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SpringerSeriesin materials science 70 SpringerSeriesin materials science Editors: R.Hull R.M.Osgood,Jr. J.Parisi The Springer Series in Materials Science covers the complete spectrum of materials physics, includingfundamentalprinciples,physicalproperties,materialstheoryanddesign.Recognizing theincreasingimportanceofmaterialsscienceinfuturedevicetechnologies,thebooktitlesin thisseriesreflectthestateoftheartinunderstandingandcontrollingthestructureandproperties ofallimportantclassesofmaterials. 61 FatigueinFerroelectricCeramics 70 ApplicationsoftheIsotopicEffect andRelatedIssues inSolids ByD.C.Lupascu ByV.G.Plekhanov 62 Epitaxy 71 DissipativePhenomena PhysicalPrinciples inCondensedMatter andTechnicalImplementation SomeApplications ByM.A.Herman,W.Richter,andH.Sitter ByS.DattaguptaandS.Puri 63 Fundamentals 72 PredictiveSimulation ofIon-IrradiatedPolymers ofSemiconductorProcessing ByD.Fink StatusandChallenges Editors:J.DabrowskiandE.R.Weber 64 MorphologyControlofMaterials andNanoparticles 73 SiCPowerMaterials AdvancedMaterialsProcessing DevicesandApplications andCharacterization Editor:Z.C.Feng Editors:Y.WasedaandA.Muramatsu 74 PlasticDeformation 65 TransportProcesses inNanocrystallineMaterials inIon-IrradiatedPolymers ByM.Yu.GutkinandI.A.Ovid’ko ByD.Fink 75 WaferBonding 66 MultiphasedCeramicMaterials ApplicationsandTechnology ProcessingandPotential Editors:M.AlexeandU.Go¨sele Editors:W.-H.TuanandJ.-K.Guo 76 SpirallyAnisotropicComposites 67 Nondestructive ByG.E.Freger,V.N.Kestelman, MaterialsCharacterization andD.G.Freger WithApplicationstoAerospaceMaterials 77 ImpuritiesConfined Editors:N.G.H.Meyendorf,P.B.Nagy, inQuantumStructures andS.I.Rokhlin ByP.O.HoltzandQ.Zhao 68 DiffractionAnalysis 78 MacromolecularNanostructured oftheMicrostructureofMaterials Materials Editors:E.J.MittemeijerandP.Scardi Editors:N.UeyamaandA.Harada 69 Chemical–MechanicalPlanarization ofSemiconductorMaterials Editor:M.R.Oliver Volumes10–60arelistedattheendofthebook. V.G. Plekhanov Applications of the Isotopic Effect in Solids With151Figuresand24Tables 123 ProfessorVladimirG.Plekhanov ComputerScienceCollege ErikaStreet7a,Tallinn 10416Estonia E-mail:[email protected] SeriesEditors: ProfessorRobertHull ProfessorJürgenParisi UniversityofVirginia Universita¨tOldenburg,FachbereichPhysik Dept.ofMaterialsScienceandEngineering Abt.Energie-undHalbleiterforschung ThorntonHall Carl-von-Ossietzky-Strasse9–11 Charlottesville,VA22903-2442,USA 26129Oldenburg,Germany ProfessorR.M.Osgood,Jr. ProfessorHansWarlimont MicroelectronicsScienceLaboratory Institutfu¨rFestko¨rper- DepartmentofElectricalEngineering undWerkstofforschung, ColumbiaUniversity Helmholtzstrasse20 SeeleyW.MuddBuilding 01069Dresden,Germany NewYork,NY10027,USA ISSN0933-033X ISBN 978-3-642-62137-6 ISBN 978-3-642-18503-8 (eBook) DOI 10.1007/978-3-642-18503-8 LibraryofCongressCataloging-in-PublicationData: Plekhanov,VladimirG. Applicationsoftheisotopiceffectinsolids/V.G.Plekhanov.p.cm.–(Springerseriesinmaterialsscience, ISSN0933-033X;70)Includesbibliographicalreferencesandindex.ISBN 978-3-642-62137-6(acid-freepaper) 1.Solid-statephysics.2.Isotopes.I.Title.II.Springerseriesinmaterialsscience;v.70) QC176.P542004 530.4’1–dc22 2004040798 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationor partsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,inits currentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violationsareliable toprosecutionundertheGermanCopyrightLaw. springeronline.com ©Springer-VerlagBerlinHeidelberg2004 Originally published by Springer-Verlag Berlin HeidelbergNew Yo rk in 2004 Softcover reprint of the hardcover 1st edition 2004 Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsand regulationsandthereforefreeforgeneraluse. FinalprocessingbyPTP-BerlinProtago-TeX-ProductionGmbH,Germany Coverconcept:eStudioCalamarSteinen Coverproduction:design&productionGmbH,Heidelberg Printedonacid-freepaper SPIN:10825876 57/3141/YU 543210 To the memory of my parents Preface Thisisthefirstbookinworldliteraturedevotedtoapplicationsoftheisotopic effect in solids. It is accessible to physicists, chemists, electronic engineers, and material scientists alike. This book is intended both as tutorial and as reference. Readers seeking to learn the basics of application of the isotopic effect in solids should start by reading the first few overview chapters, and thendigintodescriptionsofspecificapplicationstoseehowtheyreallywork. It is hoped that it will be useful to undergraduate and graduate students of physics and optics as well as engineers, physicists, material scientists, and medical doctors who are interested in investigation or applications of the isotopic effect in solids. This book is a state-of-the-art introduction to very recent activity in solid-state physics which has developed in the main during the last half century and promises a new technology of isotopic engineering. Importantapplicationsaretobeexpectedforinformationstorageanddevel- oping materials for computer memory, quantum computers, isotopic fibers, isotopic optoelectronics, and quantum electronics as well as UV lasers. The references I cite are those with which I am most familiar and which have helped us understand the subject as presented here. There has been no attempttogivecredittoeachcontributor,butIhavetriedtocitetheoriginal papers, which brought new and important results (methods) to applications of the isotopic effect in solids, covered in this text. Iwishtothankalltheauthorscitedthroughoutthetextfortheirpermis- sion to use the figures from their work and also the publishers concerned for allowing reproduction. I would like to express thanks to my many students who have contributed to this investigations in various ways over the years. Last but by no means least I owe a great debt to my wife and my children fortheirpatienceandencouragementoverthelongperiodspentinpreparing this book and I thank their most sincerely. I thank my many friends for their help stimulation and the Produc- tion and Editorial Staff of Springer-Verlag, especially Dr. C. Asheron and Ms. A. Duhm, and also the staff of PTP-Berlin for their continual and very long assistance in preparing the copy for publication of my manuscript. Tallinn, May 2004 V.G. Plekhanov Contents 1 Introduction.............................................. 1 2 Phonon Spectra of Solids: Indicator of Their Isotope Purity ......................... 5 2.1 Theory of Lattice Dynamics ............................. 5 2.2 Elastic Properties ...................................... 16 2.2.1 Theoretical Background of Elastic Constant Measurements .................. 16 2.2.2 Experimental Results and Interpretation ............ 17 2.3 Vibrational Properties .................................. 27 2.3.1 Phonon Dispersion and Density of Phonon States..... 27 2.3.2 Low Concentrations: Localized, Resonant, and Gap Modes .................................. 36 2.3.3 Phonon Spectra of Isotopically Mixed Crystals ....... 40 2.3.4 Isotopically Induced Disorder Effects in Vibrational Spectra ............................ 48 3 Thermal Properties....................................... 55 3.1 Dependence of the Thermal Conductivity on the Isotopic Composition ............................. 55 3.1.1 Theoretical Models ............................... 58 3.1.2 Experimental Results ............................. 63 3.1.3 High Thermal Conductivity Silicon ................. 70 3.2 Lattice Constant Dependence on Temperature and Isotopic Composition................................ 73 4 Isotopic Renormalization of the Electronic Excitation Energy Spectrum ............ 81 4.1 Exciton States ......................................... 81 4.2 Exciton–Phonon Interaction ............................. 87 4.3 Giant Isotopic Effect in the Energy Spectrum of Wannier–Mott Exciton in LiH Crystals ................. 93 4.4 Nonlinear Dependence of Band-Gap Energy on the Isotopic Effect ................................... 99 4.5 Renormalization of Binding Energy of Wannier–Mott Excitons by Isotopic Effect............... 101 X Contents 4.6 Nonlinear Dependence of Binding Energy on Isotopic Concentration ............................... 104 4.7 Isotopic Effect in the Luminescence Spectrum.............. 107 5 Process of Self-Diffusion in Isotopically Pure Materials and Heterostructures ..................................... 111 5.1 General Remarks....................................... 111 5.2 The Relation of Diffusion Experiments to the Mathematics of Diffusion .......................... 112 5.3 The Self-Diffusion Process ............................... 117 5.4 The SIMS-Technique.................................... 120 5.5 Self-Diffusion of Li and H in LiH Crystals ................. 122 5.6 Self-Diffusion in Intrinsic Ge ............................. 127 5.7 Self- and Interdiffusion of Ga and Al in Isotopically Pure and Doped Heterostructures ............................. 134 6 Neutron Transmutative Doping........................... 155 6.1 The NTD Process: A New Reactor Technology ............. 155 6.2 Reactor Facilities for Transmutative Doping ............... 161 6.3 Nuclear Reaction Under the Influence of Charged Particles .................................... 173 6.4 Nuclear Reaction Under the Action of the γ-Rays .......... 175 6.5 Nuclear Reactions Under the Influence of Neutrons ......... 176 6.6 The Influence of Dopants................................ 178 6.7 Atomic Displacement Effects in NTD ..................... 180 6.8 Experimental Results ................................... 183 6.8.1 Ge ............................................. 183 6.8.2 Silicon .......................................... 199 6.8.3 Other Compounds................................ 206 7 Optical Fiber ............................................. 219 7.1 Optical Communication ................................. 219 7.2 Maxwell’s Equations .................................... 220 7.2.1 Planar Geometry................................. 222 7.2.2 Cylindrical Geometry ............................. 224 7.2.3 The Electromagnetic Wave Equation................ 225 7.3 Geometric Optics of Fibers .............................. 226 7.4 Waveguide Mode Propagation............................ 232 7.5 Pulse Spreading ........................................ 239 7.6 Materials for Optical Fibers ............................. 249 7.6.1 Absorptive Losses in Glasses....................... 252 7.6.2 Rayleigh Scattering............................... 253 7.7 Fiber Preparation ...................................... 256 7.8 Isotopes in Fibers ...................................... 259 Contents XI 8 Laser Materials........................................... 261 8.1 Some General Remarks.................................. 261 8.2 Absorption and Induced Emission ........................ 262 8.3 Semiconductor Lasers ................................... 264 8.3.1 Heterojunction Lasers............................. 264 8.3.2 Study of Excitons Lasing.......................... 270 8.4 Nonlinear Properties of Excitons in Isotopically Mixed Crystals............................ 278 9 Other Unexplored Applications of Isotopic Engineering... 285 9.1 Isotopic Information Storage ............................. 285 9.2 Isotopic Structuring for Fundamental Studies .............. 287 9.3 Other Possibilities ...................................... 287 10 Conclusion ............................................... 289 References.................................................... 293 Index......................................................... 315 1 Introduction The availability of isotopically pure crystals with low carrier and impurity concentrations has allowed the investigation of isotopic effects on lattice dy- namic and electronic properties of solids in the last three decades [23]. Due to zero-point motion, the atoms in a solid feel the anharmonicity [28] of the interatomicpotential,evenatlowtemperatures.Therefore,thelatticeparam- eters of two chemically identical crystals formed by different isotopes do not coincide [23,106,428]; heavier isotopes have smaller zero-point delocalization (as expected in a harmonic approximation) and smaller lattice parameters (ananharmoniceffect).Moreover,phonon-relatedpropertiessuchasthermal conductivity, thermal expansion, and melting temperature are expected to depend on isotope mass. We start with the fact that phonon frequency is directly affected by changes in the average mass of the whole crystal or its sublattice (the VCA- model), even if we look upon them as noninteracting particles, i.e., as har- monicoscillators.Thedirectinfluenceoftheisotopicmassonthefrequencies of coupled phonon modes may be(cid:2)us(cid:3)ed to determine their eigenvectors. Sec- ond,themeansquareamplitude u2 ofphononsdependsonisotopicmasses only at low temperature, and they are determined only by the temperature T,onceT becomeslargerthantheDebyetemperature.Arefinementofthese effectsmusttakeplacewhentakinginteractionsamongphononsintoaccount. These interactions lead to finite phonon lifetimes and additional frequency renormalization. The underlying processes can be divided into two classes: (1) anharmonic interactions in which a zone center phonon decays into two phonons or more with wave-vector and energy conservation and (2) elastic scattering in which a phonon scatters into phonons of similar energies but different wave vectors. The former processes arise from cubic and quartic terms in the expansion of lattice potential [28], whereas the latter are due to the relaxed wave-vector conservation rule in samples that are isotopically disordered and thus not strictly translationally invariant. Since the vast majority of compounds de- rives from elements that have more than one stable isotope, it is clear that both processes are present most of the time. Unfortunately, their absolute sizes and relative importance cannot be predicted easily. However, isotopic enrichment allows one to suppress the elastic scattering induced by isotopic V. Plekhanov, Applications of the Isotopic Effect in Solids © Springer-Verlag Berlin Heidelberg, 2004