A maior rede de estudos do Brasil

Grátis
370 pág.
Kuno M - Introduction to Nanoscience and Nanotechnology_ A Workbook (2005)

Pré-visualização | Página 1 de 44

Introduction to Nanoscience and Nanotechnology:
A Workbook
M. Kuno
August 22, 2005
2
Contents
1 Introduction 1
2 Structure 11
3 Length scales 37
4 Excitons 45
5 Quantum mechanics review 57
6 Confinement 75
7 Nondegenerate perturbation theory 107
8 Density of states 121
9 More density of states 129
10 Even more density of states 139
11 Joint density of states 151
12 Absorption 165
13 Interband transitions 173
14 Emission 195
15 Bands 213
16 K · P Approximation
(Pronounced k dot p) 235
i
ii CONTENTS
17 Tunneling 261
18 The WKB approximation 279
19 Synthesis 307
20 Tools 325
21 Applications 333
Acknowledgments 355
List of Figures
1.1 CdSe quantum dot . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Quantum confinement . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Size dependent absorption and emission of CdSe . . . . . . . 8
1.5 Artificial solid . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 14 3D Bravais lattices . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Atoms per unit cell . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Atom sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 FCC unit cell . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 BCC unit cell . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Hexagonal unit cell . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Diamond structure unit cell . . . . . . . . . . . . . . . . . . . 18
2.8 Zincblende or ZnS structure unit cell . . . . . . . . . . . . . . 19
2.9 NaCl structure unit cell . . . . . . . . . . . . . . . . . . . . . 20
2.10 CsCl structure unit cell . . . . . . . . . . . . . . . . . . . . . 21
2.11 Wurtzite unit cell . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.12 Miller index examples . . . . . . . . . . . . . . . . . . . . . . 23
2.13 More Miller index examples . . . . . . . . . . . . . . . . . . . 24
2.14 Simple cubic . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.15 FCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1 Exciton types . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Exciton absorption . . . . . . . . . . . . . . . . . . . . . . . . 46
6.1 Particle in an infinite box . . . . . . . . . . . . . . . . . . . . 76
6.2 Half a harmonic oscillator . . . . . . . . . . . . . . . . . . . . 78
6.3 Various 1D potentials . . . . . . . . . . . . . . . . . . . . . . 79
6.4 Particle in a finite box . . . . . . . . . . . . . . . . . . . . . . 80
6.5 Particle in a finite box: solutions . . . . . . . . . . . . . . . . 81
iii
iv LIST OF FIGURES
6.6 Particle in a finite well: Mathcad solutions . . . . . . . . . . . 85
6.7 Particle in an infinite circle . . . . . . . . . . . . . . . . . . . 87
6.8 Particle in a sphere . . . . . . . . . . . . . . . . . . . . . . . . 92
8.1 3D density of states . . . . . . . . . . . . . . . . . . . . . . . 123
8.2 2D density of states . . . . . . . . . . . . . . . . . . . . . . . 125
8.3 1D density of states . . . . . . . . . . . . . . . . . . . . . . . 126
8.4 0D density of states . . . . . . . . . . . . . . . . . . . . . . . 127
9.1 3D density of CB and VB states . . . . . . . . . . . . . . . . 134
9.2 3D Fermi level . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.1 2D density of CB states . . . . . . . . . . . . . . . . . . . . . 140
10.2 2D density of VB states . . . . . . . . . . . . . . . . . . . . . 142
10.3 1D density of CB states . . . . . . . . . . . . . . . . . . . . . 144
10.4 1D density of VB states . . . . . . . . . . . . . . . . . . . . . 147
11.1 Vertical transitions . . . . . . . . . . . . . . . . . . . . . . . . 153
11.2 3D joint density of states . . . . . . . . . . . . . . . . . . . . 155
11.3 2D joint density of states . . . . . . . . . . . . . . . . . . . . 158
11.4 1D joint density of states . . . . . . . . . . . . . . . . . . . . 161
11.5 Summary, joint density of states . . . . . . . . . . . . . . . . 162
14.1 Einstein A and B coefficients . . . . . . . . . . . . . . . . . . 196
14.2 Derived emission spectrum: Einstein A and B coefficients . . 209
14.3 Pulsed experiment and lifetime . . . . . . . . . . . . . . . . . 209
14.4 Radiative decay of excited state . . . . . . . . . . . . . . . . . 211
14.5 Multiple pathway decay of excited state . . . . . . . . . . . . 211
15.1 Kronig-Penney rectangular potential . . . . . . . . . . . . . . 213
15.2 Kronig-Penney delta function potential . . . . . . . . . . . . . 224
15.3 General Kronig Penney model: Mathcad solutions . . . . . . 227
15.4 General Kronig Penney model continued: Mathcad solutions 228
15.5 Kronig Penney model revisited: Mathcad solutions . . . . . . 229
15.6 Kronig Penney model, delta functions: Mathcad solutions . . 230
15.7 Kronig Penney model, delta functions continued: Mathcad
solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
15.8 From metals to insulators . . . . . . . . . . . . . . . . . . . . 232
17.1 Potential step . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
17.2 Potential step (ε > V ) . . . . . . . . . . . . . . . . . . . . . . 262
LIST OF FIGURES v
17.3 Potential step (ε < V ) . . . . . . . . . . . . . . . . . . . . . . 263
17.4 Potential barrier . . . . . . . . . . . . . . . . . . . . . . . . . 269
17.5 Potential barrier (ε > V ) . . . . . . . . . . . . . . . . . . . . . 269
17.6 Potential barrier (ε < V ) . . . . . . . . . . . . . . . . . . . . . 275
17.7 Semiconductor junction . . . . . . . . . . . . . . . . . . . . . 278
18.1 Arbitrary potential step . . . . . . . . . . . . . . . . . . . . . 281
18.2 Arbitrary potential drop . . . . . . . . . . . . . . . . . . . . . 286
18.3 Arbitrary potential barrier . . . . . . . . . . . . . . . . . . . . 290
18.4 Field emission . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
18.5 Shottky barrier . . . . . . . . . . . . . . . . . . . . . . . . . . 300
18.6 Parabolic barrier . . . . . . . . . . . . . . . . . . . . . . . . . 301
18.7 Linear barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
18.8 Parabolic barrier . . . . . . . . . . . . . . . . . . . . . . . . . 304
19.1 Cartoon of a MBE apparatus . . . . . . . . . . . . . . . . . . 308
19.2 Cartoon of a MOCVD apparatus . . . . . . . . . . . . . . . . 309
19.3 Colloidal synthesis apparatus . . . . . . . . . . . . . . . . . . 311
19.4 LaMer model . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
19.5 LaMer model: size distribution . . . . . . . . . . . . . . . . . 319
20.1 Transmission electron microscopy . . . . . . . . . . . . . . . . 326
20.2 Secondary electron microscopy . . . . . . . . . . . . . . . . . 327
20.3 Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . 328
20.4 Scanning tunneling microscopy . . . . . . . . . . . . . . . . . 329
20.5 Dip pen nanolithography . . . . . . . . . . . . . . . . . . . . . 330
20.6 Microcontact printing . . . . . . . . . . . . . . . . . . . . . . 331
21.1 Nanowire device . . . . . . . . . . . . . . . . . . . . . . . . . 334
21.2 Nanowire sensor . . . . . . . . . . . . . . . . . . . . . . . . . 335
21.3 Quantum dot/dye photobleaching . . . . . . . . . . . . . . . . 337
21.4 Quantum dot/dye absorption/emission spectra . . . . . . . . 338
21.5 Density of states for lasing . . . . . . . . . . . . . . . . . . . . 340
21.6 Solar spectrum and QD absorption/emission spectra . . . . . 342
21.7 Quantum dot LED schematic . . . . . . . . . . . . . . . . . . 344
21.8 Orthodox model of single electron tunneling . . . . . . . . . . 346
21.9 Coulomb Staircase . . . . . . . . . . . . . . . . . . . . . . . . 350
vi LIST OF FIGURES
List of Tables
2.1 Common metals . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2 Group IV semiconductors . . . . . . . . . . . . . . . . . . . . 25
2.3 Group III-V semiconductors . . . . . . . . . . . . . . . . . . . 26
2.4 Group II-VI semiconductors