Introduction to Nanoscience and Nanotechnology: A Workbook

246 Pages·2004·12.11 MB·English

Introduction to Nanoscience and Nanotechnology:
A Workbook
M. Kuno
May 14, 2004
2
Contents
1 Introduction 1
2 Structure 11
3 Length scales 29
4 Confinement 35
5 Density of states 57
6 More density of states 65
7 Even more density of states 73
8 Joint density of states 85
9 Emission 97
10 Bands 115
11 Tunneling 137
12 The WKB approximation 155
13 Synthesis 183
14 Tools 201
15 Applications 209
Acknowledgments 231
i
ii CONTENTS
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 Primitive 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 . . . . . . . . . . . . . . . . . . . . . 19
2.10 CsCl structure unit cell . . . . . . . . . . . . . . . . . . . . . 20
2.11 Primitive wurtzite unit cell . . . . . . . . . . . . . . . . . . . 20
2.12 Miller index examples . . . . . . . . . . . . . . . . . . . . . . 22
2.13 More Miller index examples . . . . . . . . . . . . . . . . . . . 23
4.1 Particle in an infinite box . . . . . . . . . . . . . . . . . . . . 36
4.2 Half a harmonic oscillator . . . . . . . . . . . . . . . . . . . . 38
4.3 Particle in a finite box . . . . . . . . . . . . . . . . . . . . . . 39
4.4 Particle in a finite box: solutions . . . . . . . . . . . . . . . . 40
4.5 Particle in a finite well: Mathcad solutions . . . . . . . . . . . 44
4.6 Particle in an infinite circle . . . . . . . . . . . . . . . . . . . 45
4.7 Particle in a sphere . . . . . . . . . . . . . . . . . . . . . . . . 49
5.1 3D density of states . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 2D density of states . . . . . . . . . . . . . . . . . . . . . . . 61
iii
iv LIST OF FIGURES
5.3 1D density of states . . . . . . . . . . . . . . . . . . . . . . . 62
5.4 0D density of states . . . . . . . . . . . . . . . . . . . . . . . 63
6.1 3D density of CB and VB states . . . . . . . . . . . . . . . . 70
6.2 3D Fermi level . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.1 2D density of CB states . . . . . . . . . . . . . . . . . . . . . 74
7.2 2D density of VB states . . . . . . . . . . . . . . . . . . . . . 76
7.3 1D density of CB states . . . . . . . . . . . . . . . . . . . . . 78
7.4 1D density of VB states . . . . . . . . . . . . . . . . . . . . . 81
8.1 Vertical transitions . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2 3D joint density of states . . . . . . . . . . . . . . . . . . . . 89
8.3 2D joint density of states . . . . . . . . . . . . . . . . . . . . 92
8.4 1D joint density of states . . . . . . . . . . . . . . . . . . . . 95
8.5 Summary, joint density of states . . . . . . . . . . . . . . . . 96
9.1 Einstein A and B coefficients . . . . . . . . . . . . . . . . . . 98
9.2 Derived emission spectrum: Einstein A and B coefficients . . 110
9.3 Pulsed experiment and lifetime . . . . . . . . . . . . . . . . . 110
9.4 Radiative decay of excited state . . . . . . . . . . . . . . . . . 112
9.5 Multiple pathway decay of excited state . . . . . . . . . . . . 112
10.1 Kronig-Penney rectangular potential . . . . . . . . . . . . . . 115
10.2 Kronig-Penney delta function potential . . . . . . . . . . . . . 126
10.3 General Kronig Penney model: Mathcad solutions . . . . . . 129
10.4 General Kronig Penney model continued: Mathcad solutions 130
10.5 Kronig Penney model revisited: Mathcad solutions . . . . . . 131
10.6 Kronig Penney model, delta functions: Mathcad solutions . . 132
10.7 Kronig Penney model, delta functions continued: Mathcad
solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
10.8 From metals to insulators . . . . . . . . . . . . . . . . . . . . 134
11.1 Potential step . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
11.2 Potential step (ε > V) . . . . . . . . . . . . . . . . . . . . . . 138
11.3 Potential step (ε < V) . . . . . . . . . . . . . . . . . . . . . . 139
11.4 Potential barrier . . . . . . . . . . . . . . . . . . . . . . . . . 144
11.5 Potential barrier (ε > V). . . . . . . . . . . . . . . . . . . . . 145
11.6 Potential barrier (ε < V). . . . . . . . . . . . . . . . . . . . . 150
11.7 Semiconductor junction . . . . . . . . . . . . . . . . . . . . . 153
LIST OF FIGURES v
12.1 Arbitrary potential step . . . . . . . . . . . . . . . . . . . . . 157
12.2 Arbitrary potential drop . . . . . . . . . . . . . . . . . . . . . 162
12.3 Arbitrary potential barrier . . . . . . . . . . . . . . . . . . . . 166
12.4 Field emission . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
12.5 Shottky barrier . . . . . . . . . . . . . . . . . . . . . . . . . . 176
12.6 Parabolic barrier . . . . . . . . . . . . . . . . . . . . . . . . . 177
12.7 Linear barrier . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
12.8 Parabolic barrier . . . . . . . . . . . . . . . . . . . . . . . . . 180
13.1 Cartoon of a MBE apparatus . . . . . . . . . . . . . . . . . . 184
13.2 Cartoon of a MOCVD apparatus . . . . . . . . . . . . . . . . 185
13.3 Colloidal synthesis apparatus . . . . . . . . . . . . . . . . . . 187
13.4 LaMer model . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
13.5 LaMer model: size distribution . . . . . . . . . . . . . . . . . 195
14.1 Transmission electron microscopy . . . . . . . . . . . . . . . . 202
14.2 Secondary electron microscopy . . . . . . . . . . . . . . . . . 203
14.3 Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . 204
14.4 Scanning tunneling microscopy . . . . . . . . . . . . . . . . . 205
14.5 Dip pen nanolithography. . . . . . . . . . . . . . . . . . . . . 206
14.6 Microcontact printing . . . . . . . . . . . . . . . . . . . . . . 207
15.1 Nanowire device . . . . . . . . . . . . . . . . . . . . . . . . . 210
15.2 Nanowire sensor . . . . . . . . . . . . . . . . . . . . . . . . . 211
15.3 Quantum dot/dye photobleaching . . . . . . . . . . . . . . . . 213
15.4 Quantum dot/dye absorption/emission spectra . . . . . . . . 214
15.5 Density of states for lasing . . . . . . . . . . . . . . . . . . . . 216
15.6 Solar spectrum and QD absorption/emission spectra . . . . . 218
15.7 Quantum dot LED schematic . . . . . . . . . . . . . . . . . . 220
15.8 Orthodox model of single electron tunneling . . . . . . . . . . 222
15.9 Coulomb Staircase . . . . . . . . . . . . . . . . . . . . . . . . 226
vi LIST OF FIGURES
List of Tables
2.1 Common metals . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Group IV semiconductors . . . . . . . . . . . . . . . . . . . . 24
2.3 Group III-V semiconductors . . . . . . . . . . . . . . . . . . . 24
2.4 Group II-VI semiconductors . . . . . . . . . . . . . . . . . . . 25
2.5 Group IV-VI semiconductors . . . . . . . . . . . . . . . . . . 25
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viii LIST OF TABLES