Quantum Physics of Semiconductor Materials and Devices PDF
Preview Quantum Physics of Semiconductor Materials and Devices
QUANTUM PHYSICS OF SEMICONDUCTOR MATERIALS AND DEVICES Quantum Physics of Semiconductor Materials and Devices D. Jena CornellUniversity GreatClarendonStreet,Oxford,OX26DP, UnitedKingdom OxfordUniversityPressisadepartmentoftheUniversityofOxford. ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship, andeducationbypublishingworldwide.Oxfordisaregisteredtrademarkof OxfordUniversityPressintheUKandincertainothercountries ©DebdeepJena2022 Themoralrightsoftheauthorhavebeenasserted Impression:1 Allrightsreserved.Nopartofthispublicationmaybereproduced,storedin aretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthe priorpermissioninwritingofOxfordUniversityPress,orasexpresslypermitted bylaw,bylicenceorundertermsagreedwiththeappropriatereprographics rightsorganization.Enquiriesconcerningreproductionoutsidethescopeofthe aboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,atthe addressabove Youmustnotcirculatethisworkinanyotherform andyoumustimposethissameconditiononanyacquirer PublishedintheUnitedStatesofAmericabyOxfordUniversityPress 198MadisonAvenue,NewYork,NY10016,UnitedStatesofAmerica BritishLibraryCataloguinginPublicationData Dataavailable LibraryofCongressControlNumber:2021952780 ISBN978–0–19–885684–9(hbk) ISBN978–0–19–885685–6(pbk) DOI:10.1093/oso/9780198856849.001.0001 Printedandboundby CPIGroup(UK)Ltd,Croydon,CR04YY LinkstothirdpartywebsitesareprovidedbyOxfordingoodfaithand forinformationonly.Oxforddisclaimsanyresponsibilityforthematerials containedinanythirdpartywebsitereferencedinthiswork. ”IamoneofthosewhothinklikeNobel,thathumanitywilldrawmoregood thanevilfromnewdiscoveries.”–MarieCurie ”Noproblemcanbesolvedfromthesamelevelofconsciousnessthatcreated it. Wemustlearntoviewtheworldanew.”–AlbertEinstein ”Oneshouldntworkonsemiconductors,thatisafilthymess;whoknows whetheranysemiconductorsexist”–WolfgangPauli ”Iamthinkingofsomethingmuchmoreimportantthanbombs. Iam thinkingaboutcomputers”–JohnvonNeumann ”Itisfrequentlysaidthathavingamore-or-lessspecificpracticalgoalin mindwilldegradethequalityofresearch. Idonotbelievethatthisis necessarilythecaseandtomakemypointinthislectureIhavechosenmy examplesofthenewphysicsofsemiconductorsfromresearchprojectswhich wereverydefinitelymotivatedbypracticalconsiderations...”–William Shockley,NobelLecture(1956) ”Somepeoplecandoonethingmagnificently,likeMichelangelo. Others makethingslikesemiconductors,orbuild747airplanes-thattypeofwork requireslegionsofpeople. Inordertodothingswell,thatcan’tbedoneby oneperson,youmustfindextraordinarypeople”–SteveJobs Preface Semiconductorelectronicsrequiresforitsfoundationprimarilywavemechan- icsandstatistics. However,crystallography,thermodynamics,andchemistry 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 WalterSchottky Several excellent books and monographs have been written about the physics of semiconductors and nanostructures. I could not resist reproducingtheaboveparagraphfromanearlyclassic,Spenke’sElec- 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 onthistopicinthe1950s,whenthefieldwasinitsinfancy. Consider the simplest physical processes that occur in semiconduc- tors: electronorholetransportinbandsandoverbarriers, collisionof 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- timesbecomeroadblockstowardsadeeperunderstandingandappre- ciation of the richness of the subject. A typical introductory course on semiconductor physics would then require prerequisites of quan- tummechanics,statisticalphysicsandthermodynamics,materialssci- ence,andelectromagnetism. Rarelywouldastudenthaveallthisback- groundwhen(s)hetakesacourseofthisnatureinmostuniversities. Whathaschangedsince1950s? Semiconductordeviceshavebecome 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 connectionofthephysicstotoday’sinformationsystemssuchastran- 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. viii Preface The quantum physics of semiconductors is not abstract, but mea- suredroutinelyascurrentsandvoltagesindiodesandtransistors,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- tumphysicsofsemiconductorsandnanostructuresondisplayrightin front of our very eyes. Asher Peres captured this philosophy beauti- fullyinhisquote: ”Quantum Phenomena do not occur in a Hilbert space. They occur in a laboratory.”–AsherPeres 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 almostimmediateintheformofusefulsemiconductordevices. Ihave had the opportunity to work on both sides of the fence – on the fun- damental materials science and quantum physics of semiconductors, andintheirapplicationsinsemiconductorelectronicandphotonicde- vices. Drawingfromthisexperience,Ihavemadeaneffortinthisbook tomakeeachtopicastangibleaspossible. Theconceptsaredeveloped from their experimental roots, with historical trails, personalities, and stories where possible, to reflect the subject as a human adventure. Themathematicalstructureisthendevelopedtoexplainexperimental observations,andthenpredictnewphenomenaanddevices. Ibelieve this is a unique approach towards a book on this subject, one that distinguishesitfromothersinthefield. Thebookisaimedatthirdandfourthyearundergraduatestudents, and graduate students in Electrical Engineering, Materials Sciences andEngineering,AppliedPhysics,Physics,andMechanicalandChem- icalEngineeringdepartmentsthatoffersemiconductorrelatedcourses. It will be of interest to scientists and engineers in the industry, and in variousresearchlaboratories. Thebookisdividedintofourmodules. Module I, in seven chapters, presents the fundamentals rigorously, coveringthecoreprinciplesofquantummechanics,statisticalthermo- dynamics, and the physics of free electrons. The last two chapters of Module I develop perturbation theory techniques without which one isoftendisadvantagedinunderstandingsemiconductorphysics. ModuleII,inninechaptersintroducestheconceptsofbands,gaps, effectivemasses,andBlochtheory,developsafewmethodstocalculate andunderstandsemiconductorbandstructures,anddevelopsmethods tohandlearangeofsemiconductorquantumheterostructures. 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, andFermiGoldenrulefortransitions. High-fieldtransport,tunneling, and quantummagnetotransport phenomenaround offthis moduleof ninechapters. ix Module IV focuses on semiconductor photonics, by starting from a descriptionoftheMaxwellequationsandlight,trackingtheinteraction ofphotonswithsemiconductors,andculminatinginthedescriptionof semiconductorheterostructurephotonicdevices. 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 tosolveasmanyexercisesastimepermits. 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- signedasprojects),Chapters20-24inModuleIII,andChapters27and 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- conductorsofModulesIandII,theprogressthroughModulesIIIand IV can be rapid. I have provided a table and guidance for instructors andstudentslaterinthisprefaceforpotentialusageofthebook. 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. Becausemuchofsemiconductorphysicsoriginatedfromatomicquan- tumtheory,suchexamplesabound,buthavebeen”lostintranslation” 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 exceededitsintendedpedagogicalpurpose. 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 physicstoelectricalengineers,appliedphysicists,andmaterialsscien- tistswhoworkonsemiconductors,byusingsemiconductordevicesin thebackdrop. Itismysincerehopethatthisbookfillsthatvoid. DebdeepJena Ithaca,NewYork,March2022.
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