SEVENTH EDITION ELECTRONIC DEVICES AND CIRCUIT THEORY ROBERT BOYLESTAD LOUIS NASHELSKY PRENTICE HALL Upper Saddle River, New Jersey Columbus, Ohio Contents v 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 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 vii Contents 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 ix Contents 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 OTHER TWO-TERMINAL DEVICES 810 20.1 Introduction 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 xi Contents 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. 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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 C H A P T E R 1 Semiconductor Diodes 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- tics shown in Figs. 1.1a and b, respectively. 1 Figure 1.1 Ideal diode: (a) symbol; (b) characteristics. 2 Chapter 1 Semiconductor Diodes 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 RF   V IF F   0  (short circuit) 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, RR   V IR R     (open-circuit) 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. 5, 20, or any reverse-bias potential  0 mA 0 V  2, 3, mA, . . . , or any positive value Figure 1.2 (a) Conduction and (b) nonconduction states of the ideal diode as determined by the applied bias. D V – + D V + – D I 0 D I D V = 0 (limited by circuit) Open circuit Short circuit (a) (b) D I 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 3 p n the resulting current has the opposite direction, as shown in Fig. 1.3b, the open- circuit equivalent is appropriate. 1.3 Semiconductor Materials Figure 1.3 (a) Conduction and (b) nonconduction states of the ideal diode as determined by the direction of conventional current established by the network. D I = 0 (b) D I D I D I (a) 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):    R l A   () c ( m cm2)  ⇒ -cm (1.1) 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: R    A l     ( ( 1 1 c c m m 2 ) )  ohms 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 Figure 1.4 Defining the metric units of resistivity. 4 Chapter 1 Semiconductor Diodes 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- conductors, germanium and silicon, are shown in Fig. 1.6. 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. Figure 1.5 Ge and Si single-crystal structure. 5 p n 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 Figure 1.6 Atomic structure: (a) germanium; (b) silicon. Figure 1.7 Covalent bonding of the silicon atom. 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. 6 Chapter 1 Semiconductor Diodes p n Figure 1.8 Energy levels: (a) discrete levels in isolated atomic structures; (b) conduction and valence bands of an insulator, semiconductor, and conductor. Energy Energy Energy E > 5 eV g Valence band Conduction band Valence band Conduction band Conduction band The bands overlap Electrons "free" to establish conduction Valence electrons bound to the atomic stucture E = 1.1 eV (Si) g E = 0.67 eV (Ge) g E = 1.41 eV (GaAs) g Insulator Semiconductor (b) g E Valence band Conductor Energy gap Energy gap etc. Valance Level (outermost shell) Second Level (next inner shell) Third Level (etc.) Energy Nucleus (a) 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 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 7 1.5 Extrinsic Materials—n- and p-Type p n – Antimony (Sb) impurity Si – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – Si Si Si Sb Si Si Si Si Fifth valence electron of antimony 8 Chapter 1 Semiconductor Diodes p n 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. Figure 1.10 Effect of donor impurities on the energy band structure. Energy Conduction band Valence band Donor energy level gE = 0.05 eV (Si), 0.01 eV (Ge) E as before g 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. 9 1.5 Extrinsic Materials—n- and p-Type p n 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. 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. 10 Chapter 1 Semiconductor Diodes p n Figure 1.13 (a) n-type material; (b) p-type material. + – + + – – – – + – – – – – – – + Minority carrier Minority carrier p-type n-type Donor ions Majority carriers Acceptor ions Majority carriers + + + + + + + + + – + – – – – – – + + + + – – + + – – + + – – – + + + – + + + (a) (b) 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. 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. 11 1.6 Semiconductor Diode p n Figure 1.14 p-n junction with no external bias. 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- itive terminal is connected to the n-type material and the negative terminal is con- 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. 12 Chapter 1 Semiconductor Diodes Figure 1.17 Reverse-bias conditions for a semiconductor diode. Figure 1.15 No-bias conditions for a semiconductor diode. 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- tion of Is is against the arrow of the symbol. Note also that the negative potential is 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. Figure 1.16 Reverse-biased p-n junction. p n 13 p n 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- 1.6 Semiconductor Diode Figure 1.18 Forward-biased p-n junction. Figure 1.19 Silicon semiconductor diode characteristics. 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 0.3 0.5 0.7 1 –10 –20 –30 –40 ID (mA) (V) D V D V – + Defined polarity and direction for graph Forward-bias region (V > 0 V, I > 0 mA) D I D D s I – 0.2 uA – 0.3 uA – 0.4 uA µ 0 No-bias (VD = 0 V, ID = 0 mA) – 0.1 uA µ µ µ Reverse-bias region (VD < 0 V, ID = –Is ) Eq. (1.4) Actual commercially available unit 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(e kVD/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  Ise kVD/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  e x appearing in Fig. 1.20. At VD  0 V, Eq. (1.4) becomes ID  Is(e 0  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- 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 Even though the scale of Fig. 1.19 is in tens of volts in the negative region, there is a point where the application of too negative a voltage will result in a sharp change 14 Chapter 1 Semiconductor Diodes Figure 1.20 Plot of ex. Figure 1.21 Forward-bias conditions for a semiconductor diode. 15 1.6 Semiconductor Diode 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   1 2mv 2) 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 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 1.23 Comparison of Si and Ge semiconductor diodes. 17 1.7 Resistance Levels 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. 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: RD   V ID D (1.5) 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). 18 Chapter 1 Semiconductor Diodes p n 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. 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 Solution (a) At ID  2 mA, VD  0.5 V (from the curve) and RD   V ID D   2 0. m 5 V A   250  EXAMPLE 1.1 Figure 1.26 Example 1.1 19 p n Figure 1.28 Determining the ac resistance at a Q-point. 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, rd    V I d d  where  signifies a finite change in the quantity. (1.6) 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 lower voltage) the higher the ac resistance. (b) At ID  20 mA, VD  0.8 V (from the curve) and RD   V ID D  2 0 0 .8 m V A  40  (c) At VD  10 V, ID  Is  1 A (from the curve) and RD   V ID D   1 10 V A   10 M 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. 1.7 Resistance Levels p n 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: rd     V Id d  0 4 .1 m 1 A V  27.5  (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 rd     V Id d  1 0 0 .0 m 2 V A  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. 20 Chapter 1 Semiconductor Diodes EXAMPLE 1.2 Figure 1.29 Example 1.2 V (V) D I (mA) D 0 5 10 15 20 25 30 2 4 0.1 0.3 0.5 0.7 0.9 1 0.8 0.6 0.4 0.2 ∆ d I ∆ d I ∆ d V ∆ d V 21 1.7 Resistance Levels p n (c) For ID  2 mA, VD  0.7 V and RD   V ID D   2 0. m 7 V A   350  which far exceeds the rd of 27.5 . For ID  25 mA, VD  0.79 V and RD   V ID D  2 0 5 .7 m 9 V A  31.62  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  dV d D (ID)  d d V [Is(e kVD/TK  1)] and  d d V ID D    T k K (ID  Is) following a few basic maneuvers of differential calculus. In general, ID  Is in the vertical slope section of the characteristics and  d d V ID D    T k K ID Substituting   1 for Ge and Si in the vertical-rise section of the characteristics, we obtain k  11,  600  11, 1 600  11,600 and at room temperature, TK  TC  273°  25°  273°  298° so that  T k K   11 2 , 9 6 8 00   38.93 and  d d V ID D   38.93ID Flipping the result to define a resistance ratio (R  V/I) gives us  d d V ID D   0. I 0 D 26  or rd  26 ID mV  Ge,Si (1.7) 22 Chapter 1 Semiconductor Diodes 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. r d  26 ID mV  rB ohms (1.8) 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 rd  26 ID mV  2 2 5 6 m mV A  1.04  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), rd  226ID mV  222 6 m m A V   2(13 )  26  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- 23 1.7 Resistance Levels p n 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), rav     V Id d  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 with rav     V Id d  0 1 . 5 07 m 5 A V  5  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. Figure 1.30 Determining the average ac resistance between indicated limits. D (V) V I (mA) D 0 5 10 15 20 0.1 0.3 0.5 0.7 0.9 0.2 0.4 0.6 0.8 1 ∆ d V ∆ d I 24 Chapter 1 Semiconductor Diodes p n TABLE 1.2 Resistance Levels Special Graphical Type Equation Characteristics Determination DC or static RD   V ID D Defined as a point on the characteristics AC or rd     V Id d  26 ID mV  Defined by a dynamic tangent line at the Q-point Average ac rav     V Id d pt. to pt. Defined by a straight 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 approximation to the actual behavior of the device. For the sloping section of the equivalence the average ac resistance as in- troduced in Section 1.7 is the resistance level appearing in the equivalent circuit of Fig. 1.32 next to the actual device. In essence, it defines the resistance level of the device when it is in the “on” state. The ideal diode is included to establish that there is only one direction of conduction through the device, and a reverse-bias condition will re- 25 1.8 Diode Equivalent Circut p n sult in the open-circuit state for the device. Since a silicon semiconductor diode does not reach the conduction state until VD reaches 0.7 V with a forward bias (as shown in Fig. 1.31), a battery VT opposing the conduction direction must appear in the equiv- alent circuit as shown in Fig. 1.32. The battery simply specifies that the voltage across the device must be greater than the threshold battery voltage before conduction through the device in the direction dictated by the ideal diode can be established. When con- duction is established the resistance of the diode will be the specified value of rav. Keep in mind, however, that VT in the equivalent circuit is not an independent voltage source. If a voltmeter is placed across an isolated diode on the top of a lab bench, a reading of 0.7 V will not be obtained. The battery simply represents the hor- izontal offset of the characteristics that must be exceeded to establish conduction. The approximate level of rav can usually be determined from a specified operat- ing point on the specification sheet (to be discussed in Section 1.9). For instance, for a silicon semiconductor diode, if IF  10 mA (a forward conduction current for the diode) at VD  0.8 V, we know for silicon that a shift of 0.7 V is required before the characteristics rise and rav     V Id d  pt. to pt.  1 0 0 .8 m V A   0 0 .7 m V A  1 0 0 .1 m V A  10  as obtained for Fig. 1.30. Simplified Equivalent Circuit For most applications, the resistance rav is sufficiently small to be ignored in com- parison to the other elements of the network. The removal of rav from the equivalent Figure 1.32 Components of the piecewise-linear equivalent circuit. D V D I + – av r T V 0.7 V 10 Ω D V Ideal diode + – D I Figure 1.31 Defining the piecewise-linear equivalent circuit using straight-line segments to approximate the characteristic curve. 26 Chapter 1 Semiconductor Diodes p n circuit is the same as implying that the characteristics of the diode appear as shown in Fig. 1.33. Indeed, this approximation is frequently employed in semiconductor cir- cuit analysis as demonstrated in Chapter 2. The reduced equivalent circuit appears in the same figure. It states that a forward-biased silicon diode in an electronic system under dc conditions has a drop of 0.7 V across it in the conduction state at any level of diode current (within rated values, of course). Ideal Equivalent Circuit Now that rav has been removed from the equivalent circuit let us take it a step further and establish that a 0.7-V level can often be ignored in comparison to the applied voltage level. In this case the equivalent circuit will be reduced to that of an ideal diode as shown in Fig. 1.34 with its characteristics. In Chapter 2 we will see that this approximation is often made without a serious loss in accuracy. In industry a popular substitution for the phrase “diode equivalent circuit” is diode model—a model by definition being a representation of an existing device, object, system, and so on. In fact, this substitute terminology will be used almost exclusively in the chapters to follow. Figure 1.34 Ideal diode and its characteristics. Summary Table For clarity, the diode models employed for the range of circuit parameters and appli- cations are provided in Table 1.3 with their piecewise-linear characteristics. Each will be investigated in greater detail in Chapter 2. There are always exceptions to the gen- eral rule, but it is fairly safe to say that the simplified equivalent model will be em- ployed most frequently in the analysis of electronic systems while the ideal diode is frequently applied in the analysis of power supply systems where larger voltages are encountered. Figure 1.33 Simplified equivalent circuit for the silicon semiconductor diode. – Ω D V D I 0 T V = 0.7 V av r = 0 D I + D V Ideal diode VT = 0.7 V 27 1.9 Diode Specification Sheets p n 1.9 DIODE SPECIFICATION SHEETS Data on specific semiconductor devices are normally provided by the manufacturer in one of two forms. Most frequently, it is a very brief description limited to perhaps one page. Otherwise, it is a thorough examination of the characteristics using graphs, artwork, tables, and so on. In either case, there are specific pieces of data that must be included for proper utilization of the device. They include: 1. The forward voltage VF (at a specified current and temperature) 2. The maximum forward current IF (at a specified temperature) 3. The reverse saturation current IR (at a specified voltage and temperature) 4. The reverse-voltage rating [PIV or PRV or V(BR), where BR comes from the term “breakdown” (at a specified temperature)] 5. The maximum power dissipation level at a particular temperature 6. Capacitance levels (as defined in Section 1.10) 7. Reverse recovery time trr (as defined in Section 1.11) 8. Operating temperature range Depending on the type of diode being considered, additional data may also be provided, such as frequency range, noise level, switching time, thermal resistance lev- els, and peak repetitive values. For the application in mind, the significance of the data will usually be self-apparent. If the maximum power or dissipation rating is also provided, it is understood to be equal to the following product: PDmax  VD ID (1.10) where ID and VD are the diode current and voltage at a particular point of operation. TABLE 1.3 Diode Equivalent Circuits (Models) Type Conditions Model Characteristics Piecewise-linear model Simplified model Rnetwork  rav Ideal device Rnetwork  rav Enetwork  VT 28 Chapter 1 Semiconductor Diodes p n If we apply the simplified model for a particular application (a common occur- rence), we can substitute VD  VT  0.7 V for a silicon diode in Eq. (1.10) and de- termine the resulting power dissipation for comparison against the maximum power rating. That is, Pdissipated  (0.7 V)ID (1.11) Figure 1.35 Electrical characteristics of a high-voltage, low-leakage diode. 29 1.9 Diode Specification Sheets p n An exact copy of the data provided for a high-voltage/low-leakage diode appears in Figs. 1.35 and 1.36. This example would represent the expanded list of data and characteristics. The term rectifier is applied to a diode when it is frequently used in a rectification process to be described in Chapter 2. Figure 1.36 Terminal characteristics of a high-voltage diode. Specific areas of the specification sheet have been highlighted in blue with a let- ter identification corresponding with the following description: A: The minimum reverse-bias voltage (PIVs) for a diode at a specified reverse saturation current. B: Temperature characteristics as indicated. Note the use of the Celsius scale and the wide range of utilization [recall that 32°F  0°C  freezing (H2O) and 212°F  100°C  boiling (H2O)]. C: Maximum power dissipation level PD  VDID  500 mW. The maximum power rating decreases at a rate of 3.33 mW per degree increase in tempera- ture above room temperature (25°C), as clearly indicated by the power derating curve of Fig. 1.36. D: Maximum continuous forward current IFmax  500 mA (note IF versus tem- perature in Fig. 1.36). E: Range of values of VF at IF  200 mA. Note that it exceeds VT  0.7 V for both devices. F: Range of values of VF at IF  1.0 mA. Note in this case how the upper lim- its surround 0.7 V. G: At VR  20 V and a typical operating temperature IR  500 nA  0.5 A, while at a higher reverse voltage IR drops to 5 nA  0.005 A. H: The capacitance level between terminals is about 8 pF for the diode at VR  VD  0 V (no-bias) and an applied frequency of 1 MHz. I: The reverse recovery time is 3 s for the list of operating conditions. A number of the curves of Fig. 1.36 employ a log scale. A brief investigation of Section 11.2 should help with the reading of the graphs. Note in the top left figure how VF increased from about 0.5 V to over 1 V as IF increased from 10 A to over 100 mA. In the figure below we find that the reverse saturation current does change slightly with increasing levels of VR but remains at less than 1 nA at room tempera- ture up to VR  125 V. As noted in the adjoining figure, however, note how quickly the reverse saturation current increases with increase in temperature (as forecasted earlier). In the top right figure note how the capacitance decreases with increase in reverse- bias voltage, and in the figure below note that the ac resistance (rd) is only about 1  at 100 mA and increases to 100  at currents less than 1 mA (as expected from the discussion of earlier sections). The average rectified current, peak repetitive forward current, and peak forward surge current as they appear on the specification sheet are defined as follows: 1. Average rectified current. A half-wave-rectified signal (described in Section 2.8) has an average value defined by Iav  0.318Ipeak. The average current rating is lower than the continuous or peak repetitive forward currents because a half-wave current waveform will have instantaneous values much higher than the average value. 2. Peak repetitive forward current. This is the maximum instantaneous value of repet- itive forward current. Note that since it is at this level for a brief period of time, its level can be higher than the continuous level. 3. Peak forward surge current. On occasion during turn-on, malfunctions, and so on, there will be very high currents through the device for very brief intervals of time (that are not repetitive). This rating defines the maximum value and the time in- terval for such surges in current level. 30 Chapter 1 Semiconductor Diodes p n 31 1.10 Transition and Diffusion Capacitance p n The more one is exposed to specification sheets, the “friendlier” they will become, especially when the impact of each parameter is clearly understood for the applica- tion under investigation. 1.10 TRANSITION AND DIFFUSION CAPACITANCE Electronic devices are inherently sensitive to very high frequencies. Most shunt ca- pacitive effects that can be ignored at lower frequencies because the reactance XC  1/2 fC is very large (open-circuit equivalent). This, however, cannot be ignored at very high frequencies. XC will become sufficiently small due to the high value of f to introduce a low-reactance “shorting” path. In the p-n semiconductor diode, there are two capacitive effects to be considered. Both types of capacitance are present in the forward- and reverse-bias regions, but one so outweighs the other in each region that we consider the effects of only one in each region. In the reverse-bias region we have the transition- or depletion-region capaci- tance (CT), while in the forward-bias region we have the diffusion (CD) or storage capacitance. Recall that the basic equation for the capacitance of a parallel-plate capacitor is defined by C  A/d, where  is the permittivity of the dielectric (insulator) between the plates of area A separated by a distance d. In the reverse-bias region there is a de- pletion region (free of carriers) that behaves essentially like an insulator between the layers of opposite charge. Since the depletion width (d) will increase with increased reverse-bias potential, the resulting transition capacitance will decrease, as shown in Fig. 1.37. The fact that the capacitance is dependent on the applied reverse-bias po- tential has application in a number of electronic systems. In fact, in Chapter 20 a diode will be introduced whose operation is wholly dependent on this phenomenon. Although the effect described above will also be present in the forward-bias re- gion, it is overshadowed by a capacitance effect directly dependent on the rate at which charge is injected into the regions just outside the depletion region. The result is that increased levels of current will result in increased levels of diffusion capaci- tance. However, increased levels of current result in reduced levels of associated re- sistance (to be demonstrated shortly), and the resulting time constant (  RC ), which is very important in high-speed applications, does not become excessive. Figure 1.37 Transition and diffusion capacitance versus applied bias for a silicon diode. 0 0.25 0.5 5 10 15 20 25 – – – – – (V) C 5 10 15 Forward-bias (C ) D Reverse-bias (C ) T (pF) 32 Chapter 1 Semiconductor Diodes p n The capacitive effects described above are represented by a capacitor in parallel with the ideal diode, as shown in Fig. 1.38. For low- or mid-frequency applications (except in the power area), however, the capacitor is normally not included in the diode symbol. 1.11 REVERSE RECOVERY TIME There are certain pieces of data that are normally provided on diode specification sheets provided by manufacturers. One such quantity that has not been considered yet is the reverse recovery time, denoted by trr . In the forward-bias state it was shown earlier that there are a large number of electrons from the n-type material progress- ing through the p-type material and a large number of holes in the n-type—a re- quirement for conduction. The electrons in the p-type and holes progressing through the n-type material establish a large number of minority carriers in each material. If the applied voltage should be reversed to establish a reverse-bias situation, we would ideally like to see the diode change instantaneously from the conduction state to the nonconduction state. However, because of the large number of minority carriers in each material, the diode current will simply reverse as shown in Fig. 1.39 and stay at this measurable level for the period of time ts (storage time) required for the minor- ity carriers to return to their majority-carrier state in the opposite material. In essence, the diode will remain in the short-circuit state with a current Ireverse determined by the network parameters. Eventually, when this storage phase has passed, the current will reduce in level to that associated with the nonconduction state. This second pe- riod of time is denoted by tt (transition interval). The reverse recovery time is the sum of these two intervals: trr  ts  tt. Naturally, it is an important consideration in high- speed switching applications. Most commercially available switching diodes have a trr in the range of a few nanoseconds to 1 s. Units are available, however, with a trr of only a few hundred picoseconds (1012). Figure 1.38 Including the effect of the transition or diffusion capacitance on the semiconductor diode. Figure 1.39 Defining the reverse recovery time. D I t forward I reverse I Change of state (on off) required at t = t1 Desired response 1 t s t t t rr t 1.12 SEMICONDUCTOR DIODE NOTATION The notation most frequently used for semiconductor diodes is provided in Fig. 1.40. For most diodes any marking such as a dot or band, as shown in Fig. 1.40, appears at the cathode end. The terminology anode and cathode is a carryover from vacuum- tube notation. The anode refers to the higher or positive potential, and the cathode refers to the lower or negative terminal. This combination of bias levels will result in a forward-bias or “on” condition for the diode. A number of commercially available semiconductor diodes appear in Fig. 1.41. Some details of the actual construction of devices such as those appearing in Fig. 1.41 are provided in Chapters 12 and 20. 33 1.13 Diode Testing p n 1.13 DIODE TESTING The condition of a semiconductor diode can be determined quickly using (1) a digi- tal display meter (DDM) with a diode checking function, (2) the ohmmeter section of a multimeter, or (3) a curve tracer. Diode Checking Function A digital display meter with a diode checking capability appears in Fig. 1.42. Note the small diode symbol as the bottom option of the rotating dial. When set in this po- sition and hooked up as shown in Fig. 1.43a, the diode should be in the “on” state and the display will provide an indication of the forward-bias voltage such as 0.67 V (for Si). The meter has an internal constant current source (about 2 mA) that will de- fine the voltage level as indicated in Fig. 1.43b. An OL indication with the hookup of Fig. 1.43a reveals an open (defective) diode. If the leads are reversed, an OL indi- cation should result due to the expected open-circuit equivalence for the diode. In general, therefore, an OL indication in both directions is an indication of an open or defective diode. Figure 1.40 Semiconductor diode notation. or •, K, etc. Anode Cathode p n Figure 1.41 Various types of junction diodes. [(a) Courtesy of Motorola Inc.; and (b) and (c) Courtesy International Rectifier Corporation.] 34 Chapter 1 Semiconductor Diodes p n Ohmmeter Testing In Section 1.7 we found that the forward-bias resistance of a semiconductor diode is quite low compared to the reverse-bias level. Therefore, if we measure the resistance of a diode using the connections indicated in Fig. 1.44a, we can expect a relatively low level. The resulting ohmmeter indication will be a function of the current estab- lished through the diode by the internal battery (often 1.5 V) of the ohmmeter circuit. The higher the current, the less the resistance level. For the reverse-bias situation the reading should be quite high, requiring a high resistance scale on the meter, as indi- cated in Fig. 1.44b. A high resistance reading in both directions obviously indicates an open (defective device) condition, while a very low resistance reading in both di- rections will probably indicate a shorted device. Curve Tracer The curve tracer of Fig. 1.45 can display the characteristics of a host of devices, in- cluding the semiconductor diode. By properly connecting the diode to the test panel at the bottom center of the unit and adjusting the controls, the display of Fig. 1.46 Figure 1.44 Checking a diode with an ohmmeter. Figure 1.42 Digital display meter with diode checking capability. (Courtesy Computronics Technology, Inc.) Figure 1.43 Checking a diode in the forward-bias state. 35 1.14 Zener Diodes p n can be obtained. Note that the vertical scaling is 1 mA/div, resulting in the levels in- dicated. For the horizontal axis the scaling is 100 mV/div, resulting in the voltage lev- els indicated. For a 2-mA level as defined for a DDM, the resulting voltage would be about 625 mV  0.625 V. Although the instrument initially appears quite complex, the instruction manual and a few moments of exposure will reveal that the desired re- sults can usually be obtained without an excessive amount of effort and time. The same instrument will appear on more than one occasion in the chapters to follow as we investigate the characteristics of the variety of devices. 1.14 ZENER DIODES The Zener region of Fig. 1.47 was discussed in some detail in Section 1.6. The char- acteristic drops in an almost vertical manner at a reverse-bias potential denoted VZ. The fact that the curve drops down and away from the horizontal axis rather than up and away for the positive VD region reveals that the current in the Zener region has a direction opposite to that of a forward-biased diode. Figure 1.47 Reviewing the Zener region. Figure 1.45 Curve tracer. (Courtesy of Tektronix, Inc.) Figure 1.46 Curve tracer response to 1N4007 silicon diode. 36 Chapter 1 Semiconductor Diodes p n TABLE 1.4 Electrical Characteristics (25°C Ambient Temperature Unless Otherwise Noted) Zener Max Maximum Maximum Maximum Voltage Test Dynamic Knee Reverse Test Regulator Typical Nominal, Current, Impedance, Impedance, Current, Voltage, Current, Temperature VZ IZT ZZT at IZT ZZK at IZK IR at VR VR IZM Coefficient (V) (mA) () () (mA) ( A) (V) (mA) (%/°C) 10 12.5 8.5 700 0.25 10 7.2 32 0.072 This region of unique characteristics is employed in the design of Zener diodes, which have the graphic symbol appearing in Fig. 1.48a. Both the semiconductor diode and zener diode are presented side by side in Fig. 1.48 to ensure that the direction of conduction of each is clearly understood together with the required polarity of the ap- plied voltage. For the semiconductor diode the “on” state will support a current in the direction of the arrow in the symbol. For the Zener diode the direction of conduction is opposite to that of the arrow in the symbol as pointed out in the introduction to this section. Note also that the polarity of VD and VZ are the same as would be obtained if each were a resistive element. The location of the Zener region can be controlled by varying the doping levels. An increase in doping, producing an increase in the number of added impurities, will decrease the Zener potential. Zener diodes are available having Zener potentials of 1.8 to 200 V with power ratings from 14 to 50 W. Because of its higher temperature and current capability, silicon is usually preferred in the manufacture of Zener diodes. The complete equivalent circuit of the Zener diode in the Zener region includes a small dynamic resistance and dc battery equal to the Zener potential, as shown in Fig. 1.49. For all applications to follow, however, we shall assume as a first approx- imation that the external resistors are much larger in magnitude than the Zener-equiv- alent resistor and that the equivalent circuit is simply the one indicated in Fig. 1.49b. A larger drawing of the Zener region is provided in Fig. 1.50 to permit a descrip- tion of the Zener nameplate data appearing in Table 1.4 for a 10-V, 500-mW, 20% diode. The term nominal associated with VZ indicates that it is a typical average value. Since this is a 20% diode, the Zener potential can be expected to vary as 10 V  20% Figure 1.48 Conduction direc- tion: (a) Zener diode; (b) semi- conductor diode. Figure 1.49 Zener equivalent circuit: (a) complete; (b) approxi- mate. Figure 1.50 Zener test characteristics. 37 1.14 Zener Diodes p n or from 8 to 12 V in its range of application. Also available are 10% and 5% diodes with the same specifications. The test current IZT is the current defined by the  1 4 power level, and ZZT is the dynamic impedance at this current level. The maximum knee im- pedance occurs at the knee current of IZK. The reverse saturation current is provided at a particular potential level, and IZM is the maximum current for the 20% unit. The temperature coefficient reflects the percent change in VZ with temperature. It is defined by the equation TC  VZ (T  1 V  Z T0)  100% %/°C (1.12) where VZ is the resulting change in Zener potential due to the temperature varia- tion. Note in Fig. 1.51a that the temperature coefficient can be positive, negative, or even zero for different Zener levels. A positive value would reflect an increase in VZ with an increase in temperature, while a negative value would result in a decrease in value with increase in temperature. The 24-V, 6.8-V, and 3.6-V levels refer to three Zener diodes having these nominal values within the same family of Zeners. The curve for the 10-V Zener would naturally lie between the curves of the 6.8-V and 24-V de- vices. Returning to Eq. (1.12), T0 is the temperature at which VZ is provided (nor- mally room temperature—25°C), and T1 is the new level. Example 1.3 will demon- strate the use of Eq. (1.12). EXAMPLE 1.3 Figure 1.51 Electrical characteristics for a 10-V, 500-mW Zener diode. –0.12 0.01 Temperature coefficient – (%/˚C) Temperature coefficient versus Zener current –0.08 –0.04 0 +0.04 +0.08 Zener current, IZ – (mA) 0.1 1 10 100 0.05 0.5 5 50 C T (a) 3.6 V 6.8 V 24 V +0.12 1 0.1 Dynamic impedence versus Zener current Dynamic impedance, Z Z – ( )Ω 2 5 10 20 50 100 200 500 1 k Ω 2 0.2 5 50 100 10 1 20 0.5 6.8 V (b) 3.6 V 24 V Zener current, IZ – (mA) Determine the nominal voltage for the Zener diode of Table 1.4 at a temperature of 100°C. Solution From Eq. 1.12, VZ   T 1 C 0 V 0 Z (T1  T0) 38 Chapter 1 Semiconductor Diodes p n Substitution values from Table 1.4 yield VZ  (0.07 1 2 0 )( 0 10 V)  (100°C  25°C)  (0.0072)(75)  0.54 V and because of the positive temperature coefficient, the new Zener potential, defined by V Z, is VZ  VZ  0.54 V  10.54 V The variation in dynamic impedance (fundamentally, its series resistance) with current appears in Fig. 1.51b. Again, the 10-V Zener appears between the 6.8-V and 24-V Zeners. Note that the heavier the current (or the farther up the vertical rise you are in Fig. 1.47), the less the resistance value. Also note that as you drop below the knee of the curve, the resistance increases to significant levels. The terminal identification and the casing for a variety of Zener diodes appear in Fig. 1.52. Figure 1.53 is an actual photograph of a variety of Zener devices. Note that their appearance is very similar to the semiconductor diode. A few areas of applica- tion for the Zener diode will be examined in Chapter 2. Figure 1.52 Zener terminal identification and symbols. Figure 1.53 Zener diodes. (Courtesy Siemens Corporation.) 1.15 LIGHT-EMITTING DIODES The increasing use of digital displays in calculators, watches, and all forms of in- strumentation has contributed to the current extensive interest in structures that will emit light when properly biased. The two types in common use today to perform this function are the light-emitting diode (LED) and the liquid-crystal display (LCD). Since the LED falls within the family of p-n junction devices and will appear in some of 39 1.15 Light-Emitting Diodes p n the networks in the next few chapters, it will be introduced in this chapter. The LCD display is described in Chapter 20. As the name implies, the light-emitting diode (LED) is a diode that will give off visible light when it is energized. In any forward-biased p-n junction there is, within the structure and primarily close to the junction, a recombination of holes and elec- trons. This recombination requires that the energy possessed by the unbound free elec- tron be transferred to another state. In all semiconductor p-n junctions some of this energy will be given off as heat and some in the form of photons. In silicon and ger- manium the greater percentage is given up in the form of heat and the emitted light is insignificant. In other materials, such as gallium arsenide phosphide (GaAsP) or gallium phosphide (GaP), the number of photons of light energy emitted is sufficient to create a very visible light source. The process of giving off light by applying an electrical source of energy is called electroluminescence. As shown in Fig. 1.54 with its graphic symbol, the conducting surface connected to the p-material is much smaller, to permit the emergence of the maximum number of photons of light energy. Note in the figure that the recombination of the injected carriers due to the forward-biased junction results in emitted light at the site of re- combination. There may, of course, be some absorption of the packages of photon en- ergy in the structure itself, but a very large percentage are able to leave, as shown in the figure. Figure 1.54 (a) Process of electroluminescence in the LED; (b) graphic symbol. The appearance and characteristics of a subminiature high-efficiency solid-state lamp manufactured by Hewlett-Packard appears in Fig. 1.55. Note in Fig. 1.55b that the peak forward current is 60 mA, with 20 mA the typical average forward current. The test conditions listed in Fig. 1.55c, however, are for a forward current of 10 mA. The level of VD under forward-bias conditions is listed as VF and extends from 2.2 to 3 V. In other words, one can expect a typical operating current of about 10 mA at 2.5 V for good light emission. Two quantities yet undefined appear under the heading Electrical/Optical Char- acteristics at TA  25°C. They are the axial luminous intensity (IV) and the luminous efficacy (v). Light intensity is measured in candela. One candela emits a light flux of 4 lumens and establishes an illumination of 1 footcandle on a 1-ft2 area 1 ft from the light source. Even though this description may not provide a clear understanding of the candela as a unit of measure, its level can certainly be compared between sim- ilar devices. The term efficacy is, by definition, a measure of the ability of a device to produce a desired effect. For the LED this is the ratio of the number of lumens generated per applied watt of electrical energy. The relative efficiency is defined by 40 Chapter 1 Semiconductor Diodes p n Figure 1.55 Hewlett-Packard subminiature high-efficiency red solid-state lamp: (a) appearance; (b) absolute maximum ratings; (c) electrical/optical characteristics; (d) relative intensity versus wave- length; (e) forward current versus forward voltage; (f) relative luminous intensity versus forward cur- rent; (g) relative efficiency versus peak current; (h) maximum peak current versus pulse duration; (i) relative luminous intensity versus angular displacement. (Courtesy Hewlett-Packard Corporation.) the luminous intensity per unit current, as shown in Fig. 1.55g. The relative intensity of each color versus wavelength appears in Fig. 1.55d. Since the LED is a p-n junction device, it will have a forward-biased characteristic (Fig. 1.55e) similar to the diode response curves. Note the almost linear increase in rel- ative luminous intensity with forward current (Fig. 1.55f). Figure 1.55h reveals that the longer the pulse duration at a particular frequency, the lower the permitted peak current (after you pass the break value of tp). Figure 1.55i simply reveals that the intensity is greater at 0° (or head on) and the least at 90° (when you view the device from the side). 41 1.15 Light-Emitting Diodes p n Figure 1.55 Continued. Green Yellow GaAsP Red High efficiency Red T = 25˚C A Relative intensity Wavelength–nm 0 0.5 1.0 500 550 600 650 700 750 (d) I – Forward current – mA 0 5 10 15 20 0 1.0 2.0 3.0 0.5 1.5 2.5 V – Forward voltage – V F I F T = 25˚C A (e) Relative luminous intensity (normalized at 10 mA) 0 1.0 2.0 3.0 0 5 10 15 20 I – Forward current – mA F (f) T = 25˚C A Relative efficiency (normalized at 10 mA dc) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 0 20 40 60 10 30 50 I – Peak current – mA peak (g) 1.0 10 100 1000 10,000 1 2 3 4 5 6 Ratio of maximum tolerable peak current to maximum tolerable dc current I max I max peak I dc I – t – Pulse duration – µs p p t T (h) 100 kH z 30 kH z 10 kH z 100 H z 300 H z 3 kH z 1 kH z 20˚ 60˚ 100˚ 40˚ 80˚ 0.2 0.4 0.6 0.8 0˚ 10˚ 20˚ 30˚ 40˚ 50˚ 60˚ 70˚ 80˚ 90˚ (i)