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Electronic States in Crystals of Finite Size: Quantum Confinement of Bloch Waves 2nd ed. 2017 [Kietas viršelis]

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  • Formatas: Hardback, 283 pages, aukštis x plotis: 235x155 mm, weight: 5738 g, 42 Illustrations, black and white; XVI, 283 p. 42 illus., 1 Hardback
  • Serija: Springer Tracts in Modern Physics 270
  • Išleidimo metai: 14-Sep-2017
  • Leidėjas: Springer Verlag, Singapore
  • ISBN-10: 9811047162
  • ISBN-13: 9789811047169
Kitos knygos pagal šią temą:
Electronic States in Crystals of Finite Size: Quantum Confinement of Bloch Waves 2nd ed. 2017Didesnis paveikslėlis
  • Formatas: Hardback, 283 pages, aukštis x plotis: 235x155 mm, weight: 5738 g, 42 Illustrations, black and white; XVI, 283 p. 42 illus., 1 Hardback
  • Serija: Springer Tracts in Modern Physics 270
  • Išleidimo metai: 14-Sep-2017
  • Leidėjas: Springer Verlag, Singapore
  • ISBN-10: 9811047162
  • ISBN-13: 9789811047169
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9789811047169.html
Raktažodžiai:
This book presents an analytical theory of the electronic states in ideal low dimensional systems and finite crystals based on a differential equation theory approach. It provides precise and fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and offers new insights into some of the basic problems in low-dimensional systems, such as the surface states and quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community. Many previous predictions have been confirmed in subsequent investigations by other authors on various relevant problems. In this new edition, the theory is further extended to one-dimensional photonic crystals and phononic crystals, and a general theoretical formalism for investigating the existence and properties of surface states/modes in semi-infinite one-dimensional crystals is developed. In addition, there are various revisions and improvements, including using the Kronig-Penney model to illustrate the analytical theory and make it easier to understand. This book is a valuable resource for solid-state physicists and material scientists.

Part I Why a Theory of Electronic States in Crystals of Finite Size Is Needed
1 Introduction
3(18)
1.1 Electronic States Based on the Translational In variance
4(2)
1.2 Energy Band Structure of Several Typical Crystals
6(1)
1.3 Fundamental Difficulties of the Theory of Electronic States in Conventional Solid-State Physics
7(2)
1.4 The Effective Mass Approximation
9(2)
1.5 Some Numerical Results
11(2)
1.6 Subject of the Book and Main Findings
13(8)
References
17(4)
Part II One-Dimensional Semi-infinite Crystals and Finite Crystals
2 The Periodic Sturm-Liouville Equations
21(30)
2.1 Elementary Theory and Two Basic Sturm Theorems
22(5)
2.2 The Floquet Theory
27(4)
2.3 Discriminant and Linearly Independent Solutions
31(2)
2.4 The Spectral Theory
33(7)
2.4.1 Two Eigenvalue Problems
34(1)
2.4.2 The Function D(λ)
35(5)
2.5 Band Structure of Eigenvalues
40(4)
2.6 Zeros of Solutions
44(7)
References
49(2)
3 Surface States in One-Dimensional Semi-infinite Crystals
51(16)
3.1 Basic Considerations
52(2)
3.2 Two Qualitative Relations
54(2)
3.3 Surface States in Ideal Semi-infinite Crystals
56(3)
3.4 Cases Where Vout Is Finite
59(3)
3.5 A General Theoretical Formalism
62(2)
3.6 Comparisons with Previous Work and Discussions
64(3)
References
65(2)
4 Electronic States in Ideal One-Dimensional Crystals of Finite Length
67(24)
4.1 Basic Considerations
67(2)
4.2 Two Types of Electronic States
69(6)
4.3 τ-Dependent States
75(3)
4.4 Stationary Bloch States
78(1)
4.5 Electronic States in One-Dimensional Finite Symmetric Crystals
78(2)
4.6 Comments on the Effective Mass Approximation
80(2)
4.7 Comments on the Surface States
82(3)
4.8 Two Other Comments
85(1)
4.8.1 A Comment on the Formation of the Energy Bands
85(1)
4.8.2 A Comment on the Boundary Locations
86(1)
4.9 Summary
86(5)
References
87(4)
Part III Low-Dimensional Systems and Finite Crystals
5 Electronic States in Ideal Quantum Films
91(28)
5.1 A Basic Theorem
93(4)
5.2 Consequences of the Theorem
97(2)
5.3 Basic Considerations on the Electronic States in an Ideal Quantum Film
99(1)
5.4 Stationary Bloch States
99(4)
5.4.1 The Simplest Cases
100(1)
5.4.2 More General Cases
101(2)
5.5 τ3-Dependent States
103(2)
5.6 Several Practically More Interesting Films
105(3)
5.6.1 (001) Films with an fcc Bravais Lattice
105(1)
5.6.2 (110) Films with an fcc Bravais Lattice
106(1)
5.6.3 (001) Films with a bcc Bravais Lattice
107(1)
5.6.4 (110) Films with a bcc Bravais Lattice
108(1)
5.7 Comparisons with Previous Numerical Results
108(5)
5.7.1 Si (001) Films
108(2)
5.7.2 Si (110) Films and GaAs (110) Films
110(3)
5.8 Further Discussions
113(6)
References
118(1)
6 Electronic States in Ideal Quantum Wires
119(26)
6.1 Basic Considerations
120(1)
6.2 Further Quantum Confinement of ψn(k, x; τ3)
121(4)
6.3 Further Quantum Confinement of ψn, j3(k, x; τ3)
125(5)
6.4 Quantum Wires of Crystals with a sc, tetr, or ortho Bravais Lattice
130(2)
6.5 fcc Quantum Wires with (110) and (001) Surfaces
132(7)
6.5.1 fcc Quantum Wires Obtained from (001) Films Further Confined by Two (110) Surfaces
132(2)
6.5.2 fcc Quantum Wires Obtained from (110) Films Further Confined by Two (001) Surfaces
134(3)
6.5.3 Results Obtained by Combining Sects. 6.5.1 and 6.5.2
137(2)
6.6 fcc Quantum Wires with (110) and (110) Surfaces
139(2)
6.7 bcc Quantum Wires with (001) and (010) Surfaces
141(1)
6.8 Summary and Discussions
142(3)
References
144(1)
7 Electronic States in Ideal Finite Crystals or Quantum Dots
145(32)
7.1 Basic Considerations
146(1)
7.2 Further Quantum Confinement of ψn(k, x; τ2, τ3)
146(4)
7.3 Further Quantum Confinement of ψn, j3(k, x; τ2, τ3)
150(3)
7.4 Further Quantum Confinement of ψn, j2(k, x; τ2, τ3)
153(3)
7.5 Further Quantum Confinement of ψn, j2, j3(k, x; τ2, τ3)
156(4)
7.6 Finite Crystals or Quantum Dots with a sc, tetr, or ortho Bravais Lattice
160(2)
7.7 fee Finite Crystals with (001), (110), and (110) Surfaces
162(3)
7.8 bee Finite Crystals with (100), (010), and (001) Surfaces
165(3)
7.9 Summary and Discussions
168(9)
References
173(4)
Part IV Epilogue
8 Concluding Remarks
177(12)
8.1 Summary and Brief Discussions
177(6)
8.2 Some Relevant Systems
183(2)
8.2.1 Other Finite Periodic Systems
183(2)
8.2.2 Electronic States in Ideal Cavity Structures
185(1)
8.3 Could a More General Theory Be Possible?
185(4)
References
187(2)
Appendix A The Kronig-Penney Model 189(22)
Appendix B Electronic States in One-Dimensional Symmetric Finite Crystals with a Finite Vout 211(6)
Appendix C Layered Crystals 217(8)
Appendix D Analytical Expressions of ∂Λ/∂τ and ∂Λ/∂σ 225(6)
Appendix E One-Dimensional Phononic Crystals 231(16)
Appendix F One-Dimensional Photonic Crystals 247(22)
Appendix G Electronic States in Ideal Cavity Structures 269(12)
Index 281
Shang Yuan REN pursued his graduate study with Professor Kun HUANG at Peking University(PKU), worked on theoretical semiconductor physics after  he  graduated  from  PKU  in  1963.   He  worked  with  Professor  Walter A. Harrison at Stanford University on theoretical solid state physics from 1978-1980, as one of earliest visiting scholars from P. R. China to the United States.  Then he worked as a research associate at University of  Missouri at Kansas City, University of Illinois at Urbana-Champaign.  He was back to the University of Science and Technology of China(USTC) in 1981 and worked as an associate professor and then a professor of physics at USTC. He worked as a visiting professor at University of Notre Dame, and a research professor at Arizona State University.  He joined PKU as a professor of physics since 1994.  He is now an emeritus professor at PKU. He  has  published  about  100  research  articles.   His  research  interests  include Low-Dimensional Physics, Theoretical Solid State Physics, Physics of Semiconductors/Semiconductor Devices, MØobius Inversions and Their Applications  in  Science  and  Engineering,  Electronic  Structure  of  Biological Macromolecules.