Index

0–9 1D channel 104, 106, 108–110, 112, 118,

119, 125, 129, 130, 150, 152, 153, 155, 160, 238, 179, 180, 181, 189, 226, 247, 227, 281, 286, 365

1D localization 280, 281, 283 2D conductance 72

A Aharonov-Bohm effect 168, 210, 274, 276,

279 annihilation operator 242, 334 armchair nanotube 304, 307–309, 312, 316,

379, 380 atomic force microscope (AFM) 118, 119,

219, 279, 280 atomic level 44, 293, 344 autocorrelation 227–230, 233, 234, 243, 248

B backscattering 93, 107, 112, 145, 147, 148,

284, 285, 380 band

conduction 24, 28, 30, 31, 37, 58, 64, 69, 95, 97, 220, 293, 298–302, 305, 306, 313, 314, 317, 318, 321, 378

energy 22, 24, 25, 30, 37, 43, 44, 48, 49, 51, 54, 56, 63–65, 69, 97, 105, 106, 113, 147, 150 184, 294, 306, 378, 379

forbidden 24 structure 22, 24, 43, 45, 56, 88, 97, 291–

295, 300, 304, 307, 308, 312, 314–316, 321, 322, 326, 327, 329

valence 24, 28, 30, 69, 298–301, 305, 306, 314, 317, 318

base vector 23, 327, 329 basic vector 327, 329 binomial probability law 349 Bloch

oscillations 28, 29 theorem 23, 25, 30, 330 wave 23, 24, 26, 43, 45, 47, 49, 295, 330

Boltzmann constant 36, 61, 353 distribution 71, 72

bonding 1, 39, 293, 294, 321, 378, 379 Born-von Karmann (BVK) boundary

conditions 57–59, 62, 69, 89, 99, 110, 305 bra 12 Breit-Wigner formula 192–194 Brillouin zone 24, 27–29, 47, 50, 97, 295,

296, 298, 300, 301, 306, 307, 309, 310, 329, 330

Büttiker formula 130, 131, 132, 134, 141, 364, 365, 367, 368

Electron Transport in Nanostructures and Mesoscopic Devices: An Introduction Thieny Ouisse

Copyright 0 2008, ISTE Ltd.

384 Electron Transport in Nanostructures and Mesoscopic Devices

C carbon

atom 291–294, 296–298, 304, 305, 321 nanotube 4, 6, 210, 291, 292, 304, 305,

309, 313–322, 351 chemical potential 61, 105, 107, 108, 112,

115, 123–128, 142, 143, 147–149, 151, 183, 240, 286

chirality 304, 307, 309 circumference 79, 304, 305, 307, 308, 315,

351, 352 coherent states 137–140 collision 29, 66, 67, 68, 73, 80, 105, 110,

143, 237, 287, 317, 318, 380, 381 commutator 13, 325 conductance matrix 134, 149, 151–154, 156,

361, 362, 364, 365, 368 conductivity 67, 75, 82, 93, 94, 104, 110,

122, 123, 127, 281, 320 confinement 36, 37, 42, 55, 59, 60, 78, 235,

291 contact resistance 103, 107, 123, 127, 149,

281, 366 Coulomb blockade 2, 4, 62, 218, 249–251,

253, 254, 257, 258, 263–265, 267, 268, 270, 271, 319, 323, 376, 380

Coulomb diamond 263–266, 271 coupled quantum well 37, 44, 379 creation operator 334 crystalline cell 55, 56 current

fluctuations 234, 243 noise 2, 71, 225, 234, 236, 238, 241

cyclotron 73, 80, 150, 302

D de Broglie

relation 16, 19 thermal wavelength 36, 37

degenerate 37, 38, 39, 43, 44, 55, 61, 63, 69, 71, 72, 79, 80, 85, 97, 301, 322, 338–341, 344

density of states 57–59, 81, 89, 99, 110, 114, 115, 125, 150, 151, 171, 179, 206, 209, 301, 313, 314, 318, 322, 357, 360, 369, 370, 380

depletion 99, 108, 247 determinant 33, 346 diffusion

coefficient 71–73 current 72

Dirac point 299, 301, 306, 310, 311, 317, 380

discrete state 42, 79, 201–203, 206, 207, 209–211

dispersion 27, 28, 30, 47, 53, 55, 56, 92, 97, 147, 151, 152, 295, 298, 300–302, 304, 306–309, 313–315, 329, 330, 363, 379

dissipation 103, 104, 107, 110, 111, 123, 126, 144, 147, 256

drift velocity 68, 69, 73 double-slit experiment 117, 225 Drude model 67, 68, 73

E edge state 145, 147, 148, 149, 155, 156 effective mass 25, 27–31, 34, 43, 47, 49, 51,

55, 56, 69, 92, 95, 97, 179, 188, 220, 269, 299, 306, 313–315

approximation 25, 31, 43, 49, 55, 56 eigenstate 13–15, 18, 20, 39, 79, 84, 85,

140, 170, 171, 202, 207, 330, 332–334, 336–341, 344

eigenvalue 13–16, 18, 22, 52, 204, 332, 333, 336, 338, 344

Einstein relationship 71 elastic scattering 137, 140, 283 electric field 3, 25–30, 40–43, 62, 64, 68–

73, 75, 94, 97–99, 103, 110, 143, 193, 199, 231, 235, 236, 255, 300, 316, 317, 323, 338, 357–359, 380, 381

electrostatic energy 26, 252, 255, 259, 269 energy gap 24, 42, 306 ergodicity 226–228 expectation value 15, 43, 45, 48, 194, 195,

287, 295, 345, 346 extended state 22, 24, 89, 321

Index 385

F Fano resonance 169, 201, 210, 212–214,

216–218, 319 Fermi

level 71, 80–82, 99, 109, 145, 149, 150, 153, 173, 279, 293, 298, 323, 360, 369, 378, 380

wavelength 65, 114–116, 179 Fermi’s golden rule 201, 209, 210, 221, 222,

370, 371 Fermi-Dirac

distribution 61, 240, 243 statistics 60

Feynman path 287 flux quantum 277, 278, 280 four-terminal 134, 135, 154, 156 Fourier transform 16, 17, 21, 22, 52, 53, 95,

138, 228–230, 309, 348, 355, 358

G gallium arsenide (GaAs) 24, 31, 34, 35, 37,

40, 64, 95, 99, 109, 150, 152, 153, 155, 179, 179, 180 184, 199, 200, 220, 279, 292, 367

gauge 84, 85, 100, 361 generator 236, 237, 253, 255, 260–262, 268,

269 graphene 4, 43, 48, 49, 291, 292–306, 309,

313–316, 318, 321, 326, 328, 329, 379 Green’s function 5, 6, 170, 273, 274 ground state 38, 40, 96, 97, 332, 333, 344,

359, 371 group velocity 20, 22, 25, 88, 100, 293, 299,

301

H Hamiltonian 14–18, 38, 43, 45, 51, 52, 55,

76, 79, 85, 202, 203, 207, 331–333, 336, 340, 344, 345

harmonic oscillator 79, 86–88, 91, 330, 333 hermitian operator 14, 325 heterostructure 30, 31, 35, 36, 64, 65, 80,

82, 99, 109, 143, 279

High Electron Mobility Transistor (HEMT) 64, 73

hole 29, 30, 35, 150, 201, 301, 306, 315

I incoherent state 136, 139, 140 inelastic scattering 108, 137, 140, 286 input channel 161, 171, 178, 180, 181, 212,

222, 223 interference 2, 10, 13, 66, 67, 69, 116–118,

120, 129, 168, 169, 189, 201, 202, 207, 210, 215, 217, 218, 273, 274, 278–286, 299, 300, 320

inverter 266–268

K, L ket 12, 15 kinetic energy 25, 30, 64, 93, 94, 110, 123,

129, 180, 183, 275, 299, 381 Lagrange multipliers 342, 343, 345 Lagrangian 76, 273–275, 343, 345 Landau

band 80–82, 88–90, 99, 145, 148, 149, 150, 304, 360

level 80, 146, 148, 150, 301, 304 Landauer formula 114, 116, 120, 122, 126,

130, 181, 187, 278, 282, 318 Landauer-Büttiker formalism 104 lifetime 43, 196, 199, 201, 207, 209, 212,

221, 223, 372, 373 linear combination of atomic orbitals

(LCAO) 43, 344 localized state 150, 361 Lorentz force 26, 73, 75, 88, 132, 360 Lorentzian 192, 197, 198, 206, 371

M, N magnetoresistance 286 mean free path 3, 66, 67, 71, 80, 122, 123,

283, 286, 291, 316 measurement process 13, 66, 120, 225 Metal-Oxide-Semiconductor Field Effect

Transistor (MOSFET) 3, 4, 62, 64, 78, 80, 82, 83, 109, 140, 143, 144

mobility 64, 66, 67, 69, 73, 75, 83, 99, 304

386 Electron Transport in Nanostructures and Mesoscopic Devices

momentum mean free path 67, 71, 237 relaxation time 68, 285

non-ballistic conductor 237

O observable 12–16, 196, 214, 251, 257, 258,

283, 325, 326 occupation number 240, 241, 243 Onsager reciprocity relations 361 orbit 73, 78–80, 88, 150, 241, 276, 278, 361 output channel 171 overlap integral 345

P pass-band filter 230 Pauli exclusion principle 235, 240–243, 245 periodic lattice 22, 24, 25, 27, 30, 31, 43,

44, 56, 326, 327 perturbation

degenerate 338 first order 219, 337, 338, 369 non-degenerate 336

phase coherence 66, 67, 80, 128, 169, 189, 201 coherence length 66, 120, 169 relaxation 67, 281, 283, 285, 286

phonon 66, 67, 291, 316–318, 323, 380, 381 Planck constant 11, 353 Poisson process 233, 234, 350, 351 power spectral density 228–231, 234, 239,

245, 348 probability

current 18, 19, 136, 139, 141, 241, 243 density 13, 18, 19, 22, 95, 129, 179,

226, 244, 285, 355

Q quantized Hall resistance 150 quantum

coherent 4, 43, 49, 137, 161, 167, 169, 170, 212, 238, 291, 316, 318, 368

dot 210, 219, 315, 318, 319

level 34, 42 mechanics 1, 2, 4, 5, 9–14, 16, 23, 30,

67, 78, 183, 225, 273, 274, 276 point contact 109, 116, 118 ring 166, 169, 178, 179, 212, 215–218,

222, 223, 372 well 13, 18, 30, 31, 34–38, 40, 41, 43,

44, 95, 96, 99, 120, 171, 183, 184, 185, 193, 194, 196, 199–202, 221, 249, 330 342, 360, 370, 371, 379

wire 36, 104, 181, 283 quantum-mechanical operator 77 quasi-Fermi level 71

R reciprocal

lattice 27, 295, 296, 328–330 lattice vector 27, 50, 294, 296, 328–330

reciprocity 132, 133, 151, 152, 161, 278, 361, 363

reflection coefficient 138, 151, 161, 165, 168, 187, 188, 193

ring 57, 166, 168, 169, 178, 179, 212, 215–218, 222, 223, 241, 276–278, 280, 372, 373

S scanning tunneling microscope (STM) 293,

314, 369 scatterer 119–124, 126, 136, 139, 194, 243,

277, 280, 281 scattering 28, 64, 80, 93, 107, 108, 111–113,

121, 122, 124, 126, 128, 130, 137, 139, 140, 159, 160, 168, 169, 200, 214, 215, 278, 281, 283, 286, 287, 300, 316, 317

Schrödinger equation 9, 11, 12, 14, 17, 19, 20, 31, 32, 51, 84, 85, 97, 146, 169, 170, 171, 200, 251, 273, 274, 336, 357

screening (electron) 65 secular equation 38, 339, 346 self-adjoint (operator) 14 semi-classical approximation 25, 26, 115,

116, 301, 317

Index 387

semiconductor 2–5, 18, 22, 24, 25, 28, 30, 34, 35, 43, 49, 57, 62, 67, 69, 73, 78, 109, 119, 151, 276, 277, 280, 283, 291, 293, 338, 369, 379

Sharvin conductance 116 shot noise 71, 226, 230, 234, 235, 237–241,

245–247 classical 231, 241, 245 quantum 137, 240, 242, 247

Shubnikov-de Haas (SdH) oscillations 78, 82, 83

silicon (Si) 3, 24, 25, 35, 37, 42, 43, 62–64, 67, 82, 83, 97, 109, 140, 155, 265–271, 292, 293, 316, 320, 322, 357, 359, 367

single-electron transistor (SET) 63, 250, 258, 264–271

s-matrix 159–171, 175, 177, 178, 181, 212, 213, 215–217, 222, 223

spectral noise density 228 spin 6, 58, 60, 89, 110, 148, 149, 298, 300,

313, 319, 342, 365, 367, 368, 378 square well 34, 39, 41, 95, 356 stark effect 40, 42, 43 state vector 12–15, 18, 332 stationarity 226, 227 stationary perturbation theory 336 stationary state 17, 18, 110, 139, 179, 180,

193, 201–203, 207, 219, 373 subband 58–62, 65, 82, 83, 86, 89, 94, 99,

106, 109, 110, 120, 129, 141, 147, 173, 180, 242, 305–309, 313–315, 322, 360, 380

symmetric (state) 39

T thermal noise 240, 245 tight-binding 45, 48, 295, 308, 309, 312,

347 approximation 37, 43, 49, 299, 300, 321,

327, 378, 379 Bloch waves 295

transmission coefficient 112, 129, 131, 135, 136, 138,

140, 143, 149, 151, 152, 154–156, 167, 169, 171, 178, 181, 183, 189, 213–217, 222, 223, 238, 245, 281

conductance 103, 111, 184, 280 probability 105, 112, 114, 121, 122,

135, 136, 141, 185, 188, 191–194, 197, 212, 214, 224, 240, 243, 245, 257, 278, 281, 287, 364, 366

transverse (mode) 316 tunneling

resonant 3, 4, 40, 143, 169, 179, 181, 183, 184, 189, 196, 199, 200, 207, 210, 212, 215, 216, 220–223, 249, 319, 372, 373

single barrier 183, 185

U, V uncertainty principle 2, 20, 116, 303, 325 unitarity 164 universal conductance fluctuations (UCFs)

62, 286 variational method 344 variational principle 43, 45, 48, 344 vector potential 76, 274–277, 286 voltage probe 127, 129, 132

W–Z Wannier function 49–55 wave matching 130, 170 wave packet 22, 26, 241, 242, 246 weak localization 210, 274, 283, 285 Wiener-Khintchine theorem 228, 229, 348 Wigner-Seitz cell 327, 330 Y-junction 160, 161, 164, 166, 168, 212,

213, 215, 222–224, 372 zig-zag nanotube 304, 307