SpringerBriefs in Physics Editorial Board Egor Babaev, University of Massachusetts, USA Malcolm Bremer, University of Bristol, UK Xavier Calmet, University of Sussex, UK Francesca Di Lodovico, Queen Mary University of London, London, UK Maarten Hoogerland, Universiy of Auckland, Auckland, New Zealand Eric Le Ru, Victoria University of Wellington, Wellington, New Zealand James Overduin, Towson University, USA Vesselin Petkov, Concordia University, Canada Charles H.-T. Wang, University of Aberdeen, UK Andrew Whitaker, Queen’s University Belfast, UK For furthervolumes: http://www.springer.com/series/8902 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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyrightLawofthePublisher’slocation,initscurrentversion,andpermissionforusemustalways beobtainedfromSpringer.PermissionsforusemaybeobtainedthroughRightsLinkattheCopyright ClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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