Preface ......................................................... v
List of Contributors ......................................... xvii
1 Thermodynamics and Kinetics of Quantum Dot Growth
Vitaly Shchukin, Eckehard Schöll and Peter Kratzer ......... 1
1.1. Introduction ............................................... 2
1.1.1. Length and Time Scales .............................. 3
1.1.2. Multiscale Approach to the Modeling of
Nanostructures ...................................... 4
1.2. Atomistic Aspects of Growth ................................ 5
1.2.1. Diffusion of Ga Atoms on GaAs(OOl) .................. 5
1.2.2. Energetics of As2 Incorporation During
Growth .............................................. 5
1.2.3. Kinetic Monte Carlo Simulation of GaAs
Homoepitaxy ......................................... 6
1.2.4. Wetting Layer Evolution ............................. 9
1.3. Size and Shapes of Individual Quantum Dots ................ 11
1.3.1. Hybrid Approach to Calculation of the Equilibrium
Shape of Individual Quantum Dots ................... 11
1.3.2. Role of High-Index Facets in the Shape of Quantum
Dots ............................................... 13
1.3.3. Shape Transition During Quantum Dot Growth ......... 14
1.3.4. Constraint Equilibrium of Quantum Dots with a
Wetting Layer ...................................... 15
1.4. Thermodynamics and Kinetics of Quantum Dot Ensembles ...... 19
1.4.1. Equilibrium Volume of Strained Islands versus
Ostwald Ripening ................................... 19
1.4.2. Crossover from Kinetically Controlled to
Thermodynamically Controlled Growth of Quantum
Dots ............................................... 22
1.4.3. Tunable Metastability of Quantum Dot Arrays ........ 25
1.4.4. Evolution Mechanisms in Dense Arrays of
Elastically Interacting Quantum Dots ............... 27
1.5. Quantum Dot Stacks ........................................ 29
1.5.1. Transition between Vertically Correlated and
Vertically Anticorrelated Quantum Dot Growth ....... 29
1.5.2. Finite Size Effect: Abrupt Transitions between
Correlated and Anticorrelated Growth ............... 31
1.5.3. Reduction of a Size of a Critical Nucleus in the
Second Quantum Dot Layer ........................... 32
1.6. Summary and Outlook ....................................... 34
References ..................................................... 35
2 Control of Self-Organized In(Ga)As/GaAs Quantum Dot Growth
Udo W. Pohl and André Strittmatter ........................ 41
2.1. Introduction .............................................. 41
2.2. Evolution and Strain Engineering of InGaAs/GaAs Quantum
Dots ...................................................... 42
2.2.1. Evolution of InGaAs Dots ........................... 42
2.2.2. Engineering of Single and Stacked InGaAs QD
Layers ............................................. 46
2.3. Growth Control of Equally Shaped InAs/GaAs Quantum Dots ... 50
2.3.1. Formation of Self-Similar Dots with a Multimodal
Size Distribution .................................. 51
2.3.2. Kinetic Description of Multimodal Dot-Ensemble
Formation .......................................... 54
2.4. Epitaxy of GaSb/GaAs Quantum Dots ......................... 56
2.4.1. Onset and Dynamics of GaSb/GaAs Quantum-Dot
Formation .......................................... 56
2.4.2. Structure of GaSb/GaAs Quantum Dots ................ 58
2.5. Device Applications of InGaAs Quantum Dots ................ 60
2.5.1. Edge-Emitting Lasers ............................... 60
2.5.2. Surface-Emitting Lasers ............................ 61
2.6. Conclusion ................................................ 62
References ..................................................... 63
3 In-Situ Monitoring for Nano-Structure Growth in MOVPE
Markus Pristovsek and Wolfgang Richter .................... 67
3.1. Introduction .............................................. 67
3.2. Reflectance ............................................... 69
3.3. Reflectance Anisotropy Spectroscopy (RAS) ................. 71
3.3.1. RAS Spectra and Surface Reconstruction ............. 72
3.3.2. Monolayer Oscillations ............................. 74
3.3.3. Monitoring of Carrier Concentration ................ 79
3.4. Scanning Tunneling Microscopy (STM) ....................... 82
3.5. Conclusion ................................................ 84
References ..................................................... 85
4 Bottom-up Approach to the Nanopatterning of Si(001)
R. Koch ................................................... 87
4.1. Quantum Dot Growth on Semiconductor Templates ............. 87
4.2. (2 x n) Reconstruction of Si(001) ......................... 88
4.3. Monte Carlo Simulations on the (2 x n) Formation .......... 90
4.4. Scanning Tunneling Microscopy Results ..................... 92
4.5. Summary and Outlook ....................................... 94
References ..................................................... 95
5 Structural Characterisation of Quantum Dots by X-Ray
Diffraction and ТЕМ
R. Köhler, W. Neumann, M. Schmidbauer, M. Hanke,
D. Grigoriev, P. Schäfer, H. Kirmse, I. Hausler
and R. Schneider .......................................... 97
5.1. Introduction .............................................. 97
5.2. Liquid Phase Epitaxy of SiGe/Si: A Model System for the
Stranski-Krastanow Process ................................ 99
5.2.1. Dot Evolution in a Close-to-Equilibrium Regime ..... 99
5.3. (In,Ga)As Quantum Dots on GaAs ........................... 103
5.3.1. Shape, Size, Strain and Composition Gradient in
InGaAs QD Arrays .................................. 103
5.3.2. Chemical Composition of (In,Ga)As QDs Determined
by ТЕМ ............................................ 107
5.3.3. Controlling 3D Ordering in (In,Ga)As QD Arrays
through GaAs Surface Orientation .................. 109
5.4. Ga(Sb,As) Quantum Dots on GaAs ........................... 113
5.4.1. Structural Characterisation of Ga(Sb,As) QDs by
High-Resolution ТЕМ Imaging ....................... 117
5.4.2. Chemical Characterisation of Ga(Sb,As) QDs by
HAADF STEM Imaging ................................ 118
References .................................................... 119
6 The Atomic Structure of Quantum Dots
Mario Dähne, Holger Eisele and Karl Jacobi ............... 123
6.1. Introduction ............................................. 123
6.2. Experimental Details ..................................... 124
6.3. STM Studies of InAs Quantum Dots on the Growth Surface ... 124
6.4. XSTM Studies of Buried Nanostructures .................... 127
6.4.1. InAs Quantum Dots ................................. 127
6.4.2. InGaAs Quantum Dots ............................... 131
6.4.3. GaSb Quantum Dots ................................. 134
6.5. Conclusion ............................................... 135
References .................................................... 136
7 Theory of Excitons in InGaAs/GaAs Quantum Dots
Andrei Schliwa and Momme Winkelnkemper ................... 139
7.1. Introduction ............................................. 139
7.2. Interrelation of QD-Structure, Strain and
Piezoelectricity, and Coulomb Interaction ................ 140
7.2.1. The Binding Energies of the Few Particle
Complexes ......................................... 140
7.3. Method of Calculation .................................... 143
7.3.1. Calculation of Strain ............................. 144
7.3.2. Piezoelectricity and the Reduction of Lateral
Symmetry .......................................... 145
7.3.3. Single Particle States ............................ 147
7.3.4. Many-Particle States .............................. 148
7.3.5. The Configuration Interaction Model ............... 148
7.3.6. Interband Spectra ................................. 150
7.4. The Investigated Structures: Variation of Size, Shape
and Composition .......................................... 150
7.5. The Impact of QD Size .................................... 151
7.5.1. The Role of the Piezoelectric Field ............... 153
7.6. The Aspect Ratio ......................................... 155
7.6.1. Vertical Aspect Ratio ............................. 155
7.6.2. Lateral Aspect Ratio .............................. 157
7.7. Different Composition Profiles ........................... 157
7.7.1. Inverted Cone-Like Composition Profile ............ 157
7.7.2. Annealed QDs ...................................... 159
7.7.3. InGaAs QDs with Uniform Composition ............... 159
7.8. Correlation vs. QD Size, Shape and Particle Type ......... 159
7.9. Conclusions .............................................. 162
References .................................................... 163
8 Phonons in Quantum Dots and Their Role in Exciton
Dephasing
F. Grosse, E.A. Muljarov and R. Zimmermann ............... 165
8.1. Introduction ............................................. 165
8.2. Structural Properties of Semiconductor Nanostructures .... 166
8.3. Theory of Acoustic Phonons in Quantum Dots ............... 166
8.3.1. Continuum Elasticity Model of Phonons ............. 167
8.3.2. Phonons in Quantum Dots ........................... 170
8.4. Exciton-Acoustic Phonon Coupling in Quantum Dots ......... 171
8.5. Dephasing of the Exciton Polarization in Quantum Dots .... 173
8.5.1. Single Exciton Level: Independent Boson Model ..... 174
8.5.2. Multilevel System: Real and Virtual Phonon-
Assisted Transitions .............................. 176
8.5.3. Application to Coupled Quantum Dots ............... 182
8.6. Summary .................................................. 184
References .................................................... 185
9 Theory of the Optical Response of Single and Coupled
Semiconductor Quantum Dots
C. Weber, M. Richter, S. Ritter and A. Knorr ............. 189
9.1. Introduction ............................................. 189
9.2. Theory ................................................... 190
9.2.1. Quantum Dot Model ................................. 190
9.2.2. Hamiltonian ....................................... 191
9.2.3. Mathematical Formalisms ........................... 193
9.3. Single Quantum Dot Response .............................. 196
9.3.1. Linear Absorption Spectra and Quantum Optics ...... 196
9.3.2. Semiclassical Nonlinear Dynamics .................. 199
9.4. Two Coupled Quantum Dots ................................. 201
9.4.1. Absorption Spectra ................................ 202
9.4.2. Excitation Transfer ............................... 202
9.4.3. Rabi Oscillations ................................. 203
9.4.4. Pump-Probe/Differential Transmission Spectra ...... 204
9.5. Multiple Quantum Dots .................................... 205
9.5.1. Four-Wave-Mixing: Photon Echo in Quantum Dot
Ensembles ......................................... 205
9.5.2. Absorption of Multiple Coupled Quantum Dots ....... 205
9.5.3. Energy Transfer of Multiple Coupled Quantum
Dots .............................................. 206
9.6. Conclusion ............................................... 206
References .................................................... 207
10 Theory of Nonlinear Transport for Ensembles of Quantum
Dots
G. Kießilich, A. Wacker and E. Schöll .................... 211
10.1.Introduction ............................................. 211
10.2.Coulomb Interaction within a Quantum Dot Layer ........... 211
10.3.Transport in Quantum Dot Stacks .......................... 213
10.4.Current Fluctuations and Shot Noise ...................... 214
10.5.Full Counting Statistics and Decoherence in Coupled
Quantum Dots.............................................. 216
10.6.Conclusion ............................................... 218
References .................................................... 219
11 Quantum Dots for Memories
M. Geller and A. Marent .................................. 221
11.1.Introduction ............................................. 221
11.2.Semiconductor Memories ................................... 222
11.2.1.Dynamic Random Access Memory (DRAM)................ 222
11.2.2.Nonvolatile Semiconductor Memories (Flash) ........ 223
11.2.3.A QD-based Memory Cell ............................ 224
11.3.Charge Carrier Storage in Quantum Dots ................... 226
11.3.1.Experimental Technique ............................ 226
11.3.2.Carrier Storage in InGaAs/GaAs Quantum Dots ....... 228
11.3.3.Hole Storage in GaSb/GaAs Quantum Dots ............ 229
11.3.4.InGaAs/GaAs Quantum Dots with Additional AlGaAs
Barrier ........................................... 230
11.4.Conclusion and Outlook ................................... 233
References .................................................... 235
12 Visible-Bandgap II-VI Quantum Dot Heterostructures
llya Akimov, Joachim Puis, Michael Rabe and Fritz
Henneberger .............................................. 237
12.1.Introduction ............................................. 237
12.2.Epitaxial Growth ......................................... 238
12.3.Few-Particles States and Their Fine Structure ............ 241
12.3.1.Excitons and Biexcitons ........................... 241
12.3.2.Trions in Charged Quantum Dots .................... 243
12.4.Coherent Control of the Exciton-Biexciton System ......... 245
12.5.Spin Relaxation of Excitons, Holes, and Electrons ........ 247
12.5.1.Exciton Quantum Coherence ......................... 247
12.5.2.Hole Spin Lifetime ................................ 248
12.5.3.Spin Dynamics of the Resident Electron ............ 249
12.6.Diluted Magnetic Quantum Dots ............................ 251
References .................................................... 253
13 Narrow-Gap Nanostructures in Strong Magnetic Fields
T. Tran-Anh and M. Ortenberg ............................. 255
13.1.Introduction ............................................. 255
13.2.Materials: HgSe/HgSe:Fe .................................. 256
13.3.Fabrication of HgSe/HgSe:Fe Nanostructures ............... 256
13.3.1.Quantum Wells ..................................... 257
13.3.2.Roof-Ridge Quantum Wires .......................... 258
13.3.3.Quantum Dots ...................................... 259
13.4.Electronic Characterization of the HgSe/HgSe:Fe
Nano-Structures in Strong Magnetic Fields ................ 262
13.4.1.High-Field Magneto Transport ...................... 262
13.4.2.Infrared Magneto-Resonance Spectroscopy ........... 263
13.5.Summary .................................................. 267
References .................................................... 267
14 Optical Properties of III-V Quantum Dots
Udo W. Pohl, Sven Rodt and Axel Hoffmann ................. 269
14.1.Introduction ............................................. 269
14.2.Confined States and Many-Particle Effects ................ 270
14.2.1.Renormalization ................................... 270
14.2.2.Phonon Interaction ................................ 274
14.2.3.Electronic Tuning by Strain Engineering ........... 276
14.2.4.Multimodal InAs/GaAs Quantum Dots ................. 278
14.3.Single InAs/GaAs Quantum Dots ............................ 281
14.3.1.Spectral Diffusion ................................ 281
14.3.2.Size-Dependent Anisotropic Exchange
Interaction ....................................... 282
14.3.3.Binding Energies of Excitonic Complexes ........... 285
14.3.4.Data Storage Using Confined Trions ................ 286
14.3.5.Electronic Tuning by Annealing .................... 287
14.4.Optical Properties of InGaN/GaN Quantum Dots ............. 288
14.4.1.Time-Resolved Studies on Quantum Dot Ensembles .... 289
14.4.2.Single-Dot Spectroscopy ........................... 292
14.5.Summary .................................................. 296
References .................................................... 298
15 Ultrafast Coherent Spectroscopy of Single Semiconductor Quantum
Dots
Christoph Lienau and Thomas Elsaesser .................... 301
15.1.Introduction ............................................. 301
15.2.Interface Quantum Dots ................................... 303
15.3.Coherent Spectroscopy of Interface Quantum Dots:
Experimental Technique ................................... 305
15.4.Coherent Control in Single Interface Quantum Dots ........ 308
15.4.1.Ultrafast Optical Nonlinearities of Single
Interface Quantum Dots ............................ 308
15.4.2.Rabi Oscillations in a Quantum Dot ................ 312
15.4.3.Optical Stark Effect: Ultrafast Control of
Single Exciton Polarizations ...................... 315
15.5.Coupling Two Quantum Dots via the Dipole-Dipole
Interaction .............................................. 319
15.6.Summary and Conclusions .................................. 323
References .................................................... 325
16 Single-Photon Generation from Single Quantum Dots
Matthias Scholz, Thomas Aichele and Oliver Benson ........ 329
16.1.Introduction ............................................. 329
16.2.Single Quantum Dots as Single-Photon Emitters ............ 331
16.2.1.Photon Statistics of Single-Photon Emitters ....... 331
16.2.2.Micro-Photoluminescence ........................... 332
16.2.3.Single Photons from InP Quantum Dots .............. 333
16.3.Multiphoton Emission from Single Quantum Dots ............ 334
16.4.Realization of the Ultimate Limit of a Light Emitting
Diode .................................................... 339
16.5.Applications in Quantum Information Processing ........... 343
16.5.1.Quantum Key Distribution .......................... 343
16.5.2.Quantum Computing ................................. 344
16.6.Outlook .................................................. 346
References .................................................... 347
Index ......................................................... 351
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