Isotope Low-Dimensional Structures: Elementary Excitations and Applications

103 Pages·2012·3.47 MB·English

by  Vladimir G. Plekhanov

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For furthervolumes:
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Vladimir G. Plekhanov
Isotope Low-Dimensional
Structures
Elementary Excitations and Applications
123
Vladimir G.Plekhanov
Mathematics and PhysicsDepartment
Computer Science College
Erika Street7a
10416Tallinn
Estonia
ISSN 2191-5423 ISSN 2191-5431 (electronic)
ISBN 978-3-642-28612-4 ISBN 978-3-642-28613-1 (eBook)
DOI 10.1007/978-3-642-28613-1
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012936757
(cid:2)TheAuthor(s)2012
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Preface
The experience of the past shows that throughout constant technology improve-
ment electronics (optoelectronics) has become more reliable, faster, more pow-
erful, and less expensive by reducing the dimensions of integrated circuits. These
advantages will lead to the development of modern microelectronics. The long-
term goal of this development will lead to nanoelectronics. Advancing to the
nanoscale is not just a step toward miniaturization, but requires the introduction
and consideration of many additional phenomena. At the nanoscale, most phe-
nomenaandprocessesaredominatedbyquantumphysicsandtheyexhibitunique
behavior. Nanotechnology includes the integration of man-made nanostructures
intolargermaterialcomponentsandsystems(see,e.g.[1–4]).Importantly,within
these larger scale systems, the active elements of the system will remain at
nanoscale.
Low-dimensional structures have become one of the most active research not
only in nanoscience and nanotechnology but also isotopetronics. Quantum wells,
quantum wires, and quantum dots structures produced in the main by epitaxial
growth techniques (mainly molecular beam epitaxy (MBE) and metal-organic
chemical vapor deposition (MOCVD) and their various variations such as che-
mical beam epitaxy (CBE), atomic layer epitaxy (ALE), etc. (see, e.g. [5–10]).
MBE and MOCVD are of considerable technological interest since they are used
asactivecomponentsinmoderndevices.Thesedevicesarehigh-electron-mobility
transistors,diodesandlasers,aswellasquantumdotsfromquantumcomputations
and communications perspectives.
The seminal works of Esaki and Tsu [11] and others on the semiconductor
superlattice stimulated a vast international research effort to understand the fab-
rication and electronic properties of superlattice, quantum wells, quantum wires,
and quantum dots (see, for example, [1–4]). The dimensional scale of such sam-
plesbetween10and100 nmwhicharethesubjectofnanoscience—isabroadand
interdisciplinary field of emerging research and development. Nanoscience and
nanotechnology are concerned with materials, structures, and systems whose
componentsexhibitnovelandsignificantlymodifiedphysical,chemicalproperties
v
vi Preface
due to their nanoscale sizes. The new direction of nanoscience is isotope-
engineeredmaterials,whichisstudiedthemorelow-dimensionalinsize,asarule
the sizes of the sample of isotope-engineered materials compare with the atomic
size. Nuclear technology—neutron irradiation [12]—is a very useful method for
preparinglow-dimensionalstructure:quantumwells,quantumwires,andquantum
dots[13].Aprincipalgoalofisotope-engineeredmaterialsasnewdirectionsofthe
nanotechnology is to control and exploit their new properties in structures and
devicesatatomic,threemolecular,andsupramolecularlevels.Theminituarization
requiredbymodernelectronicsisoneofthedrivingforcesforisotope-engineered
materials (isotopetronics)—new direction of nanotechnology (see, also [14]).
Modern nanoscience and nanotechnology is a fertile ground for teaching, as it
brings together the quantum theory of materials, novel physics in the electronic
andopticalpropertiesofsolids,theengineeringofsmallstructures,andthedesign
of high performance electronic, photonic, and optoelectronic systems. The treat-
ments attempt to be introductory, comprehensive, and phenomenological in the
main. The new physics described in this book comes from one important con-
sideration—lengthscale(see,also[1,2,15,16])especiallyinmesoscopicphysics.
As we all know, mesoscopic physics deals with structures which have a size
betweenthemacroscopicandthemicroscopicoratomicone.Thesestructuresare
also called mesoscopic systems, or nanostructures [3] in a more colloquial way
since their size usually ranges from a few nanometers to about 100 nm. The
electronsinsuchmesoscopicsystemsshowtheirwavelikeproperties[15,16]and
thereforetheirbehaviorismarkedlydependentonthegeometryofthesamples.In
this case, the states of the electrons are wave-like and somewhat similar to elec-
tromagnetic waves (see, e.g. [16]).
Asmentionedaboveforthedescriptionofthebehaviorofelectronsinsolids,it
is very convenient to define a series of characteristic lengths. If the dimension of
thesolidsinwhichtheelectronembeddedisoftheorderof,orsmallerthanthese
characteristic lengths (k de Broglie wavelength, or a —exciton radius, etc.) the
B ex
materialmightshownewproperties,whichingeneralaremoreinterestingthanthe
corresponding ones in macroscopic materials. On the contrary, a mesoscopic
systemapproachesitsmacroscopiclimitifitssizeisseveraltimesitscharacteristic
length.
As mentioned above, when the dimensions of the solid get reduced to a size
comparable with, or smaller k , then the particles behave wavelike and quantum
B
mechanicsshouldbeused.Letussupposethatwehaveanelectronconfinedwithin
a box of dimensions L , L , L. If the characteristic length is l, we can have the
x y z
following situations:
1. l h L , L , L. In this case the electron behaves as in regular 3D bulk
x y z
semiconductor (insulator).
2. l i L and L hh L , L. In this situation we have a 2D semiconductor perpen-
x x y z
diculartothex-axis.Thismesoscopicsystemisalsocalledaquantumwell(for
details see Chap. 3).
Preface vii
3. l i L , L and L , L hh L. This case corresponds to a 1D semiconductor or
x y x y z
quantum wire, located along the z-axis.
4. liiL ,L ,L.Inthiscaseitissaidthatwehavea0Doraquantumdot[1,2].
x y z
Ingeneral,wesayinmesoscopicphysicsthatasolid,veryoftenacrystal,isof
reduced dimensionality if at least one of its dimensions L is smaller than the
i
characteristiclength.Forinstance,ifL andL aresmallerthanlwehaveacrystal
x y
of dimensionality equal to one. We could also have the case that l is comparable,
oralittlelarger,thanoneofthedimensionsofthesolidbutmuchsmallerthanthe
othertwo. Thenwehave aquasi 2Dsystem,which inpractice is averythinfilm,
but not thin enough to show quantum size effect (for details see Chap. 3).
This review is organized into four chapters. In Chap. 1, I review the present
statusofelementaryexcitationsinsolids.Preparationmethodsoflow-dimensional
structures are described in Chap. 2. Chapter 3 deals with physics of low-dimen-
sional structure. In this chapter of the most frequently structures—quantum dots
are revised. The applications of low-dimensional structures is done in Chap. 4.
Tallinn Vladimir G. Plekhanov
Acknowledgments
Many thanks are due to Prof. W. Reder for carefully reading the manuscript as
wellastoDr.N.WriteforimprovingmyEnglish.Iappreciatetheinvaluablehelp
givenbyMr.M.T.Kivi(Dr.ofMedicine)duringmydifficultperiod.Againitisa
pleasure to thank the Staff of Springer, in particular Dr. C. Ascheron and Elke
Sauer, for the continued excellent cooperation. I deeply thank the authors and
publisherswhohavekindlypermittedustoreproducefiguresandtablesfromtheir
papers and books. In a few cases I have been unable to contact the authors, and I
wouldbegratefuliftheywouldneverthelessretrospectivelygivemethenecessary
permission. I wish to express my deep gratitude to my family for their patience
during the long preparation of this book.
Tallinn Vladimir G. Plekhanov
ix
Contents
1 Elementary Excitations of Isotope: Mixed Crystals . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Energy Band Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Phonon States and Raman Spectra. . . . . . . . . . . . . . . . . . . . . . 5
2 Methods of the Preparation of Low-Dimensional Structures . . . . . 15
2.1 Molecular Beam Epitaxy and Metal-Organic Chemical
Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Nanolitography and Etching Technologies . . . . . . . . . . . . . . . . 18
2.3 Techniques for Characterization of Nanostructures . . . . . . . . . . 21
2.4 Nuclear Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Electron Excitations in Low-Dimensional Structures. . . . . . . . . . . 31
3.1 Wave-Like Properties of Electrons . . . . . . . . . . . . . . . . . . . . . 31
3.2 Dimensionality and Density of States. . . . . . . . . . . . . . . . . . . . 34
3.3 Electron in Quantum Dot. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.4 Excitons in Nanostructures. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.1 Excitons in Quantum Wells . . . . . . . . . . . . . . . . . . . . . 43
3.4.2 Excitons in Quantum Wires . . . . . . . . . . . . . . . . . . . . . 48
3.4.3 Excitons in Quantum Dots. . . . . . . . . . . . . . . . . . . . . . 51
3.5 Biexcitons in Quantum Dots. . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.6 Electron–Phonon Interaction in Low-Dimensional Structures . . . 57
3.7 Exciton–Phonon Interaction in Low-Dimensional Structures. . . . 62
4 Applications of Low-Dimensional Structures. . . . . . . . . . . . . . . . . 71
4.1 Resonant Tunneling Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Field Effect Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 Single-Electron-Transistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Light-Emitting Diodes and Lasers. . . . . . . . . . . . . . . . . . . . . . 75
4.5 Isotope-Based Quantum Computers. . . . . . . . . . . . . . . . . . . . . 79
xi
xii Contents
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Chapter 1
Elementary Excitations of Isotope:
Mixed Crystals
1.1 Introduction
Themodernviewofsolid-statephysicsisbasedonthepresentationofelementary
excitations, having mass, quasiimpuls, electrical charge and so on (see, e.g. [17]).
Accordingtothispresentationtheelementaryexcitationsofnon-metallicmaterials
areelectrons(holes),excitons(polaritons[18]),andphonons[19].Thelatterarethe
elementaryexcitationsofthecrystallattice,thedynamicsofwhichisdescribedin
harmonicapproximation(seee.g.[20]).Asiswellknown,thebasisofsuchaview
onsolidsisthemultiparticleapproach.Insuchaview,thequasiparticlesofsolidsare
idealgas,whichdescribethebehaviorofthesystem,e.g.noninteractingelectrons.
Weshouldincludesuchapproachtoconsiderthetheoryofelementaryexcitationsas
asuitablemodelfortheapplicationofthecommonmethodsofquantummechanics
for the solution of solid-state physics tasks. In this part of our review we briefly
considernotonlythemanifestationsoftheisotopeeffectindifferentsolids,butalso
bring the new accurate results, showing the quantitative changes of different char-
acteristicsofphononsandelectrons(excitons)insolidswithisotopicalsubstitution
(see,also[21]).Theisotopiceffectbecomesmorepronouncedwhenwedealwith
solids.Forexample,onsubstitutionofHwithDthechangeinenergyoftheelectron
transitioninsolidstate(e.g.LiH)istwoordersofmagnitudelargerthaninatomic
hydrogen(see,e.g.[22]).Theuseofelementaryexcitationstodescribethecompli-
catedmotionofmanyparticleshasturnedouttobeanextraordinarilyusefuldevice
incontemporaryphysics,anditistheviewofasolidwhichwedescribeinthispart
ofthebook.
ThebasicHamiltonianofoursolidmodelisoftheform[21]
H=Hion+Helectron+Helectron−ion (1.1)
where
(cid:2) p2 1(cid:2)
H = i + V(R − R ), (1.2)
ion i j
2m 2
i i(cid:2)=j
V.G.Plekhanov,IsotopeLow-DimensionalStructures,SpringerBriefsinPhysics, 1
DOI:10.1007/978-3-642-28613-1_1,©TheAuthor(s)2012