Table Of ContentPRINCIPLES OF
SEMICONDUCTOR
DEVICES
SECOND EDITION
SIMA DIMITRIJEV
Griffith University
NewYork Oxford
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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
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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.
