Table Of ContentV044
ISBN-13 978-981-4241-68-7
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WorldScientificBook-9.75inx6.5in 00-Fu-prelims
CRC Press
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Contents
List of Figures ix
List of Tables xxi
Preface xxiii
1. Electrons in Nanostructures 1
1.1 ATOMS AND SOLIDS . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 CRYSTALLINE NATURE OF SOLIDS . . . . . . . . . . . . . . . 8
1.3 ELECTRONS IN SOLID . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 EIGHT-BAND k·p MODEL . . . . . . . . . . . . . . . . . . . . . 13
1.5 HETEROSTRUCTURE MATERIALS . . . . . . . . . . . . . . . . 18
1.5.1 Envelop Function . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.2 Effective Mass Approximation . . . . . . . . . . . . . . . . 22
1.6 DIMENSIONALITY OF ENERGY DENSITY OF STATES . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2. Light-Matter Interactions 33
2.1 TIME-DEPENDENT PERTURBATION THEORY . . . . . . . . 33
2.1.1 The Golden Rule . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.2 Exponential Decay . . . . . . . . . . . . . . . . . . . . . . 37
2.2 ELECTROMAGNETIC FIELD. . . . . . . . . . . . . . . . . . . . 39
2.3 GENERALIZED GOLDEN RULE . . . . . . . . . . . . . . . . . . 43
2.4 LIGHT–MATTER INTERACTION . . . . . . . . . . . . . . . . . 45
2.4.1 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4.2 Electron in Electromagnetic Field . . . . . . . . . . . . . . 46
2.4.3 The Composite System . . . . . . . . . . . . . . . . . . . . 47
2.5 OPTICAL SPECTRUM . . . . . . . . . . . . . . . . . . . . . . . . 51
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
v
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vi Contents
3. Exciton and Exciton Photogeneration 55
3.1 QUANTUM CONFINEMENT IN NANOPARTICLES . . . . . . . 55
3.1.1 Free Carrier and Infinite Potential Well . . . . . . . . . . . 59
3.1.2 Spherical Square Well . . . . . . . . . . . . . . . . . . . . . 60
3.1.3 Cylindrical Quantum Wire . . . . . . . . . . . . . . . . . . 62
3.1.4 Colloidal Quantum Dots . . . . . . . . . . . . . . . . . . . 64
3.2 EFFECTIVE MASS THEORY OF EXCITON . . . . . . . . . . . 66
3.3 EXCITON BINDING ENERGY . . . . . . . . . . . . . . . . . . . 70
3.4 OPTICAL TRANSITION OF EXCITON . . . . . . . . . . . . . . 73
3.5 RADIATIVE AND NONRADIATIVE RECOMBINATIONS . . . 76
3.5.1 Spontaneous Emission. . . . . . . . . . . . . . . . . . . . . 77
3.5.2 Electron–Phonon Interaction . . . . . . . . . . . . . . . . . 78
3.5.3 Radiative Lifetime . . . . . . . . . . . . . . . . . . . . . . . 79
3.6 MULTIPHOTON PROCESSES. . . . . . . . . . . . . . . . . . . . 82
3.7 AUGER RECOMBINATION AND IMPACT IONIZATION . . . . 91
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4. Exciton Polariton 105
4.1 EXCITON EXCITATION . . . . . . . . . . . . . . . . . . . . . . . 105
4.2 EXCITONIC POLARIZATION . . . . . . . . . . . . . . . . . . . . 109
4.3 DAMPING RATE . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.4 MICROCAVITY AND FOUR-WAVE MIXING . . . . . . . . . . . 115
4.5 EXCITONIC PHOTONIC GAP . . . . . . . . . . . . . . . . . . . 120
4.5.1 Atomic Lattice . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.5.2 Photonic Band in QD Lattice . . . . . . . . . . . . . . . . 124
4.6 QD DIMER SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.6.1 Optical Excitation of QD . . . . . . . . . . . . . . . . . . . 130
4.6.2 Low-Loss Negative Dielectric Constant . . . . . . . . . . . 132
4.6.3 Photonic Band of QD-based Negative Dielectric Medium . 134
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5. Optoelectronic Devices 141
5.1 LIGHT EMITTING DIODE . . . . . . . . . . . . . . . . . . . . . 142
5.2 LASER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.2.1 The Generation of Laser Radiation . . . . . . . . . . . . . 150
5.2.2 Optical Cavity . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.2.3 Heterojunction Semiconductor Structure . . . . . . . . . . 156
5.2.4 Quantum Wells . . . . . . . . . . . . . . . . . . . . . . . . 159
5.2.5 Buried Heterostructure Semiconductor Laser . . . . . . . . 160
5.2.6 Quantum Cascade Laser . . . . . . . . . . . . . . . . . . . 162
5.3 PHOTODETECTOR . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.3.1 Optimizing Material Growth Direction . . . . . . . . . . . 163
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Contents vii
5.3.2 Optical Diffraction Grating . . . . . . . . . . . . . . . . . . 168
5.3.3 QD Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.3.4 Thermal Photovoltaics by Polymer Conjugated QDs . . . . 178
5.3.5 QD Bioimaging . . . . . . . . . . . . . . . . . . . . . . . . 179
5.4 INTEGRATED CIRCUITS . . . . . . . . . . . . . . . . . . . . . . 180
5.5 PHOTON STORAGE . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.6 WAVEGUIDES AND MODULATORS. . . . . . . . . . . . . . . . 181
5.7 QUANTUM OPTICS . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.7.1 Sensitivity and Resolution . . . . . . . . . . . . . . . . . . 184
5.7.2 Quantum Nondemolition Measurement . . . . . . . . . . . 186
5.7.3 Quantum Information . . . . . . . . . . . . . . . . . . . . . 187
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
6. Basics of Plasmonics 195
6.1 CLASSICAL ELECTRODYNAMICS IN MATTER . . . . . . . . 197
6.1.1 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.1.2 Maxwell’s Equations in Matter . . . . . . . . . . . . . . . . 198
6.2 SOLID STATE THEORY FOR OPTICAL CONSTANT
OF METAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6.3 Drude–Sommerfeld model . . . . . . . . . . . . . . . . . . . . . . . 202
6.3.1 Plasmon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
6.3.2 Plane Waves in a Metal . . . . . . . . . . . . . . . . . . . . 205
6.3.2.1 Dispersion relation . . . . . . . . . . . . . . . . . 205
6.3.2.2 Phase and group velocity . . . . . . . . . . . . . . 206
6.4 SURFACE PLASMON POLARITON AT ONE INTERFACE . . . 207
6.4.1 TM Surface Plasmon–Polaritons . . . . . . . . . . . . . . . 208
6.4.2 Phase and Group Velocity . . . . . . . . . . . . . . . . . . 209
6.4.3 TE Surface Modes . . . . . . . . . . . . . . . . . . . . . . . 211
6.5 SURFACE PLASMON–POLARITON COUPLED BETWEEN
TWO INTERFACES . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.6 FINITE-WIDTH SPP WAVEGUIDE. . . . . . . . . . . . . . . . . 212
6.7 NUMERICAL APPROACHES . . . . . . . . . . . . . . . . . . . . 212
6.7.1 The Fourier Modal Method . . . . . . . . . . . . . . . . . . 213
6.7.2 The Finite-Difference Time-Domain Method . . . . . . . . 215
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7. Surface Plasmonics Devices 223
7.1 PASSIVE SURFACE PLASMONICS DEVICES . . . . . . . . . . 223
7.1.1 Plasmonic Lens . . . . . . . . . . . . . . . . . . . . . . . . 223
7.1.2 Nano Optic Beam Splitter . . . . . . . . . . . . . . . . . . 226
7.1.3 Surface Plasmonics Waveguide . . . . . . . . . . . . . . . . 226
7.1.4 Corner Plasmonic Waveguides . . . . . . . . . . . . . . . . 227
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7.1.5 General Properties of Corner Modes . . . . . . . . . . . . . 230
7.1.6 The Effect of Geometry . . . . . . . . . . . . . . . . . . . . 233
7.1.7 The Chromatic Properties . . . . . . . . . . . . . . . . . . 236
7.1.8 Realistic Metal-Corner Waveguides . . . . . . . . . . . . . 237
7.1.9 Plasmonic Resonator Channel Drop Filters . . . . . . . . . 239
7.1.10 Broadband Plasmonic Coupler . . . . . . . . . . . . . . . . 245
7.2 DEEP-SUBWAVELENGTH PLASMONIC WAVEGUIDE . . . . . 248
7.2.1 General Consideration . . . . . . . . . . . . . . . . . . . . 248
7.2.2 Realistic Design and Simulation . . . . . . . . . . . . . . . 249
7.3 HYBRID PLASMONIC AND INDEX-GUIDING WAVEGUIDE . 253
7.3.1 1D Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 254
7.3.2 2D Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 257
7.3.2.1 Waveguide for quasi-TE operation . . . . . . . . . 257
7.3.2.2 Waveguide for quasi-TM operation . . . . . . . . 260
7.3.3 Further Considerations . . . . . . . . . . . . . . . . . . . . 262
7.4 ACTIVE SURFACE PLASMONICS DEVICES . . . . . . . . . . . 262
7.4.1 Plasmonic Light Sources . . . . . . . . . . . . . . . . . . . 262
7.4.2 Active Plasmonic Devices . . . . . . . . . . . . . . . . . . . 263
7.5 NANOSTRUCTURE SURFACE PLASMONICS . . . . . . . . . . 264
7.5.1 Surface Plasmon Polaritons in Periodic Nano Hole Arrays. 265
7.5.2 Localized Plasmon Resonances in Metal Nanoparticles . . 268
7.6 BARRIERS AND FRONTIERS . . . . . . . . . . . . . . . . . . . 272
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Index 283
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List of Figures
1.1 IntheBohrmodelofthehydrogenatomthenegativelychargedelectron
e− is in a circular orbit around the positively charged proton p+. . . . . 3
1.2 The energy level diagram for hydrogen atom. Light is emitted or ab-
sorbed when an electron makes a transition between two states. . . . . . 5
1.3 (a)Astwoatomsarebroughtclosertogether,asingleatomiclevelsplits
into two states with different energies. (b) A single atomic level splits
into five when five atoms are in close proximity. (c) In a crystal each
atomic level splits into an essentially continuous band of energies.. . . . 7
1.4 Face-centered cubic lattice and the zincblende crystal structure.. . . . . 8
1.5 FirstBrillouinzonesforsimplecubiclattice(left)andfcc(right)lattice.
Points and lines of symmetry are indicated. . . . . . . . . . . . . . . . . 11
1.6 SchematicdiagramillustratingthegrowthofanAlGaAs/GaAsmultiple
quantum well sample by molecular beam epitaxy. Deposition of (a)
(Al,Ga)As, (b) GaAs. The system is under high vacuum. . . . . . . . . 12
1.7 Energy band structures of (a) Si and (b) InAs. . . . . . . . . . . . . . . 14
1.8 A schematic illustration of one-dimensional square-well barrier model
for conduction-band (CB) electrons and valence-band (VB) holes in
GaAs/AlxGa1−xAs multiple quantum well system. . . . . . . . . . . . . 23
1.9 Conductionbandedgeandenvelopfunction(verticallyshiftedupbythe
energy position of the ground sublevel) of a GaAs/AlGaAs asymmetri-
callycoupledquantum-wellsystem. Solidlines: L=0.1˚A;dottedlines:
L=5.1˚A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.10 Dimensionality of energy density of states. . . . . . . . . . . . . . . . . . 28
2.1 Wavelength–frequency spectrum of electromagnetic wave (photon). . . . 39
2.2 Optical spectra of low-dimensional GaAs nanostructures. L = 100 ˚A,
T =300K.Integer0,1,2,and3indicatethedimensionalityofthesystem. 53
3.1 Lattice structures of a GaAs nano cluster. . . . . . . . . . . . . . . . . . 57
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