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El. knyga: Quantum Tunneling and Field Electron Emission Theories [World Scientific e-book]

(Sun Yat-sen Univ, China)
  • Formatas: 408 pages
  • Išleidimo metai: 04-Feb-2014
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814440226
Kitos knygos pagal šią temą:
  • World Scientific e-book
  • Kaina: 150,61 €*
  • * this price gives unlimited concurrent access for unlimited time
Quantum Tunneling and Field Electron Emission TheoriesDidesnis paveikslėlis
  • Formatas: 408 pages
  • Išleidimo metai: 04-Feb-2014
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789814440226
Kitos knygos pagal šią temą:
World Scientific e-booksMore info about World Scientific e-books
Partnerių interneto svetainė: http://www.worldscientific.com/worldscibooks/10.1142/8663#t=toc
Quantum tunneling is an essential issue in quantum physics. Especially, the rapid development of nanotechnology in recent years promises a lot of applications in condensed matter physics, surface science and nanodevices, which are growing interests in fundamental issues, computational techniques and potential applications of quantum tunneling.The book involves two relevant topics. One is quantum tunneling theory in condensed matter physics, including the basic concepts and methods, especially for recent developments in mesoscopic physics and computational formulation. The second part is the field electron emission theory, which covers the basic field emission concepts, the Fowler-Nordheim theory, and recent developments of the field emission theory especially in some fundamental concepts and computational formulation, such as quantum confinement effects, Dirac fermion, Luttinger liquid, carbon nanotubes, coherent emission current, quantum tunneling time problem, spin polarized field electron emission and non-equilibrium Green's function method for field electron emission.This book presents in both academic and pedagogical styles, and is as possible as self-complete to make it suitable for researchers and graduate students in condensed matter physics and vacuum nanoelectronics.
Preface vii
1 Introduction
1(4)
Quantum Tunneling Theory
5(330)
2 Quantum Physics and Quantum Formalism
7(16)
2.1 Quantum Phenomena
7(1)
2.2 Quantum Characteristics
7(1)
2.3 Quantum Formalism
8(6)
2.4 Probability Current and Current Conservation
14(2)
2.5 Quantum Physics versus Classical Physics
16(2)
2.6 Mesoscopic Physics and Characteristic Length
18(3)
2.6.1 Characteristic Length
18(2)
2.6.2 Characteristic Transports
20(1)
2.7 Mathematics in Classical and Quantum Worlds
21(2)
3 Basic Physics of Quantum Scattering and Tunneling
23(14)
3.1 Definitions of Quantum Scattering and Tunneling
23(1)
3.2 Description of Quantum Scattering and Tunneling
24(2)
3.3 Basic Physical Quantities in Quantum Tunneling
26(1)
3.3.1 Transmission and Reflection Coefficients
26(1)
3.3.2 Conductance: Landauer-Buttiker Formula
26(1)
3.3.3 Charge Current
27(1)
3.4 Relationships between Transmission Coefficient and Scattering Matrix
27(2)
3.5 Basic Properties of Scattering and Transfer Matrices
29(6)
3.6 Constraints of Scattering and Transfer Matrices
35(2)
4 Wave Function Matching Method
37(24)
4.1 Square Barrier Model
38(2)
4.2 Asymmetric Square Barrier Model
40(3)
4.3 Double Square Barrier Model
43(2)
4.4 Multi-Mode Square Barrier Model
45(2)
4.5 Triangle Barrier
47(4)
4.6 Lattice Models
51(10)
4.6.1 One-dimensional Model
51(3)
4.6.2 Two-chain Model
54(4)
4.6.3 2D Square Lattice
58(3)
5 WKB Method
61(10)
5.1 Mathematics of WKB Method
61(2)
5.2 Validity
63(1)
5.3 Solution of Schrodinger Equation
63(1)
5.4 Quantum Tunneling
64(1)
5.5 Triangle Barrier
65(2)
5.6 Triangle and Image Potential Barrier
67(4)
6 Lippmann-Schwinger Formalism
71(12)
6.1 Lippmann-Schwinger Equation
71(2)
6.2 Wave Function and S Matrix
73(1)
6.3 Green's Function and T Matrix
74(2)
6.4 S Matrix
76(1)
6.5 Adiabatic Transport Model
77(2)
6.6 Quantum Tunneling in Time-Dependent Barrier
79(4)
6.6.1 Floquet Theory
79(1)
6.6.2 Time-Dependent Barrier
80(3)
7 Non-Equilibrium Green's Function Method
83(14)
7.1 Basic Physics of Non-Equilibrium Transport Problems
83(1)
7.2 Model of Nanodevices
84(2)
7.3 Green's Functions and Self-Energy
86(2)
7.4 Spectral Function, Density of States, and Correlation Function
88(2)
7.5 Definitions and Relationships
90(1)
7.6 Current
91(2)
7.7 Tunneling Model and Master Equation
93(4)
8 Spin Tunneling
97(22)
8.1 Tunneling Magnetoresistance Phenomena
97(1)
8.2 Julliere Model
98(3)
8.3 Giant Magnetoresistance
101(1)
8.4 Spin Tunneling in Spin-Orbital Coupling Semiconductors
102(8)
8.4.1 Model and Issue
102(2)
8.4.2 Ferromagnetic Nanowires
104(2)
8.4.3 Spin-Orbital Coupling Semiconductor
106(4)
8.5 Spin Polarization
110(7)
8.6 Remarks
117(2)
9 Applications
119(22)
9.1 Josephson Effect
119(2)
9.2 Theory of Scanning Tunneling Microscopy
121(4)
9.2.1 Quantum Electron Tunneling and Bardeen's Formula
122(1)
9.2.2 Tersoff-Hamann Formula
123(2)
9.2.3 Non-Equilibrium Green's Function Method
125(1)
9.3 Conductance of Graphene
125(7)
9.3.1 Graphene Nanoribbons Model
127(1)
9.3.2 Impurity Effects
128(2)
9.3.3 Vacancy and Impurity
130(1)
9.3.4 Conclusion
131(1)
9.4 Charge Transfer in DNA
132(8)
9.4.1 G4-DNA Model
133(2)
9.4.2 TG4 and Their Classifications
135(1)
9.4.3 Anomalous Conductance in. NCM(H)TG4
136(2)
9.4.4 Topological Structure Transition versus Telomerase Activation and Inhibition
138(1)
9.4.5 Conclusion
139(1)
9.5 Remarks
140(1)
Field Electron Emission Theory
141(2)
10 Introduction
143(8)
10.1 Field Electron Emission Phenomenon
143(1)
10.2 Brief Histroy of Field Electron Emission
143(1)
10.3 Basic Concepts of Field Electron Emission
144(2)
10.3.1 Electron Emissions from Solids
144(1)
10.3.2 Work Function and Field Emission Condition
145(1)
10.3.3 Basic Experiment Components of Field Emission
145(1)
10.3.4 Applications of Field Emission
146(1)
10.4 Basic Issues of Field Electron Emission
146(2)
10.4.1 Theoretical Issues
146(1)
10.4.2 Engineering Issues
147(1)
10.5 Novel Phenomena and Challenges of Field Emission
148(3)
10.5.1 New Phenomena
148(1)
10.5.2 Challenging Problems
149(2)
11 Theoretical Model and Methodology
151(6)
11.1 Theoretical Model of Field Emission
151(1)
11.2 Theoretical Methodology
152(1)
11.2.1 Model and Analytic Solution
153(1)
11.2.2 Computer Simulation
153(1)
11.2.3 Empirical Method
153(1)
11.3 Remarks
153(4)
12 Fowler-Nordheim Theory
157(52)
12.1 Assumptions of Fowler-Nordheim Theory
157(1)
12.2 Fowler-Nordheim Theory
158(9)
12.2.1 Field Emission Equation I: Fowler-Nordheim Method
160(3)
12.2.2 Field Emission Equation II: Young-Gadzuk's Method
163(1)
12.2.3 Field Emission Equation III: R. Forbes' Method
164(2)
12.2.4 Field Emission Equation VI: A. Haug's Method
166(1)
12.3 Remarks
167(1)
12.4 Beyond Triangular Vacuum Potential Barrier
168(10)
12.4.1 General Formalism
169(2)
12.4.2 Generalized Triangular Barrier
171(1)
12.4.3 Schottky-Nordheim Barrier: Image Potential Effect
172(3)
12.4.4 Beyond Gamow Exponent Form
175(1)
12.4.5 Emitter Curvature and Field Enhancement Factor
175(1)
12.4.6 Space Charge Effect
176(2)
12.4.7 Small-Scale Effect of Emitter
178(1)
12.4.8 Emission Area and Total Emission Current
178(1)
12.5 Energy Band Effect
178(4)
12.5.1 Supply Function Density
179(1)
12.5.2 Transmission Coefficient and Total Energy Distribution
179(2)
12.5.3 Emission Current Density
181(1)
12.6 Finite Temperature Effect
182(2)
12.7 Basic Characteristic of Current-Field Relation
184(7)
12.7.1 Current-Field Characteristic
184(1)
12.7.2 Maximum Emission Current Density
185(1)
12.7.3 FN Plot
186(5)
12.8 Energy Distribution of Emission Electrons
191(13)
12.8.1 Total Energy Distribution (TED)
191(2)
12.8.2 Normal Energy Distribution (NED)
193(1)
12.8.3 Basic Characteristics of TED and NED
194(8)
12.8.4 Measurement of Energy Distributions
202(2)
12.9 Nottingham Effect
204(5)
13 Field Emission from Semiconductors
209(12)
13.1 Basic Properties of Semiconductors
210(2)
13.1.1 Energy Band Structure
210(1)
13.1.2 Temperature Dependence of Energy Band Gap
210(1)
13.1.3 Carrier Concentration
211(1)
13.2 Model of Field Emission from Semiconductors
212(1)
13.3 Supply Function Density
213(1)
13.4 Vacuum Potential Barrier and Transmission Coefficient
213(2)
13.5 Total Energy Distribution
215(2)
13.6 Basic Characteristics of Total Energy Distribution
217(1)
13.7 Emission Current Density
218(3)
14 Surface Effects and Resonance
221(10)
14.1 Field Emission Model with Surface Effects
221(1)
14.2 Double-Barrier Vacuum Potential and Transmission Coefficient
222(4)
14.3 Total Energy Distribution
226(1)
14.4 Emission Current Density
227(4)
15 Thermionic Emission Theory
231(6)
15.1 The Richardson Theory of Thermionic Emission
231(2)
15.2 Boundary of Field Emission and Thermionic Emission
233(4)
16 Theory of Dynamical Field Emission
237(10)
16.1 Adiabatic Process and Dynamic Field Emission Model
237(1)
16.2 Supply Function and Time-Dependent Transmission Coefficient
238(1)
16.3 Dynamic Total Energy Distribution
239(1)
16.4 Dynamic Normal Energy Distribution
240(1)
16.5 Dynamic Emission Current
241(1)
16.6 Quantum Tunneling Time
242(5)
17 Theory of Spin Polarized Field Emission
247(24)
17.1 Basic Physics of Spin Polarized Field Emission
247(2)
17.2 Energy Band Spin-Split Model
249(5)
17.2.1 Supply Function and Transmission Coefficient
249(1)
17.2.2 Total Energy Distribution
250(1)
17.2.3 Normal Energy Distribution
251(1)
17.2.4 Emission Current Density and Spin Polarization
252(2)
17.3 Spin-Dependent Triangular Potential Barrier Model
254(5)
17.3.1 Spin-dependent Triangular Potential Barrier and Transmission Coefficient
254(2)
17.3.2 Total Energy Distribution
256(1)
17.3.3 Normal Energy Distribution
256(1)
17.3.4 Emission Current Density and Spin Polarization
257(2)
17.4 Spin-Dependent Image Potential Barrier Model
259(4)
17.4.1 Spin-dependent Image Potential Barrier and Transmission Coefficient
259(1)
17.4.2 Total and Normal Energy Distributions
260(1)
17.4.3 Emission Current Density and Spin Polarization
261(2)
17.5 Finite Temperature Effects
263(2)
17.5.1 Energy-Band Spin-Split Model
263(1)
17.5.2 Spin-Dependent Triangular Potential Barrier Model
264(1)
17.5.3 Spin-Dependent Image Potential Barrier Model
264(1)
17.6 Comparison of Spin Polarizations
265(1)
17.7 A Scheme of Pure Spin Polarized Electron Emission Induced by Quantum Spin Hall Effect
266(2)
17.8 Difficulties and Possibilities of Spin Polarized Field Emission
268(3)
18 Theory of Field Electron Emission from Nanomaterials
271(34)
18.1 Basic Physics of Field Emission from Nanoemitters
271(2)
18.2 Formulation of Field Emission Current Density
273(6)
18.2.1 Supply Function Density
274(1)
18.2.2 Current Density
274(1)
18.2.3 Density of States
274(1)
18.2.4 Transmission Coefficient
274(4)
18.2.5 Distribution Function
278(1)
18.2.6 Total Energy Distribution
278(1)
18.2.7 Emission Current Density
279(1)
18.3 Computational Framework
279(1)
18.4 Special Case I: Sommerfeld Model
280(1)
18.5 Special Case II: Nanowires
280(4)
18.6 Special Case III: Coupled Nanowires
284(6)
18.7 Thermionic Emission of Nanowires
290(2)
18.8 Theory of Field Electron Emission from Carbon Nanotubes
292(11)
18.8.1 Energy Dispersion and Density of States
293(1)
18.8.2 Density of States and Group Velocity
293(1)
18.8.3 Supply Function and Transmission Coefficient
294(1)
18.8.4 Total Energy Distribution
295(1)
18.8.5 Emission Current Density
295(6)
18.8.6 Finite Temperature Effect
301(1)
18.8.7 Thermionic Emission
301(2)
18.9 Theory of Luttinger Liquid Field Emission
303(2)
19 Computer Simulations of Field Emission
305(18)
19.1 Basic Idea on Computer Simulation
305(1)
19.2 Formulation of Field Emission Based on Non-Equilibrium Green's Function Method
306(3)
19.2.1 Generalized Supply Function
307(1)
19.2.2 Transmission Coefficient
308(1)
19.2.3 Total Energy Distribution and Emission Current Density
308(1)
19.3 Tight-Binding Approach
309(10)
19.3.1 Computational Formulation
309(1)
19.3.2 Carbon Nanotubes
310(2)
19.3.3 Total Energy Distribution and Emission Current
312(1)
19.3.4 Computational Framework
313(1)
19.3.5 Basic Properties of Field Emission of SWCN
314(5)
19.4 Cap and Doping Effects
319(1)
19.5 Field Penetration Effect and Field Enhancement Factor
320(1)
19.6 First-Principle Method
321(2)
19.6.1 The Multi-Scale Technique
321(1)
19.6.2 The ab-initio Tight-Binding Method
322(1)
19.6.3 Lippman-Schwinger Scattering Formalism
322(1)
20 The Empirical Theory of Field Emission
323(4)
20.1 The Empirical Theory of Field Emission
323(1)
20.2 The Generalized Empirical Theory of Field Emission
324(1)
20.3 The Empirical Theory of Thermionic Emission
325(1)
20.4 Connection between Empirical Theory and Experimental Data
325(2)
21 Fundamental Physics of Field Electron Emission
327(8)
21.1 Field Emission Behavior and Material Properties
327(1)
21.2 Equilibrium and Non-Equilibrium Currents
328(1)
21.3 Many-Body Effect
329(1)
21.4 Coherent and Non-Coherent Emission Currents
330(1)
21.5 Electron Emission Mechanism: Nano versus Bulk Effects
330(1)
21.6 Universality versus Finger Effects
331(1)
21.7 Open Problems and Difficulties
332(1)
21.8 Perspectives
333(2)
Appendix A Appendices
335(40)
A.1 Basic Properties of S and M Matrices
335(5)
A.1.1 Proof of Theorem 3.5
335(1)
A.1.2 Proof of Theorem 3.7
336(1)
A.1.3 Proof of Theorem 3.8
336(2)
A.1.4 Proof of Theorem 3.9
338(2)
A.2 Spin Tunneling
340(3)
A.2.1 Proof of Claim 8.1b and Claim 8.2b
340(1)
A.2.2 Proof of Claim 8.2
341(1)
A.2.3 Proof of Theorem 8.1
341(1)
A.2.4 Proof of Theorem 8.2
342(1)
A.2.5 Proof of Theorem 8.3
343(1)
A.3 Derivations in Non-Equilibrium Green's Function Method
343(3)
A.3.1 Basic Relationships
343(1)
A.3.2 Non-Equilibrium Current
344(2)
A.4 Models of Solids
346(5)
A.4.1 Sommerfeld Model of Metals
346(2)
A.4.2 Crystal Lattice Model and Bloch Theorem
348(1)
A.4.3 Tight-Binding Model
349(2)
A.4.4 Remarks of Solid Model
351(1)
A.5 Density of States
351(3)
A.5.1 Definition of Density of States
351(1)
A.5.2 Sommerfeld Model (Electron Gas)
351(1)
A.5.3 Beyond Sommerfeld Model
352(1)
A.5.4 Non-Equilibrium Cases
353(1)
A.6 Fermi Wave Vector and Fermi Wavelength
354(2)
A.6.1 Definitions of Fermi Wave Vector and Fermi Wavelength
354(1)
A.6.2 Sommerfeld Model
355(1)
A.7 The Widths of TED and NED
356(2)
A.7.1 TED
356(1)
A.7.2 NED
357(1)
A.8 Spin Polarized Field Emission
358(2)
A.9 Field Emission from Nanomaterials
360(3)
A.9.1 Nanowire Integration
360(1)
A.9.2 Coupled Nanowire
361(2)
A.10 Carbon Nanotubes
363(8)
A.10.1 Graphene
363(1)
A.10.2 Lattice Structure of Single-Wall Carbon Nanotubes (SWCN)
364(1)
A.10.3 Unit Cell and Brillouin Zone of SWCN
365(1)
A.10.4 Energy Dispersion Relation of SWCN
366(1)
A.10.5 Energy Gap
367(1)
A.10.6 Density of States of SWCN
368(1)
A.10.7 Multi Wall Carbon Nanotubes (MWCN)
368(3)
A.11 Physical Constants
371(1)
A.12 Field Emission Constants
372(1)
A.13 Epilogue
373(2)
Bibliography 375(10)
Index 385
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