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## Physics of Semiconductor Devices

This volume originates from the lectures on Solid-State Electronics and Microelectronics that I have been giving since 1978 at the School of Engineering of the University of Bologna. Its scope is to provide the reader with a book that, starting from the elementary principles of classical mechanics and electromagnetism, introduces the concepts of quantum mechanics and solid-state theory, and describes the basic physics of semiconductors including the hierarchy of transport models, ending up with the standard mathematical model of semiconductor devices and the analysis of the behavior of basic devices. The ambition of the work has been to write a book, self contained as far as possible, that would be useful for both students and researchers; to this purpose, a strong effort has been made to elucidate physical concepts, mathematical derivations, and approximation levels, without being verbose.

The book is divided into eight parts. Part I deals with analytical mechanics and electromagnetism; purposedly, the material is not given in the form of a resumé:quantum-mechanics and solid-state theory’s concepts are so richly intertwined with the classical ones that presenting the latter in an abridged form may make the reading unwieldy and the connections more difficult to establish. Part II provides the introductory concepts of statistical mechanics and quantum mechanics, followed by the description of the general methods of quantum mechanics. The problem of bridging the classical concepts with the quantum ones is first tackled using the historical perspective, covering the years from 1900 to 1926. The type of statistical description necessary for describing the experiments, and the connection with the limiting case of the same experiments involving massive bodies, is related to the properties of the doubly-stochastic matrices. Part III illustrates a number of applications of the Schrödinger equation: elementary cases, solutions by factorization, and time-dependent perturbation theory. Part IV analyzes the properties of systems of particles, with special attention to those made of identical particles, and the methods for separating the equations. The concepts above are applied in Part V to the analysis of periodic structures, with emphasis to crystals of the cubic type and to silicon in particular, which, since the late 1960s, has been and still is the most important material for the fabrication of integrated circuits. Part VI illustrates the single-electron dynamics in a periodic structure and derives the semiclassical Boltzmann Transport Equation; from the latter, the hydrodynamic and drift-diffusion models of semiconductor devices are obtained using the moments expansion. The drift-diffusion model is used in Part VII to work out analytically the electrical characteristics for the basic devices of the bipolar and MOS type. Finally, Part VIII presents a collection of items which, although important per se, are not in the book’s mainstream: some of the fabrication-process steps of integrated circuits (thermal diffusion, thermal oxidation, layer deposition, epitaxy), and methods for measuring the semiconductor parameters.

In the preparation of the book I have been helped by many colleagues. I wish to thank, in particular, Giorgio Baccarani, Carlo Jacoboni, and Rossella Brunetti, who gave me important suggestions about the matter’s distribution in the book, read the manuscript and, with their observations, helped me to clarify and improve the text; I wish also to thank, for reading the manuscript and giving me their comments,

Giovanni Betti Beneventi, Fabrizio Buscemi, Gaetano D’Emma, Antonio Gnudi, Elena Gnani, Enrico Piccinini, Susanna Reggiani, Paolo Spadini.

Last, but not least, I wish to thank the students, undergraduate, graduate, and postdocs, who for decades have accompanied my teaching and research activity with stimulating curiosity. Many comments, exercises, and complements of this book are the direct result of questions and comments that came from them.

## Modern Physics for Scientists and Engineers, 4th Edition

Our objective in writing this book was to produce a textbook for a modern physics course of either one or two semesters for physics and engineering students. Such a course normally follows a full-year, introductory, calculus-based physics course for freshmen or sophomores. Before each edition we have the publisher send a questionnaire to users of modern physics books to see what needed to be changed or added. Most users like our textbook as is, especially the complete coverage of topics including the early quantum theory, subfi elds of physics, general relativity, and cosmology/astrophysics. Our book continues to be useful for either a one- or two-semester modern physics course. We have made no major changes in the order of subjects in the fourth edition.

**Coverage**

The first edition of our text established a trend for a contemporary approach to the exciting, thriving, and changing field of modern science. After briefly visiting the status of physics at the turn of the last century, we cover relativity and quantum theory, the basis of any study of modern physics. Almost all areas of science depend on quantum theory and the methods of experimental physics. We have included the name Quantum Mechanics in two of our chapter titles (Chapters 5 and 6) to emphasize the quantum connection. The latter part of the book is devoted to the subfields of physics (atomic, condensed matter, nuclear, and particle) and the exciting fi elds of cosmology and astrophysics. Our experience is that science and engineering majors particularly enjoy the study of modern physics after the sometimes-laborious study of classical mechanics, thermodynamics, electricity, magnetism, and optics. The level of mathematics is not difficult for the most part, and students feel they are fi nally getting to the frontiers of physics. We have brought the study of modern physics alive by presenting many current applications and challenges in physics, for example, nanoscience, high-temperature superconductors, quantum teleportation, neutrino mass and oscillations, missing dark mass and energy in the universe, gamma-ray bursts, holography, quantum dots, and nuclear fusion. Modern physics texts need to be updated periodically to include recent advances. Although we have emphasized modern applications, we also provide the sound theoretical basis for quantum theory that will be needed by physics majors in their upper division and graduate courses.

**Changes for the Fourth Edition**

Our book continues to be the most complete and up-to-date textbook in the modern physics market for sophomores/juniors. We have made several changes for the fourth edition to aid the student in learning modern physics. We have added additional end-ofchapter questions and problems and have modifi ed many problems from earlier editions, xt-stroke-width: 0px; “> with an emphasis on including more real-world problems with current research applications whenever possible. We continue to have a larger number of questions and problems than competing textbooks, and for users of the robust Thornton/Rex *Modern Physics for* *Scientists and Engineers, *third edition course in WebAssign, we have a correlation guide of the fourth edition problems to that third edition course.

We have added additional examples to the already large number in the text. The pedagogical changes made for the third edition were highly successful. To encourage and support conceptual thinking by students, we continue to use conceptual examples and strategy discussion in the numerical examples. Examples with numerical solutions include a discussion of what needs to be accomplished in the example, the procedure to go through to find the answer, and relevant equations that will be needed. We present the example solutions in some detail, showing enough steps so that students can follow the solution to the end.

We continue to provide a signifi cant number of photos and biographies of scientists who have made contributions to modern physics. We have done this to give students a perspective of the background, education, trials, and efforts of these scientists. We have also updated many of the Special Topic boxes, which we believe provide accurate and useful descriptions of the excitement of scientifi c discoveries, both past and current.

Chapter-by-Chapter Changes We have rewritten some sections in order to make the explanations clearer to the student. Some material has been deleted, and new material has been added. In particular we added new results that have been reported since the third edition. This is especially true for the chapters on the subfields of physics, Chapters 8–16. We have covered the most important subjects of modern physics, but we realize that in order to cover everything, the book would have to be much longer, which is not what our users want. Our intention is to keep the level of the textbook at the sophomore/junior undergraduate level. We think it is important for instructors to be able to

supplement the book whenever they choose—especially to cover those topics in which they themselves are expert. Particular changes by chapter include the following:

• Chapter 2: we have updated the search for violations of Lorentz symmetry and added some discussion about four vectors.

• Chapter 3: we have rewritten the discussion of the Rayleigh-Jeans formula and Planck’s discovery.

• Chapter 9: we improved the discussion about the symmetry of boson wave functions and its application to the Fermi exclusion principle and Bose-Einstein condensates.

• Chapter 10: we added a discussion of classes of superconductors and have updated our discussion concerning applications of superconductivity. The latter includes how superconductors are now being used to determine several fundamental constants.

• Chapter 11: we added more discussion about solar energy, Blu-ray DVD devices, increasing the number of transistors on a microchip using new semiconductor materials, graphene, and quantum dots. Our section on nanotechnology is especially complete.

• Chapter 12: we updated our discussion on neutrino detection and neutrino mass, added a description of nuclear magnetic resonance, and upgraded our discussion on using radioactive decay to study the oldest terrestrial materials.

• Chapter 13: we updated our discussion about nuclear power plants operating in the United States and the world and presented a discussion of possible new, improved reactors. We discussed the tsunami-induced tragedy at the Fukushima Daiichi nuclear power plant in Japan and added to our discussion of searches for new elements and their discoveries.

• Chapter 14: we upgraded our description of particle physics, improved and expanded the discussion on Feynman diagrams, updated the search for the Higgs boson, discussed new experiments on neutrino oscillations, and added discussion on matter-antimatter, supersymmetry, string theory, and M-theory. We mention that the LHC has begun operation as the Fermilab Tevatron accelerator is shutting down.

• Chapter 15: we improved our discussion on gravitational wave detection, added to our discussion on black holes, and included the fi nal results of the Gravity Probe B satellite.

## Physics by Computer Programming of Physical Problems Using Mathematica and C

Using computers to solve problems and model physical problems has fast become an integral part of undergraduate and graduate education in physics. This 3rd year undergraduate and subsequent graduate course is a supplement to courses in theoretical physics and develops problem-solving techniques using the computer. It makes use of the newest version of Mathematica (3.0) while still remaining compatible with older versions The programs using Mathematica 3.0 and C are written for both PCs and workstations, and the problems, source files, and graphic routines help students gain experience from the very beginning.

Nowadays the computer is an important tool in physics. The acquisition and analysis of extensive experimental data and the control of complex experiments are hardly imaginable without the use of computers. In theoretical

physics the computer has turned from a mere calculator to a comprehensive tool. Graphical displays, numerical and algebraic solutions of equations, and extensive simulations of microscopic models have become important methods for the exploration of the laws of physics.

The computer, however, is not just a tool, it also offers new perspectives and opens new areas of research. Until recently physicists generally described nature with differential equations; nowadays discrete algorithms are also used.

For some apparently simple physical models there are only numerical answers so far. We know universal laws that any high school student can reproduce on a pocket calculator, for which there is, however, no analytical theory (yet?).

In addition to this, the computer opens up new fields to physics: neural networks, combinatorial optimization, biological evolution, formation of fractal structures, and self-organized criticality are just some of the topics from the growing field of complex systems.

Almost every advanced undergraduate or graduate physics student uses a computer at one time or another. Nonetheless, computer training and the use of computers in teaching are still by no means the expected norm, but rather the exception. The literature in this field is correspondingly sparse.

**The goal of our textbook is to contribute to filling this gap.**

This book evolved out of lectures at the University of Wiirzburg, Germany, for physics majors after their fourth semester – those having completed the introductory coursework in theoretical physics. It is conceived as a text book in computational physics but may also serve as a supplement to the traditional physics classes in which the possibilities of computer use have so far been underutilized. We would like to show the reader how to solve physics problems using the computer. Experience with computers and computer languages is helpful, but not necessary, for we want to present an introduction and explain the first steps with computers and algorithms. This book does not contain many details about numerical mathematics, it does not offer a course on programming languages, nor does it teach advanced methods of

computer-oriented theoretical physics. It does, however, introduce numerous physics problems, some of which are at the cutting edge of research, and tries to solve them with simple algorithms.

One goal is to encourage our readers to do their own programming. Although a CD-ROM with finished programs is enclosed with the book, they are not meant as user-friendly experimental environments. We hope that instead they can be taken as a starting-point, and we encourage our readers to modify them, or better yet to rewrite them more efficiently. Exercises accompany every section of this introductory book.

We have received suggestions from many colleagues and students, to whom we wish to express our thanks. We would like especially to mention M. Biehl, H. Dietz, A. Engel, A. Freking, Th. Hahn, W. Hanke, G. Hildebrand, A. Jung, A. Karch, U. Krey, B. Lopez, J. Nestler, M. Opper, M. Schreckenberg, and D. Stauffer. Special thanks go to the following three people: Martin Liiders developed the program package Xgraphics, Martin Schroder wrote the section on Unix, and Ursula Eitelwein typed the manuscript of this book in UTEX.

Finally we would like to thank Martin Clajus for valuable suggestions in the course of translating this textbook into English.

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