Diodes and Transistors - Stem2

1 Diodes and Transistors James Emery Edited: 8/17/2016. Contents 1 Prologue 4. 2 Introduction to Electronics 4. 3 Semiconductors 6. 4 The Hall Effect 7. 5 Probability Theory 8. Introduction .. 9. 6 A Quantum Particle Gas 14. 7 The Band Theory of Solids 15. 8 Lagrange Multipliers 15. 9 Particle Statistics 15. 10 Sterling's Approximation 17. 11 Fermi-Dirac Statistics 17. 12 A Derivation of the Fermi-Dirac Distribution Function 18. 13 More on the Fermi Level 21. 1. 14 Thermodynamic Temperature and Statistical Mechanics 22. The Definition of Temperature and Entropy .. 22. Heat .. 24. The Energy Probability Distribution .. 25. 15 The Partition Function 26. 16 The Kronig-Penney Model for the Crystal Lattice Potential 27. 17 Feynman Approach to the Problem of an Electron in a Crys- tal lattice 27. 18 The Thermal Voltage 28. 19 Drift and Diffusion in Semiconductors 28. Drift, the Continuity Equation, Ohm's Law and Mobility .. 28. The Equation of Continuity for Charge Density .. 29. Mobility.

2 30. Diffusion and the Einstein Relation .. 31. 20 Diodes 34. The diode Junction, Current Flow Through a diode .. 34. The Shockley diode Equation .. 35. 21 Transistors 41. 22 The NPN transistor 42. 23 The Ebbers-Moll Model of the NPN transistor 43. 24 The NPN Common Emitter transistor Amplifier 44. 25 Hands-On Transistors 47. Checking Diodes and Transistors With a Meter .. 47. Measuring transistor Characteristics .. 49. Creating the transistor Data Table With MatLab .. 52. 26 Regions of Operation of the NPN Bipolar Junction Transis- tor 54. 2. 27 The Thyristor, SCR (Silicon Controlled Rectifier), Triac 55. 28 transistor Graphical Analysis and the Design of a Common- Emitter Amplifier 55. 29 A Description of the transistor Amplifier Program transis- 63. 30 A transistor Curves File 63. 31 Program Output 65. 32 A Listing of 66. 33 Appendix A: Quantum Mechanics 80. Particle in a Bounded Box .. 80. 34 Bibliography 80. 35 Glossary 84. List of Figures 1 diode Equation. This is a plot of the diode Equation I(vd ) = Is (exp(vd /vt ) 1), where Is = 1 10 11 amperes, and vt = mV.

3 36. 2 Common-Emitter Amplifier. In this amplifier configura- tion, the input signal at the base, and the output signal at the collector, are both referenced to a common point from the emitter. This version uses the NPN transistor . In the section on the common-emitter, we derive various properties of this amplifier, including the amplification factor.. 45. 3 transistor Test. In this test using the 2N3904 NPN transis- tor, the power supply voltage VCC = 12 volts, R1 and R2 are 10k resistors, P1 is a 500k potentiometer, RC and RE are 180. ohm resistors. The meters measure the current into the base, and the current out of the emitter. The results are shown in the table.. 50. 3. 4 transistor Amplifier. Based on the circuit diagram found in the book Principles of Electrical Engineering by D'Azzo and Houpis, Fig .. 56. 5 transistor Curves for the 2N3241. See Principles of Electrical Engineering by D'Azzo and Houpis, Fig , For base currents 0 a, 20 a, 40 a, 60 a, 80 a, 100 a, and 120 a.

4 The 120 a curve is the top one. The DC load line has smaller slope, the AC load line larger slope.. 57. 1 Prologue This document is in the process of being written. I write because by writing I organize my thoughts and learn. To learn the brain must exercise, not just record. Education is not simply record and playback. I recommend both writing and brain exercising very highly. But let us reverse the tangent, and return to an introduction to this docu- ment. This document is still very incomplete, and can be considered a draft, and very possibly not free from typos, errors, and bad sources, which can be quite bad indeed. The logic and mathematics used in many physics derivations tends to be weak, nebulous, overly complicated, and quite maddening for those of us with a rigorous mathematical bent, for it forces us to spend a lot of unnecessary time decoding the arguments, and separating the logical from the empirical, the physical from the metaphysical. In summary, as anonymous has said, The best way to learn a subject is to teach a course on it, to write a book about it, to experiment with it, to try it out.

5 Check back from time to time. There is a growing bibliography at the end of the document. 2 Introduction to Electronics Electronics may be studied at many levels; all levels contain some lies, . many egregious. The elementary levels contain the most. For example, in the history of atomic physics we start with the early ideas of the Greek Dem- ocritus on indivisible atoms. Then 200 or 300 years later we come upon the 4. ideas of the Roman Lucretius, who in his work De Rerum Natura, described matter as made up of indivisible atoms that swirl around in varying ways giving the various forms of matter their distinct characteristics. John Dalton (September 6, 1766 - July 27, 1844) reintroduced the atomic theory around 1800, in connection with his work on the properties of gases, and on the law of multiple proportions in chemistry. The unit of atomic mass is now called the Dalton named in his honor. Much later, in the early 20th century, came the Bohr quantum theory of the atom, where electrons orbit the nu- cleus like little planets, and shortly after that, a better theory comes along, called Quantum Mechanics, where an electron is both particle and wave, and where an electron has only a probable location.

6 Should we call these early explanations lies? Perhaps more properly, we should call them early knowl- edge within the ignorance. However, some models such as the Bohr Model we retain, because although we know it is not strictly true, it is simple and intuitive, and even accurate for the hydrogen atom. Much elementary explanation of physics uses analogies to avoid mathe- matics, although perhaps this is an aid to understanding for some completely ignorant of mathematics, it can lead to long term confusion. This is a high penalty to pay for not providing often simple mathematical explanation. For example, in first learning Special Relativity, one should definitely avoid pop- ular books on the subject to prevent serious mind corruption, which might later require painful surgical intervention. I speak from youthful experience. The book Understanding Basic Electronics by Larry D. Wolfgang, American Radio Relay League, 1996, is a good survey of Electronics, espe- cially good for refreshing old knowledge, and good for the beginner.

7 It is especially suitable for those who like simplicity, but want at least some ac- curacy, avoiding the most blatant lies. It has nice drawings and attractive cartoons. There are many similar treatments, but this is one of the better elements of this mendacious set of elementary books, without the most outra- geous analogies, such as that of electrons running around in pipes with little feet. You should know that electrons do not have feet, at least according to our current understanding. Another useful book, which presents electronics by simple experiments with simple circuits, is Make: Electronics, by Charles Platt, O'Reilly, 2010. As we have said the study of Transistors and electronics can be approached from many levels. One can approach this at a relatively deep level with a 5. book like Physics of Semiconductor Devices, by S. M. Sze, 2nd Edi- tion, Wiley Interscience, 1981. Or one can approach this at a deeper level through advanced physics books on subjects such as Solid State Physics (a subject which is now known as Condensed Matter Physics), Quantum Mechanics, Crystallography, and Statistical Mechanics.

8 Some such books are listed in the bibliography. An intermediate approach is to take the electrical engineering view and learn the practical and hands-on behavior of Transistors in circuits, with minimal concern with the underlying Quantum Mechanics of crystals, as in the book, Electrical Engineering Fundamentals, by Vincent Del Toro, Prentice-Hall, 2nd ed, 1986. The book Hands-On Electronics is written by two physicists for uni- versity science student who need to use electronics in their experimental work. It presents experimental projects together with background theory and a guide to practical details, with some material on the use of electronic test equipment. 3 Semiconductors A semiconductor is a crystalline solid with a conductivity between that of a conductor, and an insulator. The principal semiconductor materials are silicon and germanium. These elements are group IV elements in the periodic table. They form a crystal structure like that of diamond, a regular lattice with each atom covalently bounded to four neighboring atoms in the form of a tetrahedron.

9 Because each atom is covalently bounded to four neighboring atoms, we may represent this in a symbolic planar image. However, we note that this is one of those lies, because the bonding is three dimensional. The four neighbors of a carbon atom to which it is bonded do not lie in a plane, although it is convenient to represent them thus on the page of a book. The unit cell of a diamond lattice is shown on page 169 of Linus Pauling's General Chemistry, Dover republication, 1988 (where a person temporarily cross-eyed might see it in 3d), in the book by Willian Shockley, Electrons and Holes in Semiconductors, which has a nice picture of the unit cell on page six, and a very nice picture in Gray and Searle on page 49, showing all bonds of the atoms in the unit cell. A similar figure is in Levine Sumner N, Principles of Solid-State Microelectronics on page 20. One 6. might view my VRML file , which can be rotated and examined with a free VRML viewing program, such as Flux Player. This file can be found using the following link: These silicon or germanium lattices may be doped by adding a small amount of another element from either group III of the periodic table, Gal- lium or Indium, or group V of the periodic table, Arsenic or Antimony, to produce a P type, or an N type semiconductor.

10 This causes a disruption in the stable covalent bonding octet. But these semiconductors are still electri- cally neutral, the free conducting charges are due to the bonding anomaly. The P type results by doping with a III type element, where there would be one missing electron in the crystal structure at the dopant atom, whereas in the case of a type V dopant, there would be an extra electron. So there will be either an excess of holes, positive charges in the conduction band, pro- ducing a P type semiconductor,or an excess of electrons in the conduction band, producing a N type semiconductor. Now the behavior of semiconduc- tors requires a Quantum Mechanical explanation, and the usual elementary classical description is a bit of a lie. The crystal lattice must be treated like a giant molecule where electrons can jump between energy levels. However the number of energy levels is huge, so a simplification is made using the theory of energy bands in crystals, where sets of very closely spaced levels are called bands.