Introduction to Isotopic Materials Science

298 Pages·2018·12.972 MB·English

by  Vladimir G. Plekhanov

Springer Series in Materials Science 248
Vladimir G. Plekhanov
Introduction
to Isotopic
Materials
Science
Springer Series in Materials Science
Volume 248
Series editors
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Yoshiyuki Kawazoe, Sendai, Japan
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Zhiming M. Wang, Chengdu, China
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More information about this series at http://www.springer.com/series/856
Vladimir G. Plekhanov
Introduction to Isotopic
Materials Science
123
Vladimir G.Plekhanov
Mathematics andPhysics Department
Computer Science College
Tallinn, Estonia
ISSN 0933-033X ISSN 2196-2812 (electronic)
SpringerSeries inMaterials Science
ISBN978-3-319-42260-2 ISBN978-3-319-42261-9 (eBook)
https://doi.org/10.1007/978-3-319-42261-9
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Preface
This book describes new trends in the nanoscience of isotopic materials science.
Assuming a background in graduate condensed matter physics and covering the
fundamentalaspectsofisotopicmaterialssciencefromtheverybeginning,itequips
readers to engage inhigh-level professional research inthis area. The book’s main
objective is to share in the question of why solids are the way they are, either
becauseofhowtheiratomsarebondedwithoneanother,becauseofdefectsintheir
structure, or because of how they are produced or processed. Accordingly, it
explores the science of how atoms interact, connects the results to real materials
properties, and demonstrates the engineering concepts that can be used to produce
or improve semiconductors by design. In addition, it shows how the concepts
discussed are applied in the laboratory.
The book addresses the needs of researchers, graduate students, and senior
undergraduate students alike. Although primarily written for a materials science
audience,itwillbeequallyusefultothoseteachingelectricalengineering,materials
science,orevenchemicalengineeringorphysicscurricula.Inordertomaintainthe
focusonmaterialsconcepts,thedetailsofmanyofthederivationsandequationsare
leftoutofthebook.Similarly,theauthordoesnotdelveintothedetailsofelectrical
engineering topics in as much detail as an electrical engineer might wish. It is
assumed that readers have a basic command of these topics.
Tallinn, Estonia Vladimir G. Plekhanov
v
Acknowledgements
The list of acknowledgements has to be necessarily long since the author has
received a great amount of help from many person. I owe all of them a great deal
and I would like to express my sincere grateful to each one. Most of them appear
explicitly as authors in the references. Nevertheless, first of all I would like to
acknowledgeProf.F.F.Gavrilov,whofirstintroducedtheauthorinthephysicsof
isotopes. Thank you very much Prof. G. I. Pilipenko for a very long and warm
collaboration.Ideeplythanktheauthorsandpublisherswhohavekindlypermitted
ustoreproducefiguresandtablesfromtheirpapersandbooks.InafewcasesIhave
been unable to contact the authors, and I would be grateful if they would never-
theless retrospectively give me the necessary permission. Again it is a pleasure to
thank the staff of Springer, in particular Dr. C. Ascheron and Elke Sauer, for
continued excellent cooperation. Many thanks are due to Prof. D. Reder for care-
fully reading my manuscript. I also would like to acknowledge Dr. D. Jonson for
his helpin improving theEnglish style of the mymanuscript and Mr. R. Ermakov
for technical assistants. It is very pity that Estonia State has never supported my
scientificinvestigations.Iwishtoexpressmydeepgratitudekidsandgrandchildren
for their patience during the time preparation of this book.
Tallinn, Estonia Vladimir G. Plekhanov
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Energy Band Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Electronic Band Structure of Bulk Samples . . . . . . . . . . . . . . . . 5
2.1.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Energy Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Density of States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Effective Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Optical Properties of Isotope-Mixed Substances . . . . . . . . . . . . . 16
2.4.1 Isotope Renormalization of the Fundamental Gap’s
Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.2 Exciton Emission Spectra . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Electron Excitations in Low-Dimensional Structures. . . . . . . . . . 28
2.5.1 Wavelike Properties of Electrons. . . . . . . . . . . . . . . . . . 28
2.5.2 Dimensionality and Density of States . . . . . . . . . . . . . . 32
2.5.3 Electron in Quantum Dot . . . . . . . . . . . . . . . . . . . . . . . 35
2.6 Excitons in Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6.1 Excitons in Quantum Wells . . . . . . . . . . . . . . . . . . . . . 38
2.7 Biexcitons in Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3 Phonon States in Bulk and Low-Dimensional Structures . . . . . . . . . 53
3.1 Hamiltonian of Perfect Crystals. . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 The Adiabatic and Harmonic Approximations . . . . . . . . . . . . . . 55
3.3 The Anharmonic Crystal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4 Disordered Crystals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Model of Virtual Crystal Approximation . . . . . . . . . . . . 65
3.4.2 Model of Coherent Potential Approximation . . . . . . . . . 66
3.5 The Dispersion Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
ix
x Contents
3.6 Measurement of Phonon Dispersion by the Method
of Inelastic Neutron Scattering. . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.6.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.7 Raman Spectra of Isotope-Mixed Crystals . . . . . . . . . . . . . . . . . 84
3.8 Disorder Shift and Broadening of the Line in the Raman
Spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.9 Vibrations in Low-Dimensional Structures . . . . . . . . . . . . . . . . . 99
3.9.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.9.2 Elastic Continuum Model of Phonons . . . . . . . . . . . . . . 101
3.9.3 Dielectric Continuum Model of Phonons. . . . . . . . . . . . 103
3.10 Optical and Acoustic Phonons in Nanostructures . . . . . . . . . . . . 105
3.11 Experimental Manifestation of Phonons in Low-Dimensional
Structures of Different Kinds. . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.11.1 Electron–Phonon Interaction in Low-Dimensional
Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.11.2 Exciton–Phonon Interaction in Low-Dimensional
Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4 Application of Isotopic Materials Science in Bulk
and Low-Dimensional Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.2 Nonlinear Excitons in Bulk Isotope-Mixed Materials . . . . . . . . . 142
4.2.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.2.2 Free-Exciton Emission from Diamond at Room
Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.2.3 UV Emission from a Diamond p–n Junction . . . . . . . . . 146
4.3 Exciton Lasing in LiHxD1(cid:1)x Crystals. . . . . . . . . . . . . . . . . . . . . 149
4.4 Phonon-Related Isotope Effects . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.4.1 Isotope Dependence of the Thermal Expansion
Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.4.2 Effect of the Isotope Composition of a Crystal
Lattice on the Specific Heat . . . . . . . . . . . . . . . . . . . . . 165
4.4.3 Dependence of Thermal Conductivity on the Isotope
Composition of Materials . . . . . . . . . . . . . . . . . . . . . . . 172
4.4.4 Influence of the Isotope Composition Materials
on the Lattice Constant. . . . . . . . . . . . . . . . . . . . . . . . . 179
4.4.5 Isotopic Fiber Optics . . . . . . . . . . . . . . . . . . . . . . . . . . 189
4.5 Isotope-Mixed Graphene and Its Application . . . . . . . . . . . . . . . 194
4.6 Chemical Mechanisms Bandgap Engineering in Graphene. . . . . . 205
Contents xi
4.7 Low-Dimensional Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
4.7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
4.7.2 Resonant-Tunneling Diodes . . . . . . . . . . . . . . . . . . . . . 217
4.7.3 Field-Effect Transistor . . . . . . . . . . . . . . . . . . . . . . . . . 219
4.7.4 Single-Electron Transistor. . . . . . . . . . . . . . . . . . . . . . . 221
4.7.5 Graphene Quantum Dots Electronics . . . . . . . . . . . . . . . 226
4.7.6 Light-Emitting Diodes and Lasers . . . . . . . . . . . . . . . . . 229
4.7.7 Radiation Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
4.8 Isotope-Based Quantum Computers . . . . . . . . . . . . . . . . . . . . . . 239
4.8.1 General Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
4.8.2 Current Status: The Di Vincenzo Criteria. . . . . . . . . . . . 240
4.8.3 Elementary Gates for Quantum Computation . . . . . . . . . 242
4.8.4 A Physical Models for a Quantum Computer. . . . . . . . . 251
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 279