Electronic and optical properties of quantum dots [Elektronische Ressource] : a tight binding approach / von Stefan Schulz

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• Physik

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• Publié par: universitat_bremen
• Publié le: 01 janvier 2007
• Nombre de lectures: 31
• Langue: English
• Poids de l'ouvrage: 3 Mo

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Electronic and Optical Properties
of Quantum Dots:
A Tight-Binding Approach
byStefan Schulz
May, 2007
ITP FB 1
University of Bremen Institute for Theoretical PhysicsElectronic and Optical Properties
of Quantum Dots:
A Tight-Binding Approach
Dem Fachbereich für Physik und Elektrotechnik
der Universität Bremen
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften (Dr. rer. nat.)
genehmigte Dissertation
von
Dipl. Phys. Stefan Schulz
aus Delmenhorst
1. Gutachter: Prof. Dr. rer. nat. G. Czycholl
2. Gutachter: Prof. Dr. rer. nat. F. Jahnke
Eingereicht am: 29.05.2007
Tag des Promotionskolloquiums: 17.07.2007Persönlichkeiten werden nicht durch schöne Reden geformt,
sondern durch Arbeit und eigene Leistung.
Albert EinsteinAbstract
In this thesis the electronic and optical properties of semiconductor quantum dots
are investigated by means of tight-binding (TB) models combined with configuration
interaction calculations.
In the first part, an empirical TB model is used to investigate the electronic states
of group II-VI semiconductor quantum dots with a zinc blende structure. TB matrix
elements up to second nearest neighbors and spin-orbit coupling are included. Within
this approach we study pyramidal-shaped CdSe quantum dots embedded in a ZnSe
matrix as well as spherical CdSe nanocrystals. Lattice distortions are included by an
appropriate model strain field. Within the TB model, the influence of strain on the
bound electronic states, in particular their spatial orientation, are investigated. The
theoretical results for spherical nanocrystals are compared with data from tunneling
and optical spectroscopy.
Additionally to the quantum dots based on II-VI materials, we investigate the electronic
and optical properties of self-assembled nitride quantum dots. Coulomb and dipole ma-
trix elements are calculated from the single-particle wave functions, which fully include
the atomistic wurtzite structure. These matrix elements serve as an input for the cal-
culation of optical spectra. For the investigated InN/GaN material system, the optical
selection rules are found to be strongly affected by band-mixing effects. Within this
framework, excitonic absorption and emission as well as multi-exciton emission spectra
are analyzed for different lens-shaped quantum dots. A dark exciton and biexciton
ground state for small quantum dots is found. For larger structures, the strong elec-
trostatic built-in fields lead to a level reordering for the hole states, which results in a
bright exciton ground state.
Furthermore the electronic and optical properties of truncated pyramidal GaN/AlN
QDs with zinc blende structure are studied. The influence of the strain field on the
single-particle states and energies is discussed. Coulomb and dipole matrix elements are
calculated from the single-particle wave functions and the excitonic absorption spec-
trum is analyzed. This analysis reveals a strong anisotropy in the polarization of the
energetically lowest inter-band transition. In addition, the results of our atomistic TB
description are compared with approaches based on continuum models.Contents
1 Prologue v
Part I Basic Considerations
2 Modeling Semiconductor Quantum Dots 1
2.1 QuantumDots ......... .......... .......... .. 2
2.2 Theoretical Approaches for the Calculation of Electronic Properties . . 5
2.2.1 Effective-Mass Approximation and k· p-Models ....... .. 5
2.2.2 PseudopotentialModel . . ......... .......... . . 6
2.2.3 Tight-BindingModel . . . .. 7
3 Tight-Binding Models 9
3.1 Tight-BindingModelforBulkMaterials . .... .......... .. 9
3.1.1 Spin-OrbitCoupling . . . ......... .. 17
3.2 Tight-Binding Model for Semiconductor Quantum Dots . . . . . . . . . 19
3.2.1 Strainfields . ...... .......... .......... .. 22
3.2.2 Piezoelectricity ..... . ......... .. 24
3.2.3 Numerical Determination of Eigenvalues: The Folded Spectrum
Method ......... .......... .......... . . 26
4 Short Introduction in Group Theory 29
4.1 GeneralConsiderations ..... . ......... .. 29
4.2 SymmetryPropertiesofEnergyBands ...... .......... .. 36
4.3 TimeReversalSymmetry.... .......... . . 40
4.3.1 DegeneraciesduetoTimeReversalSymmetry ........ .. 43
iContents
Part II Electronic Properties of CdSe Nanostructures with
Zinc Blende Structure
5 Introduction to Part II 49
6 Crystals with a Zinc Blende Structure 51
6.1 CrystalStructure . ........ .......... ........... 51
6.2 Symmetry Considerations and Bulk Band Structure for Zinc Blende
Semiconductors . . . . . . . . . . 52
36.3 Tight-binding Model with s p Basis . ....... 54c a
7 Results for CdSe Nanostructures 59
7.1 ResultsforaPyramidalCdSeQDsEmbeddedinZnSe ......... 59
7.1.1 QuantumDotGeometryandstrain ..... ........... 59
7.1.2 Single-ParticleProperties .......... 61
7.2 ResultsforCdSeNanocrystals .. 69
7.2.1 QuantumDotGeometryandStrain..... 69
7.2.2 Single-particle Properties and Comparison with Experimental Re-
sults . . .......... . ......... ........... 69
Part III Electronic and Optical Properties of Nitride
Quantum Dots with a Wurtzite Structure
8 Introduction to Part III 77
9 Crystals with a Wurtzite Structure 79
9.1 CrystalStructure . ........ .......... ........... 79
9.2 Symmetry Considerations and Bulk Band Structure for Wurtzite Semi-
conductors . . . . . . . . . . . . . . . . . . . . . . . . . ......... 81
9.3 SpontaneousPolarization..... . ......... 84
39.4 Tight-binding Model with sp Basis ........... 85
10 Results for InN/GaN Quantum Dots 89
10.1Single-ParticleProperties..... . ......... 89
10.1.1 QuantumDotGeometryandStrain..... ........... 89
10.1.2 TheElectrostaticBuilt-InField ....... 91
10.1.3 Single-ParticleStatesandEnergies ..... 93
10.1.4 Influence of Crystal Field Splitting and Spin-Orbit Coupling . . 97
10.2Many-ParticleProperties ..... . ......... ........... 101
10.2.1 Many-BodyHamiltonianandLight-MatterInteraction ..... 102
ii