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IntroductiontoOpticalandOptoelectronicPropertiesofNanostructures
Get to grips with the fundamental optical and optoelectronic properties of nano-
structures.Thiscomprehensiveguidemakesawidevarietyofmoderntopicsacces-
sible,includingup-to-datematerialontheopticalpropertiesofmonolayercrystals,
plasmonics, nanophotonics, ultraviolet quantum well lasers, and wide-bandgap
materials and heterostructures. The unified, multidisciplinary approach makes it
idealforthoseindisciplinesspanningnanoscience,physics,materialsscience,and
optical,electrical,andmechanicalengineering.
BuildingonworkfirstpresentedinQuantumHeterostructures(Cambridge1999),
this volume draws on years of research and teaching experience. Rigorous cover-
age of basic principles makes it an excellent resource for senior undergraduates,
and detailed mathematical derivations illuminate concepts for graduate students,
researchers, and professional engineers. The examples with solutions included in
thetextandend-of-chapterproblemsallowstudentstousethistexttoenhancetheir
understanding.
VladimirV.MitinisaSUNYDistinguishedProfessorintheDepartmentofElectrical
Engineering and in the Department of Physics at the University at Buffalo, State
UniversityofNewYork.
Viacheslav A. Kochelap is Professor of Theoretical Physics and Head of the The-
oretical Physics Department at the Institute of Semiconductor Physics, National
AcademyofSciencesofUkraine.
MitraDuttaistheViceChancellorforResearchandaUniversityDistinguishedPro-
fessor at the University of Illinois at Chicago and also holds appointments in the
DepartmentsofElectronicandComputerEngineeringandPhysics.
MichaelA.StroscioisaUniversityDistinguishedProfessorandRichardandLoan
HillProfessorattheUniversityofIllinoisatChicagoandalsoholdsappointments
intheDepartmentsofElectricalandComputerEngineering,Bioengineering,and
Physics.
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Introduction to Optical and
Optoelectronic Properties
of Nanostructures
VLADIMIR V. MITIN
UniversityatBuffalo,StateUniversityofNewYork
VIACHESLAV A. KOCHELAP
LashkaryovInstituteofSemiconductorPhysics,Ukraine
MITRA DUTTA
UniversityofIllinoisatChicago
MICHAEL A. STROSCIO
UniversityofIllinoisatChicago
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108428149
DOI:10.1017/9781108674522
©CambridgeUniversityPress2019
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Firstpublished2019
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Contents
Preface pageix
1 SomeTrendsinOptoelectronics 1
2 MaterialsforOptoelectronicApplications 9
2.1 Introduction 9
2.2 Semiconductors 9
2.3 CrystalLattices:BondinginCrystals 12
2.4 ElectronEnergyBands 18
2.5 SemiconductorHeterostructures 28
2.6 Lattice-MatchedandLattice-MismatchedMaterials 31
2.7 Lattice-Matched and Pseudomorphic Heterostructures, Si/Ge
Heterostructures,andLattice-MatchedIII–VHeterostructures 37
2.8 Wide-BandgapMaterialsandHeterostructures 40
2.9 QuantumDots 45
2.10 Two-Dimensional Monolayer Crystals (Graphene, Silicene,
Germanene, Tinene, Black Phosphorus, Monochalcogenides,
Dichalcogenides,Trichalcogenides,andBoronNitrides) 50
2.11 ClosingRemarkstoChapter2 56
2.12 ControlQuestions 58
3 ElectronsinQuantumStructures 60
3.1 Introduction 60
3.2 QuantumWells 61
3.3 ElectronsinSingle-andFew-MonolayerCrystals 69
3.4 QuantumWires 80
3.5 QuantumDots 84
3.6 CouplingbetweenQuantumWells 90
3.7 Superlattices 98
3.8 ExcitonsinQuantumStructures 104
3.9 Nanostructure-BasedMaterialsAreReconfigurableNanomaterials 114
3.10 ClosingRemarkstoChapter3 122
3.11 ControlQuestions 124
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vi Contents
4 Light–SemiconductorMaterialsInteraction 125
4.1 Introduction 125
4.2 ElectromagneticWavesandPhotons 125
4.3 LightInteractionwithMatter:Phototransitions 136
4.4 OpticalPropertiesofBulkSemiconductors 142
4.5 ClosingRemarkstoChapter4 166
4.6 ControlQuestions 166
5 OpticsofQuantumStructures 168
5.1 Introduction 168
5.2 OpticalPropertiesofQuantumStructures 168
5.3 IntrabandTransitionsinQuantumStructures 182
5.4 OpticalPropertiesofTwo-Dimensional(Few-Monolayer)Crystals 193
5.5 TheOpticsofQuantumDots 205
5.6 ClosingRemarkstoChapter5 208
5.7 ControlQuestions 209
6 Electro-OpticsandNonlinearOptics 211
6.1 Introduction 211
6.2 Electro-OpticsinSemiconductors 212
6.3 TerahertzCoherentOscillationsofElectronsinanElectricField 225
6.4 NonlinearOpticsinHeterostructures 228
6.5 PlasmonicsanditsPeculiaritiesinNanostructures 238
6.6 ClosingRemarkstoChapter6 257
6.7 ControlQuestions 258
7 Light-EmittingDevicesBasedonInterbandPhototransitionsin
QuantumStructures 260
7.1 Introduction 260
7.2 LightAmplificationinSemiconductors 260
7.3 Light-EmittingDiodesandLasers 279
7.4 BlueandUltravioletLight-EmittingDiodes 297
7.5 QuantumWireandQuantumDotEmittersandLasers 317
7.6 ClosingRemarkstoChapter7 329
7.7 ControlQuestions 330
8 DevicesBasedonIntrabandPhototransitionsinQuantumStructures
andSiliconOptoelectronics 331
8.1 Introduction 331
8.2 UnipolarIntersubbandQuantum-CascadeLasers 332
8.3 TerahertzCascadeLasers 336
8.4 PhotodetectorsBasedonIntrabandPhototransitions 340
8.5 SiliconPhotonics 349
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Contents vii
8.6 PerspectivesofOptoelectronicDevicesBasedon
Two-DimensionalCrystals 353
8.7 AdaptivePhotodetectors 360
8.8 ClosingRemarkstoChapter8 370
8.9 ControlQuestions 370
AppendixABasicStatementsandFormulaeofQuantumPhysics 373
AppendixBTablesofUnits 386
AppendixC ListofPertinentSymbols 389
FurtherReading 391
Index 401
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Preface
Therearemanymonographsandtextbooksdevotedtonanostructuresandnano-
electronics.Itisgenerallyacceptedthatmicrostructurescienceandtechnologydeal
withmicrostructureswithsizesdownto0.1micrometer,whilesizesbelow100nm
(0.1micrometer)areconsideredinnanoscienceandnanoelectronics.Nanoelectron-
ics was and is predominantly driven by applications in processors and memories
ofcomputersandtheirfollow-onsystems.Thisiswhytheoverwhelmingmajority
oftextbooksdealwiththeprogressinthetechnology,coveringso-calledtop-down
technologywhichproducesnanostructuresandnanostructuredeviceswhosecritical
dimensionsarereducedtolessthan100nm.Textbookshavedevotedlessattention
totheopticalpropertiesandoptoelectronicsofnanostructures,thesubjectofthis
book.
A new burst of basic research and applications of nanostructures was stimu-
latedin2004bya“scotchtape”technologyinwhichasinglelayerofgraphenewas
obtainedbypeelingitfromagraphitesurface.Thesimplicityof“scotchtape”tech-
nologyandtheveryunusualpropertiesofgrapheneinitiatedinterestinstructures
withathicknessofoneatomiclayer.Manymaterialshaveweakbondingbetween
the layers, and monolayers or bilayers can easily be produced with “scotch tape”
technology.Inspiteofthefactthatthe“scotchtape”technologyisnotapplicable
forindustrialproduction,itisconvenientandinexpensiveforwideuseinresearch.
Thesemonolayerstructuresdemonstratedinterestingelectrical,optical,andopto-
electronicproperties.Todaydifferentmethodsoffabricationofgraphenehavebeen
developed, including epitaxial technologies. A number of other one-atom-thick
material structures have been discovered and studied. These monolayer materials
constitute a new class of two-dimensional crystals which complements conven-
tional two-dimensional heterostructures. Industrially applicable technologies for
thesestructuresarecurrentlyunderactivedevelopment.
Modern educational programs need to address the rapidly evolving facets of
nanoscience and nanotechnology. A new generation of researchers, technologists,
andengineershastobetrainedintheemergingnano-disciplines.Withthepurpose
ofcontributingtoeducationinthenano-fields,wepresentthistextbookproviding
aunifyingframeworkforthebasicideasneededtounderstandrecentdevelopments
underlyingtheopticalandoptoelectronicpropertiesofnanostructures.Thisbook
grew out of the authors’ research and teaching experience in these subjects. We
havefoundthatmanyoftheideasandachievementscanbeexplainedinarelatively
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x Preface
simplesetting.Wehavedesignedthistextbookprimarilyforseniorundergraduate
students and first-year graduate students, who will have been trained in different
fields,includingnanoscience,physicsandopticalengineering,materialsscienceand
engineering,andmechanicalengineering.Toreachsuchabroadaudience,materials
arepresentedinsuchawaythataninstructorcanchoosethelevelofpresentation
dependingonthebackgroundsofthestudents.Weincludedetailsofderivationsand
themathematicaljustificationofconceptsinsomesections.Thesedetailedsections
may be omitted in an undergraduate curriculum. The book contains some solved
examplesinthetextandcontrolquestionsforstudentself-evaluationattheendof
eachchapter.
Althoughthisbookhasbeenwrittenbasicallyforthestudent,thematerialpre-
sentedinChapters4–8shouldbeusefulforawideaudienceofresearchersworking
ondifferentsubjectswithinthemultidisciplinaryareaofnanoscience.Thecoreof
this textbook is in Chapters 4–8 but, in order to make the book self-contained,
we give in Chapters 1–3 the relevant background material on nanostructures and
their electronic properties. Appendix A discusses the Schrödinger wave equation
forparticlesandcontainsmajorrelationsandequationsfromquantummechanics.
AppendixBincludestablesofunitsaswellasmajorphysicalconstants.
In Chapter 1, we present in concise form the main subject of the book, namely
the recent and diverse trends in nanotechnologies; novel concepts of nanodevices
arealsoreviewedbriefly.Thesetrendsmakeitclearwhyunderstandingthefunda-
mentalsoftheopticsandoptoelectronicsofnanostructuresisofgreatimportance.
Chapters 2 and 3 have been written for students who have not taken courses in
nanoelectronics.
InChapter2,wepresentanoverviewofthebasicmaterialsthatareexploitedin
nanoelectronics.Weintroducethemajorpropertiesofsemiconductorsandmateri-
alsthatdemonstrategreatpotentialforapplicationinnanoelectronicsandoptoelec-
tronics. Special attention is paid to carbon nanotubes, graphene, transition-metal
dichalcogenidesandothersingle-atomic-layermaterials.
In Chapter 3, we discuss the basic physical concepts related to the behavior of
particlesinthenanoworld.Keepinginmindthediversevariantsofnanostructures,
we analyze a number of particular examples which highlight important quantum
properties of particles in heterostructures. Recently, substantial efforts in research
have been made in the area of reconfigurable materials. The last section in Chap-
ter 3 briefly describes three examples of reconfigurable materials based on nanos-
tructures, namely on graphene, quantum wells, and quantum dots. Many of the
examples analyzed can serve as the simplest underlying models of nanostructures
thatareexploitedinlaterchapters.
For supplemental information on the fundamentals presented in Chapters 2
and 3, students can refer to the following recent books: Quantum Mechanics for
Nanostructures, V. Mitin, D. Sementsov, and N. Vagidov, Cambridge University
Press,2010,IntroductiontoNanoelectronics:Nanotechnology,Engineering,Science,
and Applications, V. Mitin, V. Kochelap, and M. Stroscio, Cambridge University
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Preface xi
Press, 2008, and Quantum Heterostructures: Microelectronics and Optoelectronics,
V.Mitin,V.Kochelap,andM.Stroscio,CambridgeUniversityPress,1999.
Chapter4coversthepropertiesoflightandlight–semiconductorinteractions.We
start with a brief review of the basic concepts of electromagnetic fields. We define
the classical characteristics of electromagnetic fields, such as the energy, intensity,
anddensityofstates,andweintroducetheconceptofthequantaofthesefields–the
photons.Byanalyzingelectromagneticfieldsinfreespaceandinopticalresonators,
weshowthatresonatorsdrasticallychangethestructureandthebehaviorofelec-
tromagnetic fields. Next we study the interaction of light with matter and define
three principal optical processes: spontaneous emission, stimulated emission, and
stimulatedabsorption.Wereviewtheopticalpropertiesofbulksemiconductorsand
define the major optical characteristics of semiconductors, with specific emphasis
ontheIII–Vcompounds.
Chapter 5 emphasizes that the electrodynamics of heterostructures differs from
thatofbulkmaterials.Thespatialnonuniformitycausesspecificcharacteristicsof
the interaction of light with matter, including light propagation, absorption, etc.
We introduce several parameters which characterize the interaction of light with
matterfordifferentcasesoflightpropagation.Theparametersforlightabsorption
are calculated for type-I heterostructure quantum wells. The optical properties of
monolayermaterialsarediscussed.Variousfactorsaffectingtheopticalproperties
of low-dimensional electrons, such as the broadening of spectra due to intraband
scatteringprocesses,excitoniceffects,etc.,areanalyzedinthischapter.
Chapter 6 discusses the influence of an external electric field on the refractive
index and the absorption coefficient, i.e., the effect of the electric field on the
propagation of light through a material or on the reflection of the light, which is
known as the electro-optical effect. We study the electro-optical effect for quan-
tumheterostructuresincludingquantumwells,double-andmultiple-quantum-well
structures, and superlattices. We consider the quantum-confined Stark effect, the
Burstein–Moss effect, and the effect of destroying excitons in gated heterostruc-
tures. We show that electro-optical effects have great potential for optoelectronic
applications using the electric field to control light and for realizing the tunable
generation of microwave emission. We consider nonlinear optical effects in quan-
tum heterostructures that occur at high intensities of light. Also in Chapter 6 we
present a new emerging branch of the subject – plasmonics for optoelectronics.
We discuss subwavelength light phenomena, which involve surface plasmons and
plasmonexcitationinlow-dimensionalelectrongases.
Chapters7and8aredevotedtotheapplicationsofnanostructures.Weanalyze
theeffectofopticalconfinement.Ourdiscussionfocusesonheterostructureswhich
facilitatethesimultaneousformationofopticalmodesandtherealizationoflaser
oscillations which convert electric power into laser emission. A variety of differ-
ent laser designs are analyzed, such as: quantum well and quantum wire lasers,
includingdevicesoperatingintheterahertz(THz),infrared,visible,andultraviolet
spectralregions;thequantumcascadelaser;andsingle-monolayerphotodetectors
and emitters. In particular, we consider ultraviolet-emitting devices based on the
