PRINCIPLES OF SEMICONDUCTOR DEVICES SECOND EDITION SIMA DIMITRIJEV Griffith University NewYork Oxford OXFORD UNIVERSITY PRESS OxfordUniversityPress,Inc.,publishesworksthatfurtherOxfordUniversity’s objectiveofexcellenceinresearch,scholarship,andeducation. Oxford NewYork Auckland CapeTown DaresSalaam HongKong Karachi KualaLumpur Madrid Melbourne MexicoCity Nairobi NewDelhi Shanghai Taipei Toronto Withofficesin Argentina Austria Brazil Chile CzechRepublic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore SouthKorea Switzerland Thailand Turkey Ukraine Vietnam Copyright 2012,2006byOxfordUniversityPress,Inc. FortitlescoveredbySection112oftheU.S.HigherEducationOpportunity Act,pleasevisitwww.oup.com/us/heforthelatestinformationaboutpricing andalternateformats. PublishedbyOxfordUniversityPress,Inc. 198MadisonAvenue,NewYork,NewYork10016 http://www.oup.com OxfordisaregisteredtrademarkofOxfordUniversityPress Allrightsreserved.Nopartofthispublicationmaybereproduced, storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans, electronic,mechanical,photocopying,recording,orotherwise, withoutthepriorpermissionofOxfordUniversityPress. LibraryofCongressCataloging-in-PublicationData Dimitrijev,Sima,1958– Principlesofsemiconductordevices/SimaDimitrijev.—2nded. p.cm.—(TheOxfordseriesinelectricalandcomputerengineering) ISBN978-0-19-538803-9(hardback) 1. Semiconductors. I. Title. TK7871.85.D546972011 (cid:2) 621.38152—dc22 2010048450 Printingnumber:9 8 7 6 5 4 3 2 1 PrintedintheUnitedStatesofAmerica onacid-freepaper PREFACE This edition of Principles of Semiconductor Devices maintains the main aims of the previous edition—to offer a student-friendly text for senior undergraduate and graduate studentsofelectricalandcomputerengineeringthatprovidesacomprehensiveintroduction tosemiconductordevices.Relatedtothestudent-friendlyaspect,theaimistoprovidethe bestexplanationsoftheunderlyingphysics,deviceoperationprinciples,andmathematical models used for device and circuit design and to supportthese explanationsby intuitive figures.Thecomprehensivecharacterofthetextemergesfromthelinksthatitestablishes betweentheunderlyingprinciplesandmodernpracticalapplications,includingthelinkto theSPICEmodelsandparametersthatarecommonlyusedduringcircuitdesign. New to This Edition The aim oflinkingdevicephysicsto modernapplicationssets the needforchangesthat aremadeinthisedition.Thedimensionsofmodernsemiconductordevicesarereducedto the pointwhere electronic engineershave to question applicability of the basic concepts and models presented in semiconductor textbooks. For example, the average number of minority-current carriers is smaller than one carrier (N<1) in almost all modern semiconductor devices, which calls into question the concepts of continuous particle concentrationandcontinuouscurrentasfundamentalelementsofstandardsemiconductor theory. Further questions are due to increasing practical manifestations of quantum- mechanical effects in nanoscale devices and potential applications of nanowires and carbon nanotubes that exhibit one-dimensionaltransport. The answer to these questions shouldnotbetosimplydisregardwell-establishedstandardsemiconductortheoryandasa consequencetodisregardallthedesigntoolsandpracticesbasedonthistheorythathave beendevelopedoverseveraldecades.ThiseditionofPrinciplesofSemiconductorDevices is the first textbook to address these questions by specifying the fundamental principles and by logical application of these principles to upgrade the standard theory for proper interpretationandmodelingoftheeffectsinmoderndevices. Followingisasummaryofthenewelementsandmainchangesinthisedition: • Anewchapter—thefirstinsemiconductortextbooks—onthephysicsofnanoscale devices, including the physics of single-carrier events, two-dimensional transport in MOSFETs and HEMTs, and one-dimensional ohmic and ballistic transport in nanowiresandcarbonnanotubes. • Fully revised andupgradedmaterialon crystals to introducegrapheneand carbon nanotubes as two-dimensional crystals and to link them to the standard three- dimensionalcrystalsthroughtheunderlyingatomic-bondconcepts. • RevisedP–Njunctionchaptertoemphasizethecurrentmechanismsthatarerelevant inmoderndevices. xvii xviii Preface • JFETsandMESFETspresentedinaseparatechapter. • Revisedchapterontheenergy-bandmodel. • 57newproblemsand11newexamples. Course Organization The organization of the text is such that the core material is presented in Part I (semiconductor physics) and Part II (fundamental device structures). This will be quite sufficient for introductory undergraduatecourses. Selected sections from Part III can be used in courses that are focused on the core material in different ways: (1) as read- only material, (2) as material for assignments, (3) as reference material, and (4) as supportingmaterial for computer and/or laboratoryexercises. Many courses will require fullintegrationofselectedsectionsfromPartIII.Theorderofthesectionsinthebookdoes notimplythesequencetobefollowedinthesecourses.Selectedspecific/advancedsections can be read immediately after the relevant fundamental material. A typical example is the electronics-oriented material, such as the equivalent circuits and SPICE parameter measurements,presentedinChapter11.Tointegratetheequivalentcircuitsintoacourse, thesectionsonequivalentcircuitsofdiodescanbeusedasextensionsofthediodechapter, thesectionsonequivalentcircuitsofMOSFETscanbeusedasextensionsoftheMOSFET chapter,and the sections on equivalentcircuits of BJTs can be used as extensionsof the BJTchapter.Similarly,iftheICtechnologysectionsfromChapter16aretobeintegrated, theycanbeusedasextensionsofthediode,MOSFET,andBJTchapters.Anotherexample relates to the JFET and MESFET sectionsin Chapter 13.If these devicesare an integral partofa course,thenthesesectionscanbeincludedaftertheMOSFETchaptertocreate integrated coverage of FET devices. For courses that integrate photonic devices, the specific material from Chapter 12 can be included after the diode chapter. Analogously, forcoursesthatneedtoaddressissuesthatarespecificforpowerelectronics,thesections onpowerdiodesandpowerMOSFETsfromChapter14canbeusedasextensionsofthe diodeandMOSFETchapters,respectively. Acknowledgments I valueverymuch the feedbackI receivedaboutthe first editionof the book,and I wish to thankeverybodywhosentmecomments,suggestions,anderrata.I amindebtedto all anonymousreviewersfromdifferentstagesofthedevelopmentofthisbook,becausethey providedabsolutelyessentialfeedbackandextremelyvaluablecommentsandsuggestions. Iamespeciallygratefultothereviewers,whoseopinionsandcommentsdirectlyinfluenced thedevelopmentofthisedition: PetruAndrei,FloridaStateUniversity TerenceBrown,MichiganStateUniversity GodiFischer,RhodeIslandUniversity SiddharthaGhosh,UniversityofIllinoisatChicago MatthewGrayson,NortheasternUniversity Ying-ChengLai,ArizonaStateUniversity Preface xix It is my pleasure to acknowledge that a large team from Oxford University Press is behind this project and I am most thankful for their continuing support. The project started with important decisions and involvement by John Challice, publisher, Danielle Christensen,developmenteditor,andRachaelZimmermann,associateeditor,andcrucially relied on the work and expertise of Claire Sullivan, editorial assistant, Barbara Mathieu, senior productioneditor, Claire Sullivan, editorial assistant, Brenda Griffing, copyeditor, andJillCrosson,copywriter. Finally,Iwouldliketoacknowledgethesupportofmyfamily,inparticularmywife, Vesna,becauseitprovidedmewithalotofnecessarytimeandinspiration. SimaDimitrijev 1 Introduction to Crystals and Current Carriers in Semiconductors: The Atomic-Bond Model Electriccurrentinbothmetalsandsemiconductorsisduetotheflowofelectrons,although many electrons are tied to the parent atoms and are unable to contribute to the electric current. The regular placement of atoms in metal and semiconductor crystals, shown in Fig. 1.1 for the case of silicon crystal, provides the conditions for some electrons to be sharedbyalltheatomsinthecrystal.Itistheseelectronsthatcanmakeelectriccurrentand are referredto ascurrentcarriers.The effectsof regularatom placementonthe essential properties of the current carriers in semiconductors are progressively introduced in two steps: (1)atthe leveloftheatomic-bondmodelinthischapterand(2)atthe levelofthe energy-bandmodelinthenextchapter. This chapter begins with a description of atomic bonds and then proceeds to the important concepts related to spatial placement of atoms in both three-dimensional and two-dimensional crystals (including graphene and carbon nanotubes). This chapter also Figure1.1 Imageofsiliconcrystalobtainedby transmission-electronmicroscopy. 0.543 nm 1 2 CHAPTER1 INTRODUCTIONTOCRYSTALSANDCURRENTCARRIERSINSEMICONDUCTORS introducescurrentcarriersinsemiconductorstothelevelthatispossiblewiththeatomic- bond model. Although lacking certain important details, this level is a very important initialstep.Theusualmodelofcurrentconductioninmetalshastobegraduallyupgraded to introduce the model of conduction by carriers of two types: free electrons and holes among bound electrons. It is the existence of two types of carrier that distinguishes semiconductors from metals. Given that semiconductor devices utilize combinations of layers with predominantly electron-based conduction (N-type layers) and layers with predominantlyhole-basedconduction(P-typelayers),the conceptsandeffectsofN-type andP-typedopingarealso introducedin thischapter.Theeffectsofdopingareessential becausesemiconductorsaredistinguishedfrominsulatorsbytheabilitytoachieveN-type and P-typelayers. Finally,to roundupthe introductionto semiconductorsatthe atomic- bond level, the last section briefly presents the basic techniques of crystal growth and doping. † 1.1 INTRODUCTION TO CRYSTALS 1.1.1 Atomic Bonds Certain atoms can pack spontaneously into an orderly pattern called a crystal lattice. If this were not so, it would be practically impossible to create even one cubic millimeter ofa crystallinematerial,asthiswouldrequirethe placementofmorethan1019 atomsin almostperfectorder.Clearly,there are naturalforcesthat holdthe atoms ofa crystalline materialtogether.Theseforcesarerelatedtothestabilityoftheelectronicconfigurationof individualatoms.Forexample,thereareatomswithquitestableelectronicconfigurations; theyarereferredtoasthenoblegases,andtheyarechemicallyinert.Helium,thenoblegas elementwiththesmallestnumberofelectrons,hastwoelectronswithsphericalsymmetry and opposite spins. The next noble gas element, neon, has 10 electrons. In neon, two electrons are in the first shell (as in the case of helium), which is usually denoted by 1s2 (1indicates the first shell and s2 indicates the two electrons in the spherical orbital labeledbys).Theremainingeightelectronsfillthesecondshell—onepairwithspherical symmetry(s2)andthreepairsat porbitalswithx-, y-,andz-symmetries(p2p2p2 = p6). x y z The shapes and symmetries of 2s and 2p electron orbitals are illustrated in Fig. 1.2. Accordingly, the complete electronic configuration of neon is expressed as 1s22s22p6. Sodium is the eleventh element, with the eleventh electron placed in the s orbital of the third shell: 1s22s22p63s1. To reach the stability of the electronic configuration found in neon, sodium tends to give the eleventh electron away. On the other hand, chlorine, the seventeenth, element, can reach the stability of argon (the next noble gas element) by accepting an extra electron. Therefore, sodium and chlorine atoms relatively easily exchangeelectrons,creatingpositivesodiumionsandnegativechlorineions.Theattractive forcesbetweenthepositiveandnegativeions(ionicbonds)holdtheatomsofNaClcrystals together. †Sectionsmarkedbyadaggercanbeusedasread-onlysections. 1.1 IntroductiontoCrystals 3 Figure1.2 Theshapesandsymmetriesof2sand 2pelectronorbitals. 2s 2p 2p 2p x y z The atoms in metal crystals are held together by another type of bond, the metallic bond.Inthiscase,theatomssimplygivetheextraelectronsawaytoreachstableelectronic configurations.Theextraelectronsaresharedbyalltheatoms(positiveions)inthecrystal, sothatwecanthinkofionssubmergedinaseaofelectrons.Theseaofelectronsholdsthe crystaltogether;butbecausetheseelectronsaresharedbyalltheatoms,theymovethrough thecrystalwhenanelectricfieldisapplied.Consequently,metalsareexcellentconductors ofelectriccurrent. The atoms with half-filled shells can reach stable electronic configurations in two symmetric ways: (1) by giving the electrons from the half-filled shell away or (2) by acceptingelectronsfromneighboringatomstofillthehalf-emptyshell.Thefirstelement that exhibits a half-filled shell is hydrogen: it has one electron in the first shell that canaccommodatetwo electrons.Two hydrogenatomsformahydrogenmolecule,where one of the hydrogen atoms gives its electron away (to eliminate the unstable electronic configurationassociated with a single electron)and the other hydrogenatom acceptsthe electron(toreachthestableelectronicconfigurationofhelium).Becauseofthesymmetry of this situation, the hydrogen atom that gives and the hydrogen atom that accepts an electronareindistinguishable.Thistypeofbond,whichisclearlydifferentfromboththe ionicandmetallicbonds,isthecovalentbond. The next atom that has a half-filled shell is carbon. Carbon has six electrons: two electrons completely fill the first shell, with the remaining four electrons appearing in the second shell, which can accommodate eight electrons: 1s22s22p2. The four valence electronsinthesecondshell,whicharetheunstableoractiveelectrons,makecarbonthe firstelementinthefourthgroupoftheperiodictableofelements(asshowninTable1.1).A carbonatomcanformfourcovalentbondswithfourhydrogenatoms,whichcreatesastable methanemolecule(CH ). In a methanemolecule,the carbonatomeither givesaway the 4 fourvalenceelectrons(toreachthestableelectronicconfigurationofhelium)oracceptsthe fourelectronsfromthe fourhydrogenatoms(toreachthestable electronicconfiguration of neon). The four covalent bonds in a methane molecule are indistinguishable because ofthesymmetryofthismolecule,whichisnotconsistentwiththedifferencebetweenthe two s electrons and the two p electrons in the 2s22p2 configuration of the second shell of a carbonatom.A carbonatomcan formfoursymmetricalcovalentbondsbecausethe 2s, 2p , 2p , and 2p orbitals (Fig. 1.2) can be transformed into the four symmetrical x y z hybrid orbitals illustrated in Fig. 1.3a. This transformation is called hybridization, and the four symmetric hybridorbitals are called sp3 hybrid orbitals; the label sp3 indicates that these orbitals are the result of hybridization of one s (2s) and three p (2p , 2p , x y and 2p ) orbitals. Figure 1.3b illustrates the interaction between the four sp3 orbitals of z the carbon atom and the 1s orbitals of the four hydrogenatoms in a methane molecule, 4 CHAPTER1 INTRODUCTIONTOCRYSTALSANDCURRENTCARRIERSINSEMICONDUCTORS TABLE1.1 SemiconductorRelatedElements inthePeriodicTable(withAtomic NumberandAtomicWeight) III IV V (cid:2)3 (cid:2)4 (cid:2)5 5 B 6 C 7 N Boron Carbon Nitrogen 10.82 12.01 14.008 13 Al 14 Si 15 P Aluminum Silicon Phosphorus 26.97 28.09 31.02 31 Ga 32 Ge 33 As Gallium Germanium Arsenic 69.72 72.60 74.91 49 In 50 Sn 51 Sb Indium Tin Antimony 114.8 118.7 121.8 H H C C σ b o n d H H H H H H (a) (b) (c) Figure1.3 Hybridelectronicconfigurationthatenablesfoursymmetricalcovalentbondsofacarbonatom:(a)theshape andtetrahedralsymmetryofsp3hybridorbitals,(b)theinteractionsofthefoursp3orbitalswith1sorbitalsoffourhydrogen atomsthatformthefourcovalentbondsofaCH molecule,and(c)thethree-dimensionalatomic-bondmodeloftheCH 4 4 molecule. whereasFig.1.3cshowstheatomic-bondmodelofthismoleculeinthreedimensions.As indicatedinFig.1.3c,covalentatomicbondsofthistypearecalledσ bonds. Another important hybridization of the 2s, 2p , 2p , and 2p orbitals in carbon is x y z called sp2 hybridization. In this case, the s orbital and two p orbitals, say p and p , x y are transformed into three sp2 orbitals with triangular planar symmetry (Fig. 1.4a); the p orbitalremainsunhybridized.Carbonatomswithsp2 hybridorbitalsformσ covalent z bondswith planar(two-dimensional)structures.The simplest structurefromthis class is the ethylene molecule, C H . Figure 1.4b illustrates that the sp2 orbitals form σ bonds 2 4 (four bonds with the s orbitals of four hydrogen atoms and one bond between two sp2 1.1 IntroductiontoCrystals 5 sp2 pz sp2 C σπ bboonndd H C H sp2 H H (a) (b) H C π bond C H σ bond H H (c) Figure1.4 Hybridelectronicconfigurationofacarbonatomthatresultsintriangularplanarbonds: (a)theshapeandtriangularsymmetryofsp2hybridorbitals,(b)σ bondformedbytwosp2orbitals andπ bondformedbytheunhybridizedporbitalsoftwocarbonatomsinaC H molecule,and(c) 2 4 theatomic-bondmodeloftheC H molecule. 2 4 orbitalsoftwocarbonatoms),whereastheunhybridizedporbitalsofthetwocarbonatoms formamuchweakerπ bond. Covalent bonds between carbon and hydrogen atoms result in molecules that form hydrocarbongasesofdifferenttypes.However,thesituationisverydifferentwhencovalent bondingislimitedtocarbonatomsthemselves.Considersp3-hybridizedcarbonatoms(as in Fig. 1.3a) and replace the four hydrogenatoms with identical, sp3-hybridizedcarbon atoms. The carbonatom in the center of the tetrahedronwill be stable owingto the four σ covalent bonds with the four neighboring carbon atoms. As distinct from hydrogen atoms in the corners of the tetrahedron, carbon atoms in the corners need to form three extra covalentbondseach to be stable. This means that each of the corner carbonatoms needs four carbon neighbors in analogous tetrahedral structures, so that each of these atomsappearsinthecenterofitsowntetrahedron.Thisarrangementrequirescontinuous replication of the tetrahedral pattern, which is the basic or primitive cell, in all three dimensions in space. Accordingly, sp3-hybridizedcarbon atoms form three-dimensional crystals with the tetrahedral primitive cell, which is the diamond version (polytype) of solid carbon. Silicon and germanium, as the second and third elements in the fourth column of the periodic table, respectively,also form three-dimensionalcrystals with the samediamond-typelattice.Section1.1.2considersthemostimportantthree-dimensional crystalsfordeviceapplicationsinmoredetail. Consider now sp2-hybridized carbon atoms (as in Fig. 1.4a) and replace the four hydrogen atoms with identical sp2-hybridized carbon atoms. The replacement of a hydrogen atom by an sp2 carbon atom means that this atom will have to connect to two additional sp2 carbon atoms to be stable, symmetrically to the carbon atoms in the ethylene molecule. In this case, the triangular planar structure is replicated to form a two-dimensionalcrystalknownasgraphene.Section1.1.2describesthetwo-dimensional structureofgrapheneandtherelatedcarbonnanotubes.