Electronic Transport in Mesoscopic SystemsCambridge University Press, 15 mai 1997 - 377 pages Recent advances in semiconductor technology have made possible the fabrication of structures whose dimensions are much smaller than the mean free path of an electron. This book gives the first thorough account of the theory of electronic transport in such mesoscopic systems. Beginning with coverage of fundamental concepts, the book presents a detailed account of transmission function formalism which is used to describe three key topics in mesoscopic physics: the quantum Hall effect, localization, and double-barrier tunneling. Other sections include a discussion of optical analogies to mesoscopic phenomena, followed by a concluding description of the non-equilibrium Green's function formalism and its relation to the transmission formalism. Complete with problems and solutions, the book will be of great interest to graduate students of mesoscopic physics and nanoelectronic device engineering, as well as to established researchers in these fields. |
Table des matières
Acknowledgements | xii |
A few common symbols | xiii |
Introductory remarks | 1 |
Preliminary concepts | 6 |
11 Twodimensional electron gas 2DEG | 7 |
12 Effective mass density of states etc | 10 |
13 Characteristic lengths | 16 |
14 Lowfield magnetoresistance | 23 |
Exercises | 194 |
Localization and fluctuations | 196 |
51 Localization length | 197 |
52 Weak localization | 201 |
53 Effect of magnetic field | 210 |
54 Conductance fluctuations | 215 |
55 Diagrammatic perturbation theory | 222 |
Summary | 242 |
15 Highfield magnetoresistance | 26 |
16 Transverse modes or magnetoelectric subbands | 29 |
17 Drift velocity or Fermi velocity? | 37 |
Summary | 44 |
Exercises | 45 |
Conductance from transmission | 48 |
21 Resistance of a ballistic conductor | 50 |
22 Landauer formula | 57 |
23 Where is the resistance? | 65 |
24 What does a voltage probe measure? | 74 |
25 Nonzero temperature and bias | 86 |
26 Exclusion principle? | 93 |
27 When can we use the LandauerButtiker formalism? | 102 |
Summary | 110 |
Exercises | 112 |
Transmission function Smatrix and Greens functions | 117 |
31 Transmission function and the Smatrix | 119 |
32 Combining Smatrices | 125 |
a brief introduction | 132 |
34 Smatrix and the Greens function | 139 |
or the method of finite differences | 141 |
36 Selfenergy | 151 |
37 Relation to other formalisms | 157 |
38 Feynman paths | 163 |
Summary | 168 |
Exercises | 170 |
Quantum Hall effect | 175 |
41 Origin of zero resistance | 176 |
42 Effect of backscattering | 188 |
Summary | 193 |
Doublebarrier tunneling | 246 |
61 Coherent resonant tunneling | 247 |
62 Effect of scattering | 256 |
63 Singleelectron tunneling | 266 |
Summary | 272 |
Exercises | 273 |
Optical analogies | 276 |
72 Linear optics | 279 |
73 Nonlinear optics | 285 |
74 Coherent sources | 288 |
Summary | 290 |
Exercises | 291 |
Nonequilibrium Greens function formalism | 293 |
81 Correlation and scattering functions | 294 |
82 Selfenergy and the Greens function | 300 |
83 Kinetic equation | 304 |
84 Calculating the selfenergy | 306 |
85 Summary of solution procedure | 311 |
86 Current flow and energy exchange | 315 |
87 Relation to the LandauerButtiker formalism | 319 |
88 Relation to the Boltzmann formalism | 322 |
89 Strongly interacting systems | 328 |
resonant tunneling with phonon scattering | 330 |
Summary | 338 |
Exercises | 339 |
Concluding remarks | 343 |
Solutions to exercises | 345 |
375 | |
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Expressions et termes fréquents
amplitude assume backscattering ballistic conductor barriers bias Büttiker calculate Chapter coherent concepts conductor confining potential correlation function current flow described device diagrams discussion effect electrochemical potential electron density energy range equilibrium Fermi energy Feynman paths given Green's function ħ² Hall resistance Hamiltonian Hence I₁ inside the conductor interactions Landau levels lattice lead longitudinal magnetic field matrix mean free path measured mesoscopic momentum relaxation NEGF formalism Note number of modes obtain oscillations peak phase phase-breaking phase-coherent phase-relaxation length phonon Phys Physics quantization quantum Hall quantum Hall effect quasi-Fermi level relation resonant tunneling resonant tunneling diode result S-matrix sample scattering functions Schrödinger equation Section self-energy self-energy function semiconductors shown in Fig spatial spectral function subbands T₁ T₂ terminal tion transmission function transmission probability transport transverse modes V₁ vector potential velocity vertical flow voltage probes wave wavefunction weak localization write zero μ₁