WIXLIB

Preface to the Second EditionWe have so far received many comments and feedback on our book from allquarters including students, instructors and, of course, many friends. We aremost grateful to them not only for their compliments but also for their valuable criticism. We also received many requests for an instructor manual andsolutions to the problems at the end of each chapter. We realize that semiconductor physics has continued to evolve since the publication of this book andthere is a need to continue to update its content. To keep our readers informedof the latest developments we have created a Web Page for this book. Its address (as of the writing of this preface) is: http://pauline.berkeley.edu/textbook.At this point this Web Page displays the following information:1) Content, outline and an excerpt of the book.2) Reviews of the book in various magazines and journals.3) Errata to both first and second printing (most have been corrected inthe second edition as of this date).4) Solutions to selected problems.5) Additional supplementary problems.The solutions in item (4) are usually incomplete. They are supposed to serveas helpful hints and guides only. The idea is that there will be enough leftfor the students to do to complete the problem. We hope that these solutionswill satisfy the need of both instructors and students. We shall continue to addnew materials to the Web Page. For example, a list of more recent referencesis planned. The readers are urged to visit this Web Page regularly to find outthe latest information. Of course, they will be welcomed to use this Web Pageto contact us.While the present printing of this book was being prepared, the 1998 International Conference on the Physics of Semiconductors (ICPS) was being heldin Jerusalem (Israel). It was the 24th in a biannual series that started in 1950in Reading (U.K.), shortly after the discovery of the transistor by Shockley,Bardeen and Brattain in 1948. The ICPS conferences are sponsored by the International Union of Pure and Applied Physics (IUPAP). The proceedings ofthe ICPS’s are an excellent historical record of the progress in the field andthe key discoveries that have propelled it. Many of those proceedings appearin our list of references and, for easy identification, we have highlighted inred the corresponding entries at the end of the book. A complete list of allconferences held before 1974, as well as references to their proceedings, can

XPreface to the Second Editionbe found in the volume devoted to the 1974 conference which was held inStuttgart [M. H. Pilkuhn, editor (Teubner, Stuttgart, 1974) p. 1351]. The nextICPS is scheduled to take place in Osaka, Japan from Sept. 18 to 22 in theyear 2000.The Jerusalem ICPS had an attendance of nearly 800 researchers from 42different countries. The subjects covered there represent the center of the current interests in a rapidly moving field. Some of them are already introducedin this volume but several are still rapidly developing and do not yet lendthemselves to discussion in a general textbook. We mention a few keywords:Fractional quantum Hall effect and composite fermions.Mesoscopic effects, including weak localization.Microcavities, quantum dots, and quantum dot lasers.III–V nitrides and laser applications.Transport and optical processes with femtosecond resolution.Fullerites, C60 -based nanotubes.Device physics: CMOS devices and their future.Students interested in any of these subjects that are not covered here, willhave to wait for the proceedings of the 24th ICPS. Several of these topics arealso likely to find a place in the next edition of this book.In the present edition we have corrected all errors known to us at thistime and added a few references to publications which will help to clarify thesubjects under discussion.Stuttgart and Berkeley,November 1998Peter Y. YuManuel Cardona

Preface to the First EditionI, who one day was sand but am today a crystalby virtue of a great fireand submitted myself to the demanding rigorof the abrasive cut,today I have the powerto conjure the hot flame.Likewise the poet, anxiety and word:sand, fire, crystal, strophe, rhythm.– woe is the poem that does not light a flameDavid Jou, 1983(translated from the Catalan original)The evolution of this volume can be traced to the year 1970 when one of us(MC) gave a course on the optical properties of solids at Brown Universitywhile the other (PYY) took it as a student. Subsequently the lecture noteswere expanded into a one-semester course on semiconductor physics offeredat the Physics Department of the University of California at Berkeley. Thecomposition of the students in this course is typically about 50 % from thePhysics Department, whereas the rest are mostly from two departments in theSchool of Engineering (Electrical Engineering and Computer Science; Materials Science and Mineral Engineering). Since the background of the studentswas rather diverse, the prerequisites for this graduate-level course were keptto a minimum, namely, undergraduate quantum mechanics, electricity andmagnetism and solid-state physics. The Physics Department already offers atwo-semester graduate-level course on condensed matter physics, therefore itwas decided to de-emphasize theoretical techniques and to concentrate onphenomenology. Since many of the students in the class were either growingor using semiconductors in device research, particular emphasis was placed onthe relation between physical principles and device applications. However, toavoid competing with several existing courses on solid state electronics, discussions of device design and performance were kept to a minimum. This coursehas been reasonably successful in “walking this tight-rope”, as shown by thefact that it is offered at semi-regular intervals (about every two years) as aresult of demands by the students.One problem encountered in teaching this course was the lack of an adequate textbook. Although semiconductor physics is covered to some extentin all advanced textbooks on condensed matter physics, the treatment rarelyprovides the level of detail satisfactory to research students. Well-establishedbooks on semiconductor physics are often found to be too theoretical by experimentalists and engineers. As a result, an extensive list of reading materialsinitially replaced the textbook. Moreover, semiconductor physics being a mature field, most of the existing treatises concentrate on the large amount of

XIIPreface to the First Editionwell-established topics and thus do not cover many of the exciting new developments. Soon the students took action to duplicate the lecture notes, whichdeveloped into a “course reader” sold by the Physics Department at cost. Thisvolume is approximately “version 4.0” (in software jargon) of these lecturenotes.The emphasis of this course at Berkeley has always been on simple physical arguments, sometimes at the expense of rigor and elegance in mathematics. Unfortunately, to keep the promise of using only undergraduate physicsand mathematics course materials requires compromise in handling specialgraduate-level topics such as group theory, second quantization, Green’s functions and Feynman diagrams, etc. In particular, the use of group theory notations, so pervasive in semiconductor physics literature, is almost unavoidable.The solution adopted during the course was to give the students a “five-minutecrash course” on these topics when needed. This approach has been carriedover to this book. We are fully aware of its shortcomings. This is not too serious a problem in a class since the instructor can adjust the depth of the supplementary materials to satisfy the need of the students. A book lacks suchflexibility. The readers are, therefore, urged to skip these “crash courses”, especially if they are already familiar with them, and consult the references forfurther details according to their background.The choice of topics in this book is influenced by several other factors.Most of the heavier emphasis on optical properties reflects the expertise of theauthors. Since there are already excellent books emphasizing transport properties, such as the one by K. H. Seeger, our book will hopefully help to filla void. One feature that sets this book apart from others on the market isthat the materials science aspects of semiconductors are given a more important role. The growth techniques and defect properties of semiconductors arerepresented early on in the book rather than mentioned in an appendix. Thisapproach recognizes the significance of new growth techniques in the development of semiconductor physics. Most of the physics students who took thecourse at Berkeley had little or no training in materials science and hence abrief introduction was found desirable. There were some feelings among thosephysics students that this course was an easier way to learn about materialsscience! Although the course offered at Berkeley lasted only one semester,the syllabus has since been expanded in the process of our writing this book.As a result it is highly unlikely that the volume can now be covered in onesemester. However, some more specialized topics can be omitted without lossof continuity, such as high field transport and hot electron effects, dynamiceffective ionic charge, donor–acceptor pair transitions, resonant Raman andBrillouin scattering, and a few more.Homework assignment for the course at Berkeley posed a “problem” (excuse our pun). No teaching assistant was allocated by the department to helpwith grading of the problem sets. Since the enrollment was typically over thirtystudents, this represented a considerable burden on the instructor. As a “solution” we provide the students with the answers to most of the questions.Furthermore, many of the questions “lead the student by the hand” through

Preface to the First Editionthe calculation. Others have hints or references where further details can befound. In this way the students can grade their own solutions. Some of thematerial not covered in the main text is given in the form of “problems” to beworked out by the student.In the process of writing this book, and also in teaching the course, wehave received generous assistance from our friends and colleagues. We are especially indebted to: Elias Burstein; Marvin Cohen; Leo Esaki; Eugene Haller;Conyers Herring; Charles Kittel; Neville Smith; Jan Tauc; and Klaus von Klitzing for sharing their memories of some of the most important developments inthe history of semiconductor physics. Their notes have enriched this book bytelling us their “side of the story”. Hopefully, future students will be inspiredby their examples to expand further the frontiers of this rich and productivefield. We are also grateful to Dung-Hai Lee for his enlightening explanationof the Quantum Hall Effect.We have also been fortunate in receiving help from the over one hundredstudents who have taken the course at Berkeley. Their frank (and anonymous)comments on the questionnaires they filled out at the end of the course havemade this book more “user-friendly”. Their suggestions have also influencedthe choice of topics. Many postdoctoral fellows and visitors, too numerous toname, have greatly improved the quality of this book by pointing out errorsand other weaknesses. Their interest in this book has convinced us to continuein spite of many other demands on our time. The unusually high quality of theprinting and the color graphics in this book should be credited to the following people: H. Lotsch, P. Treiber, and C.-D. Bachem of Springer-Verlag,Pauline Yu and Chia-Hua Yu of Berkeley, Sabine Birtel and Tobias Ruf ofStuttgart. Last but not the least, we appreciate the support of our families.Their understanding and encouragement have sustained us through many difficult and challenging moments. PYY acknowledges support from the John S.Guggenheim Memorial Foundation in the form of a fellowship.Stuttgart and Berkeley,October 1995Peter Y. YuManuel CardonaXIII

XIVPreface to the First EditionA SEMI-CONDUCTOR

Contents1.2.Introduction11.12223344455678A Survey of Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.1Elemental Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.2Binary Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.3Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.4Layered Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.5Organic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.6Magnetic Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . .1.1.7Other Miscellaneous Semiconductors . . . . . . . . . . . . . . . . .1.2 Growth Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.1Czochralski Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.2Bridgman Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.3Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . .1.2.4Molecular Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2.5Fabrication of Self-Organized Quantum Dotsby the Stranski–Krastanow Growth Method . . . . . . . . . . .1.2.6Liquid Phase Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Periodic Table of “Semiconductor-Forming” Elements . . . . . . . . . . . . . .11131415Electronic Band Structures172.12.22.3182025252.42.5Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Translational Symmetry and Brillouin Zones . . . . . . . . . . . . . . . . .A Pedestrian’s Guide to Group Theory . . . . . . . . . . . . . . . . . . . . .2.3.1Definitions and Notations . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.2Symmetry Operations of the Diamondand Zinc-Blende Structures . . . . . . . . . . . . . . . . . . . . . . . .2.3.3Representations and Character Tables . . . . . . . . . . . . . . .2.3.4Some Applications of Character Tables . . . . . . . . . . . . . . .Empty Lattice or Nearly Free Electron Energy Bands . . . . . . . . .2.4.1Nearly Free Electron Band Structurein a Zinc-Blende Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . .2.4.2Nearly Free Electron Energy Bands in Diamond CrystalsBand Structure Calculations by Pseudopotential Methods . . . . . .2.5.1Pseudopotential Form Factorsin Zinc-Blende- and Diamond-Type Semiconductors . . . .2.5.2Empirical and Self-Consistent Pseudopotential Methods303240484852586166

XVIContents2.63.The k·p Method of Band-Structure Calculations . . . . . . . . . . . . . .2.6.1Effective Mass of a Nondegenerate BandUsing the k·p Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.6.2Band Dispersion near a Degenerate Extremum:Top Valence Bands in Diamondand Zinc-Blende-Type Semiconductors . . . . . . . . . . . . . . .2.7 Tight-Binding or LCAO Approach to the Band Structureof Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.7.1Molecular Orbitals and Overlap Parameters . . . . . . . . . . .2.7.2Band Structure of Group-IV Elementsby the Tight-Binding Method . . . . . . . . . . . . . . . . . . . . . . .2.7.3Overlap Parameters and Nearest-Neighbor Distances . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .879496105Vibrational Properties of Semiconductors,and Electron–Phonon Interactions1073.13.24.6869718383Phonon Dispersion Curves of Semiconductors . . . . . . . . . . . . . . .Models for Calculating Phonon Dispersion Curvesof Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.1Force Constant Models . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.2Shell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.3Bond Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.4Bond Charge Models . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3 Electron–Phonon Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.1Strain Tensor and Deformation Potentials . . . . . . . . . . . .3.3.2Electron–Acoustic-Phonon Interactionat Degenerate Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.3Piezoelectric Electron–Acoustic-Phonon Interaction . . . .3.3.4Electron–Optical-PhononDeformation Potential Interactions . . . . . . . . . . . . . . . . .3.3.5Fröhlich Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.6Interaction Between Electrons and Large-WavevectorPhonons: Intervalley Electron–Phonon Interaction . . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135137158Electronic Properties of Defects1594.14.21601611621661714.3Classification of Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Shallow or Hydrogenic Impurities . . . . . . . . . . . . . . . . . . . . . . . . .4.2.1Effective Mass Approximation . . . . . . . . . . . . . . . . . . . . .4.2.2Hydrogenic or Shallow Donors . . . . . . . . . . . . . . . . . . . .4.2.3Donors Associated with Anisotropic Conduction Bands4.2.4Acceptor Levels in Diamondand Zinc-Blende-Type Semiconductors . . . . . . . . . . . . . .Deep Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110114114114115117121122127130131133174180

Contents4.3.1Green’s Function Methodfor Calculating Defect Energy Levels . . . . . . . . . . . . . . .4.3.2An Application of the Green’s Function Method:Linear Combination of Atomic Orbitals . . . . . . . . . . . . .4.3.3Another Application of the Green’s Function Method:Nitrogen in GaP and GaAsP Alloys . . . . . . . . . . . . . . . .4.3.4Final Note on Deep Centers . . . . . . . . . . . . . . . . . . . . . . .Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.6.183188192197198202Electrical Transport2035.15.2203206206207Quasi-Classical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Carrier Mobility for a Nondegenerate Electron Gas . . . . . . . . . .5.2.1Relaxation Time Approximation . . . . . . . . . . . . . . . . . . .5.2.2Nondegenerate Electron Gas in a Parabolic Band . . . . .5.2.3Dependence of Scattering and Relaxation Timeson Electron Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.4Momentum Relaxation Times . . . . . . . . . . . . . . . . . . . . .5.2.5Temperature Dependence of Mobilities . . . . . . . . . . . . .5.3 Modulation Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4 High-Field Transport and Hot Carrier Effects . . . . . . . . . . . . . . .5.4.1Velocity Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4.2Negative Differential Resistance . . . . . . . . . . . . . . . . . . .5.4.3Gunn Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.5 Magneto-Transport and the Hall Effect . . . . . . . . . . . . . . . . . . . .5.5.1Magneto-Conductivity Tensor . . . . . . . . . . . . . . . . . . . . .5.5.2Hall Effect . . . . . . . . . . . . . .

in semiconductor physics is our understanding of the class of deep defect cen-ters known as the DX centers. During the preparation of the first edition, the physics behind these centers was not universally accepted and not all its pre-dicted properties