these 4 valence electrons is lower than that required for any other electron in the struc- ture. In a pure germanium or silicon crystal these 4 valence electrons are bonded to 4 adjoining atoms, as shown in Fig. 1.7 for silicon. Both Ge and Si are referred to as tetravalent atoms because they each have four valence electrons. A bonding of atoms, strengthened by the sharing of electrons, is called cova- lent bonding. 4 Chapter 1 Semiconductor Diodes  p n Figure 1.6 Atomic structure: (a) germanium; Figure 1.7 Covalent bonding of the silicon (b) silicon. atom. Although the covalent bond will result in a stronger bond between the valence electrons and their parent atom, it is still possible for the valence electrons to absorb sufficient kinetic energy from natural causes to break the covalent bond and assume the “free” state. The term free reveals that their motion is quite sensitive to applied electric fields such as established by voltage sources or any difference in potential. These natural causes include effects such as light energy in the form of photons and thermal energy from the surrounding medium. At room temperature there are approx- imately 1.5  1010 free carriers in a cubic centimeter of intrinsic silicon material. Intrinsic materials are those semiconductors that have been carefully refined to reduce the impurities to a very low level—essentially as pure as can be made available through modern technology. The free electrons in the material due only to natural causes are referred to as intrinsic carriers. At the same temperature, intrinsic germanium material will have approximately 2.5  1013 free carriers per cubic centimeter. The ratio of the num- ber of carriers in germanium to that of silicon is greater than 103 and would indi- cate that germanium is a better conductor at room temperature. This may be true, but both are still considered poor conductors in the intrinsic state. Note in Table 1.1 that the resistivity also differs by a ratio of about 10001, with silicon having the larger value. This should be the case, of course, since resistivity and conductivity are inversely related. An increase in temperature of a semiconductor can result in a substantial in- crease in the number of free electrons in the material. As the temperature rises from absolute zero (0 K), an increasing number of va- lence electrons absorb sufficient thermal energy to break the covalent bond and con- tribute to the number of free carriers as described above. This increased number of carriers will increase the conductivity index and result in a lower resistance level. Semiconductor materials such as Ge and Si that show a reduction in resis- tance with increase in temperature are said to have a negative temperature coefficient. You will probably recall that the resistance of most conductors will increase with temperature. This is due to the fact that the numbers of carriers in a conductor will 1.3 Semiconductor Materials 5  p n not increase significantly with temperature, but their vibration pattern about a rela- tively fixed location will make it increasingly difficult for electrons to pass through. An increase in temperature therefore results in an increased resistance level and a pos- itive temperature coefficient. 1.4 ENERGY LEVELS In the isolated atomic structure there are discrete (individual) energy levels associated with each orbiting electron, as shown in Fig. 1.8a. Each material will, in fact, have its own set of permissible energy levels for the electrons in its atomic structure. The more distant the electron from the nucleus, the higher the energy state, and any electron that has left its parent atom has a higher energy state than any electron in the atomic structure. Energy Valance Level (outermost shell) Energy gap Second Level (next inner shell) Energy gap Third Level (etc.) etc. Nucleus (a) Energy Energy Energy Electrons Conduction band "free" to establish Conduction band conduction The bands Conduction band overlap E g > 5 eV Eg Valence band Valence electrons Valence band bound to Valence band the atomic stucture E g = 1.1 eV (Si) E g = 0.67 eV (Ge) Figure 1.8 Energy levels: (a) E g = 1.41 eV (GaAs) discrete levels in isolated atomic structures; (b) conduction and Insulator Semiconductor Conductor valence bands of an insulator, semiconductor, and conductor. (b) Between the discrete energy levels are gaps in which no electrons in the isolated atomic structure can appear. As the atoms of a material are brought closer together to form the crystal lattice structure, there is an interaction between atoms that will re- sult in the electrons in a particular orbit of one atom having slightly different energy levels from electrons in the same orbit of an adjoining atom. The net result is an ex- pansion of the discrete levels of possible energy states for the valence electrons to that of bands as shown in Fig. 1.8b. Note that there are boundary levels and maxi- mum energy states in which any electron in the atomic lattice can find itself, and there remains a forbidden region between the valence band and the ionization level. Recall 6 Chapter 1 Semiconductor Diodes  p n that ionization is the mechanism whereby an electron can absorb sufficient energy to break away from the atomic structure and enter the conduction band. You will note that the energy associated with each electron is measured in electron volts (eV). The unit of measure is appropriate, since W  QV eV (1.2) as derived from the defining equation for voltage V  W/Q. The charge Q is the charge associated with a single electron. Substituting the charge of an electron and a potential difference of 1 volt into Eq. (1.2) will result in an energy level referred to as one electron volt. Since energy is also measured in joules and the charge of one electron  1.6  1019 coulomb, W  QV  (1.6  1019 C)(1 V) and 1 eV  1.6  1019 J (1.3) At 0 K or absolute zero (273.15°C), all the valence electrons of semiconductor materials find themselves locked in their outermost shell of the atom with energy levels associated with the valence band of Fig. 1.8b. However, at room temperature (300 K, 25°C) a large number of valence electrons have acquired sufficient energy to leave the valence band, cross the energy gap defined by Eg in Fig. 1.8b and enter the conduction band. For silicon Eg is 1.1 eV, for germanium 0.67 eV, and for gallium arsenide 1.41 eV. The obviously lower Eg for germanium accounts for the increased number of carriers in that material as compared to silicon at room temperature. Note for the insulator that the energy gap is typically 5 eV or more, which severely limits the number of electrons that can enter the conduction band at room temperature. The conductor has electrons in the conduction band even at 0 K. Quite obviously, there- fore, at room temperature there are more than enough free carriers to sustain a heavy flow of charge, or current. We will find in Section 1.5 that if certain impurities are added to the intrinsic semiconductor materials, energy states in the forbidden bands will occur which will cause a net reduction in Eg for both semiconductor materials—consequently, increased carrier density in the conduction band at room temperature! 1.5 EXTRINSIC MATERIALS— n- AND p-TYPE The characteristics of semiconductor materials can be altered significantly by the ad- dition of certain impurity atoms into the relatively pure semiconductor material. These impurities, although only added to perhaps 1 part in 10 million, can alter the band structure sufficiently to totally change the electrical properties of the material. A semiconductor material that has been subjected to the doping process is called an extrinsic material. There are two extrinsic materials of immeasurable importance to semiconductor device fabrication: n-type and p-type. Each will be described in some detail in the following paragraphs. n-Type Material Both the n- and p-type materials are formed by adding a predetermined number of impurity atoms into a germanium or silicon base. The n-type is created by introduc- ing those impurity elements that have five valence electrons (pentavalent), such as an- timony, arsenic, and phosphorus. The effect of such impurity elements is indicated in 1.5 Extrinsic Materials—n- and p-Type 7  p n – – – – Si – – Si – – Si – – – – Fifth valence electron of antimony – – – – – Si – – Sb – – Si – – – – Antimony (Sb) impurity – – – – Si – – Si – – Si – – – – Figure 1.9 Antimony impurity in n-type material. Fig. 1.9 (using antimony as the impurity in a silicon base). Note that the four cova- lent bonds are still present. There is, however, an additional fifth electron due to the impurity atom, which is unassociated with any particular covalent bond. This re- maining electron, loosely bound to its parent (antimony) atom, is relatively free to move within the newly formed n-type material. Since the inserted impurity atom has donated a relatively “free” electron to the structure: Diffused impurities with five valence electrons are called donor atoms. It is important to realize that even though a large number of “free” carriers have been established in the n-type material, it is still electrically neutral since ideally the number of positively charged protons in the nuclei is still equal to the number of “free” and orbiting negatively charged electrons in the structure. The effect of this doping process on the relative conductivity can best be described through the use of the energy-band diagram of Fig. 1.10. Note that a discrete energy level (called the donor level) appears in the forbidden band with an Eg significantly less than that of the intrinsic material. Those “free” electrons due to the added im- purity sit at this energy level and have less difficulty absorbing a sufficient measure of thermal energy to move into the conduction band at room temperature. The result is that at room temperature, there are a large number of carriers (electrons) in the conduction level and the conductivity of the material increases significantly. At room temperature in an intrinsic Si material there is about one free electron for every 1012 atoms (1 to 109 for Ge). If our dosage level were 1 in 10 million (107), the ratio (1012/107  105) would indicate that the carrier concentration has increased by a ra- tio of 100,0001. Energy Conduction band E g = 0.05 eV (Si), 0.01 eV (Ge) E g as before Donor energy level Valence band Figure 1.10 Effect of donor impurities on the energy band structure. 8 Chapter 1 Semiconductor Diodes  p n p-Type Material The p-type material is formed by doping a pure germanium or silicon crystal with impurity atoms having three valence electrons. The elements most frequently used for this purpose are boron, gallium, and indium. The effect of one of these elements, boron, on a base of silicon is indicated in Fig. 1.11. Figure 1.11 Boron impurity in p-type material. Note that there is now an insufficient number of electrons to complete the cova- lent bonds of the newly formed lattice. The resulting vacancy is called a hole and is represented by a small circle or positive sign due to the absence of a negative charge. Since the resulting vacancy will readily accept a “free” electron: The diffused impurities with three valence electrons are called acceptor atoms. The resulting p-type material is electrically neutral, for the same reasons described for the n-type material. Electron versus Hole Flow The effect of the hole on conduction is shown in Fig. 1.12. If a valence electron ac- quires sufficient kinetic energy to break its covalent bond and fills the void created by a hole, then a vacancy, or hole, will be created in the covalent bond that released the electron. There is, therefore, a transfer of holes to the left and electrons to the right, as shown in Fig. 1.12. The direction to be used in this text is that of conven- tional flow, which is indicated by the direction of hole flow. Figure 1.12 Electron versus hole flow. 1.5 Extrinsic Materials—n- and p-Type 9  p n Majority and Minority Carriers In the intrinsic state, the number of free electrons in Ge or Si is due only to those few electrons in the valence band that have acquired sufficient energy from thermal or light sources to break the covalent bond or to the few impurities that could not be re- moved. The vacancies left behind in the covalent bonding structure represent our very limited supply of holes. In an n-type material, the number of holes has not changed significantly from this intrinsic level. The net result, therefore, is that the number of electrons far outweighs the number of holes. For this reason: In an n-type material (Fig. 1.13a) the electron is called the majority carrier and the hole the minority carrier. For the p-type material the number of holes far outweighs the number of elec- trons, as shown in Fig. 1.13b. Therefore: In a p-type material the hole is the majority carrier and the electron is the minority carrier. When the fifth electron of a donor atom leaves the parent atom, the atom remaining acquires a net positive charge: hence the positive sign in the donor-ion representation. For similar reasons, the negative sign appears in the acceptor ion. The n- and p-type materials represent the basic building blocks of semiconductor devices. We will find in the next section that the “joining” of a single n-type mater- ial with a p-type material will result in a semiconductor element of considerable im- portance in electronic systems. Donor ions Acceptor ions + –– + – + – Majority + + + – carriers + – – – + +– – + – + + – –+ + – – – + + + + + – + – + + – + – Minority Majority + – + – + – – + carrier carriers – + – + – Minority n-type p-type carrier (a) (b) Figure 1.13 (a) n-type material; (b) p-type material. 1.6 SEMICONDUCTOR DIODE In Section 1.5 both the n- and p-type materials were introduced. The semiconductor diode is formed by simply bringing these materials together (constructed from the same base—Ge or Si), as shown in Fig. 1.14, using techniques to be described in Chapter 20. At the instant the two materials are “joined” the electrons and holes in the region of the junction will combine, resulting in a lack of carriers in the region near the junction. This region of uncovered positive and negative ions is called the depletion re- gion due to the depletion of carriers in this region. Since the diode is a two-terminal device, the application of a voltage across its terminals leaves three possibilities: no bias (VD  0 V), forward bias (VD 0 V), and reverse bias (VD 0 V). Each is a condition that will result in a response that the user must clearly understand if the device is to be applied effectively. 10 Chapter 1 Semiconductor Diodes  p n Figure 1.14 p-n junction with no external bias. No Applied Bias (VD  0 V) Under no-bias (no applied voltage) conditions, any minority carriers (holes) in the n-type material that find themselves within the depletion region will pass directly into the p-type material. The closer the minority carrier is to the junction, the greater the attraction for the layer of negative ions and the less the opposition of the positive ions in the depletion region of the n-type material. For the purposes of future discussions we shall assume that all the minority carriers of the n-type material that find them- selves in the depletion region due to their random motion will pass directly into the p-type material. Similar discussion can be applied to the minority carriers (electrons) of the p-type material. This carrier flow has been indicated in Fig. 1.14 for the mi- nority carriers of each material. The majority carriers (electrons) of the n-type material must overcome the at- tractive forces of the layer of positive ions in the n-type material and the shield of negative ions in the p-type material to migrate into the area beyond the depletion re- gion of the p-type material. However, the number of majority carriers is so large in the n-type material that there will invariably be a small number of majority carriers with sufficient kinetic energy to pass through the depletion region into the p-type ma- terial. Again, the same type of discussion can be applied to the majority carriers (holes) of the p-type material. The resulting flow due to the majority carriers is also shown in Fig. 1.14. A close examination of Fig. 1.14 will reveal that the relative magnitudes of the flow vectors are such that the net flow in either direction is zero. This cancellation of vectors has been indicated by crossed lines. The length of the vector representing hole flow has been drawn longer than that for electron flow to demonstrate that the mag- nitude of each need not be the same for cancellation and that the doping levels for each material may result in an unequal carrier flow of holes and electrons. In sum- mary, therefore: In the absence of an applied bias voltage, the net flow of charge in any one direction for a semiconductor diode is zero. 1.6 Semiconductor Diode 11  p n The symbol for a diode is repeated in Fig. 1.15 with the associated n- and p-type regions. Note that the arrow is associated with the p-type component and the bar with the n-type region. As indicated, for VD  0 V, the current in any direction is 0 mA. Reverse-Bias Condition (VD 0 V) If an external potential of V volts is applied across the p-n junction such that the pos- Figure 1.15 No-bias conditions itive terminal is connected to the n-type material and the negative terminal is con- for a semiconductor diode. nected to the p-type material as shown in Fig. 1.16, the number of uncovered posi- tive ions in the depletion region of the n-type material will increase due to the large number of “free” electrons drawn to the positive potential of the applied voltage. For similar reasons, the number of uncovered negative ions will increase in the p-type material. The net effect, therefore, is a widening of the depletion region. This widen- ing of the depletion region will establish too great a barrier for the majority carriers to overcome, effectively reducing the majority carrier flow to zero as shown in Fig. 1.16. Figure 1.16 Reverse-biased p-n junction. The number of minority carriers, however, that find themselves entering the de- pletion region will not change, resulting in minority-carrier flow vectors of the same magnitude indicated in Fig. 1.14 with no applied voltage. The current that exists under reverse-bias conditions is called the reverse sat- uration current and is represented by Is. The reverse saturation current is seldom more than a few microamperes except for high-power devices. In fact, in recent years its level is typically in the nanoampere range for silicon devices and in the low-microampere range for germanium. The term saturation comes from the fact that it reaches its maximum level quickly and does not change significantly with increase in the reverse-bias potential, as shown on the diode characteristics of Fig. 1.19 for VD 0 V. The reverse-biased conditions are depicted in Fig. 1.17 for the diode symbol and p-n junction. Note, in particular, that the direc- Figure 1.17 Reverse-bias tion of Is is against the arrow of the symbol. Note also that the negative potential is conditions for a semiconductor diode. connected to the p-type material and the positive potential to the n-type material—the difference in underlined letters for each region revealing a reverse-bias condition. Forward-Bias Condition (VD 0 V) A forward-bias or “on” condition is established by applying the positive potential to the p-type material and the negative potential to the n-type material as shown in Fig. 1.18. For future reference, therefore: A semiconductor diode is forward-biased when the association p-type and pos- itive and n-type and negative has been established. 12 Chapter 1 Semiconductor Diodes  p n Figure 1.18 Forward-biased p-n junction. The application of a forward-bias potential VD will “pressure” electrons in the n-type material and holes in the p-type material to recombine with the ions near the boundary and reduce the width of the depletion region as shown in Fig. 1.18. The re- sulting minority-carrier flow of electrons from the p-type material to the n-type ma- terial (and of holes from the n-type material to the p-type material) has not changed in magnitude (since the conduction level is controlled primarily by the limited num- ber of impurities in the material), but the reduction in the width of the depletion re- gion has resulted in a heavy majority flow across the junction. An electron of the n-type material now “sees” a reduced barrier at the junction due to the reduced de- pletion region and a strong attraction for the positive potential applied to the p-type material. As the applied bias increases in magnitude the depletion region will con- tinue to decrease in width until a flood of electrons can pass through the junction, re- ID (mA) 20 19 Eq. (1.4) Actual commercially 18 available unit 17 16 15 14 13 12 Defined polarity and 11 direction for graph 10 VD + – 9 8 ID 7 Forward-bias region 6 (V VD > 0 V, II D > 0 mA) 5 4 3 2 Is 1 –40 –30 –20 –10 0 0.3 0.5 0.7 1 V D (V) – 0.1 µ uA – 0.2 µ uA No-bias Reverse-bias region (VD = 0 V, ID = 0 mA) (VD < 0 V, ID = –Is ) – 0.3 µ uA – 0.4 µ uA Figure 1.19 Silicon semiconductor diode characteristics. 1.6 Semiconductor Diode 13  p n sulting in an exponential rise in current as shown in the forward-bias region of the characteristics of Fig. 1.19. Note that the vertical scale of Fig. 1.19 is measured in milliamperes (although some semiconductor diodes will have a vertical scale mea- sured in amperes) and the horizontal scale in the forward-bias region has a maximum of 1 V. Typically, therefore, the voltage across a forward-biased diode will be less than 1 V. Note also, how quickly the current rises beyond the knee of the curve. It can be demonstrated through the use of solid-state physics that the general char- acteristics of a semiconductor diode can be defined by the following equation for the forward- and reverse-bias regions: ID  Is(ekVD/TK  1) (1.4) where Is  reverse saturation current k  11,600/ with  1 for Ge and  2 for Si for relatively low levels of diode current (at or below the knee of the curve) and  1 for Ge and Si for higher levels of diode current (in the rapidly increasing sec- tion of the curve) TK  TC 273° A plot of Eq. (1.4) is provided in Fig. 1.19. If we expand Eq. (1.4) into the fol- lowing form, the contributing component for each region of Fig. 1.19 can easily be described: ID  IsekVD/TK  Is For positive values of VD the first term of the equation above will grow very quickly and overpower the effect of the second term. The result is that for positive values of VD, ID will be positive and grow as the function y  ex appearing in Fig. 1.20. At VD  0 V, Eq. (1.4) becomes ID  Is(e0  1)  Is(1  1)  0 mA as ap- pearing in Fig. 1.19. For negative values of VD the first term will quickly drop off be- low Is, resulting in ID  Is, which is simply the horizontal line of Fig. 1.19. The break in the characteristics at VD  0 V is simply due to the dramatic change in scale from mA to A. Note in Fig. 1.19 that the commercially available unit has characteristics that are shifted to the right by a few tenths of a volt. This is due to the internal “body” resis- tance and external “contact” resistance of a diode. Each contributes to an additional voltage at the same current level as determined by Ohm’s law (V  IR). In time, as production methods improve, this difference will decrease and the actual characteris- Figure 1.20 Plot of e x. tics approach those of Eq. (1.4). It is important to note the change in scale for the vertical and horizontal axes. For positive values of ID the scale is in milliamperes and the current scale below the axis is in microamperes (or possibly nanoamperes). For VD the scale for positive values is in tenths of volts and for negative values the scale is in tens of volts. Initially, Eq. (1.4) does appear somewhat complex and may develop an unwar- ranted fear that it will be applied for all the diode applications to follow. Fortunately, however, a number of approximations will be made in a later section that will negate the need to apply Eq. (1.4) and provide a solution with a minimum of mathematical difficulty. Before leaving the subject of the forward-bias state the conditions for conduction (the “on” state) are repeated in Fig. 1.21 with the required biasing polarities and the resulting direction of majority-carrier flow. Note in particular how the direction of conduction matches the arrow in the symbol (as revealed for the ideal diode). Zener Region Figure 1.21 Forward-bias conditions for a semiconductor Even though the scale of Fig. 1.19 is in tens of volts in the negative region, there is diode. a point where the application of too negative a voltage will result in a sharp change 14 Chapter 1 Semiconductor Diodes  p n Figure 1.22 Zener region. in the characteristics, as shown in Fig. 1.22. The current increases at a very rapid rate in a direction opposite to that of the positive voltage region. The reverse-bias poten- tial that results in this dramatic change in characteristics is called the Zener potential and is given the symbol VZ. As the voltage across the diode increases in the reverse-bias region, the velocity of the minority carriers responsible for the reverse saturation current Is will also in- crease. Eventually, their velocity and associated kinetic energy (WK  12mv2) will be sufficient to release additional carriers through collisions with otherwise stable atomic structures. That is, an ionization process will result whereby valence electrons absorb sufficient energy to leave the parent atom. These additional carriers can then aid the ionization process to the point where a high avalanche current is established and the avalanche breakdown region determined. The avalanche region (VZ) can be brought closer to the vertical axis by increasing the doping levels in the p- and n-type materials. However, as VZ decreases to very low levels, such as 5 V, another mechanism, called Zener breakdown, will contribute to the sharp change in the characteristic. It occurs because there is a strong electric field in the region of the junction that can disrupt the bonding forces within the atom and “generate” carriers. Although the Zener breakdown mechanism is a significant contrib- utor only at lower levels of VZ, this sharp change in the characteristic at any level is called the Zener region and diodes employing this unique portion of the characteristic of a p-n junction are called Zener diodes. They are described in detail in Section 1.14. The Zener region of the semiconductor diode described must be avoided if the re- sponse of a system is not to be completely altered by the sharp change in character- istics in this reverse-voltage region. The maximum reverse-bias potential that can be applied before entering the Zener region is called the peak inverse voltage (referred to simply as the PIV rating) or the peak reverse voltage (denoted by PRV rating). If an application requires a PIV rating greater than that of a single unit, a num- ber of diodes of the same characteristics can be connected in series. Diodes are also connected in parallel to increase the current-carrying capacity. Silicon versus Germanium Silicon diodes have, in general, higher PIV and current rating and wider temperature ranges than germanium diodes. PIV ratings for silicon can be in the neighborhood of 1000 V, whereas the maximum value for germanium is closer to 400 V. Silicon can be used for applications in which the temperature may rise to about 200°C (400°F), whereas germanium has a much lower maximum rating (100°C). The disadvantage of silicon, however, as compared to germanium, as indicated in Fig. 1.23, is the higher 1.6 Semiconductor Diode 15  p n Figure 1.23 Comparison of Si and Ge semiconductor diodes. forward-bias voltage required to reach the region of upward swing. It is typically of the order of magnitude of 0.7 V for commercially available silicon diodes and 0.3 V for germanium diodes when rounded off to the nearest tenths. The increased offset for silicon is due primarily to the factor in Eq. (1.4). This factor plays a part in de- termining the shape of the curve only at very low current levels. Once the curve starts its vertical rise, the factor drops to 1 (the continuous value for germanium). This is evidenced by the similarities in the curves once the offset potential is reached. The potential at which this rise occurs is commonly referred to as the offset, threshold, or firing potential. Frequently, the first letter of a term that describes a particular quan- tity is used in the notation for that quantity. However, to ensure a minimum of con- fusion with other terms, such as output voltage (Vo) and forward voltage (VF), the no- tation VT has been adopted for this book, from the word “threshold.” In review: VT  0.7 (Si) VT  0.3 (Ge) Obviously, the closer the upward swing is to the vertical axis, the more “ideal” the device. However, the other characteristics of silicon as compared to germanium still make it the choice in the majority of commercially available units. Temperature Effects Temperature can have a marked effect on the characteristics of a silicon semicon- ductor diode as witnessed by a typical silicon diode in Fig. 1.24. It has been found experimentally that: The reverse saturation current Is will just about double in magnitude for every 10°C increase in temperature. 16 Chapter 1 Semiconductor Diodes  p n Figure 1.24 Variation in diode characteristics with temperature change. It is not uncommon for a germanium diode with an Is in the order of 1 or 2 A at 25°C to have a leakage current of 100 A  0.1 mA at a temperature of 100°C. Current levels of this magnitude in the reverse-bias region would certainly question our desired open-circuit condition in the reverse-bias region. Typical values of Is for silicon are much lower than that of germanium for similar power and current levels as shown in Fig. 1.23. The result is that even at high temperatures the levels of Is for silicon diodes do not reach the same high levels obtained for germanium—a very im- portant reason that silicon devices enjoy a significantly higher level of development and utilization in design. Fundamentally, the open-circuit equivalent in the reverse- bias region is better realized at any temperature with silicon than with germanium. The increasing levels of Is with temperature account for the lower levels of thresh- old voltage, as shown in Fig. 1.24. Simply increase the level of Is in Eq. (1.4) and note the earlier rise in diode current. Of course, the level of TK also will be increas- ing in the same equation, but the increasing level of Is will overpower the smaller per- cent change in TK. As the temperature increases the forward characteristics are actu- ally becoming more “ideal,” but we will find when we review the specifications sheets that temperatures beyond the normal operating range can have a very detrimental ef- fect on the diode’s maximum power and current levels. In the reverse-bias region the breakdown voltage is increasing with temperature, but note the undesirable increase in reverse saturation current. 1.7 RESISTANCE LEVELS As the operating point of a diode moves from one region to another the resistance of the diode will also change due to the nonlinear shape of the characteristic curve. It will be demonstrated in the next few paragraphs that the type of applied voltage or signal will define the resistance level of interest. Three different levels will be intro- duced in this section that will appear again as we examine other devices. It is there- fore paramount that their determination be clearly understood. 1.7 Resistance Levels 17  p n DC or Static Resistance The application of a dc voltage to a circuit containing a semiconductor diode will re- sult in an operating point on the characteristic curve that will not change with time. The resistance of the diode at the operating point can be found simply by finding the corresponding levels of VD and ID as shown in Fig. 1.25 and applying the following equation: VD RD    (1.5) ID The dc resistance levels at the knee and below will be greater than the resistance levels obtained for the vertical rise section of the characteristics. The resistance lev- els in the reverse-bias region will naturally be quite high. Since ohmmeters typically employ a relatively constant-current source, the resistance determined will be at a pre- set current level (typically, a few milliamperes). Figure 1.25 Determining the dc resistance of a diode at a particu- lar operating point. In general, therefore, the lower the current through a diode the higher the dc resistance level. EXAMPLE 1.1 Determine the dc resistance levels for the diode of Fig. 1.26 at (a) ID  2 mA (b) ID  20 mA (c) VD  10 V Figure 1.26 Example 1.1 Solution (a) At ID  2 mA, VD  0.5 V (from the curve) and VD 0.5 V RD      250  ID 2 mA 18 Chapter 1 Semiconductor Diodes  p n (b) At ID  20 mA, VD  0.8 V (from the curve) and VD 0.8 V RD      40  ID 20 mA (c) At VD  10 V, ID  Is  1 A (from the curve) and VD 10 V RD      10 M ID 1 A clearly supporting some of the earlier comments regarding the dc resistance levels of a diode. AC or Dynamic Resistance It is obvious from Eq. 1.5 and Example 1.1 that the dc resistance of a diode is inde- pendent of the shape of the characteristic in the region surrounding the point of inter- est. If a sinusoidal rather than dc input is applied, the situation will change completely. The varying input will move the instantaneous operating point up and down a region of the characteristics and thus defines a specific change in current and voltage as shown in Fig. 1.27. With no applied varying signal, the point of operation would be the Q-point appearing on Fig. 1.27 determined by the applied dc levels. The des- ignation Q-point is derived from the word quiescent, which means “still or unvarying.” Figure 1.27 Defining the dynamic or ac resistance. A straight line drawn tangent to the curve through the Q-point as shown in Fig. 1.28 will define a particular change in voltage and current that can be used to deter- mine the ac or dynamic resistance for this region of the diode characteristics. An ef- fort should be made to keep the change in voltage and current as small as possible and equidistant to either side of the Q-point. In equation form, Vd rd   where  signifies a finite change in the quantity. (1.6)  Id The steeper the slope, the less the value of Vd for the same change in  Id and the less the resistance. The ac resistance in the vertical-rise region of the characteristic is therefore quite small, while the ac resistance is much higher at low current levels. In general, therefore, the lower the Q-point of operation (smaller current or Figure 1.28 Determining the ac lower voltage) the higher the ac resistance. resistance at a Q-point. 1.7 Resistance Levels 19  p n EXAMPLE 1.2 For the characteristics of Fig. 1.29: (a) Determine the ac resistance at ID  2 mA. (b) Determine the ac resistance at ID  25 mA. (c) Compare the results of parts (a) and (b) to the dc resistances at each current level. I D (mA) 30 25 ∆ Id 20 ∆Vd 15 10 5 4 2 ∆ Id 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 VD (V) ∆Vd Figure 1.29 Example 1.2 Solution (a) For ID  2 mA; the tangent line at ID  2 mA was drawn as shown in the figure and a swing of 2 mA above and below the specified diode current was chosen. At ID  4 mA, VD  0.76 V, and at ID  0 mA, VD  0.65 V. The resulting changes in current and voltage are  Id  4 mA  0 mA  4 mA and Vd  0.76 V  0.65 V  0.11 V and the ac resistance: Vd 0.11 V rd      27.5  Id 4 mA (b) For ID  25 mA, the tangent line at ID  25 mA was drawn as shown on the fig- ure and a swing of 5 mA above and below the specified diode current was cho- sen. At ID  30 mA, VD  0.8 V, and at ID  20 mA, VD  0.78 V. The result- ing changes in current and voltage are Id  30 mA  20 mA  10 mA and Vd  0.8 V  0.78 V  0.02 V and the ac resistance is Vd 0.02 V rd      2  Id 10 mA 20 Chapter 1 Semiconductor Diodes  p n (c) For ID  2 mA, VD  0.7 V and VD 0.7 V RD      350  ID 2 mA which far exceeds the rd of 27.5 . For ID  25 mA, VD  0.79 V and VD 0.79 V RD      31.62  ID 25 mA which far exceeds the rd of 2 . We have found the dynamic resistance graphically, but there is a basic definition in differential calculus which states: The derivative of a function at a point is equal to the slope of the tangent line drawn at that point. Equation (1.6), as defined by Fig. 1.28, is, therefore, essentially finding the deriva- tive of the function at the Q-point of operation. If we find the derivative of the gen- eral equation (1.4) for the semiconductor diode with respect to the applied forward bias and then invert the result, we will have an equation for the dynamic or ac resis- tance in that region. That is, taking the derivative of Eq. (1.4) with respect to the ap- plied bias will result in d d (ID)  [Is(ekVD /TK  1)] dVD dV dID k and   (ID Is) dVD TK following a few basic maneuvers of differential calculus. In general, ID  Is in the vertical slope section of the characteristics and dID k   ID dVD TK Substituting  1 for Ge and Si in the vertical-rise section of the characteristics, we obtain 11,600 11,600 k      11,600 1 and at room temperature, TK  TC 273°  25° 273°  298° k 11,600 so that     38.93 TK 298 dID and   38.93ID dVD Flipping the result to define a resistance ratio (R  V/I) gives us dVD 0.026    dID ID 26 mV or rd   (1.7) ID Ge,Si 1.7 Resistance Levels 21  p n The significance of Eq. (1.7) must be clearly understood. It implies that the dynamic resistance can be found simply by substituting the quiescent value of the diode cur- rent into the equation. There is no need to have the characteristics available or to worry about sketching tangent lines as defined by Eq. (1.6). It is important to keep in mind, however, that Eq. (1.7) is accurate only for values of ID in the vertical-rise section of the curve. For lesser values of ID,  2 (silicon) and the value of rd ob- tained must be multiplied by a factor of 2. For small values of ID below the knee of the curve, Eq. (1.7) becomes inappropriate. All the resistance levels determined thus far have been defined by the p-n junc- tion and do not include the resistance of the semiconductor material itself (called body resistance) and the resistance introduced by the connection between the semiconduc- tor material and the external metallic conductor (called contact resistance). These ad- ditional resistance levels can be included in Eq. (1.7) by adding resistance denoted by rB as appearing in Eq. (1.8). The resistance r d, therefore, includes the dynamic re- sistance defined by Eq. 1.7 and the resistance rB just introduced. 26 mV r d   rB ohms (1.8) ID The factor rB can range from typically 0.1  for high-power devices to 2  for some low-power, general-purpose diodes. For Example 1.2 the ac resistance at 25 mA was calculated to be 2 . Using Eq. (1.7), we have 26 mV 26 mV rd      1.04  ID 25 mA The difference of about 1  could be treated as the contribution of rB. For Example 1.2 the ac resistance at 2 mA was calculated to be 27.5 . Using Eq. (1.7) but multiplying by a factor of 2 for this region (in the knee of the curve  2),     26 mV 26 mV rd  2   2   2(13 )  26  ID 2 mA The difference of 1.5  could be treated as the contribution due to rB. In reality, determining rd to a high degree of accuracy from a characteristic curve using Eq. (1.6) is a difficult process at best and the results have to be treated with a grain of salt. At low levels of diode current the factor rB is normally small enough compared to rd to permit ignoring its impact on the ac diode resistance. At high lev- els of current the level of rB may approach that of rd, but since there will frequently be other resistive elements of a much larger magnitude in series with the diode we will assume in this book that the ac resistance is determined solely by rd and the im- pact of rB will be ignored unless otherwise noted. Technological improvements of re- cent years suggest that the level of rB will continue to decrease in magnitude and eventually become a factor that can certainly be ignored in comparison to rd. The discussion above has centered solely on the forward-bias region. In the re- verse-bias region we will assume that the change in current along the Is line is nil from 0 V to the Zener region and the resulting ac resistance using Eq. (1.6) is suffi- ciently high to permit the open-circuit approximation. Average AC Resistance If the input signal is sufficiently large to produce a broad swing such as indicated in Fig. 1.30, the resistance associated with the device for this region is called the aver- age ac resistance. The average ac resistance is, by definition, the resistance deter- 22 Chapter 1 Semiconductor Diodes  p n I D (mA) 20 15 ∆ Id 10 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 VD (V) ∆Vd Figure 1.30 Determining the average ac resistance between indicated limits. mined by a straight line drawn between the two intersections established by the max- imum and minimum values of input voltage. In equation form (note Fig. 1.30), Vd rav    Id  pt. to pt. (1.9) For the situation indicated by Fig. 1.30, Id  17 mA  2 mA  15 mA and Vd  0.725 V  0.65 V  0.075 V Vd 0.075 V with rav      5  Id 15 mA If the ac resistance (rd) were determined at ID  2 mA its value would be more than 5 , and if determined at 17 mA it would be less. In between the ac resistance would make the transition from the high value at 2 mA to the lower value at 17 mA. Equation (1.9) has defined a value that is considered the average of the ac values from 2 to 17 mA. The fact that one resistance level can be used for such a wide range of the characteristics will prove quite useful in the definition of equivalent circuits for a diode in a later section. As with the dc and ac resistance levels, the lower the level of currents used to determine the average resistance the higher the resistance level. Summary Table Table 1.2 was developed to reinforce the important conclusions of the last few pages and to emphasize the differences among the various resistance levels. As indicated earlier, the content of this section is the foundation for a number of resistance calcu- lations to be performed in later sections and chapters. 1.7 Resistance Levels 23  p n TABLE 1.2 Resistance Levels Special Graphical Type Equation Characteristics Determination VD DC or static RD   Defined as a ID point on the characteristics V 26 mV AC or rd  d   Defined by a Id ID dynamic tangent line at the Q-point Vd Average ac rav   Defined by a straight Id pt. to pt. line between limits of operation 1.8 DIODE EQUIVALENT CIRCUITS An equivalent circuit is a combination of elements properly chosen to best represent the actual terminal characteristics of a device, system, or such in a particular operating region. In other words, once the equivalent circuit is defined, the device symbol can be removed from a schematic and the equivalent circuit inserted in its place without se- verely affecting the actual behavior of the system. The result is often a network that can be solved using traditional circuit analysis techniques. Piecewise-Linear Equivalent Circuit One technique for obtaining an equivalent circuit for a diode is to approximate the characteristics of the device by straight-line segments, as shown in Fig. 1.31. The re- sulting equivalent circuit is naturally called the piecewise-linear equivalent circuit. It should be obvious from Fig. 1.31 that the straight-line segments do not result in an ex- act duplication of the actual characteristics, especially in the knee region. However, the resulting segments are sufficiently close to the actual curve to establish an equiv- alent circuit that will provide an excellent first approximati