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Quantum Physics of Semiconductor Materials and Devices

Quantum Physics of Semiconductor Materials and Devices PDF

Author: Debdeep Jena

Publisher: Oxford University Press


Publish Date: August 26, 2022

ISBN-10: 0198856857

Pages: 896

File Type: PDF

Language: English

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Book Preface

Semiconductor electronics requires for its foundation primarily wave mechan-ics and statistics. However, crystallography, thermodynamics, and chemistry also have a share in it and, quite generally, “it is incredible what miserable quantities of thought and mathematics are needed to provide even the sim-plest tools for daily use in semiconductor physics”.–Eberhard Spenke and Walter Schottky
Several excellent books and monographs have been written about the physics of semiconductors and nanostructures. I could not resist reproducing the above paragraph from an early classic, Spenke’s Elec-tronic Semiconductors written in 1958. Till today, each author of books on this subject struggles with the same pedagogical challenge that pi-oneers such as Spenke and Shockley faced in writing the first books on this topic in the 1950s, when the field was in its infancy.
Consider the simplest physical processes that occur in semiconduc-tors: electron or hole transport in bands and over barriers, collision of electrons with the atoms in the crystal, or when electrons and holes annihilate each other to produce a photon. The correct explanation of these processes require a quantum mechanical treatment. Any short-cuts lead to misconceptions that can take years to dispel, and some-times become roadblocks towards a deeper understanding and appre-ciation of the richness of the subject. A typical introductory course on semiconductor physics would then require prerequisites of quan-tum mechanics, statistical physics and thermodynamics, materials sci-ence, and electromagnetism. Rarely would a student have all this back-ground when (s)he takes a course of this nature in most universities.
What has changed since 1950s? Semiconductor devices have become indispensable, and integral in our daily lives. The shift towards a semiconductor electronics and photonics-powered information econ-omy occurred near the turn of the century. This was not the case when the early books on semiconductor physics were written. The connection of the physics to today’s information systems such as tran-sistors for logic, memory, and signal amplification, and light-emitting diodes and lasers for lighting and communications makes the subject far more tangible and alive than an abstract one. Practitioners of the science, technology, and art of semiconductor physics and devices are the ”quantum mechanics” of our age in the true sense of the word. They reside in several leading industries, research laboratories, and universities, and are changing the world, one bit (or photon!) at a time.

The quantum physics of semiconductors is not abstract, but mea-sured routinely as currents and voltages in diodes and transistors, and seen as optical spectra of semiconductor lasers. The glow of semi-conductor quantum well light emitting diodes in our rooms and cell phone screens puts the power and utility of understanding the quan-tum physics of semiconductors and nanostructures on display right in front of our very eyes. Asher Peres captured this philosophy beauti-fully in his quote:
”Quantum Phenomena do not occur in a Hilbert space. They occur in a laboratory.”–Asher Peres
This philosophy accurately reflects the approach I have taken in writing this book. Semiconductor physics is a laboratory to learn and discover the concepts of quantum mechanics and thermodynamics, condensed matter physics, and materials science, and the payoffs are almost immediate in the form of useful semiconductor devices. I have had the opportunity to work on both sides of the fence – on the fun-damental materials science and quantum physics of semiconductors, and in their applications in semiconductor electronic and photonic de-vices. Drawing from this experience, I have made an effort in this book to make each topic as tangible as possible. The concepts are developed from their experimental roots, with historical trails, personalities, and stories where possible, to reflect the subject as a human adventure. The mathematical structure is then developed to explain experimental observations, and then predict new phenomena and devices. I believe this is a unique approach towards a book on this subject, one that distinguishes it from others in the field.
The book is aimed at third and fourth year undergraduate students, and graduate students in Electrical Engineering, Materials Sciences and Engineering, Applied Physics, Physics, and Mechanical and Chem-ical Engineering departments that offer semiconductor related courses. It will be of interest to scientists and engineers in the industry, and in various research laboratories. The book is divided into four modules.
Module I, in seven chapters, presents the fundamentals rigorously, covering the core principles of quantum mechanics, statistical thermo-dynamics, and the physics of free electrons. The last two chapters of Module I develop perturbation theory techniques without which one is often disadvantaged in understanding semiconductor physics.
Module II, in nine chapters introduces the concepts of bands, gaps, effective masses, and Bloch theory, develops a few methods to calculate and understand semiconductor bandstructures, and develops methods to handle a range of semiconductor quantum heterostructures.
Module III starts with the quantum physics of diodes and transis-tors in the ballistic limit. It then covers several electronic phenomena on transport and scattering using the Boltzmann transport equation, and Fermi Golden rule for transitions. High-field transport, tunneling, and quantum magnetotransport phenomena round off this module of nine chapters.

Module IV focuses on semiconductor photonics, by starting from a description of the Maxwell equations and light, tracking the interaction of photons with semiconductors, and culminating in the description of semiconductor heterostructure photonic devices.
The chapter-end exercises have been tried and tested as homework assignments in classes. They considerably amplify the material dis-cussed in the chapters, and are designed to encourage deep thinking, purposeful enquiry, and thoughtful discussions. Some problems take the reader beyond the topics of the respective chapters, into current areas of research. Some problems connect to other fields such as biol-ogy, astronomy, high-energy physics, and other fields in which semi-conductors play an increasingly important role. There is no better practice to hone one’s skills to achieve mastery over the subject than to solve as many exercises as time permits.
Instructors must plan the usage of the book to fit their goals. The book has far more material than can (or should) be covered in a 1-semester course. A typical 1-semester course at Cornell offered for senior undergraduates and beginning graduate students covers all of Module I, most chapters of Module II, (Chapters 12 and 13 are as-signed as projects), Chapters 20-24 in Module III, and Chapters 27 and 29 of Module IV. To cater to the varying backgrounds of enrolled stu-dents, more time is spent on Modules I and II. Once the students are comfortable with the concepts of bands and carrier statistics in semi-conductors of Modules I and II, the progress through Modules III and IV can be rapid. I have provided a table and guidance for instructors and students later in this preface for potential usage of the book.
No claim to originality is made for most of the presented mate-rial. Nevertheless, the process of writing for pedagogical purposes allows for fresh perspectives. Readers may encounter a few uncon-ventional derivations, or connections made that were not apparent. Because much of semiconductor physics originated from atomic quan-tum theory, such examples abound, but have been ”lost in translation” over the past few decades. I have brought them back, as semicon-ductors are going back to their atomic roots in the new generation of nanostructured devices. The field is alive and kicking, new semicon-ductors and phenomena are being discovered, synthesized, and are being used for applications today. The presentation of the materials in the book take these advances into fold. If the book gives ideas, or makes connections for readers that enable them to make new discov-eries or inventions that outdate the topics discussed here, it will have exceeded its intended pedagogical purpose.
Colleagues and students I have talked to around the world agree that there is a place for a stand-alone book to introduce solid state physics to electrical engineers, applied physicists, and materials scien-tists who work on semiconductors, by using semiconductor devices in the backdrop. It is my sincere hope that this book fills that void.
Debdeep Jena
Ithaca, New York, March 2022.

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