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Mir Publishers of Moscow publishes So- viet scientific and technical literature in twenty four languages including all those most widely used. Mir translates texts into Russian, and from Russian originals pre- duces books in English, German, French, Italian, Spanish, Portuguese, Czech, Slo- vak, Finnish, Hungarian, Mongolian, Ara- bic, Persian, Hindi, Tamil, Kannada, Viet- namese, Cari, Laotian, Khmer, Bengali, Marathi, and Telugu. Titles include text- books for higher technical and vocational schools, literature on the natural sciences and mediciré (including textbooks for me- dical schocis), popular science and _ scien- ce fiction. The contributors to Mir Publi- shers’ list are leading Soviet scientists and engineers frim all fields of science and technology, among them more than forty Members arid Corresponding Members of the USSR Academy of Sciences. Skilled translators provide a high standard of translation from the original Russian. Many of the titles already issued by Mir Publi- shers have been adopted as textbooks and manuals ‘at educational establishments in France, ‘Switzerland, Cuba, Syria, India, Brasil and many other countries. Mir Publishers’ books in foreign languages ean be purchased or ordered through book- sellers in your country dealing with VO “Mezhdunarodnaya Kniga’’, the authorised exporters,
The subject-matter of the book co- vers a wide range of material specific to electronics—from the basic prin- ciples underlying it to sophisticated devices employed in a multitude of applications. Among other things, there is a fairly detailed discussion of semiconductor materials and devices, electron tubes, photocells, optoelect- ronic devices, and integrated circuits. The text is liberally illustrated and includes a discussion of reliability and testing.
The book has been conceived as an aid in the study of electronics by college students, those relying on self-education, and hobbyists. »
Docent ivan P. Zherebtsov, Cand. (Pedagog. Sc.) taught electrical en- gineering and radio engineering at secondary educational establish- ments since 1928, has been lecturing on these subjects at colleges since 1946. Is a leading Soviet authority in the field of telecommunications. Has penned over 40 books and booklets many of which have been translated into foreign languages or published outside the Soviet Union. The most important of them are Radio Engi- neering (five editions), Basic Electro- nics (four editions), . Electric and Magnetic Circuits (two editions), An {ntroduction to UHF-SHT Radio En- gineering (three editions). Honorary member of the A.S. Popov S¢ientific and Technical Society on / Radio, Electronics, and Communicatjons. -
I. Zherebtsov
electronics
Basic Electronics
VM. II. Kepe6ron
OcHOBBI 3JIEKTPOHHKH
DueproaTomu3yzatT Jlenuurpay
|. Zherebtsov Basic Electronics
AREAS a
ces s' 9
Ne, Mir Publishers Moscow
First published 1988 Revised from the 1985 Russian edition
Translated from the Russian by Boris V. KUZNETSOV
Ha aneautickom A3b1Ke
Printed in the Union of Soviet Socialist Republics
ISBN 5-03-000021-6 © DSueproatomus3yar, 1985 BN 5 © English translation, Mir Publishers, 1988
Contents
Preface 9
Introduction 10
I-1 Electronics Defined 10
I-2 A Brief Historical Outline 10
I-3 Requirements for Electronic Components 13 I-4 Semiconductor Devices in Electronics 16
Part One. Semiconductor Devices 18
Chapter | Electric Conduction in Semiconductors 18
1-1 Electrons in Solids 18
1-2 Intrinsic Electron and Hole Conduction. Drift Current 20 1-3 Extrinsic Conduction 24
1-4 Carrier Diffusion in Semiconductors 26
Chapter 2 P-N and Metal-Semiconductor Junctions 28
2-1 A P-N Junction with No External Voltage Applied 28 2-2 The Forward-Biased P-N Junction 31
2-3 The Reverse-Biased P-N Junction 33
2-4 Thé Metal-Semiconductor Junction 34
Chapter 3 Semiconductor Diodes 35
1 The Current-Voltage Characteristic of the Semiconductor Diode 35 3-2 The Capacitance of a Semiconductor Diode 37 3-3 The Temperature Behaviour of Semiconductor Diodes 38 3-4 The Operation of the Diode at Load 39 3-5 Semiconductor Diodes as Rectifiers 41 3-6 Series and Parallel Connection of Diodes 45 3-7 The Pulsed Operation of Semiconductor Diodes 47 3-8 Basic Types of Semiconductor Diodes 48
Chapter 4 Bipolar Transistors 53
4-1 General Principles 53
4-2 Physical Processes ina Transistor 54
4-3 Amplification by a Transistor 59
4-4 The Basic Circuit Configurations of Transistors 61
4-5 Bias Supply and Temperature Compensation for Transistors 64 4-6 Transistors in Amplifiers and Oscillators 67
Chapter 5 Characteristics and Parameters of Bipolar 68 Transistors
5-1 Characteristics of Transistors 68 5-2 Parameters and Equivalent Circuits of Transistors 73
Contents
Chapter 6 Dynamic Operation of Bipolar Transistors
6-1 Calculation of Dynamic Operation of Transistors 80
6-2 The Effect of Temperature on the Performance of Transistors
6-3 The Frequency Behaviour of Transistors 88
6-4 Transistors as Switches 90
6-5 Frequency Changing by Semiconductor Devices 91 6-6 Inherent Noise in Transistors 95
6-7 Basic Types of Bipolar Transistors 97
Chapter 7 Field-Effect Transistors and Thyristors
7-1 Field-Effect Transistors 102 7-2 Thyristors 109
Chapter 8 Miscellaneous Semiconductor Devices
1 The Tunnel Diode 113
8-2: Microwave Semiconductor Diodes 117 8-3 Avalanche Diodes and Gunn Diodes 119 8-4 Heterojunction Devices 121
8-5 The Unijunction Transistor 122
8-6 Semiconductor Resistors 122
Chapter 9 An Outline of Integrated Circuits
9-1 General 123 9-2 Film and Hybrid Integrated Circuits 125 9-3 Monolithic Integrated Circuits 127
9-4 Charge-Coupled Devices and Integrated Injection Logic (I7L)
Chips 135
Part Two. Electron Tubes
Chapter 10 Behaviour of Electrons in Electric and Mag-
netic Fields 10-1 The Motion of Electrons in a Uniform Electric Field
10-2 The Motion of Electrons in a Nonuniform Electric Field
10-3 The Motion of Electrons in a Uniform Magnetic Field
139
142
143
Chapter 11 The Basic Structure and Operation of Electron
Tubes
11-1 A General Outline and Classification of Electron Tubes
11-2 The Basic Structure and Operation of the Diode 146 11-3 The Basic Structure and Operation of the Triode 148
11-4 Electron Emission 149 :
11-5 The Parameters of Thermionic Cathodes 152 11-6 Cathodes 152
11-7 Directly and Indirectly Heated Cathodes 154 11-8 Anode and Grid Types for Vacuum Tubes 156 11-9 Vacuum in Vacuum Tubes. Tube Envelopes 158 11-10 Electrode Mounting and Elctrode Leads 158
Chapter 12 Diodes
12-1 Physical Processes 160
12-2' The Three-Halves Power Law 162
12-3 The Current-Voltage Characteristic of a Vacuum Diode 12-4 The Parameters of the Vacuum Diode 163
145
163
80
102
113
123
145
160
Contents
12-5 Dynamic Operation of a Vacuum Diode. Rectification of Alternating Current 165 12-6 Diode Types 166
Chapter 13 Vacuum Triodes 167
13-1 Physical Processes 167
13-2 Current Division 170
13-3 The Virtual Voltage and the Three-Halves Power Law 171
13-4 Characteristics of the Vacuum Triode 172
13-5 The Operating Conditions, Absolute Maximum Ratings and Parameters of the Vacuum Triode 175
13-6 Grid Current 181
Chapter 14 The Vacuum Triode in Operation at Load 182
14-1 General 182
14-2 An Amplifier Stage Using a Vacuum Triode 183
14-3 Amplifier Stage Parameters 187
14-4 The Analytical Method and the Equivalent Circuits of an Amplifier Stage 189
14-5 Graphical Analysis of Triode Performance at Load 192
14-6 The Vacuum Triode as an Oscillator 195
14-7 The Interelectrode Capacitances of a Vacuum Triode 195
14-8 Common-Grid and Common-Anode Stages 198
14-9 Limitations of the Vacuum Triode 199
14-10 Basic Types of Receiving-Amplifying Vacuum Triodes 199
Chapter 15 Tetrodes, Pentodes and Miscellaneous Tubes 199
15-1 The Vacuum Tetrode 199
15-2 Secondary Electron Emission in the Vacuum Tetrode 202
15-3 The Pentode 203
15-4 Current Division in the Pentode 204
15-5 Connection of Tetrodes and Pentodes in Circuits 205
15-6 The Characteristics of Tetrodes and Pentodes 206
15-7 The Parameters of Tetrodes and Pentodes 208
15-8 The Interelectrode Capacitances of Tetrodes and Pentodes 210 15-9 The Beam Power Tetrode 210
15-10 The Characteristics and Parameters of the Beam Tetrode 211 15-11 The Dynamic Operation of Tetrodes and Pentodes 212
15-12 Variable-Mu Tubes 214
15-13 Basic Types of Tetrodes and Pentodes 215
15-14 Miscellaneous Tubes 215
Chapter 16 Cathode-Ray Tubes 217
16-1 General 217
16-2 The Electrostatic CRT 217
16-3 The Supply Circuits of the CRT 218
16-4 The Electron Gun of an Electrostatic CRT 220
16-5 Electrostatic Beam Deflection 222
16-6 Measurement and Visual Observation of Alternating Voltages with a Cathode-Ray Tube 223
16-7 Image Distortion in Electrostatic CRTs 225
16-8 The Magnetic CRTs 226
16-9 The Fluorescent Screen 229
16-10 Basic Types of CRTs for Oscilloscopes and TV = 232
16-11 Shaped-Beam Character Display Tubes 233
Chapter 17 17-1 17-2 17-3 17-4 17-5 17-6 17-7 17:8
Chapter 18 18-1 18-2
Chapter 19
19-1
19-2 19-3
19-4 19-5 19-6
Chapter 20 20-1 20-2 20-3 20-4 20-5 20-6
Chapter 21 21-1 21-2
Contents
Gas-Discharge and Indicator Tubes 234
Gaseous Discharges 234
Forms of Gaseous Discharge 235
Glow Discharge 236
Voltage-Regulator Tubes 240
Circuits Using VR Tubes 242
Glow-Discharge Thyratrons 244
Character Display and Numerical Readout Devices 246 Miscellaneous Gas-Discharge Devices 249
Tube Noise 250
Sources of Tube Noise 250 The Noise Performance of Vacuum Tubes 250
Operation of Vacuum Tubes at Microwave Frequencies 252
The Effects of Interelectrode Capacitances and Lead Induc- tances 252
Electron-Inertia Effects 253
Electrostatically Induced Currents in the Circuits of Vacuum Tubes 254
The Input Resistance of and Power Dissipation in Tubes 257 Tubes in Pulse Operation 260
Microwave Vacuum Tubes 261
Advanced Types of Microwave Tubes 263
General 263
The Drift-Tube Klystron 263
The Reflex Klystron 267
The Magnetron 270
Travelling-Wave and Backward-Wave Tubes 275 The Amplitron and the Carmatron 280
Reliability and Testing of Electron Devices 281
Reliability and Testing of Semiconductor Devices 281 Reliability and Testing of Tubes 283
Part Three. Photoelectric and Optoelectronic Devices _ 286
Chapter 22 22-1 290 22-3
Chapter 23 2344 93:2 9333 23-4 23-5 23-6 23-7 23-8
Conclusion
Index
Photoelectric Devices 286
Photoelectric Emission 286 Phototubes 287 The Photomultiplier Tube 288
Semiconductor Optoelectronic Devices 290
General 290
Bulk Photoconductors (Photoresistors) 291 Photodiodes 292
Semiconductor Photovoltaic Cells 293 Phototransistors 294
Photothyristors 295
Light-Emitting Diodes (LEDs) 296 Optocouplers (Optoisolators) 298
301 303
Preface
Advances in science and technology today are inseparably linked to major breakthroughs in electronics, among them the advent of basically new designs of electron devices, both tubes and semiconductor components. A person who wishes to be well versed in state-of-the-art electronics, must above all learn how such devices operate, what characteristics and parameters they have, and how they can be used in electronic equipment. All of these matters are taken up in this book which has been written as an aid for college students, those studying telecommunications on their own, and radio amateurs.
At this writing, the number of electron device types is too large to be covered in a single book. An attempt to do would have resulted in either an unwieldy collection of data or an inadequate or even very scanty description of many devices. Quite naturally, the author has left out devices used on a very limited scale, if available commercially at all.
Semiconductor devices are discussed first because they are the heart of the equipments and circuits that most of those concerned with electronics have to do with, and for them a discourse on electron tubes would have been unnecessary.
Special emphasis in the book is placed on the matters that the author believes to be especially important. Apart from a description of the devices as such, he touches upon some of their uses. Otherwise, the reader would have acquired an incomplete idea about the component side of electronics.
This is an English translation of the fourth Russian edition. As compared with its predecessors, it has been extended to include chapters on microelectronics, photoelectronics, and optoelectronics. More material has been added on semiconductor devices while the presentation of tubes has been curtailed. Only a very brief mention is made of the devices that have fallen out of use in electronics, such as gas-filled rectifier diodes, hot-cathode thyratrons, and some others.
I wish to express my gratitude to Docent G. A. Fedotov, Cand. Sc. (Tech.), for his very careful review of the manuscript and his valuable suggestions.
Undoubtedly, the criticism voiced by N. V. Parol and V. A. Terekhov on the previous editions has served to improve the encouragement that has come from other people, and to all these people I want to express a heartfelt “Thank you”.
I. Zherebtsov
Introduction
I-1 Electronics Defined
Electronics is a field of science and technology concerned with the study, design, and use of devices that depend on the conduction of elect- ricity through a vacuum, gas, or semiconductor.
For purposes of discussion it appears conven- ient to class it into physical electronics—the division that has to do with electron and ion processes occurring in a vacuum, gases, and semiconductors, and also at the interface be- tween a vacuum or a gas and a solid or liquid, and into electronic engineering which has to do with the design and use of the devices that depend for their operation on the above proces- ses. There is a special field called industrial electronics. As its name implies, it has to do with the design and use of electron devices in indus- trial applications.
Advances in electronics have largely been prompted by those of telecommunications, no- tably radio engineering. For this reason, it was at some time customary to call the two fields collectively as radioelectronics. Electron devi- ces are the basis of telecommunication equip- ment and have a direct bearing on its perfor- mance. On the other hand, many of the pro- blems that first arose in telecommunications later led to the advent of new and an improve- ment of existing electron devices. These devices are used in radio communication, television, sound recording and reproduction, radar, radio navigation, radiotelecontrol, and elsewhere. To this we should add the fact that electronics has penetrated other divisions of today’s science, technology, and industry. Electron devices are doing many jobs in automatic control, teleope- ration, wire (or line) communication, cinemato- graphy, nuclear engineering, rocketry, astrono- my, meteorology, geophysics, medicine, biology, physics, chemistry, metallurgy, mechanical en- gineering, measurement and instrumentation, etc.
Progress in electronics has been a big help to cybernetics — the science and technology concer- ned with the study of control and information flows in artificial and natural systems, and has also served as a basis for high-speed electronic computers. Without electronics, man would not have been able to explore outer space with his probes, artificial Earth satellites, space vehicles, and unmanned interplanetary stations.
Electron devices provide powerful tools for studies and measurements, notably those which have, as such, nothing to do with electronics. Among them are electronic amplifiers, oscilla- tors, rectifiers, oscilloscopes, and measuring instruments. Apart from research and automa- tic control, they come in useful in running a great variety of production processes. Electro- nics-based techniques have advanced our know- ledge about the properties of many substances existing in nature, provided a deeper insight into the structure of matter, and have brought us closer to a proper understanding of the laws that govern the material world.
I-2 A Brief Historical Outline
The foundations for electronics as we know it today were laid by physicists back in the 18th and 19th centuries. A big impetus was given by the electronic theory of metallic conduction developed by many outstanding scientists in the late 19th and the early 20th century.
In 1887, Heinrich Hertz of Germany, known for his experiments with electromagnetic waves, discovered the photoelectric effect. In 1888, Alexander Stoletov of Russia investigated Hertz’s discovery and formulated the laws of the photoelectric effect, thus breaking ground for the design and use of photoelectronic devices. Also in 1888. Vladimir Ulyanin of Russia built the first selenium photocells. It should be noted that it was not until 1904 that the photoelectric
Introduction 1]
effect was explained by Albert Einstein who worked on a theory that the radiant energy could only be transferred in discrete packets called photons.
The year 1883 saw the discovery of thermion- ic emission by Thomas A. Edison of the United States. In fact, it was first called the Edison effect. Unfortunately, Edison knew nothing about electrons and could not explain what he had observed. For the first time, an in-depth study of thermionic emission was made by O.W. Ri- chardson of Britain, who was the first to derive, in 1912, a thermionic electron emission equation based on the classical electronic theory of metallic conduction. (In 1923, S. Dushman ap- plied the quantum theory to this same problem and derived his own version of the thermionic electron emission equation.) In 1897, Karl Braun of Germany built the first cold-cathode ray tube.
The use of electron devices for radio com- munication began in 1904 when Sir John A. Flemming of Britain produced a vacuum hot- cathode diode tube to rectify (detect) electro- magnetic waves in radio receivers. He named his device a thermionic valve (for the reason that it permits only a unilateral flow of particles from the negative to the positive electrode, much as a mechanical valve does so to a flow of liquid or gas). For this device he obtained a patent in 1904—this was the first electron tube.
At about the same time, A. Wehnelt of Ger- many discovered and investigated the increased electron emission by wires given a coat of alkali-earth metal oxides. His discovery ultima- tely led to the use of what has come to be known as the oxide cathode widely employed in state- of-the-art electron tubes. In 1905, A. Hull of the United States invented the gas-filled rectifier diode, another important milestone in the pro- gress of electronics.
In 1906, De Forest of the United States made a discovery that is rated by many as one of the greatest engineering breakthroughs of modern times, the one that gave rise to the field of electronics. He observed that current flow in a diode could be controlled by the field produced by a grid of fine wires placed as a third electrode between the cathode and the anode (or plate). De Forest’s original “Audion”, as he called his invention, was the forerunner of the modern vacuum triode. In 1907, B. Rosing of Russia proposed to use a cathode-ray tube for image
reception and later proved the viability of his invention. This places him among the origina- tors of present-day television.
In 1909-1911, V. Kovalenkov of Russia built triodes adapted to service in long-distance teleph- one repeaters. A bit later, he added a second grid to the tube to produce a tetrode, that is, a four-electrode tube, which he likewise used in long-distance telephone repeaters. Similar four- electrode, or double-grid, tubes were built by Irving Langmuir of the United States somewhat later.
In 1913, Alexander Meissner of Germany (born in Vienna) was the first to use a vacuum triode as a self-excited vacuum-tube signal gene- rator involving feedback. This had a decisive influence on the progress of radio engineering, especially in Europe; until then, undamped high-frequency oscillations had been obtainable only by means of alternators coupled to frequ- ency multipliers or by utilizing the arc discharge as a type of negative resistance.
In Russia, the first triodes for the reception of radio signals were independently built by N. D. Papalexi and M.A. Bonch-Bruyevich in 1914- 1916. In 1918, Bonch-Bruyevich headed a team at the Nizhny Novgorod Radio Laboratory in Russia to develop high-power transmitting and low-power receiving tubes. Valuable contribu- tions were made by B.A. Ostroumov, A.M. Kugushev, N.A. Nikitin, and P. A. Ostryakov among many others.
In 1918-1919, Bonch-Bruyevich published his triode theory which played an important role in the design of vacuum tubes during the subse- quent years. He also advanced a theory that explained signal amplification by the vacuum triode. Similar works better known to the Western world were independently published by Heinrich Barkhausen. In 1911, he took over the chair of communications engineering in Dres- den where he founded the first institute on this subject in Germany. He made important con- tributions to the theory of nonlinear switching elements, formulated the electron-tube coeffi- cients (and the equations relating them) that are still in use, and wrote a four-volume text on electron tubes. About the same time, W. Schot- tky of Germany added what has come to be known as the screen grid to the tube, thus producing the screen-grid tetrode. Today it is mainly of historical interest, but it was an important step in the development of the pen-
1:2
tode, the most extensively used of all types of vacuum tubes.
Special mention should be made of the wa- ter-cooled high-power transmitting tube invent- ed by Bonch-Bruyevich and developed much later outside the Soviet Union. Important steps were demountable transmitting tubes devised by A.L. Mints, N.N. Oganov and A.M. Ku- gushev also at Nizhny Novgorod. A team under V. P. Vologdin came up with several designs of high-power mercury-vapour rectifier tubes.
Large-scale R & D work in the field of electro- nics went on in Leningrad. Among the leading figures there was A. A. Chernyshev who inven- ted the indirectly heated cathode in 1921.
In 1922, O.V. Losev at Nizhny Novgorod discovered that oscillations could be generated and amplified by a crystal (semiconductor) detector. He also observed the glow discharge at the detector’s contact. Unfortunately, his find- ings were not followed up, and the inventor himself died during the Leningrad Siege. For a long time, work in this field was limited to theoretical studies of semiconductors and the design of semiconductor rectifiers.
Beween 1920 and 1930, much headway in the field of electron devices was made outside the Soviet Union, In 1926, A. Hull of the United States made far-reaching improvements in the screen-grid tetrode and in 1930 he took out a patent on the pentode which is, as already noted, the most extensively used of all types of vacuum tube. Improvements were made in gas-filled rectifier diodes, and the thyratron (a gas-filled triode) was invented. The next decade saw an impressive number of important discoveries and inventions in the field of electronics. In 1930, L. A. Kubetsky of the Soviet Union invented the photomultiplier (also known as the electron multiplier) later radically improved and com- mercialized by S.A. Vekshinsky and P. V. Ti- mofeyev of the Soviet Union. In the United States, similar devices were produced by Farns- worth. In 1930-1931, A.P. Konstantinov and S.I. Katayev of the Soviet Union, working independently of each other, came up with the idea of television pick-up (camera) tubes. In the United States, Vladimir K. Zworykin engaged in investigations in the field of photoelectric emission and television. These studies led to his conception of a new type of television pick-up tube, the iconoscope, which he developed into a form suitable for practical picture transmission.
pi Introduction
Zworykin’s second major step towards all-elec- tronic television was the development of the kinescope or the television picture tube. All this had opened up broad vistas for rapid advances in the practical use of television.
In 1933, P. V. Shmakov and P. V. Timofeyev of the Soviet Union proposed the image ico- noscope (or the superemitron), a far more sensitive TV camera pick-up tube with which the scene to be televized needs no strong light- ing. In 1939, G. V. Braude of the Soviet Union proposed a still more sensitive TV camera pick-up tube later called the image orthicon. Also in the 1930s, experiments were made with very simple TV camera tubes known today as vidicons. Their concept was first proposed by A.A. Chernyshev in 1925. The first commercial image orthicons and vidicons appeared in the United States in 1946-1950.
Speaking of the Soviet effort in the field of electronics, another direction in which out- standing discoveries and inventions were made was work on microwave devices and circuits. In 1932, D. A. Rozhansky came up with the idea of using velocity modulation in microwave devi- ces. Following his suggestions, A. N. Arsenyeva and O. Heil built the first such devices to generate and amplify microwave oscillations. Later called drift-tube klystrons, they were also worked upon by R. Varian and S. Varian in the United States. In 1940, V. F. Kovalenko of the Soviet Union invented the simpler reflex klyst- ron which is now widely used to generate and amplify microwave signals.
In 1938-1941, E.N. Daniltsev, V.K. Khokh- lov, N.D. Devyatkov and M.D. Gurevich in the USSR designed disc-seal or planar-grid tubes for use in the UHF band. The active portions of the tube structure are in the form of planes or discs. Connections to the external resonators or cavities are made by means of metal rings attached to the disc electrodes. This principle was embodied in the metal-ceramic tubes made in Germany and in the lighthouse tubes that appeared at about the same time in the United States.
High power output in the microwave region is supplied by the magnetron, a version of the thermionic vacuum tube. The single-anode magnetron was initially investigated by A. W. Hull of the United States in 1921. His work was followed up by a large group of scientists in the Soviet Union (A.A. Slutsky, M.T. Grekhova,
Introduction 13
D.S. Steinberg, V.I. Kalinin, S.A. Zusmanov- sky, V.S. Lukoshkov, and S. Ya. Braude), Ja- pan (H. Yagi and K. Okabe), France (L. Bril- louin), Germany (E. Habann), and elsewhere. In the USSR, this type of tube as we know it today dates back, however, to 1936-1937 when V. F. Alexeyev and D.E. Malyarov developed what has come to be called the multicavity magne- tron. In the United States, the first high-power microwave magnetron was built by J.T. Ran- dall and H.A.H. Boot in 1940.
The 1930s and the later years saw a very rapid advance in semiconductor electronics. In the Soviet Union, especially valuable contributions in this field were made by a team of researchers under A.F. Ioffe in Leningrad. Their work covered physical processes in semiconductors, the effects of impurities on these processes, the thermoelectric and photoelectric properties of semiconductors, the rectification of alternating current by semiconductors, and many other issues. The theory of semiconductors formula- ted by the Ioffe school was later convincingly verified by experiments made in the Soviet Union.
Mention should also be made of B.I. Davy- dov who was the first to theorize on the rectification of alternating current at the me- tal-semiconductor junction. His theory was la- ter elaborated by W. Schottky of Germany. Ya. I. Frenkel came out with a quantum theory of semiconductors, proposed the concept of movable vacancies in the crystal lattice of semiconductors (later called ‘holes’), and formu- lated a theory explaining electron-hole: pair generation.
Also in the 1930s, copper-oxide and selenium rectifiers were commercialized in the Soviet Union. Ya.I. Frenkel, L.D. Landau, B.I. Da- vydov and some others formulated a theory to explain the generation of an emf by illuminated semiconductors. A team under A. F. Ioffe built semiconductor thermo-emf batteries which la- ter found a very broad field of application. Some of them could be put around the glass chimney of a kerosene lamp in order to generate electri- city in an amount sufficient to run a portable radio transmitter-receiver. Today’s space vehi- cles widely use as sources of electric power solar batteries which are assemblies of semiconductor thermocells.
In the 1940s, germanium and silicon diodes, semiconductor thermoresistors and photoresis-
tors were commercialized in the Soviet Union. In 1948, the first type of transistor, called the point-contact transistor, was officially announ- ced by V. Bardeen and W.H. Brattain of the United States. It was very much like the old familiar crystal detector but had two contacts known as cat whiskers that made contact on a small block of germanium. In the same year 1948, W. Shockley, also of the United States, invented what we know as the junction transis- tor, a semiconductor device which consists of a sandwich of alternate layers of n- and p-type germanium or silicon. In 1949, both the point- contact type and the junction type were put in production in the USSR.
In 1958-1960, a team under V.M. Tuchke- vich of the USSR designed and commercialized high-power silicon-controlled rectifiers and thy- ristors. Ten years later, the population of these devices all over the USSR totalled around 10 million units capable of handling between them about 500 million kilowatts of power. In 1959, V.M. Wald-Perlov and A.S. Tager of the USSR invented the avalanche transit time diode adapted to generating microwave oscillations.
In 1972, V.M. Tuchkevich’s team were awar- ded the Lenin Prize for heterojunction semicon- ductor devices, that is, devices using dissimilar semiconductor materials of opposite polarity. Their work had been greatly assisted by the contributions from Zh.I. Alferov of the Soviet Union.
Since then, many more discoveries and inven- tions have been made and embodied in practical devices. Some of them will be taken up in the text.
1-3 Requirements for Electronic Components
The various electron devices fall in the class of active electronic components because they can rectify, amplify, generate, and change the frequ- ency of a.c. signals and perform other active processes. In contrast, there are passive com- ponents, such as resistors, capacitors, inductors, and transformers. Whatever the class of a given electronic component, there are some general requirements that they must all satisfy to be fit for use.
Component manufacturers, standards or spe- cifications establish ratings—safe and limiting capabilities or conditions under which the com-
14 Introduction
ponents may be operated. These include nomi- nal (or rated) voltages, currents, power dissipa- tion, and the like. Since no component can be manufactured to have the precise rating, it is customary to specify also the respective to/eran- ces usually expressed as percentages, for examp- le, + 10%.
It is vitally important for electronic compo- nents to have ample reliability. This refers to the ability of any device, component, or circuit to perform a required function under stated con- ditions for a stated period of time. This may be expressed as a probability. ‘Time’ may be con- sidered as distance, cycles, or other appropriate units. Reliability characteristics are those quan- tities used to express reliability in numerical terms. Electronic items are usually approached from the viewpoint of failure, service life, main- tainability, and shelf life.
A failure refers to a complete or partial loss of the ability to perform a required function by a device, component, circuit, or any part or sub- system that can be separately tested.
Service life, or lifetime, is usually limited by the fact that some criterion (or criteria) of an item’s performance degrades with time to a point where the item may no longer be used at all or it may be used ina less critical application, say, for educational purposes.
Maintainability refers to the ability of a device, component, or circuit to be kept in proper operating condition. Since any piece or equipment is less than 100% reliable, it is ultimately necessary to repair and maintain it. Also, in systems of any complexity, certain trimming adjustments are necessary at various stages of operation. Thus, a vital consideration in the design of the components and equipments of a system is the question of how quickly and easily a unit in that system can be adjusted or repaired. However, semiconductor devices and electron tubes fall in the class of nonrecoverable items, that is, those which cannot be brought back to a normal service status after a failure. For them, maintainability should be construed as the adaptability of an item to an easy check and replacement.
Shelf life refers to the length of time under specified conditions that a component retains its usability. It is usually found by a shelf test designed to measure the retention of serviceabi- lity after storage or transit under specified conditions of temperature.
Quantitatively, reliability may be expressed in terms of several criteria. Most often, this is done in terms of the failure rate symbolized by the Greek letter ‘lambda’ (A). One of the definitions for the failure rate is as the ratio of the number n of like devices, components, etc., failing during an interval of time ¢, to the number N of devices, components, etc., operating at the start of the interval, multiplied by the time interval, or mathematically
X= n/Nt (I-1)
If the time is in hours, the unit of A will be the hour to the minus first power (that is, the reciprocal of the hour), h~‘. In other words, the failure rate may be defined as the fraction of components failing during one hour of opera- tion. For example, if the number of components under test is N = 1000, if they operated for t = 500 h, and two components failed in the meantime, the failure rate will be
A = 2/(1000 x 500) =4 x 10-6 h7?
Or in words, the reliability is such that four components out of a million may fail during one hour of operation.
Failure is ordinarily classed according to cause, suddenness, and degree. Thus, failure can be sudden or gradual, that is, unanticipated by prior examination or anticipated. In the latter case, the primary cause is ageing or wear-out. It can also be partial, complete, or intermittent. A complete failure renders the failing component totally unfit for further use. In the case of a partial failure, the failing component may be used subject to certain limitations. There are various causes of failure: misuse failure is attribu- table to the application of stresses beyond the stated capabilities of the item; inherent weakness failure is attributable to a weakness inherent in the item itself when subjected to stresses within its stated capabilities, this weakness being due to either a poor design or to a poor workmanship.
A failure that is both sudden and complete is termed catastrophic; one that is both gradual and partial is called degradation failure.
The failure rate A of an item varies during its lifetime (Fig. I-1). In the early failure (or shake- down) period, the failure rate starts from a relatively high value due to defects passed unnoticed during quality control or misuse during the early days of operation. This is what
Introduction 15
r t 0 500 1000 hours
Fig. I-1 Failure rate-vs-operating age (‘bathtub’) curve
is known as the infant mortality, and it decreases rapidly. Next comes the period when the item is in useful operation. This period lies between the end of the shakedown period and the advent of wear-out. During this time, the failure rate of mature, well-designed equipment is at a low, nearly constant value. This period is the useful life of the item. With the advent of wear-out, the failure rate increases rapidly due to degradation processes. In the failure rate curve, sometimes called the ‘bathtub’ curve, this interval is marked as the wear-out failure period. The reliability of electronic equipment degrades on aircraft and, especially, missiles. To avoid an early failure in use, a manufacturer will operate and test an item in a process known as burn-in; it stabilizes the item’s characteristics. The period when an item is in useful operation is labelled on the failure rate curve as the constant-failure rate period.
It is vitally important for electronic devices, components, and equipments to have an ade- quate resistance to various exposures and a good parameter stability. The list of hostile exposures is topped by temperature. Electronic components must be femperature-stable—this means that their parameters should remain as constant with changes in temperature as practi- cable. In most cases, an item will be heated by the current that is flowing through it, by nearby components, and by the ambient air. This is the reason why measures should be taken to shield an item against heat uptake and to withdraw excess heat from it (by cooling or with the aid of a heat sink).
The temperature stability of a component is usually stated in terms of the respective tempe- rature coefficient. For example, in the case of resistors one uses the temperature coefficient of resistance (TCR) which is defined as the incre- mental change in the resistance of a resistor as a result of a change in thermodynamic tempera- ture by one degree and is expressed in kelvins to
the minus first power:
TCR = AR/RAt (1-2)
where AR is the change in the resistance of the resistor caused by a change in temperature by At.
For example, if TCR = 5 x 10°* K™!, this means that heating a resistor by | K will change its resistance by 5 x 10~* ofits original value. If R = 10 kQ, this change will be 5 Q per kelvin of temperature increase.
Heat resistance and frost resistance refer to the highest and the lowest temperature at which an item is still capable of performing its assigned function normally and there will be no failure.
Moisture resistance refers to the ability of an item to resist exposure to atmospheric moisture (humidity). Where there is a risk of water ingress in an electronic equipment, the latter must be made water resistant or water-proofed. Pro- tection against humidity and water is provided by the use of protective films and other coatings and also by the encapsulation of components or even of a complete equipment.
Stability towards an elevated or a reduced pressure is important for electronic components that are likely to be used under such conditions. It is important to remember that the cooling of (the heat withdrawal from) an item is impaired as the ambient pressure goes down.
In some applications, it is important for electronic components to be chemically stable. This may be the case when an item is likely to be exposed to corrosive gases or fumes or when sea water is likely to get inside an item or an equipment.
If an equipment is to be used in a dust-laden atmosphere, such as may exist in a desert, the equipment itself and all of its components must be dust-proofed.
Radiation stability refers to the ability of an item to operate normally while being exposed to visible light or ionizing radiation. Unfortuna- tely, some semiconductor devices cannot stand up properly to radiation.
An important consideration is the resistance to mechanical influences. This includes shock resistance and vibration resistance. The latter is especially important for electronic equipments carried on board ships, aircraft, and rockets.
Special mention should be made of tropicali- zation which refers to some form of design or treatment to combat the fungi that ruin electro-
16 Introduction
nic equipment in hot, humid tropical regions and also to repel attack by some dielectric- eating insects. Thus designed or treated, the items are termed tropicalized.
There are several special requirements that must be met by electronic devices, components, circuits, and equipments. Among other things, they must be able to perform normally in a desired frequency range and show an adequate speed of response. This is the reason why the data sheet of an electronic item will usually specify its operating frequency or its frequency limit.
As a rule, electronic components should pre- ferably draw as little power from their power supplies as practicable (this is especially impor- tant for portable equipments) for their operation and also dissipate negligible power as heat.
Electronic elements are required to have a specified dielectric strength (also called electric strength, breakdown strength, and electric field strength). It is usually stated as the maximum voltage that the dielectric of a given item can withstand without rupturing. Sometimes, the respective maximum current or maximum po- wer may be stated by a maker.
It is always desirable that an electronic item should be as small in size and as light in weight as achievable at the present state of the art. The reason is that today’s electronic equipments pack each a very large number of components. This objective is currently achieved through miniaturization and microminiaturization. How- ever, this approach poses a problem: the smaller an item, the lower its power rating, that is, the maximum power it can safely dissipate.
Importantly, electronic devices, components and circuits must lend themselves readily to a streamlined technology. This quality is usually referred to as producibility in the manufacturing industries. Also, they should preferably be made by a process that can easily be mechanized and automated because the huge multitude of elec- tronic components turned out currently by their makers in amazing numbers cannot be fabrica- ted with sufficient accuracy and, especially, repeatability by hand. There is an obvious advantage in the attempts by some countries to adopt common standards.
The cost of electronic components is a crucial economic factor, but they must of necessity be manufactured to the most stringent quality requirements, so their production cannot but be cost-intensive.
I-4 Semiconductor Devices in Electronics
In its early days and for several decades that followed, electronics relied almost exclusively on vacuum and gas-filled tubes. For some time past, however, semiconductor devices have come to be the basis of state-of-the-art electro- nics in nearly all of its divisions. This is the reason why we will begin our study by dis- cussing semiconductor devices, and vacuum and gas-filled tubes will come in at a later time.
Crystal detectors which are radio-frequency semiconductor diodes have been in use in electronics since the advent of radio communi- cation. Copper-oxide and selenium rectifiers have been used to rectify alternating current. For all their past records, however, the principle by which crystal detectors and rectifiers operate remained unclear for a long time.
As compared with vacuum tubes, semicon- ductor devices have several important advanta- ges to offer, namely:
— They are light in weight and small in size.
— They need no heater (or filament) power.
— They have a higher reliability and a longer service life (tens of thousands of hours or even more).
— They are more robust mechanically (they readily stand up to vibration, impacts, and other mechanical factors).
— They have a far better efficiency because very little power is dissipated in semiconductor devi- ces themselves.
— They need low voltages for their operation. — They can be used in microelectronic circuits. — They are far more cheaper to make.
However, they are prone to some limitations, namely:
— The items in a single batch of semiconductor devices may widely differ in their parameters and characteristics.
— Their behaviour and performance are strong- ly temperature-dependent.
— With time the properties and parameters of some semiconductor devices degrade (due to ageing).
— Inherent noise is sometimes greater than it is in vacuum tubes.
— Many transistor types cannot be operated at high frequencies.
— The input resistance of many transistors is only a fraction of that of vacuum tubes.
— The useful power output of transistors is so
Introduction 17
far smaller than that supplied by tubes.
— The performance of most semiconductor de- vices is strongly degraded by exposure to ra- dioactive emissions.
Extensive work is under way in all industrial- ly advanced countries on improvements in semiconductor devices and on the use of novel, often unorthodox materials. Among the new additions to the electronic components on the market are semiconductor rectifiers for currents of thousands of amperes, transistors for frequen- cies of many hundred megahertz, and novel types of semiconductor devices capable of ope- ration at frequencies running in to the gigahertz region.
Transistors are able to operate in nearly every type of electronic equipment using tubes, except some microwave equipments. As of this writing, transistors are used in amplifiers, receivers, transmitters, oscillators, TV receivers, measur- ing instruments, pulse circuits, computers, and many other applications.
Semiconductor devices offer their users huge savings in power and a chance to cut down the size and weight of their equipments many times.
The minimum power needed to drive a vacuum tube is 0.1 W and more; for a transistor it may be as low as 1 pW, that is, 1/100000th of its previous value.
In semiconductor integrated circuits (ICs), a silicon chip a few square millimetres in area can hold hundreds and even thousands of transistors. With such IC chips, one can readily build computers containing many millions of integrated components.
Transistors are the heart of miniature radio receivers and transmitters. A single flashlight battery is quite enough to sustain operation of such a set for many hours. Miniature radio components have specially been designed for use as companions for semiconductor devices, and together they have led to the advent of extremely small electronic equipment. For exa- mple, there are transceivers built into a handset and driven by the voice of the man speaking into the microphone. There are superminiature tran- sistor radio transmitters enclosed with some other equipment into a capsule that can be swallowed by a patient and relay back data about his stomach and intestines.
Part One Semiconductor Devices
Chapter One Electric Conduction in Semiconductors
1-1 Electrons in Solids
It is proved in physics that electrons in a solid cannot possess just any arbitrary energy. Each electron can only have a particular discrete energy called an energy level.
The electrons closer to the atomic nucleus have lower energies, that is, they occupy lower energy levels. If we wish to move an electron away from the nucleus, we must overcome the mutual attraction between the electron and the nucleus, and this involves the expenditure of some energy. Therefore, the more distant elec- trons are more energetic, that is, they reside at higher energy levels.
When an electron moves from a higher to a lower energy level, it releases an amount of energy called a quantum; a quantum of electro- magnetic radiation is a photon. If an atom absorbs one quantum of energy, the electron moves from a lower to a higher energy level. Thus, the energy carried by electrons can only change portionwise, that is, in quanta.
The distribution of electrons among the ener- gy levels is usually shown on a diagram such as appears in Fig. 1-1. The horizontal lines drawn across the energy diagram represent each the energy W that an electron residing at that level has,
As has been proved by the band theory of
solids, the energy levels form closely spaced groups called energy bands or, simply, bands. The electrons occupying the external shell of an atom fill a number of energy levels that form what is known as the valence band. The valence electrons take part in electrical and chemical processes. The lower energy levels are included into other electron-filled bands, but these bands (omitted in the energy diagram) do not contri- bute anything to the process of electric conduc- tion.
Metals and semiconductors have a great number of electrons occupying the higher ener- gy levels. These levels constitute the conduction band, and the electrons filling it are referred to as conduction electrons. They are moving at ran- dom, or roaming, from one atom to another. It is conduction electrons that are responsible for the high electrical conductivity of metals.
Atoms that give up their electrons to the conduction band may be viewed as positive ions. They make up an ordered arrangement called the space lattice, the ion lattice, or the crystal lattice. The state of this lattice corres- ponds to an equilibrium between the forces of interaction among its atoms, when the total energy of all particles in a specimen takes on a minimal value. Inside the lattice, conduction electrons are moving in a haphazard way.
Figure |-la shows an energy level (or energy band) diagram for a metal. It is important to
W W ——<—<—=—————= | Conduction Conduction _——$$s——_———————— | band band Forbidden = band (band gap) Valence I val SS | Vole 0 (a) fo) (b) Fig. 1-1
Energy-level (or energy-band) diagram of (a) a metal and (4) a dielectric
Ch. 1. Electric Conduction in Semiconductors 19
(a)
N T>0
_4
(b)
Fig. 1-2 Electron distribution by energy levels in a metal
stress that the actual pattern of energy bands is far more complicated, it has a very great number »f energy levels, and the levels are distributed nonuniformly. If we write the maximum energy of electrons at absolute zero (T= 0) as W,, the energy diagram may be drawn up as it appears Fig. 1-2. The energy W is laid off horizontal- ». and the vertical segments represent the sumber N of electrons that have the energy shown (actually, there is a very great number of these vertical segments). The energy diagram in Fiz 1-2a corresponds to absolute zero. It shows ‘bat the number of electrons devoid of energy is zero. The higher the value of energy, the greater ‘be number of electrons having it. The maxi- um number of electrons have an energy equal to W,. The energy diagram in Fig. 1-26 is valid or a higher temperature. Now some electrons nave an energy exceeding W, and a proportion- ately lesser number of electrons have an energy ower than W,. The number of electrons having en energy in excess of W, decreases with nereasing energy. The higher the temperature of the material, the higher the maximum energy Ww.
Figure 1-la shows that in metals there is no zap between the conduction band and the -alence band. Therefore, even at normal tempe- rature a great number of electrons in metals nave an energy sufficient for them to pass from tbe valence to the conduction band. Practically every atom of a metal donates at least one ectron to the conduction band. Quite logically, ‘ne conduction electrons in metals are as nume- rous as the atoms.
The pattern of energy bands is different in electrics. In them, the conduction band is separated from the valence band by what is called a ‘forbidden band’, that is, one where no ©ectrons can reside (Fig. 1-15). The width, AW,
«the forbidden band, or the difference in energy »etween the top level of the valence band and
the bottom level of the conduction band, is a few electron-volts (eV). At normal temperature, the conduction band of a dielectric is populated by a very small number of electrons, and so the dielectric has a negligibly small electric conduc- tivity. On heating, however, some electrons in the valence band acquire an additional energy and jump into the conduction band so that the dielectric displays a noticeable conductivity.
For semiconductors, the pattern of energy bands is similar to that shown in Fig. 1-1, but the forbidden band is narrower than it is in dielectrics, being of the order of | eV in most cases. This is the reason why semiconductors behave as dielectrics at low temperatures while at normal temperature a substantial number of electrons jump from the valence to the conduc- tion band. Electric conduction in semiconduc- tors is discussed in more detail in the sections that follow.
At this writing, semiconductor devices are most often fabricated from germanium (Ge) and silicon (Si) both of which are four-valent sub- stances, This means that the outer shells of a germanium or a silicon atom have four valence electrons. The lattice of germanium or silicon consists of atoms bound together by valence electrons. This type of linkage is known as the covalent bond and is shown in Fig. 1-3. As is seen, each pair of atoms is orbited by two valence electrons shown as small filled circles or dots. In a two-dimensional view of the lattice (Fig. 1-4), the covalent bonds are shown as straight lines, and the shared electrons as small filled circles (or they may be omitted altogether). As is seen, each atom of a pair contributes one electron to the shared pair that constitutes an ordinary chemical bond.
20 Part One. Semiconductor Devices
Fig. 1-3 Covalent bonding between germanium atoms
Fig. 1-4 Two-dimensional model of the germanium crystal
lattice
1-2 Intrinsic Electron and Hole Conduction. Drift Current
In terms of electric conductivity,* semicon- ductors stand midway between conductors and dielectrics.
At T= 300 K, the electric conductivity of conductors is 10*-10° S cm~?. (As will be recalled 1 S cm™! is the electric conductivity of 1 cm? of a material.) The figure for dielectrics is less than 10~1° Scm™!, and for semiconductors it ranges from 107 !° to 10* S cm“ ?. As is seen, the electric conductivity of semiconductors ex- tends across a very broad range. Most substan- ces occurring in nature are semiconductors. At this writing, semiconductors used for commer- cial purposes include primarily germanium and silicon, and also gallium arsenide (GaAs), indi-
* Not to be confused with ‘electric conduction’, which is the ability of a material to transmit electricity. Electric conductivity is the numerical measure of electric conduction.
um antimonide (InSb), indium phosphide (InP), and some others.
Typically, semiconductors have a negative temperature coefficient of resistance. In other words, a rise in temperature brings about a fall in the resistance of semiconductors, and not the other way around as happens with most solid conductors. Also, the resistance of semicon- ductors heavily depends on their impurity con- tent and exposure to external factors, such as light, an electric field, an ionizing radiation, etc.
Semiconductor diodes and transistors de- pend for their operation on the fact that two types of electric conduction exist in semicon- ductor materials. Like metals, they show elec- tron conduction, that is, the flow of current due to the motion of conduction electrons. At ordinary operating temperatures, any semiconductor al- ways has conduction electrons which are only loosely tied to the atomic nuclei and are in a random thermal motion among the lattice atoms. When exposed to a potential difference, these roaming electrons can constitute an or- dered flow while retaining their roaming be- haviour. This additional flow is an electric current.
The other type of conduction displayed by semiconductors but nonexistent in metals is hole conduction. Since it is a distinction of semi- conductors, hole conduction deserves a more detailed discussion.
In a semiconductor atom, thermal or other factors may cause one of the valence electrons most distant from the nucleus to jump into the conduction band. As a result, the atom will acquire a positive charge numerically equal to that on the electron. This atom may be called a positive ion, It should be borne in mind, however, that in the case of the true ionic conduction, such as is observed in electrolytes, the current is constituted by the flow of ions (the very word ‘ion’ means ‘a traveller’). In hole conduction, an entirely different mechanism is involved —the crystal lattice of semiconductors is sufficiently strong, so its ions remain sta- tionary rather than move.
The vacancy left in the valence band of a semiconductor due to an electron being lost from the band by, say, thermal excitation has come to be known as a hole. Holes behave like positive charge carriers.
The way a hole is produced can be seen in Fig. 1-5 which is the already familiar two-di-
Ch. 1. Electric Conduction in Semiconductors 21
mensional model of a semiconductor. On re- ceiving an additional energy, one of the elec- trons contributing to a covalent bond becomes a conduction electron, that is, a charge carrier which is free to move about in the crystal lattice. As it does so, it leaves behind a vacancy, that is,
a hole shown as an open circle in the figure.
Under the influence of an applied potential difference (or electric field), a hole is caused to be propagated through the lattice, which is equi- valent to the motion of a positive charge. This process is depicted in Fig. 1-6 which shows several atoms of a semiconductor material at several instants. Let, at the initial instant (Fig. 1-6a), a hole be produced in the atom on the extreme left (/) due to its loss of an electron. The electron-deficient atom (shown shaded) is positively charged and can attract an electron from one of its neighbours (2). When an electric field (or a potential difference) is applied to the material, the field tends to move electrons from the negative towards the positive potential. Therefore, during the next instant (Fig. 1-65) one electron from atom 2 jumps into atom / and fills the vacant hole, while leaving a new va- cancy, or hole, behind in atom 2. Then an electron from atom 3 will jump into atom 2 to fill its vacant hole, thereby causing a further hole to appear in atom 3 (Fig. 1-6c), and so on. This chain of events will go on until the hole has moved from the atom on the extreme left to the atom on the extreme right. In this way, the positive charge originally produced in atom ! will have moved to atom 6 (Fig. 1-6f).
Thus, as we have seen, the electric current produced in the case of hole conduction is likewise due to the motion of electrons, but their motion is more limited than in the case of electron conduction. An electron can move from an atom only to its neighbour. Also, the effective movement of the hole due to a process of continuous exchange is in the direction of the positive field, that is, opposite to the direction of electron movement.
The situation we have just described may be likened to a concert-hall with rows of chairs occupied by spectators. Suppose that a spec- tator in the first row leaves his seat and a spectator from the row next behind him fills the vacant place. In turn, a spectator in the third row moves forward and occupies the vacant seat in the second row. Finally, a spectator from the last row moves forward to take up the vacant
Fig. 1-5 Electron-hole pair generation
‘©O©OOO “© © ©© © “*©@QO@QWO®O X®™@OO©OOD® *@ © ©@QOSW "©@OOOO®O
Fig. 1-6 Hole conduction
seat in the last-but-one row. Thus, the vacant seat originally left in the first row has finally moved to the last row. In this example, the spectators act similarly to the electrons and the consecutively vacated seats similarly to the holes in our previous example. Thus, the seats (that is, ‘holes’) remained stationary, and only the spectators (that is ‘electrons’) move in succession.
The best way to explain electric conduction in semiconductors is by reference to their energy band diagram (Fig. 1-7). As we know, the width of the forbidden band (band gap) in semi- conductors is relatively small (being 0.72 eV for germanium and 1.12 eV for silicon). At absolute zero, a semiconductor free from impurities is a dielectric —it has neither conduction electrons
22 Part One. Semiconductor Devices
Conduction band Forbidden band
( band gap)
Valence band
Fig. 1-7 Pattern of energy levels in a semiconductor
nor holes. As its temperature is raised, however, the semiconductor acquires an ever greater electric conductivity because heating imparts an additional energy to the electrons in the valence band, and an_ ever’ greater number of them cross the forbidden band and jump from the valence band into the conduction band. This is illustrated in Fig. 1-7 by a solid arrow. That is how conduction electrons are produced and electron conduction takes place. Each electron moving into the conduction band leaves behind in the valence band a vacancy, or a hole. In this way, the valence band acquires conduction holes, and their number is equal to that of electrons that have moved into the conduction band. Thus, electron conduction is accompa- nied by hole conduction.
Electrons and holes that can move and bring about electric conduction are called mobile charge carriers or simply charge carriers (or still simpler, carriers). It is customary to say that thermal excitation results in the generation of electron-hole pairs. Electron-hole pair genera- tion may likewise be brought about by light, an electric field, an ionizing radiation, etc.
Both conduction electrons and holes move in a random fashion, and this is responsible for a process which is the reverse of electron-hole pair generation. Conduction electrons eventually re- occupy vacancies in the valence band, that is, recombine with holes. Quite aptly, this oc- currence is referred to as electron-hole pair recombination. During this process, an electron moves from the conduction band into the valence band as shown by the dashed arrow in Fig. 1-7. Electron-hole pair generation and re- combination occur at the same time always. Recombination limits the increase in the num- ber of electron-hole pairs, so for each particular temperature of the material there is a certain definite number of each species. In this way,
their populations are in a state of dynamic equilibrium. To state this a bit differently, ever new pairs of electrons and holes are generated all the time, and those produced ‘earlier re- combine as continuously.
A semiconductor free from impurities is called an intrinsic, or i-type, semiconductor. It possesses intrinsic electric conduction which, as has been shown, is a combination of electron conduction and hole conduction. Importantly, although an intrinsic semiconductor has equal concentra- tions of electrons and holes under conditions of thermal equilibrium, electron conduction is pre- dominant. This is because electrons have a greater mobility as compared with holes. It is easy to understand why this is so: in the case of hole conduction, the electrons are more limited (less free) to move about than in the case of electron conduction.
The electric conductivity of a semiconductor depends on its carrier concentration which is defined as the number of charge carriers per unit volume, in practice usually quoted as a number per cubic centimetre.* One way to symbolize the carrier concentration is with the letters n (for ‘negative’) in the case of electron concentration and p (for ‘positive’) in the case of hole con- centration. Obviously, in an intrinsic semicon- ductor ni = Pj where the subscript “i” indicates that we refer to an intrinsic semiconductor.
One cubic centimetre of a metal or semi- conductor specimen has a number N of atoms of the order of 1077. At a temperature close to 20°C, the (approximate) carrier concentration
for pure germanium is 3
66299 1
n, =p, = 10? cm7 and for silicon, maip = 10° om?
Thus, at room temperature the ratio of mobile carriers to the total number of atoms in an intrinsic semiconductor is about 10°7% for germanium and about 10~1°% for silicon. In metals, the number of conduction electrons is no less than that of atoms (n > N). Therefore, the electric conductivity of semiconductors is a few millionths or even a few thousand-millionths of
* Some authors term this quantity as the carrier density.— Translator’s note.
Ch. 1. Electric Conduction in Semiconductors
that of metals. For example, the resistivity at room temperature is 0.017 x 10°*Q cm for copper, about 50 Q2 cm for germanium, and about 100000 Q cm for silicon (1 Q cm is the resistance of one cubic centimetre of a material).
If no voltage is applied to a semiconductor specimen, its conduction electrons and holes will be in a chaotic thermal motion, and there will of course be no net flow of current. When a potential difference is applied to a semiconduc- tor specimen, it sets up an electric field which accelerates the electrons and holes and imparts them some translational motion which consti- tutes what is known as the conduction current.
An alternative name for the motion of charge carriers under the influence of an applied field is drift, and the associated current is referred to as the drift current, iy, The total conduction cur- rent is the sum of the electron drift current i, 4,
and the hole drift current /, 4,:
(1-1)
Although electrons and holes move in op- posite directions, the two currents are added together because the motion of holes is in effect the motion of electrons. For example, in an intrinsic semiconductor i,4,=6mA, and i,.ar = 3 mA, and so the total or net conduction current is iy, = 9 mA.
In order to establish the factors that affect the net current, it is convenient to consider the current density rather than the current itself. Obviously, the drift (net) current density J4, is the algebraic sum of the electron and hole current densities
Jar = Inde + J
lar = Un ar cE 'p,dr
(1-2)
Since current density is defined as the ratio of the current to the cross-sectional area of the current-carrying medium per second, we may write the electron current density as
p.dr
(1-3)
J yar = nyeu, where n, is the concentration of electrons, e is the charge on an electron, and u, is the average velocity at which electrons move translationally under the influence of an applied field.
It is important to remember that the average velocity takes into account the random thermal motion of electrons during which they collide with the atoms of the lattice many times. During the time interval from one collision to another each electron is accelerated by the field, and so u,,
23
is proportional to the electric field strength E: (1-4) where pL, is a proportionality coefficient called
the electron mobility. Its meaning is easy to grasp if, using Eq. (1-4), we write
Un = Hy
H, = u,/E (1-5)
As follows from Eq. (1-5), when £ = 1, the electron mobility 1, is equal to the average velocity of electrons as they move under the influence of an applied electric field of unity strength. If we express the velocity in centi- metres per second and the field strength in volts per centimetre, the unit of carrier mobility will be
(em s~4)/(V cem~') = cm? V7! 57}
For example, at room temperature the elec- tron mobility for pure germanium is 3600 cm? V~!s~!. In other words, an electric field whose intensity is 1 Vcm~? will cause the conduction electrons in a specimen of pure germanium to move in the direction of the field with an average velocity of 3600 cm s~'. Elec- tron mobility is different for different semi- conductors and tends to decrease with rising temperature because the electrons collide with the atoms of the crystal lattice far more often.
On expressing the velocity in Eq. (1-3) in terms of p,£, we get
J nde ar nep,E (1-6)
The product ne, in Eq. (1-6) is the electron conductivity whose symbol is o,. Hence, Inde = OnE (1-7)
The relations and the reasoning given above may be extended to include conduction holes as
well. Then, the hole current density will be given by
J», dr = Pen ,E (1-8)
where the product pep, is the hole conductivity G,.
Pp
Hence, the total drift (net) current in an
intrinsic semiconductor is
Jar = NiehnE + PyehpE =(o, + 0,)E (1-9) and the total conductivity, o=6,+ 6, =n,e(H, + H,) (1-10)
Thus the conductivity of a semiconductor is a function of both the carrier concentration and
24 Part One. Semiconductor Devices
the carrier mobility. In semiconductors, a rise in temperature promotes electron-hole pair gene- ration, and the mobile carrier concentration builds up faster than their mobility decreases. As a result, a rise in the temperature of a semicon- ductor specimen leads to an increase in its conductivity. By way of comparison, it may be noted that in metals the conduction electron concentration is almost independent of tempe- rature, so a rise in the temperature of a metal specimen leads to a fall in its conductivity due to a decrease in the electron mobility.
It is also to be recalled that p,, <p, always, and so o, < 6, For example, at room tempera- ture p,, = 3600 cm? V~' s~* and p, = 1820 cm? V~' s~! for germanium, and up, = 1300 cm? V~'s-* and p, = 460 cm? V~' s“' for silicon.
1-3 Extrinsic Conduction
If a semiconductor contains other substances as impurities, it will display what may be called extrinsic conduction in addition to its intrinsic conduction. It depends on the type of impurity (or impurities) present, and may be electron or hole conduction. For example, if we dope (as it is said) pure germanium which has four electrons in its valence band with a controlled amount ofa donor element having five electrons in its valence band, such as antimony (Sb), arsenic (As), or phosphorus (P), under proper physical condi- tions, atoms of the impurity element will take the places of germanium atoms in their crystal lattice, and four of the five valence electrons will perform in the manner of the four germanium valence electrons they have displaced. But the fifth valence electron of the impurity atom will be free to move on and form conduction current. Antimony, arsenic, phosphorus and other ele- ments with five valence electrons are called donors because they donate electrons to the host crystal. On giving up their fifth valence electrons, the donor atoms become positively charged. How the above process takes places in the case of antimony as the donor impurity and a germanium crystal as the host is shown in the two-dimensional lattice pattern of Fig. 1-8.
Semiconductors showing a predominance of electron conduction are called n-type semicon- ductors. An energy band diagram for an n-type semiconductor is shown in Fig. 1-9. The energy levels of the donor atoms are situated only
Fig. 1-8 Mechanism of extrinsic electron conduction
Conduction band
Donor levels
Valence band
Fig. 1-9 Energy-band diagram of an n-type semiconductor
slightly below the conduction band of the host material. Therefore, one electron from each donor atom can readily jump into the conduc- tion band, and an additional number of elect- rons, equal to that of donor atoms, is added to that band. No holes are produced in the donor atoms as a result of this process.
Now consider the elements boron (B), indium (In), and aluminium (Al). Each of them has only three electrons in their respective valence band. When controlled amounts of any one of these elements are added to highly refined germanium (Ge), their atoms will displace germanium atoms in their crystal lattice. In this case there will be one incomplete bond on a neighbouring germa- nium atom. The missing electron constitutes a hole which may be neutralized electrically by an electron jumping into it from nearby bond and thus effectively moving the hole to a new position in the germanium specimen. Boron, indium, aluminium, and other impurity elements with three valence electrons are called acceptors
Ch, 1. Electric Conduction in Semiconductors
because they take on electrons from the crystal instead of donating them as do arsenic and antimony. On capturing these electrons, the acceptor atoms are charged negatively. The process we have just described is diagrammati- cally shown in Fig. 1-10.
Semiconductors showing a predominance of hole conduction are called p-type semiconduc- tors (Fig. 1-11). The energy levels of the accep- tor atoms are located only slightly above the valence band. The electrons from the valence band where holes are thus produced can readily jump into these levels.
Semiconductor devices are mostly made of semiconductor materials containing donor or acceptor impurities, and they are called extrinsic semiconductors. In such semiconductors all of the impurity atoms contribute to extrinsic con- duction at normal operating temperatures by donating or accepting an electron each as the case may be.
For extrinsic conduction to exceed intrinsic conduction, the donor atom concentration Ng or the acceptor atom concentration N, should exceed the intrinsic carrier concentration n,; = p;. In the practical manufacture of extrinsic semi- conductors, N, or Ng is always many times n; or p,. For example, in the case of germanium which has n; = p, = 10'* cm~? at room temperature, N., and N, may range anywhere between 101° and 10!§ cm~?, which is 10? to 10° times the intrinsic carrier concentration. In our subse- guent discussion, we will give examples for germanium at room temperature.
Thus, conduction in n-type germanium at ordinary temperature is by means of electrons supplied by the donor impurity. These excess electrons are spoken of as majority carriers. Conduction in p-type germanium at ordinary temperatures is by means of holes that are created when an acceptor impurity is added. Now the ‘doped’ germanium has an excess of these ‘missing negative charges’ in its atoms. Holes are thus in the majority, and in this situation they are called the majority carriers. The remaining carriers of opposite sign in each case are called minority carriers.
If N4>>7,, we may neglect the intrinsic carrier concentration (that is, that of electrons), and then 1* = Ng. Taking n-type germanium as an
\ . * Here and elsewhere the subscripts n and p refer, respectively, to n- and p-semiconductors.
N nN
Fig. 1-10 Mechanism of extrinsic hole conduction
Conduction band
Acceptor levels
Valence band
Fig. 1-11 Energy-band diagram of a p-type semiconductor example, n, may be about 107 '® cm~ 3. Clearly, as compared with this figure, one need not consider the intrinsic carrier concentration which is n, = 1013 cm™!, or by a factor of 1000 smaller.
The minority carrier concentration in an extrinsic semiconductor decreases in the same proportion as the majority carrier concentra- tion increases. Thus, if i-type germanium has n; = p; = 10'? cm~3, and doping it with a do- nor impurity increases the figure 1000-fold to n, = 10° cm~ 3, the minority carrier (hole) con- centration will fall to 1/1000th of its previous value to become p, = 10!° cm~3, which is one millionth of the majority carrier concentration. The explanation is that when the conduction electron concentration is increased 1000-fold due to the contribution from donor atoms, the lower energy levels in the conduction band are filled full, and electrons from the valence band can now jump only to the higher energy levels of the conduction band. For this ‘jump’ to occur,
26
however, the electrons must have a greater energy than they do in an intrinsic semiconduc- tor, and so much fewer electrons are capable of doing this. The number of holes in the valence band then decreases in about the same sizeable proportion. It has been found that n-type extrin- sic semiconductors always satisfy the following equality:
NPn = Nip, =n} = pt (1-11) In our example, 10© x 101° = (1013)? = 1076
Everything said about n-type semiconductors fully applies to p-type semiconductors. In them, N, > P;, and we may deem that p, ~ N,. For example, in the case of p-type germanium the figures may be p, = 10'° and n, = 10'° cm~?. For p-type semiconductors, the equality
Pplly = Nip; = Mi = PP (1-12)
also holds always.
As we have seen, even minute amounts of an impurity can drastically change both the type of conduction and the magnitude of conductivity of a semiconductor. Indeed, with as many as 4.4 x 107? germanium atoms enclosed in every cubic centimetre of the material, an impurity concentration of 10'® cm~? will amount to adding only one impurity atom to the four-odd million germanium atoms. That is, the impurity will account for as little as 10°*% of the total material. Nevertheless, the majority carrier con- centration is increased 1000-fold and the con- ductivity is improved in the same proportion.
The manufacture of semiconductors carrying such negligible and closely controlled amounts of an impurity is a very sophisticated process. On top of that, the host material must be extremely pure—for germanium the tolerance on any unwanted impurities is not over 107 8% which works out to not more than one atom per 10 thousand million germanium atoms. In sili- con, the unwanted impurities may be present in an amount not exceeding 10°''% which is a still tighter tolerance.
The electric conductivity of extrinsic semicon- ductors is determined in the same way as for intrinsic semiconductors. If we neglect the con- ductivity due to the minority carriers, then we may write for n-type and p-type semiconductors,
o, =n,eu, and o, = p,eH, (1-13)
Part One. Semiconductor Devices
Fig. 1-12
Current in (a) an n-type semiconductor and (db) a p-type semiconductor
Consider the flow of current through each type of semiconductor, while neglecting the current due to the minority carriers for simpli- city. As before, Fig. 1-12 shows holes as open (unshaded) circles, and electrons as filled circles (or dots). The “+” and “—” signs indicate the polarity of charge on the atoms of the crystal lattice. When an emf is applied from an external source to an n-type semiconductor, it causes conduction electrons to move both in the wires connecting the specimen to the emf source and in the specimen itself. In a p-type semiconductor an applied emf will likewise cause electrons to move in the connecting wires, but the current in the semiconductor should be regarded as the motion of holes. The electrons coming from the negative side fill the holes, and the positive side receives the electrons arriving there from the adjacent regions of the specimen where holes are thus produced, and they move from the right- hand to the left-hand side of the specimen (in the picture).
In electrical engineering, it is customary to think that an electric current flows from a “+” terminal to a “—” terminal. When considering electron devices, it is convenient to consider the actual direction of current flow—from the “—” to the “+” terminal. We will indicate this direction by an arrow with a bold dot at the start, and the assumed (or conventional) direc- tion by an arrow without a dot.
1-4 Carrier Diffusion in Semiconductors
The carriers present in a semiconductor move by one of two mechanisms, drift or diffusion. Drift, as we have just seen, is the motion caused by the presence of an electric field—due to the
Ch. I. Electric Conduction in Semiconductors 27
field, the carriers acquire a directed component of motion. The sum of the directed components of drift constitute what we have called the drift current in the specimen. But carriers also move by the process of diffusion, giving rise to the diffusion current. Its cause is the difference in carrier concentration and not in potential be- tween different parts of a specimen.
If the carriers in a specimen are distributed uniformly, we have an equilibrium carrier con- centration. Some external factors may upset this equilibrium concentration so that it is higher in one region and lower in some other (a nonequi- librium concentration). For example, if we throw a beam of light on some part of a semiconductor specimen, more electron-hole pairs will be gene- rated there, and this will produce what is known as an excess concentration.
Since carriers always have a kinetic energy of their own, they always tend to move from regions of high concentration to regions of low concentration until it is the same throughout the specimen.
Diffusion is likewise displayed by species other than mobile charge carriers. It is a proven fact, for example, that molecules do diffuse in many substances. Whatever the kind of species involved, however, the cause of diffusion is always the same-—a difference in species con- centration between various regions in a sample, and the diffusion itself is effected at the expense of the energy that the species involved possess due to thermal motion or excitation.
Similarly to the conduction current, the diffu- sion current, symbolized as ig;-, may be consti- tuted by electrons or by holes. The respective densities are given by
Jn ai¢ = @D,An/Ax and Jy aig = —eD,Ap/Ax (1-14)
where the terms An/Ax and Ap/Ax are referred to as the concentration gradients, and the quanti- ues D, and D, as the diffusion coefficients.
The concentration gradient is a measure of the difference in carrier concentration (free electrons or holes) from point to point in a semiconductor per unit length. The greater the change in electron or hole concentration, An or Ap, over the distance Ax, the greater the diffu- sion current. No diffusion current exists when An = 0 or Ap = 0.
Fig. 1-13
Motion of holes in the presence of a concentration difference
The diffusion coefficient is a measure of the rate at which the process of diffusion occurs. It is proportional to the carrier mobility, differs from one material to another, and is a function of temperature, or mathematically
D = ukT/e
where pt is the carrier mobility, k is the Boltz- mann constant, Tis the thermodynamic tem- perature, and e is the electron charge. It is ex- pressed in square centimetres per second. The diffusion coefficient of electrons is always grea- ter than that of holes. Taking germanium at room temperature, it is D, = 98 cm? s_! and D, = 47cm? s~'. For silicon, the respective figures are D, = 34 cm? s~* and D, = 12 cm? Se.
The “—” sign in the equation defining the diffusion current density for holes indicates that the hole current is flowing towards a region of lower hole concentration. This is explained in Fig. 1-13 which shows that when the hole concentration builds up with increasing x, the holes are moving in a direction which is opposite to the positive x-axis. Hence, the hole current must be taken as negative.
If we let some external factor produce an excess carrier concentration in some region of a semiconductor and then remove this factor, the excess carriers will recombine and propagate by diffusion to other regions of the specimen. The excess concentration will decrease exponen- tially, as shown in the plot of Fig. 1-14 for the electron concentration. The time during which the excess concentration is reduced by a factor of 2.7, that is, falls to 0.37 of its original value, no, is called the lifetime of nonequilibrium carriers, t,,. It describes how fast the excess concentration of carriers decreases.
Nonequilibrium carriers recombine both in- side the semiconductor and on its surface, and
28 Part One. Semiconductor Devices
the recombination rate strongly depends on the amount and kind of impurities present and the surface conditions. The value of t, for germa- nium and silicon may range from a fraction of a microsecond to hundreds of microseconds or even longer, depending on the circumstances.
When nonequilibrium carriers (say, electrons) propagate through a specimen by diffusion, their concentration likewise decreases with dis- tance exponentially due to recombination (Fig. 1-15). The distance L, over which the excess concentration of nonequilibrium (usu- ally, minority) carriers is reduced by a factor of 2.7, that is, falls to 0.37 of its original value no, is called the diffusion length. It describes how the excess concentration decreases with distance. In more rigorous terms, it is defined as the average distance that the minority carriers move in a homogeneous semiconductor between genera- tion and recombination.
Thus, the excess concentration decreases both with time and distance, and so the lifetime t, and the diffusion distance L, are interconnected by a relation of the form
L, = (D, t,)"? (1-15)
All we have said about excess electrons fully applies to excess holes, but t, and L, take on different values, of course.
Conduction current and diffusion current, electron-hole pair generation and recombina- tion, changes in the excess carrier concentration
exc
Fig. 1-14 Time variations in excess charge concentration
Fig. 1-15 Spatial variations in excess charge concentration
with time and distance do not exhaust the multitude of complex processes that take place in semiconductors, but they are most important and their knowledge permits a proper insight into the workings of semiconductor devices.
Chapter Two P-N and Metal-Semiconductor Junctions
2-1 A P-N Junction with No External Voltage Applied
The term junction in our case refers to the boundary, or the region of transition, between n-type and p-type semiconductor materials; hence the name a p-n junction. A p-n junction has an unsymmetrical conductivity or, which is the same, it has a nonlinear resistance. Most semiconductor devices (diodes, transistors, etc.) depend for their operation on the properties of one or several p-n junctions. Let us take a closer look at what happens in a p-n junction.
We assume that no external voltage is applied across the p-n junction (Fig. 2-1). Because the carriers in each semiconductor move about in a random manner due to thermal excitation (that is, they have their own velocities), they diffuse from one semiconductor into the other. As with any form of diffusion, such as in gases or liquids, the carriers move from a region of high concentration to a region of low concentration. For this reason, electrons diffuse from the n-type semiconductor where their concentration is high into the p-type semiconductor where their concentration is low. Conversely, holes diffuse
Ch. 2. P-N and Metal-Semiconductor Junctions 29
Fig. 2-1 P-N junction with no external bias applied
from the p-type semiconductor where their concentration is high into the n-type semi- conductor where their concentration is low. This process is shown by the arrows in Fig. 2-la. The circles labelled with the “+” and “_” signs represent the donor and acceptor impurity atoms charged positively and nega- tively, respectively.
As a result of the diffusion process described above, charges of opposite sign are produced on each side of the boundary between the n-type and p-type material, a positive charge in the n-region and a negative charge in the p-region. The positive charge in the n-region is mainly formed by the positively charged atoms of the donor impurity and, in part, by the holes that have come across the junction. The negative charge in the p-region is mainly formed by the negatively charged atoms of the acceptor im- purity and, in part, by the electrons that have come across the boundary. For simplicity, Fig. 2-la only shows the carriers and the im- purity atoms in the transition region.
What is known as the contact potential dif- ference
Veont = 9, ia: Q,
is produced between the two charges which give rise to an electric field (field intensity vector Esont)- Figure 2-1b shows a potential diagram for the p-n junction that we have taken as an example, assuming that no external voltage is applied across the junction. In this diagram which shows the potential distribution along the x-axis perpendicular to the p-n junction, the boundary layer is assumed to be at zero po- tential. In fact, we may have taken either the n-region or the p-region to be at zero potential. The diagram in Fig. 2-1! and in the subsequent figures is shown on an exaggerated scale for ease of visualization. Actually, the p-n junction is extremely thin in comparison with the n- or p-region.
Importantly, space charges of opposite signs are produced near the boundary between the n- and p-regions, while the positive potential ,, or the negative potential ¢, is the same throughout the n-region or p-region, respectively. If different potentials existed in different parts of, say, the n- or p-region, this would produce a current which would finally equalize the potential throughout the respective region all the same. It should be remembered that charge and potential have a different physical meaning. A region at some potential need not necessarily possess a charge.
Thus, each kind of charge finds itself sur- rounded by charges of opposite sign, and re- combination takes place. Figure 2-la shows the junction after diffusion and recombination have happened. The boundary region soon becomes devoid of holes on the p-side and of electrons on the n-side. The result is an accumulation of positive charges at the border on the n-side and of negative charges on the p-side of the border. These are called bound charges by some authors. They are positive and negative ions that cannot move about. Two equal and opposite charges separated a small distance are called a dipole, and in this situation there is what is called a dipole layer. Such a layer is present in all p-n junctions.
Free electrons on the n-side cannot go over to the p-side because of the opposing forces of its negative ions, and free holes on the p-side cannot go over to the n-side because of the opposing forces of its positive ions.
As is seen, a potential barrier is produced in the p-n junction, preventing any further dif- fusion of carriers into the opposite regions. Figure 2-15 shows a potential barrier for elec-
30
trons which tend to move by diffusion from left to right (from the n- to the p-region). If we lay off the positive potential upwards, we can plot an image of a similar potential barrier for holes tending to diffuse from right to left (from the p- into the n-region).
The height of this barrier is equal to the contact potential difference and usually is a few tenths of a volt. The higher the impurity con- centration, the greater the majority carrier den- sity, and the greater the number of majority carriers that are capable of diffusing across the boundary. The space charge density increases, and the contact potential difference v,,,,, goes up, which is another way of saying that the potential barrier builds up. At the same time, the thickness d of the p-n junction is reduced because the respective space charges are formed in boundary layers of a progressively smaller thickness. Assuming an average impurity con- centration in the case of germanium, we obtain Ug4n, = 03-04 Vo and =d=107*- 10~° cm. At the high impurity concentrations produced in some semiconductor devices, Ucont © 0.7 V and d= 10° cm.
The diffusion of majority carriers across
the junction is accompanied by the reverse migration of carriers under the influence of the electric field.set up by the contact potential difference. This field moves holes from the n-region back into the p-region, and electrons -from the p-region back to the n-region. In Fig. 2-la, this drift of minority carriers is likewise shown by arrows. So long as the temperature of the specimen and of the sur- roundings remains unchanged, the p-n junction resides in a state of dynamic equilibrium. A definite number of electrons and holes diffuse every second across the boundary in the op- posite directions, and as many of them are caused to drift by the field in the respectively reverse directions.
It is easy to think up a mechanical analogy of the process if we imagine that Fig. 2-1b shows a hill, and liken electrons to balls that go up this hill at various velocities corresponding to the thermal velocities of electrons. As they move uphill due to their initial velocities, the balls gradually slow down until they come to a complete stop at some definite height, and then roll downhill by gravity. This analogy holds for holes as well.
We have defined the motion of carriers due to
Part One. Semiconductor Devices
diffusion as the diffusion current i,;-, and the motion of carriers due to the action of the field as the drift current i,,. In a steady state, that is, in a state of dynamic equilibrium, the two currents are equal in magnitude and opposite in sign. Therefore, the net current across the p-n junc- tion is zero, as it should be so long as no external voltage is applied to it. The two components may take on a range of values, depending on the carrier concentration and mobility. The height of the potential barrier is always such that a state of equilibrium is established. In other words, the diffusion current and the drift current completely balance out each-other. This can be proved as follows. Suppose that for one reason or another (say, a rise in temperature), the rate of diffusion goes up. This will bring about an increase in the diffusion current, because a greater number of carriers will diffuse across the boundary. This will in turn build up the space charges and potentials on both sides of the boundary, the contact potential difference v,,., will rise, and this will mean that the electric field across the junction will gain in strength and a higher potential barrier will result. However, an increase in the field strength brings about a proportionate increase in the drift current, that is, in the reverse migration of carriers. So long as igig Femains greater than i,,, the potential bar- rier will go up in height. In the long run, however, the increase in /,, will make it equal to igi¢s ANA Veoy Will cease building up.
Figure 2-1c shows the distribution of carrier concentration in a p-n junction. This pattern is typical of germanium. Since the concentrations of majority and minority carriers differ by about six orders of magnitude or even more, the concentrations are laid off vertically on a loga- rithmic scale. The impurity concentrations in the n- and p-regions are ordinarily different. Exactly such a case is shown in Fig. 2-Ic. It is taken that the majority and minority carrier concentrations respectively are n, = 10'8 cm~3 and p, = 10° cm~? in the n-type material, while for the p-type material where the impurity concentration is lower the respective figures are p, = 10'° cm~? and n, = 10'° cm~*.
As is seen, the electron concentration in a p-n junction gradually varies from 1018 to 10'° cm~3, and that of holes changes as gra- dually from 101° to 108 cm~>. As a result, what is known as the depletion region is formed at the interface between the two types of semicon-
Ch. 2. P-N and Metal-Semiconductor Junctions 31
ductor. For example, at the very boundary, the electron concentration is 10'* cm~? which is 1/10 000th of the figure in the v-region, and the hole concentration is 101? cm~? which is like- wise 1/10 000th of the figure in the p-region. Obviously, the electric conductivity of the p-n junction must be a minute fraction of what it is in the remaining parts of the n- and p-regions.
The depletion region may alternatively be looked upon as an outcome of the action produced by the electric field which is set up by the contact potential difference. This field push- es mobile carriers from the boundary layers so that the electrons: are moved into the n-region and the holes into the p-region.
This depletion region is also known as the barrier region. It has an extremely high re- sistance in comparison with the remaining por- tions of the n- and p-regions.
2-2 The Forward-Biased P-N Junction
Let an external voltage source be connected with its positive terminal to the p-type se- miconductor and with its negative terminal to. the n-type semiconductor that make up a p-n junction (Fig. 2-2a). This is called forward bias- ing, and the voltage producing it is referred to as the forward bias voltage v,.
With forward biasing, the applied potentials establish an electric field which drives the maj- ority carriers of each region towards the jun- ction, thereby giving rise to the forward current, i, across the junction. This process is explained in Fig. 2-25. (In this and the subsequent figures the potential diagram is shown simplified. Whatever happens in other parts of the circuit is of no interest as regards the p-n junction. Therefore, the diagrams do not show variations in potential along the n- and p-regions which implies that their resistance is arbitrarily assu- med equal to zero. Nor do they show variations in potential at the contact of the n- and p-regions with the electrodes to which the wires from the voltage source are connected.)
The electric field set up in the p-n junction by the forward biasing voltage opposes the field due to the contact difference of potential. To reflect this fact, the vectors E.,,, and &; are shown pointing in the opposite directions. The resultant field is weakened and the potential difference at the junction is brought down which is another way of saying that the height of the
Fig. 2-2 Forward-biased p-n junction
potential barrier is reduced while the diffusion current builds up because a greater number of carriers can overcome the reduced barrier. At the same time, the drift current remains nearly unchanged because it mainly depends on how many minority carriers from the n- and p-tegions are able to reach the p-n junction owing to their thermal velocities. If we neglect the voltage drop across the n- and p-regions, the voltage across the junction may be taken equal tO Ucont — Us. By way of comparison, the dashed line in Fig. 2-26 shows the potential diagram in the absence of an applied voltage.
As will be recalled, when no external voltage is applied to a p-n junction, i4;, and ij, are equal in magnitude and opposite in sign so that they cancel each other. With forward biasing, igig > gy and so the net current across the junction, that is, the forward current ip = laip — tgp > 0 (2-1) If, on the other hand, the barrier is brought down appreciably, the diffusion current will be many times the drift current, and we may deem that the forward current is approximately equal to the diffusion current, which is another way of saying that the current across a forward-biased junction is a purely diffusion current.
The introduction of excess charge carriers across the potential barrier reduced in height by forward biasing into the region where they are minority carriers is called the carrier injection. The region of a semiconductor from which such excess minority carriers are injected is called the emitter region or, simply, the emitter. The region
32 Part One.
into which excess minority carriers are injected is called the base region or, simply, the base. If the injected minority carriers are electrons, then the n-region of a semiconductor will be the emitter and its p-region, the base. With the injection of holes, the situation will be the other way around: the p-region will be the emitter, and the n-region will be the base.
As arule, the impurity concentrations and, in consequence, that of majority carriers in the n- and p-regions differ substantially. Therefore, the carrier injection is predominant from the region where these carriers are in majority. For examp- le, ifn, >> p,, the injection of electrons from the n-region into the p-region will greatly exceed that of holes in the reverse direction. Accor- dingly, the n-region will act as an emitter, and the p-region as a base, because the injection of holes is negligible by comparison.
Forward biasing reduces both the height of the potential barrier and the thickness of the barrier layer (that is, d, < d), so that its resistan- ce in the forward direction, Rr, falls to a very small value (from units to a few tens of ohms).
With no external voltage applied, the barrier potential v,,,, is just a few tenths of a volt. Therefore, the barrier height and the barrier resistance can be reduced to a very small value by applying as small a forward bias voltage (a few tenths of a volt). This is the reason why a heavy foward current can be produced with a very low forward bias voltage.
Obviously, there must be some forward bias voltage at which no potential barrier will be left in a p-n junction at all. Then the junction resistance, that is, the resistance of the barrier layer, will fall close to zero, and it may be neglected. In the circumstances, the forward current will be solely a function of the resistan- ces of the n- and p-regions of the specimen. These resistances may no longer be neglected because they determine the magnitude of current across the junction. An example will illustrate this point best of all.
Suppose that in a forward-biased diode (for when an n-type and a p-type semiconductor are alloyed together, they form a single unit—a junction diode), the resistance of the barrier layer is 200 Q, and the resistance of the n- and p-regions is 5 Q each. Clearly, the total resistan- ce of the diode is 200 + 2 x 5 = 210 Q. This is very close to the resistance of the p-n junction alone, that is, 200 Q. At some forward bias
Semiconductor Devices
voltage the barrier disappears, the junction resistance falls to 0.5 Q, and the total resistance (0.5 + 2 x 5 = 10.5 Q) may now be approxima- tely considered to consist solely of two resistan- ces of 5 Q each. In other words, we may well neglect the resistance of the junction itself.
Now let us see how the forward current flows in the various parts of the circuit (Fig. 2-2a). Electrons leaving the n-region move across the, junction into the p-region, and holes leaving the p-region move across the junction in the oppo- site direction into the n-region. Thus, we have two currents flowing at the same time: an electron current and a hole current. Of course, only the electron current can flow in the external leads of the circuit. They travel from the “—” side of the applied voltage source to the n-region and make up for the loss of electrons diffusing across the junction into the p-region. From the p-region, electrons travel towards the “+” side of the applied voltage source, leaving more holes behind in the process. This chain of events goes on non-stop, and so the forward current is flowing all the time.
The electron current is at its highest at the left-hand edge of the n-region. On moving closer to the transition region, this current falls off because an ever greater number of electrons recombine with the holes travelling across the junction towards the electrons, but the hole current, i,, goes up. The total forward current, i;, will be the same at any section of the circuit:
ip = i, + 1, = const (2-2)
This stems from the basic law for a series electric circuit. The same current is flowing in all parts of such a circuit.
Because the thickness of the barrier layer is very small and it is heavily depleted of charge carriers, very few of them recombine there, and the current in the barrier layer remains unchan- ged. Past the barrier layer, however, the elect- rons injected into the p-region recombine with holes. Therefore, as we move farther away from the junction to the right, that is, into the p-region, the electron current i, keeps falling off, and the hole current i, keeps building up. At the right-hand edge of the p-region, the electron current is a minimum, and the hole current is a maximum. Figure 2-3 shows how these currents vary along the x-axis for the case when the electron current exceeds the hole current becau- se n, > p, and the electron mobility exceeds the
Ch. 2. P-N and Metal-Semiconductor Junctions 33
hole mobility. Of course, even in a forward- biased diode, the diffusion current is accompa- nied by the drift current produced by the motion of minority carriers, but it is negligibly small.
2-3 The Reverse-Biased P-N Junction
Now we will connect the “+” side of an external voltage source to the n-region and the “_” side to the p-region of a p-n junction, or diode (Fig. 2-4a). Thus connected, the junction is said to be reverse-biased. The applied reverse bias voltage v, causes a very small reverse current, i,, to cross the junction. Why this current is small can be explained as follows. The field set up by the reverse bias voltage combines with the field due to the contact potential difference. In Fig. 2-4a this is indicated by the fact that the vectors E,,,,, and £, point in the same direction. The resultant field gains in strength so that the height of the potential barrier now is Uo, + v, (Fig. 2-46). Even a small rise in the barrier puts an end to the diffusion of majority carriers across the junction so that i4;, = 0 because the initial velocities of the carriers are not high enough for the carriers to overcome the barrier. In contrast, the con- duction (drift) current remains nearly unchan- ged because it is mainly constituted by the minority carriers reaching the p-n junction from the n- and p-regions. The removal of minority carriers across a p-n junction by the accelerating electric field set up by the reverse bias voltage is called the carrier extraction.
Thus, the reverse current i, is the conduction current produced by the movement of minority carriers. The reverse current is very small be- cause minority carriers are small in number and, also, the resistance of the barrier layer in a reverse-biased p-n junction (or diode) is very high. The point is that a rise in the reverse bias voltage builds up the field at the junction, and a greater number of majority carriers are expelled by this field from the boundary layers on each side of the boundary into the n- and p-regions. Therefore an increase in the reverse bias voltage brings about an increase not only in the height of the potential barrier, but also in the thickness of the barrier layer (d, > d). The barrier layer is depleted of carriers still more, and its resistance goes up appreciably so that R, > R,.
Even a relatively low reverse bias voltage causes the reverse current remain at some practically constant value. This is because the
Fig. 2-3
Electron and hole current distribution in a p-n junc- tion
Fig. 2-4 Reverse-biased p-n junction
number of minority carriers is limited. A rise in temperature brings about an increase in their number so that the reverse current builds up but the reverse resistance goes down.
Let us take a closer look at how the reverse current behaves after a reverse bias voltage is applied. At first, this event gives rise to transients related to the movement of majority carriers. Electrons in the n-region move towards the “+” terminal of the applied voltage source, that is, away from the p-n junction. In the p-region, holes move away from the junction. At the “—” terminal, they recombine with the electrons still coming from the conductor con- necting this electrode to the “—” terminal.
Because electrons leave the n-region, it is charged positively due to an excess of positively charged donor impurity atoms. The p-region is charged negatively because its holes are filled by the electrons coming there, and it acquires excess negatively charged acceptor impurity atoms.
34 Part One. Semiconductor Devices
The movement of majority carriers in the opposite directions we have just described goes on for a small span of time. This short-duration current is not unlike the charging current of a capacitor. Two unlike space charges are pro- duced on either side of the p-n junction, and the entire system acts similarly to a charged capa- citor with a poor dielectric and with a leakage current (its role in our case is played by the reverse current). In accord with Ohm’s law, however, the leakage current of a capacitor is proportional to the applied voltage, but the reverse current across a p-n junction only slight- ly depends on the applied bias voltage. .
2-4 The Metal-Semiconductor Junction
In addition to p-n junctions, present-day semiconductor devices use arrangements in which a metal and a semiconductor are brought into contact. Such an arrangement is called a metal-semiconductor junction, The events taking place in metal-semiconductor junctions depend on what is known as the electronic work function which is defined as the minimum energy requi- red to liberate an electron from a metal or a semiconductor at absolute zero temperature. The lower*the work function, the greater the number ofelectrons that can break loose from the specimen. Let us see how this happens in several types of metal-semiconductor junctions.
If in a junction formed by a metal and an n-type semiconductor (Fig. 2-5a) the electronic work function of the metal, ®y, is lower than the electronic work function of the semiconductor, ®,, escape of electrons from the metal into the semiconductor will be predominant. Therefore, electrons (majority carriers) are accumulated in the semiconductor layer next to the interface, and this layer becomes enriched with electrons — it has an increased concentration of electrons. The resistance of this layer will be low with either forward or reverse biasing, and so it is not capable of conducting current in one direction only. This is a nonrectifying (or ohmic) contact. A similar ohmic (or nonrectifying) contact exists when a junction is formed by a metal and a p-type semiconductor (Fig. 2-5b) if ®, < My. In this arrangement, more electrons will leave the semiconductor for the metal than the other way around. Likewise, a region enriched with holes (majority carriers) and having a low resistance is
(a) <®,
(b)
(c)
Fig. 2-5 Metal-semiconductor junction (M stands for ‘metal’)
produced in the boundary region of the semi- conductor. The two types of ohmic contact are widely used when attaching electrodes to the n- and p-regions of a semiconductor device.
The situation is different in the metal-semi- conductor junction shown in Fig. 2-5c. Here, ®, < ®,,. In the circumstances, electrons mainly move from the semiconductor into the metal, and the region produced near the interface on the semiconductor side is depleted of majority carriers and so it has a high resistance. As a result, a relatively high potential hill is formed here, with a height markedly varying according to the polarity of the applied voltage. This type of junction has the property of unidirectional conduction or rectification. This class of junc- tions was originally investigated by W. Schot- tky of Germany, and the potential! hill appearing in such cases is called the Schottky barrier, and diodes utilizing it are called Schottky diodes. In the metal part of a Schottky diode, carrier storage (or the storage effect) is nonexistent in contrast to p-n junctions, and so Schottky diodes have a faster speed of response since there is no time lag associated with the storage time (defined as the time interval between the appli- cation of the reverse bias and cessation of the reverse current surge).
Similar rectifying properties are displayed when a metal is brought in contact with a p-type semiconductor, provided ®, < Dy.
Ch. 3. Semiconductor Diodes
wy) nN
Chapter Three Semiconductor Diodes
3-1 The Current-Voltage Characteristic of the Semiconductor Diode
Whatever the type of electron device, it is important to know how its current varies with the applied voltage. Knowing this relation, we can readily find the current for any given voltage or to find the voltage for any given current.
If the resistance of a device is constant and independent of current or voltage, the two quantities may be connected by a relation of the form
i=v/R or (3-1) i= Gv
As is seen, the current through a device is directly proportional to the applied voltage. The coefficient of proportionality is called the con- ductance
G=1/R
A plot relating current to voltage is called the current-voltage (volt-ampere) characteristic, or simply, the characteristic of a device. For a device obeying Ohm’s law, it is a straight line passing through the origin of coordinates (Fig. 3-1).
The higher the resistance R, the lower the conductance G and the smaller the current at the same given voltage. Therefore, at high values of resistance the characteristic makes a smaller angle with the axis of abscissas. The resistance Ris connected to this angle a by a relation of the
Fig. 3-1 Current-voltage characteristic of a linear device
form
R=v/i=kcota (3-2)
where k is a proportionality coefficient which takes care of the units in which the quantities used in the equation are expressed, and the scale to which they are laid off along the coordinate axes.
Alternatively, we may write
G=1/R=i/v=k tana
where k’ = 1/k.
It is to be stressed that it would be wrong to write R=cota or G=tana, because R and G are physical quantities that have particular dimensions and units with which they are expressed numerically, while tan a and cot a are trigonometric functions which are expressed only numerically. Also, the angle a may be different for the same value of R if we choose different scales on the axes. Devices obeying Ohm’s law and having a straight-line current- voltage characteristic passing through the ori- gin of coordinates are called /inear.
There are devices whose resistance depends on voltage or current rather than remains unvarying. The relation between their current and voltage is not so straightforward as the simple Ohm’s law, and their current-voltage characteristic is no longer a straight line passing through the origin of coordinates. Such devices are called nonlinear.
As already noted, when an n-type semicon- ductor is alloyed with a p-type semiconductor, they form a single unit called a junction diode. The nonlinear behaviour of such a diode is evident from reference to its current-voltage characteristic. As an example, Fig. 3-2 shows the current-voltage characteristic of a low-pow- er diode. As is seen, a forward current of several tens of milliamperes is produced when the forward bias voltage is a few tenths of a volt. Therefore, the forward resistance is usually not greater than several tens of ohms. In the case of higher-power diodes, the forward current is hundreds of milliamperes or even greater at the same forward bias voltage, and R, decreases to units of ohms or even less than that.
(3-3)
36 Part One. Semiconductor Devices
For the reverse current which is small in comparison with the forward current the cha- racteristic is usually plotted on a different scale than for the forward current, as this is done in Fig. 3-2. For low-power diodes, a reverse bias voltage of several hundred volts gives rise to a reverse current of units or tens of microam- peres. This corresponds to a resistance of several hundred kilohms or even greater. Since U, > vp, the two voltages are likewise laid off on different scales. Owing to this difference in scale, the curve has a kink or inflection at the origin of coordinates. If the same scale had been used, the curve would have had no kink.
The forward current characteristic shows an appreciable amount of nonlinearity because an increase in Uy leads to a decrease in the resistance of the barrier layer. Therefore, the curve runs with a progressively greater slope. At a voltage of a few tenths of a volt, the barrier layer practically disappears, and there remains only the resistance of the n- and p-regions, which may approximately be deemed constant. For this reason, the characteristic becomes almost linear. The small nonlinearity remaining here can be explained by the fact that the n- and p-regions are heated by the flow of current, and their resistance is thus brought down.
When the reverse voltage is raised, the reverse current first increases at a high rate. This happens because even at a low reverse voltage the rise in the height of the potential barrier brings about a sudden fall in the diffusion current which opposes the conduction (drift) current. In consequence, the total current, i, = = ig, — igi, abruptly goes up. Any further in- crease in the reverse voltage, however, entails only an insignificant rise in the reverse current. The current increases due to the heating of the junction by the current, due to the leakage over the surface, and also due to the avalanche multiplication of charge carriers, that is, the increase in the number of carriers as a result of impact ionization. Impact ionization consists in that at a high reverse voltage the electrons acquire a high velocity and, on striking the atoms of the crystal lattice, they knock out of it more electrons which are in turn accelerated and knock still more electrons out of the atoms. This process builds up with rising voltage.
At a certain value of reverse voltage, the p-n junction breaks down, leading to a sudden increase in the reverse current, and the resis-
40 30 20
10 -150 -100 -50
Ye VE
0 0.2 0.4 volts
pA i,
Fig. 3-2 Current-voltage characteristic of a semiconductor
diode tance of the barrier layer abruptly decreases. A p-n junction may suffer two kinds of breakdown, electric and thermal. The electric breakdown whose region is labelled by the letters ABC in Fig. 3-2 is reversible. This means that it does not cause irreversible changes in the junction (the structure of the material remains unchan- ged). Therefore, semiconductor diodes may be operated under conditions of an electric break- down. There are special diodes, sometimes called breakdown diodes, often used for voltage stabilization, which are designed to utilize the region BC of the characteristic.
Electric breakdown may in turn be classed into the avalanche type and the Zener type. Avalanche breakdown is caused by the cumula- tive multiplication of free charge carriers under the action of an applied field which brings about impact ionization and removal of electrons from the lattice atoms by the field. This type of breakdown is typical of thick p-n junctions produced at a relatively low impurity concen- tration in the host material. The breakdown voltage for avalanche breakdown is tens or hundreds of volts.
Zener breakdown is observed in a reverse- biased p-n junction that has a very high doping concentration on both sides of the interface. The built-in field is high (over 10° V cm~!) and the depletion (or barrier) region is narrow as a result of the high doping level. The application of a small reverse voltage (just a few volts) is sufficient to cause electrons to tunnel directly from the valence band into the conduction band
Ch. 3. Semiconductor Diodes 37
without changing their energy—this is the es- sence of what is known as the tunnel effect. In more detail, the tunnel effect is discussed in Chap. 8.
Thermal breakdown occurs within the region represented by portion CD of the curve in Fig. 3-2. This is an irreversible breakdown because it is accompanied by the destruction of the material at the p-n junction. Thermal break- down occurs when the amount of heat dissipa- ted at the junction due to the flow of reverse current exceeds the amount of heat withdrawn from the junction. Asa result, the temperature of the junction rises, its resistance decreases, and the current through the junction builds up. The junction is thus overheated and destroyed by heat. An alternative name of this occurrence is, quite aptly, thermal runaway.
3-2 The Capacitance of a Semiconductor Diode
As is noted in Sec. 2-3, a reverse-biased p-n junction is not unlike a capacitor with a marked leakage current through the dielectric. The depletion layer has a high resistance and acts as a dielectric on each side of which there are two unlike space charges, + Q, and — Q,, produced by the ionized atoms of the donor and acceptor impurities. Therefore, a p-n junction has a capacitance similar to that of a two-plate flat (plane-parallel) capacitor. It is called the deple- tion-layer or barrier capacitance. In the case of d.c. voltage, it is given by
Cy = 2/0, (3-4) and in the case of a.c. voltage, by C, = AQ,/Av, (3-5)
As with the capacitance of conventional ca- pacitors, the barrier capacitance increases with increasing surface area of the p-n junction, increasing permittivity of the semiconductor and decreasing thickness of the depletion layer. Although in low-power p-n diodes the p-n junction has a small surface area, the barrier capacitance is fairly large because the depletion layer is narrow while the relative permittivity of the material is rather high (in the case of germanium, s = 16). Depending on the surface area of the p-n junction, C, may range from units to hundreds of picofarads. A distinction of the barrier capacitance is that it is nonlinear —it
Cy | PF
‘ry
volts -40 -30 -20 -10 0
Fig. 3-3
Barrier capacitance as a function of reverse bias voltage
varies with changes in the voltage across the junction. When the reverse voltage is raised, the depletion layer broadens, and C, decreases. The manner in which Cj, varies as a function of v, is shown by the plot in Fig. 3-3. As is seen, a change in v, can bring about a three-fold change in C\,.
The barrier capacitance has a detrimental effect on the rectification of alternating current because it shunts the diode and thus provides a bypass for alternating current around it at high frequencies. However, the barrier capacitance can serve a useful purpose as well. For example, it is utilized in varicaps and varactors—p-n junction semiconductor diodes designed for low losses at high frequencies. They are used as tuning capacitors in tuned circuits and also in some other circuits which depend for their operation on the properties of nonlinear capa- citance. In contrast to conventional variable capacitors in which the capacitance is changed mechanically, in varicaps this change is brought about by varying the reverse voltage applied. This control of tuned circuits is called electronic tuning.
When forward-biased, a p-n junction has what is known as the diffusion capacitance, Cir, in addition to the barrier capacitance. It is likewise nonlinear and goes up with rising forward voltage, v,. The diffusion capacitance is associated with the accumulation of mobile charge carriers in the n- and p-regions when the junction is forward-biased. So it practically exists only when a p-n junction diode is forward- biased, and a large number of carriers diffuse (are injected) over the reduced potential hill and, since they have no time to recombine, are stored in the n- and p-regions. If we assume that in a p-n junction diode the p-region acts as the emitter and the n-region as the base, then forward
38 Part One. Semiconductor Devices
(e)
Fig. 3-4
Complete and simplified equivalent circuits of a semiconductor diode
biasing can cause a great number of holes* to move across the depletion layer from the p-region into the n-region so that a positive charge is produced in the n-region. At the same time, the d.c. voltage source causes electrons to move from the circuit conductor into the n-region and, as a consequence, a negative charge is formed there. The holes and electrons in the n-region cannot recombine instantaneously, and so for each value of for- ward voltage there is a certain value for the two equal but unlike space charges, + Q4;, and —Q4gir, Stored in the n-region owing to the diffusion of carriers across the junction. In the case of d.c. voltage, Cyjr is the ratio of charge to potential difference:
Caic = Qaie/Ye In the case of a.c. voltage, it is defined as Cai = AQagic/Avy (3-7)
As v, is raised, the forward current builds up
(3-6)
* The flow of electrons from the n-region into the p-region may be neglected in this case because n, K Pp:
at a faster rate than the voltage because the current-voltage characteristic of a forward- biased p-n junction is nonlinear. Therefore, Q4;- rises faster than v,, and Cg;, increases.
The diffusion capacitance of a p-n junction is appreciably greater than its barrier capacitance, but there is no way of putting it to any use because it is shunted by the low forward resis- tance of the diode itself.
Recalling that a p-n junction diode has a capacitance, we may draw up its a.c. equivalent circuit as shown in Fig. 3-4a. The resistance Ro in this diagram is the total, relatively small resistance of the n- and p-regions, their respec- tive electrodes and leads. When the diode is forward-biased, the nonlinear resistance R,,, is equal to Rr, that is, small. When the diode is reverse-biased, R,, = R,, that is, very high. This equivalent circuit may be simplified in many cases. At low frequencies the capacitive impe- dance is very high, and the diode capacitance may be neglected. Then the equivalent circuit will only include Ry and R, under forward bias (Fig. 3-45), or only R, under reverse bias (Fig. 3-4c) because Ry « R,. At high frequen- cies, capacitances present a relatively low im- pedance. Therefore, the equivalent circuit under forward bias will take the form shown in Fig. 3-4 d (if the frequency is not very high, Cy;- has practically no effect), while under reverse bias it also includes R, and C, (Fig. 3-4e).
We should also include the capacitance bet- ween, the diode leads, C),.g, which may mar- kedly shunt the diode at very high frequencies. It is shown by the dashed lines in the figure. At microwave frequencies, the lead inductance may also have some effect.
3-3 The Temperature Behaviour of Semiconductor Diodes
Temperature has an appreciable influence on the electric conductivity of semiconductors. As the temperature goes up, a progressively greater number of electron-hole pairs is generated, the carrier concentration is raised, and so is the conductivity. This can be clearly seen from the current-voltage characteristics plotted at diffe- rent temperatures. Figure 3-5 shows them for a germanium diode. As is seen, both the forward and reverse currents rise with increasing tempe- rature. The increase is especially noticeable in the reverse current due to the increased genera-
Ch. 3. Semiconductor Diodes 39
Fig. 3-5
Effect of temperature on the current-voltage cha- racteristic of a semiconductor diode
tion of electron-hole pairs. In germanium dio- des, the reverse current nearly doubles for every 10 degrees K rise in temperature. This can be written as
x Q(t— 20)/10 (3-8) Therefore, if the temperature goes up from 20°C to 70°C, the reverse current will increase 2° (that is, 32) times. Also, an increase in temperature brings down the breakdown voltage of germa- nium diodes.
In the case of silicon diodes, an increase of 10 degrees K in temperature brings up the reverse current by a factor of 2.5, while the breakdown voltage first increases somewhat with rising temperature, but then it falls off.
Heating does not raise the forward current of a diode in the same proportion as it does in the case of the reverse current. The explanation is that the forward current is mainly due to the extrinsic conduction, but the impurity concen- tration is temperature-independent.
A rise in temperature entails an increase in the barrier capacitance of the diode. The tempera- ture coefficient of capacitance, TCC, which expresses the ratio of the change in capacitance to the original value for a unit change in temperature, is 107? = 10°* K~?.
lay = 420°)
3-4 The Operation of the Diode at Load
In practical circuits, a semiconductor diode always operates into some kind of load, say, a resistor (Fig. 3-6a). In circuit diagrams, the anode of aerystal diode is shown as a triangle,
and its cathode as a bar. There is a flow of forward current when the anode is positive with respect to the cathode. Therefore, the triangle may be regarded as the arrowhead showing the conventional direction of forward current flow. It is the direction in which holes are moving under forward bias, while electrons are moving in the opposite direction.
The behaviour of a crystal diode in operation at load differs from that at no-load in several important respects. If the diode had a linear resistance, it would be a very simple matter to determine the current in such a case because the total resistance of the circuit is the sum of the d.c. resistance of the diode Ry and of the load resistance R,. Crystal diodes, however, are not linear resistances, and their Ry varies with changes in the current that flows through. Therefore, the current around the circuit con- taining a crystal diode operating at load is found graphically. The problem may be stated thus: We know E£, R, and the diode characteristic and we are to find the current around the circuit and the voltage across the diode.
The diode characteristic should be looked upon asa plot of an equation connecting current i and voltage v. For R,, a similar equation is Ohm’s law: i= v,_/R, = (E— v)/R,
(3-9)
Fig. 3-6
Connection of a diode and load in circuit and construction of the load line
40 Part One. Semiconductor Devices
Thus, we have two equations in two un- knowns, i and v, with one of the equations given graphically. To solve this set of equations, we need to construct a plot for the second equation and to locate the intersection of the two curves.
The equation defining R, is a Ist-degree equation written in terms of i and v. Its plot is a straight line called the /oad line. The simplest way to construct it is to use two points on the coordinate axes. On setting i = 0, we get from Eq. (3-9): E-—v=0 or
which corresponds to point A in Fig. 3-65. On setting v = 0, we get
i= E/R,
We lay off this current as ordinate (point B), and join the two points, A and B, by a straight line. Thus, we get the load line. The coordinates of point Q yield the solution of our problem. It is to be noted that all the other points on line 4B do not represent any operating conditions of the diode.
As an alternative, the load line can be con- structed by using the slope angle a, because
v=E
R, =k cot a
but this approach is less convenient because we would have*to find the coefficient k so as to account for the scales used and to recover the angle a from its cotangent.
When the load line is constructed for relati- vely small values of R,, point B may fall outside the drawing. If so, lay off an arbitrary voltage V to the left of point A (Fig. 3-6c) and, starting at point C thus obtained, lay off a current equal to V/R,, (segment CD). The straight line joining points A and D will then be the load line.
Sometimes, one may know v and i (point Q) and the load resistance R,, and one is to determine £. Or one may know E and is to determine the load resistance R,. We leave it as an exercise for the reader to construct the plots for these two cases. In either case, use Eq. (3-9) as the guide.
A circuit containing a series-connected diode and a linear load resistance R, is a nonlinear circuit. The characteristic of such a circuit, called the dynamic characteristic of the diode, that is, a plot of i as a function of EF, i= J (E), can be obtained by adding together the voltages taken from the characteristics of the
0 O58 1.0
1.5 2.0 volts Fig. 3-7 Dynamic (or load) current-voltage characteristic for
a circuit consisting of a series combination of a diode and a load resistor
diode and of the load resistance R, (Fig. 3-7). The characteristic of the load resistance is in effect Ohm’s law
i= vp/R,
and is a straight line passing through the origin of coordinates. It can be plotted as follows. Mark on the plot a point corresponding to an arbitrary value of vp and vp/R,. Join this point to the origin of coordinates by a straight line. In the previous cases, the load line did not pass through the origin of coordinates because it related the current to the voltage v across the diode and not to the voltage vp.
The dynamic characteristic of the circuit, i = = f(£), can be constructed by taking the sum of v and vp for several values of current because E=v-+0p. AS an example, at a current of 3 mA we have v=0.4 V and vg =0.5 V. Adding the two voltages together, we obtain on the resultant curve a point corresponding to E=0.9 V. Acting similarly, we locate other points and draw a smooth curve through them.
The behaviour of a series circuit mainly depends on the circuit section that has the highest resistance. Therefore, the greater the value of R,, the less the nonlinearity of the resultant characteristic. It is to be noted that the operation of the diode at load need not be determined graphically if R, > Ro. If so, it is legitimate to neglect the resistance of the diode and to determine the current approximately by the equation i= E/R,.
The techniques we have used to find the d.c. voltage E may be used to determine both the peak and any instantaneous values when the anode source supplies an alternating voltage.
Ch. 3. Semiconductor Diodes 4]
3-5 Semiconductor Diodes as Rectifiers
Rectification, or the conversion of alternating current into unidirectional or direct current, is one of the principal processes used in electro- nics.
Because semiconductor diodes have the pro- perty of unidirectional conduction (they con- duct well in the forward direction and poorly, if at all, in the reverse direction), most of them are quite logically used for a.c. rectification.
An elementary rectifier circuit is shown in Fig. 3-8a. It is a series connection of a generator that supplies an a.c. emf, e, a diode D, and a load resistor R,; which may alternatively be placed in the other lead (as is shown by the dashed symbol in the diagram). The diagram shows what has come to be called a half-wave rectifier for the reason that it produces a pulsating current by passing only half the input cycle of an alternat- ing current while the other halfis blocked by the diode. It is a single-phase rectifier because the emf source is likewise single-phase. There are more elaborate rectifier circuits (two-phase, three-phase, etc.), but they are in effect a combi- nation of several single-phase rectifiers.
In rectifiers used to energize electronic equip- ment, the a. c. source is usually a power transfor- mer plugged into an a.c. power supply line (the a.c. mains) (Fig. 3-85). Sometimes, autotrans- formers are used instead of transformers. In still other cases a rectifier may be connected to the mains directly, without any transformer. In practical applications, the role of the load resistor R, shown in the diagram of Fig. 3-8 is played by the circuits or devices that are powe- red by the rectifier. In the case of r. f. rectification (or, more correctly, r.f: detection), such as in the detector stages of radio receivers, the a.c. emf source may be anr.f. transformer or a resonant tuned circuit, and the load is a high-value resistor.
An elementary rectifier operates as follows. Let us agree that the generator (source) supplies a sinusoidal emf
e= E,, sinot
and that its internal resistance may be neglected (if it may not be neglected, the internal resistance of the emf source should be accounted for in the usual way). During one half-cycle the diode is forward-biased, a current flows through it and produces a voltage drop vz across the load
Fig. 3-8
(a) je
t
| | | | | | | | | | | lg
Em
Fig. 3-9 Explaining the operation of a simple rectifier circuit
resistor R,. During the next half-cycle, the diode is reverse-biased, there is practically no current flowing, and vg = 0. Thus, a pulsating current passes through the diode, the load resistor, and the source in the form of pulses each a half-cycle long and separated by intervals likewise a half-cycle long. This is the rectified current. It produces a rectified voltage across the load resistor R,. If we trace the direction of current flow, we will readily establish its polarity or sign: the “+” terminal will be at the cathode and the “—” terminal at the anode.
The plots in Fig. 3-9 give a clear idea about the events taking place in the rectifier. The a.c. emf supplied by the source is shown as a sinewave of amplitude E,, (Fig. 3-9a). As a rule, the load resistance is many times the diode resistance, and the nonlinearity of the diode may be neglected (the dynamic characteristic is close to linear). In the circumstances, the rectified current has the form of pulses, each pulse being nearly a half-sinewave of maximum value /,,,, (Fig. 3-9b). Drawn on another scale, the same plot will show the rectified voltage vp because Vy = iR,. Multiplying the value of current by R,
42 Part One. Semiconductor Devices
will immediately yield a curve representing the rectified voltage.
The plot in Fig. 3-9c shows the voltage across the diode. Sometimes it is incorrectly regarded as sinusoidal or identified with the voltage supplied by the a. c. emf source. Actually, this is a nonsinusoidal voltage because its positive half- cycles markedly differ in amplitude from its negative half-cycles. The positive half-cycles have a very small amplitude. The explanation is that during the passage of forward current the greater proportion of source voltage is dropped across the load resistor whose resistance is many times the diode resistance. Therefore,
Ve ax ea En a, Vie max
= B— Linax Rt K Em (3-10)
For conventional semiconductor diodes, the forward voltage does not exceed 1 or 2 V.
Suppose that the source in our circuit supplies an rms voltage equal to E = 200 V and that E, = /2E=280V. If Vemax=2V, then Ve max = 278 V. If the source voltage (say, 200 V) were fully impressed on the diode, this would mean that no voltage is dropped across R,. This can only occur when R, = 0. Then the current would be excessively heavy, and the diode would be destroyed.
During the negative half-cycles of the applied voltage, there is practically no current flowing, and the voltage drop across R, is zero very nearly. All of the source voltage is applied to the diode and biases it in the reverse direction. As a result, the maximum value of reverse voltage is equal to the amplitude of the source voltage.
Let us examine the rectified voltage in more detail (everything said about it fully applies to the rectified current). As is seen from the plot in Fig. 3-9b, the rectified voltage is a strongly pulsating one so that no voltage exists during one half of each cycle. The useful part of such a voltage is its direct (constant) or average compo- nent. It is often referred to simply as the average voltage and its symbol is V,,. For a half-sine- wave pulse of maximum value V,,,,, its average over a half-cycle is
Vi, = 2Vongy/T = 0.636 Venax (3-11)
Since no voltage exists during the next half- cycle, the average over the entire cycle is half the previous value, or
Vey = Veray/T = 0.318V,
av max
(3-12)
(a) |YR V
Fig. 3-10 Direct and alternating components of rectified voltage
Approximately, V,, is 30% of the maximum value. This approximation is quite legitimate because the actual pulses always differ in wave- form from the half-sinewave. Because the volt- age drop across the diode is very small, we may take it that
Vinex © E,, and Va, + 0.3£,, (3-13)
On subtracting the average value from the pulsating rectified voltage, we obtain its alter- nating component, V,., which is nonsinewave in shape. Its datum (or zero) axis is the straight line representing the direct (constant) component (Fig. 3-10a). The half-cycles of the alternating component are shown shaded. The positive half-cycle accounts for the upper two-thirds of the half-sinewave, and the negative half-cycle is close to a trapezoid in waveform. These half- cycles differ in duration, but they bound equal areas because they do not contain a direct component any longer.
The a. c. component is an ‘unfavourable’ part of the rectified voltage. Measures are usually taken to minimize it in the load resistor, that is, to smooth the pulsations, or ripples, in the rectified voltage. One way to do this is to use what are known as smoothing filters. They are also called ripple filters or rectifier filters. In Fig. 3-105, the a.c. component is shown sepa- rately. It consists of several harmonics. The one most difficult to suppress is the first harmonic (or the fundamental), shown shaded in the figure.
A smoothing filter uses high-value capacitors which provide a bypass for the a.c. current so that as little of it could flow into the load as possible. As often, smoothing filters include chokes — high-value inductors which impede the
Ch. 3. Semiconductor Diodes 43
flow of the a.c. component into the load. As the ripple (or pulsation) frequency goes up, the reactance presented by the filter capacitor dec- reases and that due to the filter inductors increases with the net result that the filter performance is improved.
If a filter performs well in suppressing the fundamental of the ripple, it will suppress the harmonics still better. Because the harmonics are smaller in amplitude than the fundamental, practically one only needs to take care of the fundamental, the worst “offender” of all.
In the elementary rectifier we have chosen as an example, the fundamental of the ripple is very large. Its amplitude V,,, is greater than that of the useful component:
Y= OS Vaw = 1ST (3-14)
Asa rule, a rectified voltage pulsating so strong- ly can hardly be put to practical use. More elaborate rectifier circuits do reduce the ripple somewhat. The simplest way to reduce the ripple, however, is to use a filter consisting of a high-value capacitor placed in shunt with the load resistor R, (see Fig. 3-85). The inclusion of a capacitor, however, affects the performance of the diode in a very substantial way.
A capacitor will smooth the ripple well if its capacitance is such that
l/ac « R, (3-15)
During some part of a positive half-cycle when the diode is forward-biased, there is a current flowing through the diode and charging the capacitor to a voltage close to E,,. During the time interval when no current is flowing through the diode, the capacitor discharges through the load resistor R, and produces across it a voltage which falls off gradually. During every subsequent half-cycle the charge on the capacitor is restored, and the voltage across it rises again.
It takes very little time for the capacitor to charge via the relatively small resistance of the diode, but its discharge through the high-value load resistor is a far slower process. As a result, the voltage across the capacitor and across the load placed in shunt with it pulsates only slightly. Also, the capacitor builds up the direct component of the rectified voltage. In the ab- sence of a capacitor, V,, + 0.3£,,; with a capa- citor of a sufficiently high value V,, comes very closely to E,, and may be equal to 0.8 or 0.95 of
Cae vo
Fig. 3-11 Ripple reduction by a capacitor
E,, or even greater. Thus, in a single-phase half-wave rectifier a capacitor increases the rectified voltage nearly three-fold. The greater the values of C and R,, the slower the discharge of the capacitor, the smaller the ripple, and the closer V,, is to E,,. If we remove all of the load resistance from the circuit (operation at no-load, with R, = 00), a direct voltage free from any pulsations and equal to E,, will be developed across the capacitor.
The operation of a rectifier which contains a smoothing capacitor is explained in Fig. 3-11 showing the plots of the source emf e, the diode current i, and the capacitor voltage v, equal to the load voltage vp.
A better insight into what happens in a rectifier containing a capacitor may be provided by the following analogy. Suppose there is a machine which needs a steady and uniform supply of gas over a pipe. Unfortunately, the pump available to the operator can deliver the gas only portion-wise (similar to pulses in an electric circuit) because the pump draws in some gas only during the forward stroke of the piston and delivers it to the machine only during the reverse stroke. This system is not unlike a rectifier without a capacitor, with the pump motor acting similarly to the a. c. voltage source and with the pump valves acting as the rectifying diode. The situation can be improved if we install a large tank between the pump and the machine and fill it with gas. The tank will then supply the gas to the machine at a nearly constant pressure. It will pulsate only slightly because the pump will replenish the tank and maintain the average pressure in it at one and the same level. Thus, the tank operates similarly to a capacitor in a rectifier. The greater the size
44 Part One. Semiconductor Devices
of the tank and the smaller the flow rate of gas to the machine, the smaller the pulsations in the gas pressure.
The “ + ” side of the capacitor is connected to the cathode and its “ — ” side to the anode of the diode. Therefore, the diode voltage vg is equal to the difference between the source emf and the capacitor voltage Vg =e— Ue
(3-16)
Because vc is nearly equal to £,,, the diode voltage becomes a direct one only during some part of a positive half-cycle when e exceeds vc (near £,,). During these short intervals of time, the diode conducts a current in the form of pulses which restore the charge on the capacitor. During the remainder of each positive half-cycle and during the negative half-cycles, the diode voltage is reversed, there is no current flowing through the diode, and the capacitor discharges into R,.
The reverse voltage across the diode is a maximum when the amplitude of the source emf is negative, e = — E,,. Because the voltage ac- ross the capacitor is then likewise close to E,,, the maximum reverse voltage is close in value to 2E,,. When the load circuit is open-circuited (operation at no-load), the maximum reverse voltage is equal to 2£,, exactly. Thus, the use of a capacitor doubles the reverse voltage as com- pared with its value in the absence of a capaci- tor.* Therefore, it is important to choose a diode capable of standing up to this reverse voltage.
When the ripple must be kept to a very low minimum or when the load resistance is too small, a capacitor of a prohibitively high value would be required. In other words, the ripple could not then be smoothed by a capacitor alone, and one would have to add another smoothing filter consisting of a high-reactance choke and one more capacitor (or a still more elaborate filter).
It is essential to stress the danger associated with the short-circuit that may occur in the load when the filter capacitor is ruptured. Then all of the source voltage will be impressed on the diode, and it will be exposed to a prohibitively heavy current causing the thermal destruction of the diode.
Semiconductor diodes compare favourably
* This is not the case with some rectifier circuits.
with vacuum diodes not only because they need no filament (or heater) voltage for the cathode, but also because the voltage drop across the diode under forward bias is small. Whatever the current, or power, for which a semiconductor diode has been designed, its forward voltage is a few tenths of a volt or a bit higher than | V. Therefore, rectifiers using semiconductor diodes are more efficient than those using vacuum diodes. Importantly, the efficiency improves as the voltage to be rectified is increased because a loss of about 1 V across the diode itself is immaterial. For example, if the voltage to be rectified is 100 V and the voltage drop across the diode is | V, the efficiency is about 99% (the figure will of course be a bit smaller if we take into account some other losses).
Thus, semiconductor diodes are more eco- nomical than vacuum diodes and generate less heat in operation so that less damage is caused to the nearby components. Also, semiconductor diodes have a very long service life. They suffer from a disadvantage ir that they can stand up to a relatively low reverse voltage—not more than several hundred volts while the figure for H. V. vacuum diodes may be tens of kilovolts.
Semiconductor diodes may be used in any type of rectifier circuit. If, however, the front-end element of a smoothing filter is a high-value capacitor, it might pass a current pulse which may exceed the limit of forward current for the diode. To avoid this, the usual practice is to connect the diode in series with a current- limiting resistor of several units or tens of ohms.
In diodes used as rectifiers, reversal of voltage polarity may give rise to substantial pulses of reverse current (Fig. 3-12). They can arise from two causes. Firstly, the reverse voltage gives rise to a current pulse which charges the depletion- layer (barrier) capacitance of the p-n junction — the higher this capacitance, the stronger the current pulse. Secondly, the reverse voltage permits the diffusion capacitance to discharge, that is, to release the minority carriers stored in the n- and p-regions. During the flow of forward current these carriers are injected across the interface and, failing to recombine or escape, are stored in the n- and p-regions. In practice, one has to reckon most of all with the large charge stored in the base region.
For example, if the electron concentration in the n-region is substantially greater than the hole concentration in the p-region, the n-region
Ch. 3. Semiconductor Diodes 45
Fig. 3-12 Reverse current pulses in a crystal diode
will be the emitter and the p-region, the base. The injection of electrons from the n- into the p-region exceeds that of holes the other way around, so electrons are mostly stored in the p-region. When the voltage polarity is reversed, this charge is removed — the electrons move from the p- into the n-region, thereby giving rise to a reverse current pulse. The heavier the forward current, the greater the number of injected carriers (electrons in our case) and the greater the charge that they form. As a consequence, a stronger pulse of reverse current will be produc- ed. After this charge has been removed and the barrier capacitance has practically been fully charged, there will remain an extremely small reverse current which may be neglected.
The reverse current pulse gains in strength with a rise in frequency. The explanation is that the reverse voltage builds up at a progressively faster rate as the frequency is raised. In conse- quence, the barrier capacitance is charged by a heavier current, that is, in a shorter span of time. In other words, a rise in frequency brings about a decrease in capacitive reactance, and the reverse current rises in proportion. The charge produced by the injected carriers is removed likewise faster, and this also serves to build up the reverse current pulse.
At low frequencies, the reverse current pulse is very small and its duration is only a small fraction of the half-cycle. At a certain high frequency the reverse current pulse may have about the same amplitude as the forward cur- rent pulse and last throughout the half-cycle. If the forward and reverse current pulses are equal
in area, the direct component (the average rectified current) will be zero—there will be no rectification. In practice, it is recommended to use diodes for rectification up to a frequency at which the direct component of the rectified current drops by not more than 30% as compa- red with its value at low frequencies.
A rise in temperature brings about a decrease in R, and R,, but this usually has only a slight effect on rectification. The point is that the forward current is practically determined by the load resistance R, which usually is many times the forward resistance of the diode, while the reverse resistance even of a hot diode remains sufficiently large in comparison with R,, and so the reverse current remains small in comparison with the forward current.
The performance of diodes in low-frequency rectifiers can be evaluated in terms of several quantities. They include the forward current averaged over a period, I; ,,; the corresponding voltage drop across the diode, V;,,, the reverse voltage, V.,y, and the corresponding reverse current, J,,,. The current J;,, is often called the rectified current. Other important quantities are the maximum allowable (limiting) reverse vol- tage V, max, the maximum allowable (limiting) forward (or rectified) current Is max, the maxi- mum safe case temperature fcase max, and also the operating frequency limit finax.
3-6 Series and Parallel Connection of Diodes
When very high voltages are to be rectified, diodes have to be connected in series so that the reverse voltage across each diode could not exceed its safe limit. Unfortunately, it often happens that several diodes of the same type differ in reverse resistance (sometimes by a factor of tens). Because of this, the actual reverse voltage across some of the diodes may exceed their safe limit, and the diodes may break down. An example will give a better insight into the matter.
Suppose that in a rectifier the amplitude of reverse voltage is 1000 V and the diodes are chosen such that V, max = 400 V. Obviously, at least three diodes have to be connected in series. Let the reverse resistances of the diodes be such that R,; = R,2 = 1 MQ and R,3 = 3 MQ. The reverse voltage is divided in proportion to the reverse resistances, and so we find that V., =
46 Part One. Semiconductor Devices
= V,.. = 200 V and V,3 = 600 V. Thus, the reverse voltage across the third diode (which is, incidentally, the best of the three because it has the highest R,) will exceed its safe limit, and the diode may break down. If this happens, the applied voltage (1000 V) will be divided among the remaining diodes, and a voltage of 500 V will exist across each of them. Obviously, any of the two may break down, and all of the 1000 V will then be applied to the remaining single diode, and the diode will not endure it. This chain of events sometimes happens in a matter of a split second.
For the reverse voltage to be divided equally among all the diodes irrespective of their reverse resistances, resort is made to resistors that are placed in shunt with the diodes (Fig. 3-13). The shunting resistors must have the same value of Rg, which is substantially smaller than the lowest of all the reverse resistances of the diodes. On the other hand, R,, ought not to be too small, or else the reverse voltage will give rise to an excessive current, thus impairing the quality of rectification. For our example, we should take 100-kQ resistors. Then, with a reverse voltage applied to the circuit, the resistance of each section of the circuit will be somewhat less than 100 kQ, and the total reverse voltage will be divided among these sections in three nearly equal parts. The reverse voltage across each section will be lower than 400 V, and the diodes will operate reliably. As a rule, shunting resistors range in value from several tens to several hundred kilohms.
Diodes are connected in parallel when the desired forward current exceeds the current limit of a single diode. If, however, we connect several diodes of the same type simply in parallel, they will be loaded differently because of the spread in their volt-ampere characteris- tics, and the current in some of them will exceed the safe limit. The difference in forward current between diodes of the same type may be as great as tens of per cent.
As an example, Fig. 3-14a shows the charac- teristic of identical forward-biased diodes for which Imax = 0.2 A. Suppose we want these diodes to deliver a direct current of 0.4 A. If we connect them in parallel, then at a current of 0.2 A the voltage across one diode will be 0.4 V (curve /), while the current in the other diode with the same voltage applied (curve 2) will be a mere 0.05 A. Thus, the total current will be 0.25
Reh Reh Rsh D, Ds D3 Fig. 3-13
Crystal diodes connected in series
Fig. 3-14 Crystal diodes connected in parallel
A and not 0.4 A. The voltage across the diodes may not be raised because the current in the first diode would then exceed its safe limit.
It is seen from reference to the characteristics that if the second diode is to deliver a current of 0.2 A, the voltage across it must be 0.5 V which is by 0.1 V higher than it is across the first. Thus, for the diodes to operate properly, a voltage of 0.5 V must be applied and an equalizing resistor should precede the first diode (D,) so as to absorb its excess 0.1 V at a current of 0.2 A (Fig. 3-14b). Obviously, the resistance of this resistor should be Reg = 0.1/0.2 = 0.5 Q. With this resis- tor connected as shown, the two diodes will be loaded identically by a current of 0.2 A.
In practice, it occurs but seldom that more than two or three diodes are connected in parallel. Equalizing resistors with a resistance of a few tenths of an ohm or units of ohms are usually chosen by trial and error until the same current is flowing in all the diodes in operation at load. Sometimes, the resistance of the equali- zing resistors is deliberately chosen to be several times the forward resistance of the diodes. This is done in order that the current in each diode could be determined mainly by R,,. Unfortuna- tely, this brings about a further voltage drop across R.g, which is many times the forward voltage across the diodes, and the efficiency is of course impaired. If it is not desirable to include equalizing resistors, the diodes to be used must
Ch, 3. Semiconductor Diodes 47
be matched for their characteristics. Whenever possible, however, the parallel connection of diodes should preferably be avoided.
3-7 The Pulsed Operation of Semiconductor Diodes
Many state-of-the-art electronic circuits use semiconductor diodes in the pulsed mode with a pulse duration of several microseconds or even less. We will examine this mode of operation, taking as an example a diode connected in series with a load whose resistance, R,, is many times the forward resistance of the diode, R, >> Rr.
Let such a circuit be acted upon by a pulsed voltage which consists of a short forward-volta- ge pulse (a positive-going pulse) which turns on the diode, and a longer reverse-voltage pulse (a negative-going pulse) which turns off the diode reliably until the arrival of the next positive (or enabling) pulse. The voltage pulses are rectan- gular in shape (Fig. 3-15a).
The waveform of current ana of the propor- tional voltage across R, is shown in Fig. 3-15b. When a forward voltage is impressed on the diode, the current in the circuit is determined by the load resistance R,. Although the forward resistance of the diode is nonlinear, its effect is almost negligible because it is a small fraction of R,. For this reason, the forward-current pulses will be left almost undistorted. A slight distor- tion may be observed only in the case of very short pulses (with a duration of a split microse- cond).
Upon reversal of polarity, that is, when a reverse voltage is applied, the diode is not turned off at once, but during some time taken up by a reverse current pulse (Fig. 3-155) which markedly exceeds in amplitude the reverse cur- rent in a steady state, i,,,. This reverse-current pulse owes its origin to the same causes as when the diode operates at high frequencies (see Sec. 3-5). The primary cause is the discharge of the diffusion capacitance, that is, removal of the charges formed by mobile carriers in the n- and p-regions. Because the impurity concentrations in these regions are usually very different, the reverse-current pulse is mainly produced by removal of the charge stored in the base, that is, the region of a relatively low conductivity. For example, if the n-region acts as the emitter and the p-region as the base, the flow of holes in a forward-biased diode from the p- into the
ip, ss Fig. 3-15 Pulsed operation of a crystal diode
n-region may be neglected and only the flow of electrons from the n- into the p-region needs to be considered.
This diffusion current across the junction results in the accumulation and storage of electrons in the p-region because they cannot recombine or reach the p-terminal at once. Upon reversal of voltage polarity, the charge stored in the base region moves in the reverse direction, giving rise to a reverse current pulse. The heavier was the forward current, the greater the number of electrons stored in the base region and the stronger the reverse current pulse. On moving from the base back to the emitter, some of the electrons recombine with holes and some pass through the n-region and reach the metal electrode made to that region.
Removal of the space charge stored in the base lasts for some time. At the end of this time interval, the reverse current acquires its very small steady-state value, i,,,. We may describe this chain of events somewhat differently. At first the reverse diode resistance R, is relatively low, then it gradually rises and finally reaches its normal steady-state value. The time from the instant when a reverse current is produced to the instant when it falls to its steady-state value is called the reverse recovery time, T,ec. It is a very important parameter for diodes intended for use
48 ‘Part One. Semiconductor Devices
in the pulsed (or switching) mode. For switching diodes the reverse recovery time does not exceed a split microsecond. The shorter this time, the better, because the diode will then take much less time to turn off.
The other cause for the generation of a reverse current pulse is the charging of the diode capacitance by the reverse voltage. The charging current of this capacitance is added to the current associated with removal of stored car- riers and gives rise to a total reverse current pulse which increases in strength in proportion to the diode capacitance. For switching diodes, this capacitance does not exceed a few pico- farads.
If the duration of the forward current pulse is substantially longer than that of the transients we have just examined (say, several millise- conds), the reverse current pulse will be extre- mely short and it may be neglected (Fig. 3-15c).
Apart from the reverse recovery time and diode capacitance, switching diodes are charac- terized by several other important quantities. They are the direct forward voltage V, at a specified direct forward current I;, the reverse current I, at a specified reverse voltage V,, the maximum allowable reverse voltage V, max, and the maximum allowable forward current pulse
Teimax-
3-8 Basic Types of Semiconductor Diodes
Semiconductor diodes may be classed into groups in many ways. One classification is by type of semiconductor material, another by frequency, still another by function or by con- struction, etc.
A very important classification is by type of structure. Here, all semiconductor diodes are classed into the point-contact type and the junction type. In point-contact diodes, the linear dimensions determining the area of the p-n junction are comparable with the thickness of the transition region or even smaller. In junction diodes, these dimensions are markedly greater than the thickness of the junction.
Point-contact diodes have a very small capa- citance (usually less than | pF), and so they can be used at any frequencies, up to the microwave band. However, they can conduct a current of just a few units or tens of milliamperes. Junction diodes have a capacitance of tens of picofarads or even greater, depending on the junction area.
Fig. 3-16 Structure of a point-contact crystal diode
(b) .
Fig. 3-17
Germanium p-n junction diodes manufactured by (a) alloying and (5) diffusion
The current limit for junction diodes may be as high as tens of milliamperes to hundreds of amperes or even greater.
Point-contact and junction diodes are fabri- cated from semiconductor wafers sliced off a single crystal which has a regular crystal structure in all directions. The source materials for point-contact and junction diodes are most often germanium and silicon. More recently, gallium arsenide (GaAs) and other compounds have come into use for this purpose.
In sketch form, the arrangement of a point- contact diode is shown in Fig. 3-16. It has a thin pointed wire (called a catwhisker) to which a desired impurity is applied and then is welded by a current pulse to a wafer of semiconductor having a certain type of conduction. When the metal point contacts the surface of the semi- conductor, impurity atoms diffuse into the host material and produce a region of the opposite type of conduction (this step is called forming). In this way, a miniature hemispherical p-n junction is formed near the metal point. Hence the name “point contact”.
Germanium point-contact diodes are fabri- cated from n-type germanium with a relatively high resistivity. The catwhisker welded to a germanium wafer is a tungsten wire given a coat of indium which acts as an acceptor impurity for germanium. The p-region thus produced in the germanium wafer acts as the emitter. Silicon point-contact diodes are fabricated from n-type silicon, and the catwhisker is given a coat of
Ch. 3. Semiconductor Diodes
aluminium which behaves as an acceptor for silicon.
Junction diodes are mainly fabricated by alloying (or fusion) and diffusion (Fig. 3-17). The alloying process is a fabrication technique in which a small button of indium is fused at about 500°C into an n-type germanium wafer. The impurity metal alloys with the semiconductor material to form a p-type region of germanium. This p-type region has a higher impurity con- centration than the remainder of the relatively high-resistance germanium, and so it acts as the emitter. Terminal leads, usually of nickel, are then welded to the germanium wafer and the indium button. If the host material is high- resistance p-type germanium, the impurity is usually antimony. On alloying with the host material, it forms an n-type emitter.
The alloying process produces what are called abrupt p-n junctions in which the region having a higher impurity concentration is substantially narrower than the region enclosing the space charges existing at the junction.
The diffusion process is a method of pro- ducing p-n junctions by disseminating acceptors or donors into a semiconductor at a high temperature. The impurity in the diffusion pro- cess is usually in the gaseous state. For the diffusion to proceed at a high rate, the host semiconductor is heated to a far higher tempe- rature than in the alloying process. For example, an n-type germanium wafer will be heated to 900°C and placed in an atmosphere of gaseous indium. This treatment produces a layer of p-type germanium on the surface of the wafer. By varying the diffusion time, one can readily produce any desired thickness of such a layer with sufficient accuracy. On cooling, it is etched away from all parts of the wafer except one face. The diffused layer acts as the emitter. A diffused- junction diode is likewise fitted with electrodes and terminal leads which are made to the diffused layer and to the host wafer. In diffused- junction diodes, the impurity atoms penetrate to a relatively large depth into the host material, and so what is called a graded p-n junction is produced. In such diodes, the region where the impurity concentration varies is comparable in thickness with the region enclosing the space charges concentrated at the junction.
Now we will take a look at the various semiconductor diodes from the view-point of the functions they are intended to perform.
49
Rectifying junction diodes. Wide use is made of low-frequency rectifying junction diodes in- tended to rectify alternating current at frequen- cles to several kilohertz (sometimes, as high as 50 kHz). These diodes are used in rectifiers which power various equipment. Sometimes they are called power diodes. Low-frequency junction diodes are made of germanium or silicon. They are classed into low-power, me- dium-power, and high-power. The respective limits of rectified currents are 300 mA, from 300 mA to 10 A, and over 10 A. The diode ratings are usually quoted for operation at an ambient temperature of 20 + S°C.
Germanium diodes are usually fabricated by fusing indium into n-type germanium. They can stand up to a current density of as high as 100 Acm~? ata forward voltage of up to 0.8 V. The limit of reverse voltage for them does not exceed 400 V, and the reverse current usually is a few tenths or hundredths of a milliampere for low- power diodes and several amperes for medi- um-power diodes. The operating temperature for these diodes ranges from — 60° to + 75°C. If a diode has to be operated at an ambient temperature in excess of 20°C, its reverse voltage must be brought down. The devices are likely to be overheated at a reduced atmospheric pres- sure or in the case of poor cooling. In the circumstances, overheating can be avoided by running the devices at a reduced rectified cur- rent.
High-power germanium diodes use natural air cooling. They are designed for a rectified current of as high as 1000 A and a reverse voltage of up to 150 V.
Of late, there has been a steadily growing interest in rectifying silicon diodes. They are fabricated by fusing aluminium into n-type silicon or an alloy of tin and phosphorus or gold into p-type silicon. They can also be fabricated by the diffusion process. Silicon diodes offer a number of advantages over germanium diodes. Their limit of forward current density may be as high as 200 A cm~?, and the limit of reverse voltage, up to 1000 V. The operating tempera- ture ranges from — 60° to + 125°C (or even + 150°C for some makes). The forward voltage of silicon diodes may run as high as 1-1.5 V which is somewhat greater than the figure for germanium diodes. The reverse current of sili- con diodes is substantially lower than it is in germanium diodes.
SO Part One, Semiconductor Devices
High-voltage rectifiers use silicon piles enclo- sed in rectangular plastic cases which are in turn sealed with insulating resin. They can be de- signed for a current of several hundred milli- amperes and a reverse voltage of several kilo- volts. Silicon piles can be put together into larger units which can readily be assembled into various rectifier ciruits (such as bridge rectifiers or voltage doublers). Each pile in such a unit has terminal leads of its own for convenience in voltage adjustment. There are high-power sili- con diodes which can handle rectified currents from 10 to 500 A at a reverse voltage of 50 to 1000 V.
Rectifying point-contact diodes. They are widely used at high frequencies and some of them even at microwave frequencies (up to several hundred megahertz) and can perform well at low frequencies. These diodes are extre- mely versatile as they may be used in a large variety of circuit configurations. Germanium and silicon point-contact rectifying diodes may be designed for a maximum allowable reverse voltage of up to 150 V and a maximum allow- able rectified current of up to 100 mA.
Switching diodes. The manner in which these diodes operate and the quantities associated with this mode of operation have been discussed in Sec. 3-7. The most important quantity which decides whether a given diode can be used in applications involving short pulses is the reverse recovery time, T,¢¢. In order to make it as short as possible, switching diodes are fabricated so that the junction capacitance is small and the carriers can recombine fast. Switching diodes are made for pulse currents up to several hundred milliamperes and a maximum allow- able reverse voltage of a few tens of volts.
Applications involving very short pulses use what are known as mesa diodes (from the Spanish ‘mesa’ for ‘table’ or ‘plateau’). They are fabricated by a process which turns them out in large numbers at a time. As the first step in the process, a wafer of the host semiconductor is given a layer of the opposite type of conduction by the diffusion process. During the second step, a mask is deposited over the diffused layer so as to protect a multiplicity of small areas against the subsequent etching. The unmasked areas are then etched away, and the masked areas appear as plateaus above the remaining material (Fig. 3-18) to act as small p-n junctions. Finally, the wafer is sliced into chips each of which is
Fig. 3-18
Mesa diode: (/) diffused n-type layer; (2) n-region lead; (3) material removed by etching; (4) p-type semi- conductor substrate
volts 10 Vp 5 0 Vi 2pA
| / i | fee ee Imin | 10 mA Qa 20 mA euro as oe Imax I; Fig. 3-19
Reverse current-voltage characteristic of a silicon breakdown diode
a junction diode. A distinction of mesa diodes is a reduction in the volume of the base region. As a result, the storage time of a switching mesa diode is markedly cut down. Since several diodes are made from a single wafer, the spread in characteristics and parameters between them is likewise minimized.
Breakdown diodes. As has been shown, the current-voltage characteristic of breakdown diodes has a portion which may be used for voltage regulation (or stabilization). In silicon junction diodes, this portion corresponds to variations in the reverse current between broad limits. Before a breakdown occurs, the reverse current is very small, at breakdown (in the voltage stabilization mode) it is comparable in magnitude with the forward current. As of this writing, many types of breakdown (voltage reference, voltage regulator, or VR) diodes are available, but they all are made of only silicon. They owe the name ‘voltage reference’ or ‘vol- tage regulator’ to the fact that once the break- down has occurred, they will maintain their output voltage at a constant value that can be utilized as reference. Figure 3-19 shows the
Ch. 3. Semiconductor Diodes Sl
current-voltage characteristic of a typical break- down diode under reverse bias. As is seen, when the diode is operating in the avalanche break- down region (the voltage regulation mode), the output voltage changes very little. Under for- ward bias, the current voltage characteristic is the same as it is for conventional diodes.
Silicon VR diodes may be made for very low voltages (a few volts) such as are used to power many transistor circuits.
The basic parameters of silicon breakdown diodes include the following quantities. The breakdown voltage V, may range from about 5 to 200 V, the diode current may range from tens to hundreds of milliamperes. The peak power dissipation Py,ax is from hundreds of milliwatts to several watts. The dynamic resistance Ray, = Av/Ai in the VR mode may range from a few tenths of an ohm for low-voltage high-power breakdown diodes to 100-200 Q for high-voltage devices. The dynamic resistance of low-voltage, low-power breakdown diodes is from a few ohms to tens of ohms. The lower the dynamic resistance, the better the performance of the diode. In an ideal case, Ray, = 0. Since Ray, isan a.c. resistance, it ought not to be confused with the d.c. resistance of a breakdown diode, defi- ned as Ry = v/i. The value of Ry is always many times that of Ray». The temperature effect is stated in terms of the temperature coefficient of breakdown voltage, TCV, which is the ratio of the change in V, to a unit change in temperature
TCV = AV,/(V, AT) (3-17)
The temperature coefficient of voltage may range from 107* to 10-3 K~1. The value of Vg and the sign of the TCV depend on the resistivity of the host semiconductor. Breakdown diodes for voltages up to 6-7 V are made of silicon of a low resistivity, that is, with a high impurity concentration. In such diodes, the p-n junction is very narrow, the inherent field is very strong, and the breakdown mainly occurs by the Zener mechanism. This results in a negative tempera- ture coefficient of voltage. When the source material is silicon with a lower impurity con- centration, a wider p-n junction will be produ- ced. It will break down at a higher voltage by the reverse-bias avalanche mechanism. Such diodes have a positive temperature coefficient of break- down voltage.
Figure 3-20 shows a simple circuit using a breakdown diode. The load is placed in shunt
Fig. 3-20 Connection of a breakdown diode in a circuit
with the diode. Therefore, in the breakdown region when the voltage across the diode re- mains nearly constant, the same voltage will exist across the load. If the source of voltage E is unstable, any changes in E will almost comple- tely be absorbed by a limiting resistor, Rjim. Most often, breakdown diodes are used in situations where the source voltage is unstable and the load voltage must be constant. To achieve proper voltage regulation, a certain definite value must be chosen for Rj;,,. As a rule, Riim 18 calculated for the Q-point lying midway on the diode characteristic. If the source voltage E varies from Emin to Emax, the value of Riim May be found by the following equation;
Rim i (Ey P V3)/Uav I,) (3-18)
where E,y = (Emin + Emax)/2 is the arithmetic mean of source voltage, Jay = (min + Imax)/2 is the arithmetic mean of diode current, and J, = = V,/R, is the load current.
Should £ change one way or the other, the diode current would also change, but the voltage across it and, in consequence, the voltage applied to the load would remain constant very nearly.
Because any changes in the source voltage must be absorbed by the limiting resistor, the maximum change in source voltage equal to Emax — Emin Must correspond to the maximum possible change in current at which the break- down diode still retains its voltage regulation ability, that is, Imax — Jmin- It follows then that if E changes by AE, voltage regulation will be effected on satisfying the condition
AE < (Znaax os I nin) Rim (3-19)
Voltage regulation in the case of larger chan- ges in E can be retained by increasing the value of Rim. It follows from Eq. (3-18) that a higher value of Rjjm entails a lower value of I,, that is, a higher value of R,. An increase in E£,, likewise leads to an increase in Rjjm.-
Sometimes it may be necessary to obtain
52 Part One. Semiconductor Devices
a regulated voltage lower in value than that supplied by the breakdown diode used. This goal can be achieved by placing the load in series with a small resistor whose resistance can readily be found by Ohm’s law (Fig. 3-21).
Another case of voltage regulation occurs when Fis constant and R, ranges from R, min to Ry, max: For this case, R}jm can be found from the average values of currents, using the following equation:
Riim = (E — Vg)/av + Li av) where
Tuav = (ymin + Ii max)/2 Ty, min = Vp/Ry max
I, max = Vg/R. min
The operation of the circuit in the above case may be explained as follows. Because Rj, is constant and the voltage drop across it, equal to E — Vj, is likewise constant, the current in Rim, equal to I,, + J, ay, must also be constant. But this is possible only if the diode current J and the load current J, change to the same extent but in opposite senses. For example, if J, rises, the diode current J must fall by the same amount so that their sum remains unchanged.
Where high regulated voltages are needed or involved, resort is made to a series connection of breakdown diodes designed each for the same current (Fig. 3-22). It is not recommended to use parallel connection of several breakdown diodes in order to obtain a higher regulated voltage because individual devices even of the same type may greatly differ in characteristics and parameters. Parallel connection may be used only if the total power dissipation by all the diodes does not exceed the peak power of a single diode.
As an alternative, breakdown diodes may be connected in cascade (Fig. 3-23) in which case diode D, must have a higher V, than diode D,.
How well voltage regulation is performed is stated in terms of the voltage regulation ratio (or the stabilization factor), k,,,. It is defined as the ratio of a fractional change in source voltage to the fractional change in the breakdown voltage. For the simple circuit shown in Fig. 3-20 we may write
: Kreg = (AE/E)/(AV,/Vp)
(3-20)
(3-21)
Fig. 3-21
Connection of a series resistor to bring down the regulated voltage across load
Fig. 3-22 Breakdown diodes connected in series
Riim1 | Plim 2
Fig, 3-23
Cascade connection of breakdown diodes
Practical breakdown diodes have a kyeg of several tens. For a cascade connection the overall keg is the product of the individual k,.g:
(3-22)
and may be as high as several. hundreds even with two stages in cascade.
‘The voltage regulation schemes examined above suffer from a drawback which consists in that a good deal of power is dissipated in the diode itself and in the limiting resistor(s), with the result that the efficiency is heavily impaired. The losses are especially noticeable in a cascade connection.
It is to be noted that if the source voltage E is subject to fluctuations or pulsations, a break- down diode will smooth them out to a great extent. This is because a breakdown diode has a low a.c. resistance which is usually a small fraction of Rim. Therefore, the greater propor- tion of the ripple voltage will be absorbed in Rim, and only a very small fraction of this
Kreg tots Kreg 1 Kreg 2eee
Ch. 4. Bipolar Transistors 53
Fig. 3-24
Connection of a varactor in a resonant circuit as a variable capacitor
voltage will be dropped across the breakdown diode and the load.
Varactors. A varactor is a p-n junction semi- conductor diode which utilizes variations in the junction capacitance with reverse bias. In effect, varactors are variable capacitors whose capaci- tance is controlled electrically (by varying the reverse voltage) rather than mechanically.
Varactors are mainly used as tuning elements in resonant (tuned) circuits and some specialized
devices, such as parametric amplifiers. Figure 3-24 shows a diagram of a simple tuned circuit containing a varactor. By varying the reverse voltage across the varactor with a potentiome- ter, R, we can control the resonance frequency of the tuned circuit. R, is a high-value series resistor included in order to maintain the Q-fac- tor of the tuned circuit in the face of the shunting effect of the potentiometer R. Cy is a duc. blocking capacitor; without it the varactor would have been short-circuited for direct current by the tuned-circuit inductor L.
The job of varactors can well be done by silicon breakdown diodes operated at a voltage below V,, when the reverse current is still very small and, in consequence, the reverse resistance is very high.
We have examined only the most commonly used types of semiconductor diodes. There are also a number of special-purpose diodes some of which will be described in Chap. 8.
Chapter Four Bipolar Transistors
4-1 General Principles
Transistors are semiconductor devices capable of power amplification and having three or more leads. They may have two or more p-n junctions, but most common among them are those with two p-n junctions. They are called bipolar junc- tion transistors. They owe the name ‘bipolar’ to the fact that they utilize the flow of both minority and majority charge carriers through the device.
The first transistor was invented in 1948. It was a point-contact transistor. The point-con- tact transistor consisted of a small crystal of semiconductor (usually germanium) with two rectifying point contacts attached in close pro- ximity to each other and a single large-area ohmic contact at some distance from the point contacts. Unfortunately, point-contact transis- tors have proved unstable in operation and are now obsolete, being ousted by junction transis- tors which were invented in 1949.
The basic principles of a bipolar junction transistor are illustrated in Fig. 4-1. It is a wafer of germanium, silicon, or some other semicon- ductor in which three regions differing in the type of conduction have been produced. As an example, we have taken an n-p-n transistor in which the middle region has hole conduction, and the two outer regions have electron con- duction. As common are p-n-p transistors in which the outer regions have hole conduction and the middle region, electron conduction.
The middle region is called the base, one of the outer regions is called the emitter, and the other, the collector. Thus, our transistor has two p-n junctions, one between emitter and base, and the other between base and collector. The spacing between them must be very small, not more than a few micrometers and this means that the base region must be very narrow. This requirement is essential for proper operation of a transistor. Also, the impurity concentration in the base is always substantially lower than it is in the
54 Part One. Semiconductor Devices
E Cc B (b) p-n-p nSBe E Cc E Cc B B Fig. 4-1 Structure and graphical symbol of a p-n junction
transistor
collector and emitter regions. Attached to each of the three regions is a metal electrode and a lead.
The quantities associated with the base, emit- ter, and collector carry, respectively the sub- script B, E, or C. For example the base, emitter and collector currents are designated as ig, ip and i,. The voltages between the electrodes are usually supplied with two-letter subscripts. For example, the voltage between base and emitter is labelled as vgp, and that between collector and base as vc,. In the diagram (or circuit) symbols of p-n-p and n-p-n transistors the arrow shows the conventional direction of current flow (from the “+” to the “ —” terminal) in the emitter lead when the emitter-base junction is forward- biased.
A transistor can operate in any one of three regions, depending on the voltages across its
junctions. These are the active region, the cutoff
region, and the saturation region. A transistor is said to be operating in the active region when its emitter-base junction is forward-biased and its collector-base junction is reverse-biased. A tran- sistor is driven into the cutoff region by reverse- biasing both p-n junctions. When, on the other hand, the two junctions of a transistor are forward-biased, it is said to be operating in the saturation region or at saturation. The active region is the basic mode of operation. It is utilized in most amplifiers and oscillators. Therefore, we will discuss the operation of the transistor in the active region in more detail. The cutoff and saturation regions are typical of
transistors operating im the switching mode, and they will also be discussed, but at a later time.
As a rule, in any application using a transis- tor, two circuits are formed. One is the input or control circuit and the other is the output or controlled circuit. The source of the signal to be amplified is connected into the input circuit, and the load is connected to the output circuit. The quantities associated with the input circuit may carry either the letter subscript “in” or the numerical subscript “1”. The quantities associa- ted with the output circuit may be labelled “out” on <2":
4-2 Physical Processes in a Transistor
To begin with, we will see how, say, an n-p-n transistor operates with its load disconnected (static operation or operation at no-load), when only sources of direct supply voltages, £, and E,, are connected into the circuit (Fig. 4-2a). Their polarity is such that the emitter junction is forward-biased, and the collector junction is reverse-biased. Therefore, the resistance of the emitter junction is low, and for a normal current to flow across this junction it will suffice to apply a voltage, E,, of a few tenths of a volt. The resistance of the collector junction is high, and E, is usually from several volts to tens of volts. As is seen from the circuit diagram of Fig. 4-2a, the transistor voltages are connected by a simple relation of the form
(4-1)
When a transistor is operating in the active region, it is usually always that vp, is substanti- ally lower than veg, and in consequence Uc, is approximately equal to vg.
The current-voltage characteristic of the emitter junction is in effect the characteristic of a forward-biased semiconductor diode (see Fig. 3-2) and the current-voltage characteristic of the collector junction is similar to that of the reverse-biased semiconductor diode.
In basic terms, the operation of a transistor consists in that the forward voltage across the emitter junction, vg, has a strong effect on the collector current: the higher this voltage, the heavier the emitter and collector currents, and variations in the collector current are only slightly lower than those in the emitter current. In this way, the emitter-base voltage, vg_, which is the input voltage, controls the collector
Uce = Ucg t+ Upe
Ch. 4. Bipolar Transistors
Fig. 4-2
Motion of electrons and holes in an n-p-n and a p-n-p transistor
current. This is the basis of signal amplification by transistors.
Physical processes occur in a transistor as follows. An increase in the forward input voltage Ugg brings about a fall in the height of the potential barrier at the emitter junction and a proportionate increase in the current flowing across that junction, that is, in the emitter current i,. The electrons that make up this current are injected from the emitter into the base and also diffuse through the base into the collector region, thereby boosting the collector current. Because the collector junction is rever- se-biased, there appear space charges shown as encircled “ + ” and “ — ” signs in the figure, and an electric field is set up between them. This field assists in sweeping the electrons arriving here from the emitter across the collector junction or
A) Lo 4)
pulling them into the collector region.
If the base is narrow enough and its hole concentration is low, most of the electrons swept across the base will not have time to recombine with holes in the base, but will reach the collector junction. Very few of the electrons recombine with holes in the base. Recombina- tion gives rise to the base current that flows in the base lead. In a steady state, the number of holes in the base must remain unchanged. Because of recombination, so-many holes dis- appear every second, but as many new holes are produced owing to the fact that an equal number of electrons leave the base for the “ + ” terminal of the E, source. In other words, the base cannot retain very many electrons. If some of the electrons injected into the base from the emitter fail to reach the collector and remain in the base to recombine with holes, exactly as many electrons should leave the base as the base current iy. Because the collector current is smaller than the emitter current, the following relation always exists between the currents in accord with Kirchhoffs current (or first) law:
(4-2)
The base current is useless if not detrimental. Preferably, it should be as small as practicable. As a rule, i, accounts for a few per cent of the emitter current, i; < i,, and so the collector current is only slightly lower than the emitter current. In other words, we may write that i¢ is approximately equal to ip. It is for the purpose of making the base current as small as possible that the base region is made very narrow and its impurity concentration, which determines the hole concentration, is kept low. In either case, fewer electrons will be available in the base to recombine with holes.
If the base were broad and its hole concentra- tion were high, the greater proportion of the electrons that constitute the emitter current would, on diffusing across the base, recombine with holes and would fail to reach the collector junction. The collector current would not prac- tically be augmented by the electrons supplied by the emitter, and only the base current would show some increase.
When no voltage is impressed on the emitter junction, practically no current is flowing across it. In the circumstances, the collector junction presents a high resistance to direct current because the majority carriers move away from
Seng oe
the junction, and depletion layers are produced on either side of the boundary. Only a very small reverse current is then flowing across the collec- tor junction due to the minority carriers in one region moving towards those from the other, that is, electrons from the p-region and holes from the n-region.
If, however, the impressed input voltage pro- duces a substantial emitter current, the emitter will inject into the base a certain number of electrons which are minority carriers for that region. Since they have no time to recombine with holes as they diffuse through the base, they reach the collector junction. The greater the emitter current, the greater the number of electrons reaching the collector junction, and the lower its resistance. The collector current rises in proportion. In other words, a rise in the emitter current brings about an increase in the concentration of minority carriers injected from the emitter into the base. As a consequence, the increase in the number of these carriers leads to a rise in the collector current ic.
As will be recalled, we use the term ‘emitter’ (which is short for ‘emitter region’) in order to stress the fact that it is responsible for the injection of electrons through the emitter junc- tion into the base. The reference to ‘injection’ is important so that we could tell this process from electron emission as it occurs in a vacuum or a rarefied gas and produces free electrons.
To follow the above definition, we apply the name ‘emitter’ to a transistor’s region whose purpose is to inject carriers into the base. The name ‘collector’ is assigned to the region whose purpose is to extract carriers from the base. The base is the region into which the emitter injects the carriers that are minority carriers for that region.
It should be noted that the emitter and the collector may exchange places (the inverted mode of operation). However, the collector junction ofa transistor is, as a rule, larger in area than its emitter junction because it has to be able to dissipate substantially more power than the emitter junction. Therefore, if one chooses to use the emitter as a collector, the transistor would be operable, but at an appreciably lower power level, which is unattractive. If the two junctions are made the same in area (as is the case with symmetrical transistors), any of the outer regions may equally well be used as the emitter or as the collector.
56 Part One. Semiconductor Devices
Since in a transistor the emitter current is always the sum of the collector and base cur- rents, the incremental change in emitter current must likewise be always equal to the sum of the incremental changes in collector and base cur- rents:
Ai, = Aig + Aig (4-3)
An important property of transistors is that their currents are connected by an almost linear relation or, in simpler words, the three currents of a transistor vary in an approximate propor- tion to one another. Let us take as an example ig = 10 mA, ic = 9.5 mA, and i, = 0.5 mA. If the emitter current goes up by, say, 20% to become equal to 10 + 2 = 12 mA, the remaining two currents will rise likewise by 20% so that ig = 0.5+ 0.1 =0.6 mA and ip =9.54 1.9 = = 11.4 mA. This happens because the equality defined in Eq. (4-2) must always be satisfied, that is,
12 mA = 11.4mA+0.6 mA
For the incremental changes in the currents, the equality defined in Eq. (4-3) holds, that is,
2mA = 1.9 mA + 0.1 mA
We have examined physical processes occur- ring in the n-p-n type of transistor. But every- thing said fully applies to the p-n-p type except that its electrons and holes exchange their roles and the polarity (sign) of the voltages and currents are reversed (Fig. 4-25). In a p-n-p transistor, instead of electrons the emitter injects into the base holes which are minority carriers for that region. As the emitter current rises, a progressively greater number of such holes move through the base towards the collector junction. This brings down its resistance and raises the collector current.
The operation of a transistor can readily be visualized by reference to the potential diagram shown in Fig. 4-3 for an n-p-n transistor. This diagram can conveniently be used to build a mechanical model of a transistor. The emitter potential is taken as the datum or reference (zero) potential. There is a low potential barrier in the emitter junction. The greater the emit- ter-base voltage, vg,, the lower this barrier. The potential difference across the collector junction is substantial, and it accelerates the electrons. In our mechanical model, balls replace electrons; owing to their inherent velocity, they climb the hill which models the emitter junction, pass
Ch. 4. Bipolar Transistors 57
through the region simulating the base of a transistor, and roll at an ever increasing velocity (that is, are accelerated) down the slope which simulates the collector junction.
In addition to the processes we have just discussed, some other events take place in a transistor that must be taken into account.
The performance of a transistor is materially affected by the base resistance rgo*, that is the resistance that the base presents to the base current, ij. This current flows to the base electrode in a direction which is at right angles to the direction from the emitter to the collector. Because the base is very thin, its resistance seen looking from emitter to collector, that is, to ig, is very small and is usually neglected. In the direction of the base electrode, however, the base resistance, rg9, runs into hundreds of ohms because in this direction the base acts similarly to a very fine conductor. The voltage across the emitter junction is always lower than vp, be- cause some of the applied voltage is dropped across the base resistance. If we take rg, into account, a d.c. equivalent circuit for a transistor may be drawn up as shown in Fig. 4-4. In this diagram, rpg is the emitter resistance which includes the resistance of the emitter junction and the resistance of the emitter region. Low- power transistors have rp, running into tens of ohms. This is because the voltage across the emitter junction does not exceed a few tenths of a volt while the emitter current in such transistors is several milliamperes. Higher-po- wer transistors have greater values of igo and proportionately smaller values of go. Approximately, rg; can be found (in ohms) by the following equation:
Teo = 25/ig
where i, is in milliamperes.
The collector resistance rg is practically that of the collector junction and may be as high as a few kilohms to tens of kilohms. It also includes the resistance of the collector region, but it is negligibly small.
The equivalent circuit in Fig. 4-4 is a very approximate one because in an actual transis- tor, the emitter, base and collector are in contact at a multiplicity of points over the entire area of the junctions. Still, this equivalent circuit may be
(4-4)
* Here and elsewhere, the zero (0) in a subscript indicates that the quantity involved is considered under conditions of direct-current flow.
Fig. 4-3
Fig. 4-4 D.C. equivalent circuit of a transistor
used when examining many processes that oc- cur in transistors.
When the voltage applied to the collector junction is raised, what is known as the ava- lanche multiplication of carriers takes place, mainly due to impact ionization. This effect coupled with tunnelling may ultimately result in an electric breakdown. If the current is allowed to build up without bound, the electric break- down may terminate in a thermal breakdown.
A change in the voltage existing across the collector and emitter junctions is accompanied by a change in the width of the junctions. In turn, this produces a change in the base width. This is known as base width modulation. It becomes a vital factor when there is an increase in the collector-base voltage-this leads to an increase in the width of the collector junction and a decrease in the base width. Should the base be too narrow, the collector junction may spread as far as the emitter junction and the two will make electrical contact with each other —it is then said that a punch-through (or a reach- through) has occurred. The base region then disappears altogether, and the transistor ceases operating as it should.
When the carrier injection from the emitter into the base is increased, the minority carrier
58 Part One. Semiconductor Devices
concentration and charge in the base are increa- sed, too, owing to what is known as carrier storage. Conversely, a reduction in the carrier injection will cause the stored charge to be removed from the base because both the mino- rity carrier concentration and the minority carrier charge will then be brought down.
In some cases it is important to consider the flow of leakage currents over the surface of a transistor as it is accompanied by carrier recombination in the surface layer of all the regions of the device.
Let us establish the relations that exist be- tween the currents flowing in a transistor. The emitter current is controlled by the voltage existing across the emitter junction, but the current reaching the collector is somewhat smaller in value—it may be called the controlled collector current, ic,. This happens because some of the carriers injected from the emitter into the base recombine. Therefore,
(4-5)
where a is the emitter-to-collector current gain of a transistor connected in a common-base circuit (also called the alpha current factor or the common-base forward-current transfer ratio). It may range in value from 0.950 to 0.998. That is, for a junction transistor it is always less than unity. It tends to approach unity with fewer injected carriers in the base recombining. There is one more, very small current (not over a few microamperes) always flowing across the collector junction, symbolized as ic¢g (Fig. 4-5). It is called the reverse collector leakage current. It is defined as the minimum current that will flow in the collector circuit of a transistor with zero current in the emitter circuit. Thus the total collector current is
log = Olg
(4-6)
The reverse collector leakage current may be called an uncontrolled reverse current because it does not flow across the emitter junction.
In many cases, icg is a negligible fraction of i, so we may take it that i, is approximately equal to ai,. When measuring igo, the emitter circuit is opened. As follows from Eq. (4-6), when i, = 0, ic = icg:
Let us re-write Eq. (4-6) so that ig is a function of ig. On replacing i, with the sum ic + ip, we get
ig = Aig + ip) + cg
ic = Oleg + icg
Fig. 4-5 Currents in a transistor
On solving the above equation for i,, we obtain ig = iga/(1 — &) + igg/(1 — a)
On denoting a/1—a)=f68 and we may finally write ic = Big + iceo (4-7)
where B is the beta current gain factor or the current transfer ratio or gain of a transistor connected in a common-emitter circuit. It is always greater than unity and practical values up to 500 are often used.
It is interesting to compare how changes in a affect the value of B. For example, if a = 0.95, then
B = a/(1 — a) = 0.95/(1 — 0.95) = 0.95/0.05 = 19
If a = 0.99, which means an increase of 0.04 in its value, then
B = 0.99/(1 — 0.99) = 0.99/0.01 = 99
Thus, B increases more than five-fold. In other words, even minor changes in a lead to great changes in B. Similarly to a, B isa very important parameter of transistors. If we know B, we can always find a by the equation
a = BI + B)
ico/(1 — &) = icgo
(4-8)
Ch. 4. Bipolar Transistors 59
The current igo is the reverse emitter current when the base is open, that is, when i, = 0. It flows through all the three regions and the two junctions of a transistor. Thus, as follows from Eq. (4-7), if we set i, to zero, we will get ic = ioxg. This current runs into tens or even hundreds of microamperes and greatly exceeds the reverse collector leakage current icg. More specifically,
icgo = ico/(l — a)
Therefore, if we know that a/(1 — a) = B, itis an easy matter to find that
iczo = (B + Nico
Also, since f is substantially greater than unity, we get
(4-9)
The high value of icgg is due to the fact that a small fraction of uc, is applied to the emitter junction in the forward direction. In conse- quence, there is a rise in the emitter current which is, in this case, icgo.
When tc, rises too high, i¢¢g May go up abruptly and bring about an electric break- down. If Ugg is not too low and the base circuit is open, a cumulative build-up of current may occur, leading to an excessive temperature rise and causing the transistor to fail (unless there is a current-limiting resistor in the collector lead). The events taking place may be summed up as follows. Some of the collector-to-emitter volt- age, Ucp, Causes a rise in i, and in ic which is equal to it, more carriers reach the collector junction, its resistance and the voltage across it go down, leading to a higher voltage across the emitter junction, and this in turn gives rise to a further increase in the current, and so on. To avoid this occurrence, the base circuit of a transistor may never be opened in operation, unless its collector supply voltage has been turned off. Also, the base supply voltage must be turned on first and the collector supply voltage afterwards — never do this the other way around.
When a need arises to measure icg¢o, place a current-limiting resistor in the collector lead and open the base circuit.
icko © Bico
4-3 Amplification by a Transistor
Figure 4-6 shows the circuit diagram of an amplifier stage using an n-p-n transistor. This circuit is known as the common-emitter configu-
Fig. 4-6
Connection of a transistor in an amplifier stage (the common-emitter configuration)
ration (see Sec. 4-4) because the emitter is common to both the input and output circuits of the stage. The input voltage to be amplified is applied from a signal source, SS, across the emitter junction. The base also receives a posi- tive bias voltage from a bias source E£;; this is the forward voltage for the emitter junction. As a result, a current is caused to flow in the base circuit and, in consequence, the input resistance of the transistor acquires a relatively low value. To prevent some of the input a.c. voltage from being dropped across the internal resistance of the signal source, the latter is shunted by a capacitor C, which has a relatively high capacitance. Its value is chosen so that its impedance is a very small fraction of the tran- sistor’s input resistance at the lowest operating frequency.
The collector circuit (that is, the output circuit) is energized from another source, E). The amplified output voltage is taken off a load resistance, R,;. The £, source is shunted by a capacitor, C,, so as to prevent some of the amplified voltage from being lost across the internal resistance of the E, source. At the lowest operating frequency, the impedance pre- sented by this capacitor must be a very small fraction of R,. In our further discussion we will omit the capacitors C, and C, of the £, and £, sources from the diagram so as to make it simpler to read. It may be presumed that they exist inside the £, and £, sources themselves. If these sources are rectifiers, they will always contain high-value capacitors in order to smoothen the pulsations.
A transistor amplifier stage operates as fol- lows. Let the collector circuit be represented by the equivalent circuit of Fig. 4-7. The collector supply voltage E,