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Graduate Texts in Physics

Graduate Texts in PhysicsGraduate Texts in Physics publishes core learning/teaching material for graduate- andadvanced-level undergraduate courses on topics of current and emerging fields withinphysics, both pure and applied. These textbooks serve students at the MS- or PhD-level andtheir instructors as comprehensive sources of principles, definitions, derivations, experiments and applications (as relevant) for their mastery and teaching, respectively. International in scope and relevance, the textbooks correspond to course syllabi sufficiently to serveas required reading. Their didactic style, comprehensiveness and coverage of fundamentalmaterial also make them suitable as introductions or references for scientists entering, orrequiring timely knowledge of, a research field.Series EditorsProfessor H. Eugene StanleyBoston UniversityCenter for Polymer StudiesDepartment of Physics590 Commonwealth Avenue, Room 204BBoston, MA 02215, USAE-mail: [email protected] William T. RhodesGeorgia Institute of TechnologySchool of Electrical and Computer EngineeringAtlanta, GA 30332-0250, USAE-mail: [email protected]

Peter Y. YuManuel CardonaFundamentalsof SemiconductorsPhysics and Materials PropertiesFourth Edition123

Professor Dr. Peter Y. YuProfessor Dr., Dres. h.c. Manuel CardonaUniversity of CaliforniaDepartment of PhysicsBerkeley, CA 94720-7300, USAE-mail: [email protected] für FestkörperforschungHeisenbergstr. 1, 70569 Stuttgart, GermanyE-mail: [email protected] 1868-4513ISBN 978-3-642-00709-5DOI 10.1007/978-3-642-00710-1e-ISSN 1868-4521e-ISBN 978-3-642-00710-1Springer Heidelberg Dordrecht London New YorkLibrary of Congress Control Number: 2010924732 Springer-Verlag Berlin Heidelberg 1996, 1999, 2001, 2010This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting,reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication orparts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, inits current version, and permission for use must always be obtained from Springer. Violations are liable toprosecution under the German Copyright Law.The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply,even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws andregulations and therefore free for general use.Printed on acid-free paperSpringer is a part of Springer Science Business Media (springer.com).

Preface to the Fourth EditionSince the appearance of our book, Fundamentals of Semiconductors:Physics and Materials Properties, one of the questions we are askedmost frequently is this: “is there a solution manual to this book?” In preparingthe questions at the end of each chapter we have already tried to guide thereaders to derive the answers by themselves using a step-by-step approach.Clearly this strategy did not work for everyone. We recognize that many ofthe questions in this book are quite challenging and often require reading ofresearch papers to solve them. In response to readers demand we have decided to provide solutions to some of the problems in this new edition. Sinceworking through problems is an important and necessary part of the learningprocess in physics we will not give the solutions to all the problems. Instead,we hope to use the solutions to a number of selected problems in each chapter as an additional study help to the readers. We like to use these solutionsto provide more in depth discussions to topics which may be too specializedfor a typical course on semiconductor physics. By leaving enough unsolvedproblems and adding a few new ones there are still plenty of opportunities forboth the instructors to choose problems for assignments and for students totest their understanding of the text. We like to point out that, even if the solution can be found in this manual, there is usually more than one way to solvea given problem. Conscientious students should always ask whether there is abetter way to solve a problem than the one we have provided in this manual.This new addition also allows us to update and expand some topics andreferences. Finally, we hope to have taken care of the few errors still remaining in the third edition. We like to use this opportunity to thank the readerswho have identified them to us. Their support has been invaluable in our effort to improve this book.A Russian translation of our book has appeared in 2003. It joins previous translations of the book into Japanese and Chinese, making this bookavailable to a truly international readership. Last, but not least, the homepage of the book has been given a ”face lift”. Readers are encouraged tovisit the new website at: to discover new information and materials which have been added.Peter Y. Yu and M. CardonaBerkeley, CA and Stuttgart, GermanyMarch 2010

Preface to the Third EditionThe support for our book has remained high and compliments from readersand colleagues have been most heart-warming. We would like to thank all ofyou, especially the many students who have continued to send us their comments and suggestions. We are also pleased to report that a Japanese translation appeared in 1999 (more details can be obtained from a link on our Website: http://pauline.berkeley.edu/textbook). Chinesea) and Russian translationsare in preparation.Semiconductor physics and material science have continued to prosper andto break new ground. For example, in the years since the publication of thefirst edition of this book, the large band gap semiconductor GaN and relatedalloys, such as the GaInN and AlGaN systems, have all become important materials for light emitting diodes (LED) and laser diodes. The large scale production of bright and energy-efficient white-light LED may one day changethe way we light our homes and workplaces. This development may even impact our environment by decreasing the amount of fossil fuel used to produceelectricity. In response to this huge rise in interest in the nitrides we haveadded, in appropriate places throughout the book, new information on GaNand its alloys. New techniques, such as Raman scattering of x-rays, have givendetailed information about the vibrational spectra of the nitrides, availableonly as thin films or as very small single crystals. An example of the progressin semiconductor physics is our understanding of the class of deep defect centers known as the DX centers. During the preparation of the first edition, thephysics behind these centers was not universally accepted and not all its predicted properties had been verified experimentally. In the intervening yearsadditional experiments have verified all the remaining theoretical predictionsso that these deep centers are now regarded as some of the best understooddefects. It is now time to introduce readers to the rich physics behind thisimportant class of defects.The progress in semiconductor physics has been so fast that one problemwe face in this new edition is how to balance the new information with the oldmaterial. In order to include the new information we had either to expand thesize of the book, while increasing its price, or to replace some of the existingmaterial by new sections. We find either approach undesirable. Thus we havecome up with the following solution, taking advantage of the Internet in thisaThe Chinese version was published in 2002 by Lanzhou University Press (seewww.onbook.com.cn)

VIIIPreface to the Third Editionnew information age. We assume that most of our readers, possibly all, are“internet-literate” so that they can download information from our Web site.Throughout this new edition we have added the address of Web pages whereadditional information can be obtained, be this new problems or appendiceson new topics. With this solution we have been able to add new informationwhile keeping the size of the book more or less unchanged. We are sure theowners of the older editions will also welcome this solution since they canupdate their copies at almost no cost.Errors seem to decay exponentially with time. We thought that in the second edition we had already fixed most of the errors in the original edition.Unfortunately, we have become keenly aware of the truth contained in thistimeless saying: “to err is human”. It is true that the number of errors discovered by ourselves or reported to us by readers has dropped off greatly sincethe publication of the second edition. However, many serious errors still remained, such as those in Table 2.25. In addition to correcting these errors inthis new edition, we have also made small changes throughout the book toimprove the clarity of our discussions on difficult issues.Another improvement we have made in this new edition is to add manymore material parameters and a Periodic Table revealing the most commonelements used for the growth of semiconductors. We hope this book will benot only a handy source for information on topics in semiconductor physicsbut also a handbook for looking up material parameters for a wide range ofsemiconductors. We have made the book easier to use for many readers whoare more familiar with the SI system of units. Whenever an equation is different when expressed in the cgs and SI units, we have indicated in red thedifference. In most cases this involves the multiplication of the cgs unit equation by (4 Â0 ) 1 where Â0 is the permittivity of free space, or the omission ofa factor of (1/c) where c is the speed of light.Last but not least, we are delighted to report that the Nobel Prize inPhysics for the year 2000 has been awarded to two semiconductor physicists,Zhores I. Alferov and Herbert Kroemer (“for developing semiconductor heterostructures used in high-speed- and opto-electronics”) and a semiconductordevice engineer, Jack S. Kilby (“for his part in the invention of the integratedcircuit”).Stuttgart and Berkeley,January 2001Peter Y. YuManuel Cardona

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

erostructures used in high-speed- and opto-electronics”) and a semiconductor device engineer, Jack S. Kilby (“for his part in the invention of the integrated circuit”). Stuttgart and Berkeley, Peter Y. Yu January 2001 Manuel Cardona. Preface to the Second Edition We have so far received many comments and feedback on our book from all quarters including students, instructors and, of .