No description available.

No description available.

Spatial confinement of electrons and their interactions as well as confinement of the spin dimensionality often yield drastic changes of the electronic and magnetic properties of solids. Novel quantum transport and optical phenomena, involving electronic spin degrees of freedom in semiconductor heterostructures, as well as a rich variety of exotic quantum ground states and magnetic excitations in complex transition metal oxides that arise upon such confinements, belong therefore to topical problems of contemporary condensed matter physics. In this work electron spin systems in reduced dimensions are studied with Electron Spin Resonance (ESR) spectroscopy, a method which can provide important information on the energy spectrum of the spin states, spin dynamics, and magnetic correlations. The studied systems include quasi onedimensional spin chain materials based on transition metals Cu and Ni. Another class of materials are semiconductor heterostructures made of Si and Ge. Part I deals with the theoretical background of ESR and the description of the experimental ESR setups used which have been optimized for the purposes of the present work. In particular, the development and implementation of axial and transverse cylindrical resonant cavities for high-field highfrequency ESR experiments is discussed. The high quality factors of these cavities allow for sensitive measurements on μm-sized samples. They are used for the investigations on the spin-chain materials. The implementation and characterization of a setup for electrical detected magnetic resonance is presented. In Part II ESR studies and complementary results of other experimental techniques on two spin chain materials are presented. The Cu-based material Linarite is investigated in the paramagnetic regime above T > 2.8 K. This natural crystal constitutes a highly frustrated spin 1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearestneighbor interactions. The ESR data reveals that the significant magnetic anisotropy is due to anisotropy of the g-factor. Quantitative analysis of the critical broadening of the linewidth suggest appreciable interchain and interlayer spin correlations well above the ordering temperature. The Ni-based system is an organic-anorganic hybrid material where the Ni2+ ions possessing the integer spin S = 1 are magnetically coupled along one spatial direction. Indeed, the ESR study reveals an isotropic spin-1 Heisenberg chain in this system which unlike the Cu half integer spin-1/2 chain is expected to possess a qualitatively different non-magnetic singlet ground state separated from an excited magnetic state by a so-called Haldane gap. Surprisingly, in contrast to the expected Haldane behavior a competition between a magnetically ordered ground state and a potentially gapped state is revealed. In Part III investigations on SiGe/Si quantum dot structures are presented. The ESR investigations reveal narrowlines close to the free electron g-factor associated with electrons on the quantum dots. Their dephasing and relaxation times are determined. Manipulations with sub-bandgap light allow to change the relative population between the observed states. On the basis of extensive characterizations, strain, electronic structure and confined states on the Si-based structures are modeled with the program nextnano3. A qualitative model, explaining the energy spectrum of the spin states is proposed.

Polarization entangled photon pairs on demand are considered to be an important building block of quantum communication technology. It has been demonstrated that semiconductor quantum dots (QDs), which exhibit a certain spatial symmetry, can be used as a triggered, on-chip source of polarization entangled photon pairs. Due to limitations of the growth, the as-grown QDs usually do not exhibit the required symmetry, making the availability of post-growth tuning techniques essential. In this work first the QD-morphology of hundreds of QDs is correlated with the optical emission of neutral excitons confined in GaAs/AlGaAs QDs. It is presented how elastic anisotropic stress can be used to partially restore the symmetry of self-assembled GaAs/AlGaAs and InGaAs/GaAs QDs, making them as candidate sources of entangled photon pairs. As a consequence of the tuning of the QD-anisotropy we observe a rotation of the polarization of the emitted light. The joint modification of polarization orientation and QD anisotropy can be described by an anticrossing of the so-called bright excitonic states. Furthermore, it is demonstrated that anisotropic stress can be used to tune the purity of the hole states of the QDs by modifying the degree of heavy and light hole mixing. This ability might be interesting for applications using the hole spin as a so-called quantum bit.

Colloidal semiconductor nanocrystals (NCs) have attracted a great deal of interest as bright and stable chromophores for a variety of applications. Their superior physicochemical properties depend on characteristics of the inorganic core, as well as on the chemical nature and structure of the stabilizing organic ligand shell. To evaluate the promising material, a thorough knowledge of structure-property relationships is still demanded. The present work addresses this challenge to three water-soluble NC systems, namely thiol-capped CdTe, thiol-capped CdHgTe, and DNA-functionalized CdTe NCs with special emphasis on the investigation of structure, modification, and influence of the ligand shell. Remarkably, CdTe NCs show bright emission in the visible spectral region and can be synthesized in high quality directly in water. It was shown that the aqueous synthesis also facilitates the preparation of strongly near-infrared (NIR) emitting CdHgTe NCs. The current work presents a detailed study on parameters, by which the emission can be tuned, such as the growth time, the initial Cd : Hg ratio, and the choice of ligand. These insights contribute to the knowledge, which is essential for the design of highly emissive and long-term stable NIR emitting NCs. Further variations of the NC/ligand system include the modification of the ligand shell of CdTe NCs with oligonucleotides based on the strong attachment of DNA molecules to the NC. The successful functionalization of NCs with single-stranded DNA molecules is very promising for the precise and programmable assembly of NCs using DNA origami structures as templates. For both, functionality and optical properties, the surface chemistry of the NCs plays a substantial role and was subject to an extensive investigation. As there is no generally applicable technique to determine the amount of stabilizers and the structure of the ligand shell, the presented study is based on a combination of various methods particularly tailored to the analysis of water-soluble CdTe NCs capped by short-chain thiols. CdTe NCs served as a model system for the described analysis of the ligand shell, since they are thoroughly studied regarding synthesis and features of the core. Aiming for the quantification of thiols, a straightforward colorimetric assay, the Ellman\'s test, is for the first time introduced for the analysis of NCs. Accompanied by elemental analysis an approximate number of thiols per NC becomes accessible. Moreover, theoretical calculations were performed to estimate the amount of ligand that would cover the NC in a monolayer of covalently bound molecules. In contrast to these results, the experimental values point to a larger amount of thiols immobilized on the NC. Attempts to remove the ligand indicate the presence of Cd in the ligand shell and thermogravimetric studies show that the ligands are not loosely assembled in the ligand shell. The outstanding conclusion of these findings involves the presence of Cd-thiol complexes in the ligand shell. Further results unambiguously show that the amount of Cd-thiol complexes present in the NC solution strongly influences the concentration-dependent emission yield of the NCs. Additional studies dedicated to the considerable influence of the ligand shell highlight a strong effect of pH, NC concentration, type and purity of the solvent, and the number of precipitation steps on the emission of water-soluble semiconductor NCs. These substantial investigations emphasize the need to carefully control the conditions applied for handling, optical measurements, and application of NCs. In order to gain a deeper insight into the complex structure of the native ligand shell, techniques deliberately chosen for the in situ analysis were applied for thioglycolic acid-capped CdTe NCs. Information from dynamic light scattering (DLS) regarding the stability and the shell thickness are consistent with previous results showing a large ligand network on the NC surface and a decreasing stability of the NCs upon dilution. Importantly, nuclear magnetic resonance (NMR) spectroscopy allows for the distinction of bound and free ligands directly in solution and proves the presence of these species for the NCs studied. In particular, the results indicate that the ligands are not strongly bound to the NC core and that both, free and bound ligand species, consist of modified thiol molecules, such as Cd-thiol complexes. These findings support previous assumptions and allow to establish a distinct picture of the ligand shell of water-soluble semiconductor NCs. Further insights were obtained from small-angle X-ray scattering (SAXS), which facilitates the identification and the determination of the composition of NC core as well as ligand shell. Element-specific SAXS yields the final proof of the presence of Cd in the ligand shell. The model developed for the optimal fitting of the experimental scattering curves additionally confirms the findings from the other methods. In conclusion, the present work contributes to the challenging goal of a comprehensive knowledge of interactions between the NC core and the ligands. The fundamental development of a structural model of water-soluble CdTe NCs including information on stoichiometries is accomplished by the combination of the techniques presented and emphasizes the challenge to assign a clear border between the ligand shell and the Cd-thiol complexes in solution. Altogether, CdTe NCs capped by thioglycolic acid are best described by a crystalline core surrounded by a water-swollen Cd-thiolate shell that considerably affects the optical properties of the system. Notably, the results of the versatile study provide the opportunity to control the overall properties and to evaluate water-soluble semiconductor NCs for particular applications in photonics and optoelectronics.

Polarization entangled photon pairs on demand are considered to be an important building block of quantum communication technology. It has been demonstrated that semiconductor quantum dots (QDs), which exhibit a certain spatial symmetry, can be used as a triggered, on-chip source of polarization entangled photon pairs. Due to limitations of the growth, the as-grown QDs usually do not exhibit the required symmetry, making the availability of post-growth tuning techniques essential. In this work first the QD-morphology of hundreds of QDs is correlated with the optical emission of neutral excitons confined in GaAs/AlGaAs QDs. It is presented how elastic anisotropic stress can be used to partially restore the symmetry of self-assembled GaAs/AlGaAs and InGaAs/GaAs QDs, making them as candidate sources of entangled photon pairs. As a consequence of the tuning of the QD-anisotropy we observe a rotation of the polarization of the emitted light. The joint modification of polarization orientation and QD anisotropy can be described by an anticrossing of the so-called bright excitonic states. Furthermore, it is demonstrated that anisotropic stress can be used to tune the purity of the hole states of the QDs by modifying the degree of heavy and light hole mixing. This ability might be interesting for applications using the hole spin as a so-called quantum bit.

Colloidal semiconductor nanocrystals (NCs) have attracted a great deal of interest as bright and stable chromophores for a variety of applications. Their superior physicochemical properties depend on characteristics of the inorganic core, as well as on the chemical nature and structure of the stabilizing organic ligand shell. To evaluate the promising material, a thorough knowledge of structure-property relationships is still demanded. The present work addresses this challenge to three water-soluble NC systems, namely thiol-capped CdTe, thiol-capped CdHgTe, and DNA-functionalized CdTe NCs with special emphasis on the investigation of structure, modification, and influence of the ligand shell. Remarkably, CdTe NCs show bright emission in the visible spectral region and can be synthesized in high quality directly in water. It was shown that the aqueous synthesis also facilitates the preparation of strongly near-infrared (NIR) emitting CdHgTe NCs. The current work presents a detailed study on parameters, by which the emission can be tuned, such as the growth time, the initial Cd : Hg ratio, and the choice of ligand. These insights contribute to the knowledge, which is essential for the design of highly emissive and long-term stable NIR emitting NCs. Further variations of the NC/ligand system include the modification of the ligand shell of CdTe NCs with oligonucleotides based on the strong attachment of DNA molecules to the NC. The successful functionalization of NCs with single-stranded DNA molecules is very promising for the precise and programmable assembly of NCs using DNA origami structures as templates. For both, functionality and optical properties, the surface chemistry of the NCs plays a substantial role and was subject to an extensive investigation. As there is no generally applicable technique to determine the amount of stabilizers and the structure of the ligand shell, the presented study is based on a combination of various methods particularly tailored to the analysis of water-soluble CdTe NCs capped by short-chain thiols. CdTe NCs served as a model system for the described analysis of the ligand shell, since they are thoroughly studied regarding synthesis and features of the core. Aiming for the quantification of thiols, a straightforward colorimetric assay, the Ellman\'s test, is for the first time introduced for the analysis of NCs. Accompanied by elemental analysis an approximate number of thiols per NC becomes accessible. Moreover, theoretical calculations were performed to estimate the amount of ligand that would cover the NC in a monolayer of covalently bound molecules. In contrast to these results, the experimental values point to a larger amount of thiols immobilized on the NC. Attempts to remove the ligand indicate the presence of Cd in the ligand shell and thermogravimetric studies show that the ligands are not loosely assembled in the ligand shell. The outstanding conclusion of these findings involves the presence of Cd-thiol complexes in the ligand shell. Further results unambiguously show that the amount of Cd-thiol complexes present in the NC solution strongly influences the concentration-dependent emission yield of the NCs. Additional studies dedicated to the considerable influence of the ligand shell highlight a strong effect of pH, NC concentration, type and purity of the solvent, and the number of precipitation steps on the emission of water-soluble semiconductor NCs. These substantial investigations emphasize the need to carefully control the conditions applied for handling, optical measurements, and application of NCs. In order to gain a deeper insight into the complex structure of the native ligand shell, techniques deliberately chosen for the in situ analysis were applied for thioglycolic acid-capped CdTe NCs. Information from dynamic light scattering (DLS) regarding the stability and the shell thickness are consistent with previous results showing a large ligand network on the NC surface and a decreasing stability of the NCs upon dilution. Importantly, nuclear magnetic resonance (NMR) spectroscopy allows for the distinction of bound and free ligands directly in solution and proves the presence of these species for the NCs studied. In particular, the results indicate that the ligands are not strongly bound to the NC core and that both, free and bound ligand species, consist of modified thiol molecules, such as Cd-thiol complexes. These findings support previous assumptions and allow to establish a distinct picture of the ligand shell of water-soluble semiconductor NCs. Further insights were obtained from small-angle X-ray scattering (SAXS), which facilitates the identification and the determination of the composition of NC core as well as ligand shell. Element-specific SAXS yields the final proof of the presence of Cd in the ligand shell. The model developed for the optimal fitting of the experimental scattering curves additionally confirms the findings from the other methods. In conclusion, the present work contributes to the challenging goal of a comprehensive knowledge of interactions between the NC core and the ligands. The fundamental development of a structural model of water-soluble CdTe NCs including information on stoichiometries is accomplished by the combination of the techniques presented and emphasizes the challenge to assign a clear border between the ligand shell and the Cd-thiol complexes in solution. Altogether, CdTe NCs capped by thioglycolic acid are best described by a crystalline core surrounded by a water-swollen Cd-thiolate shell that considerably affects the optical properties of the system. Notably, the results of the versatile study provide the opportunity to control the overall properties and to evaluate water-soluble semiconductor NCs for particular applications in photonics and optoelectronics.

Colloidal semiconductor quantum dots (QDs) have gained substantial interest as adjustable, bright and spectrally tunable fluorophores in the past decades. Besides their in-depth analyses in the scientific community, first industrial applications as color conversion and color enrichment materials were implemented. However, stability and processability are essential for their successful use in these and further applications. Methods to embed QDs into oxides or polymers can only partially solve this challenge. Recently, our group introduced the embedding of QDs into ionic salts, which holds several advantages in comparison to polymer or oxide-based counterparts. Both gas permeability and environmental-related degradation processes are negligible, making these composites an almost perfect choice of material. To evaluate this new class of QD-salt mixed crystals, a thorough understanding of the formation procedure and the final composites is needed. The present work is focused on embedding both aqueous-based and oil-based metal-chalcogenide QDs into several ionic salts and the investigations of their optical and chemical properties upon incorporation into the mixed crystals. QDs with well-known, reproducible and high-quality synthetic protocols are chosen as emissive species. CdTe QDs were incorporated into NaCl as host matrix by using the straightforward "classical" method. The resulting mixed crystals of various shapes and beautiful colors preserve the strong luminescence of the incorporated QDs. Besides NaCl, also borax and other salts are used as host matrices. Mercaptopropionic acid stabilized CdTe QDs can easily be co-crystallized with NaCl, while thioglycolic acid as stabilizing agent results in only weakly emitting powder-like mixed crystals. This challenge was overcome by adjusting the pH, the amount of free stabilizer and the type of salt used, demonstrating the reproducible incorporation of highest-quality CdTe QDs capped with thioglycolic acid into NaCl and KCl salt crystals. A disadvantage of the "classical" mixed crystallization procedure was its long duration which prevents a straightforward transfer of the protocol to less stable QD colloids, e.g., initially oil-based, ligand exchanged QDs. To address this challenge, the "Liquid-liquid-diffusion-assisted-crystallization" (LLDC) method is introduced. By applying the LLDC, a substantially accelerated ionic crystallization of the QDs is shown, reducing the crystallization time needed by one order of magnitude. This fast process opens the field of incorporating ligand-exchanged Cd-free QDs into NaCl matrices. To overcome the need for a ligand exchange, the LLDC can also be extended towards a two-step approach. In this modified version, the seed-mediated LLDC provides for the first time the ability to incorporate oil-based QDs directly into ionic matrices without a prior phase transfer. The ionic salts appear to be very tight matrices, ensuring the protection of the QDs from the environment. As one of the main results, these matrices provide extraordinary high photo- and chemical stability. It is further demonstrated with absolute measurements of photoluminescence quantum yields (PL-QYs), that the PL-QYs of aqueous CdTe QDs can be considerably increased upon incorporation into a salt matrix by applying the "classical" crystallization procedure. The achievable PL enhancement factors depend strongly on the PL-QYs of the parent QDs and can be described by the change of the dielectric surrounding as well as the passivation of the QD surface. Studies on CdSe/ZnS in NaCl and CdTe in borax showed a crystal-induced PL-QY increase below the values expected for the respective change of the refractive index, supporting the derived hypothesis of surface defect curing by a CdClx formation as one main factor for PL-QY enhancement. The mixed crystals developed in this work show a high suitability as color conversion materials regarding both their stability and spectral tunability. First proof-of-concept devices provide promising results. However, a combination of the highest figures of merit at the same time is intended. This ambitious goal is reached by implementing a model-experimental feedback approach which ensures the desired high optical performance of the used emitters throughout all intermediate steps. Based on the approach, a white LED combining an incandescent-like warm white with an exceptional high color rendering index and a luminous efficacy of radiation is prepared. It is the first time that a combination of this highly related figures of merit could be reached using QD-based color converters. Furthermore, the idea of embedding QDs into ionic matrices gained considerable interest in the scientific community, resulting in various publications of other research groups based on the results presented here. In summary, the present work provides a profound understanding how this new class of QD-salt mixed crystal composites can be efficiently prepared. Applying the different crystallization methods and by changing the matrix material, mixed crystals emitting from blue to the near infrared region of the electromagnetic spectrum can be fabricated using both Cd-containing and Cd-free QDs. The resulting composites show extraordinary optical properties, combining the QDs spectral tunability with the rigid and tight ionic matrix of the salt. Finally, their utilization as a color conversion material resulted in a high-quality white LED that, for the first time, combines an incandescent-like hue with outstanding optical efficacy and color rendering properties. Besides that, the mixed crystals offer huge potential in other high-quality applications which apply photonic and optoelectronic components.

Spatial confinement of electrons and their interactions as well as confinement of the spin dimensionality often yield drastic changes of the electronic and magnetic properties of solids. Novel quantum transport and optical phenomena, involving electronic spin degrees of freedom in semiconductor heterostructures, as well as a rich variety of exotic quantum ground states and magnetic excitations in complex transition metal oxides that arise upon such confinements, belong therefore to topical problems of contemporary condensed matter physics. In this work electron spin systems in reduced dimensions are studied with Electron Spin Resonance (ESR) spectroscopy, a method which can provide important information on the energy spectrum of the spin states, spin dynamics, and magnetic correlations. The studied systems include quasi onedimensional spin chain materials based on transition metals Cu and Ni. Another class of materials are semiconductor heterostructures made of Si and Ge. Part I deals with the theoretical background of ESR and the description of the experimental ESR setups used which have been optimized for the purposes of the present work. In particular, the development and implementation of axial and transverse cylindrical resonant cavities for high-field highfrequency ESR experiments is discussed. The high quality factors of these cavities allow for sensitive measurements on μm-sized samples. They are used for the investigations on the spin-chain materials. The implementation and characterization of a setup for electrical detected magnetic resonance is presented. In Part II ESR studies and complementary results of other experimental techniques on two spin chain materials are presented. The Cu-based material Linarite is investigated in the paramagnetic regime above T > 2.8 K. This natural crystal constitutes a highly frustrated spin 1/2 Heisenberg chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearestneighbor interactions. The ESR data reveals that the significant magnetic anisotropy is due to anisotropy of the g-factor. Quantitative analysis of the critical broadening of the linewidth suggest appreciable interchain and interlayer spin correlations well above the ordering temperature. The Ni-based system is an organic-anorganic hybrid material where the Ni2+ ions possessing the integer spin S = 1 are magnetically coupled along one spatial direction. Indeed, the ESR study reveals an isotropic spin-1 Heisenberg chain in this system which unlike the Cu half integer spin-1/2 chain is expected to possess a qualitatively different non-magnetic singlet ground state separated from an excited magnetic state by a so-called Haldane gap. Surprisingly, in contrast to the expected Haldane behavior a competition between a magnetically ordered ground state and a potentially gapped state is revealed. In Part III investigations on SiGe/Si quantum dot structures are presented. The ESR investigations reveal narrowlines close to the free electron g-factor associated with electrons on the quantum dots. Their dephasing and relaxation times are determined. Manipulations with sub-bandgap light allow to change the relative population between the observed states. On the basis of extensive characterizations, strain, electronic structure and confined states on the Si-based structures are modeled with the program nextnano3. A qualitative model, explaining the energy spectrum of the spin states is proposed.:Abstract i Contents iii List of Figures vi List of Tables viii 1 Preface 1 I Background and Experimental 5 2 Principles of ESR 7 2.1 The Resonance Phenomenon . . . . . . . . . . . . . . . . . . . 7 2.2 ESR Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 The g -factor . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Relaxation Times . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Lineshape Properties . . . . . . . . . . . . . . . . . . . . 13 2.3 Effective Spin Hamiltonian . . . . . . . . . . . . . . . . . . . . . 15 2.4 Spin-Orbit Coupling . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 d-electrons in a Crystal Field . . . . . . . . . . . . . . . . . . . . 17 2.6 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6.1 Dipolar Coupling . . . . . . . . . . . . . . . . . . . . . . 23 2.6.2 Exchange Interaction . . . . . . . . . . . . . . . . . . . . 23 2.6.3 Superexchange . . . . . . . . . . . . . . . . . . . . . . . 24 2.6.4 Symmetric Anisotropic Exchange . . . . . . . . . . . . 25 2.6.5 Antisymmetric Anisotropic Exchange . . . . . . . . . . 25 2.6.6 Hyperfine Interaction . . . . . . . . . . . . . . . . . . . 26 3 Experimental 27 3.1 Setup for Experiments at 10GHz . . . . . . . . . . . . . . . . . 27 3.2 Implementation of an EDMR Setup . . . . . . . . . . . . . . . . 29 3.2.1 Basic Characterization . . . . . . . . . . . . . . . . . . . 31 3.3 High Frequency Setup . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.1 MillimeterWave Vector Network Analyzer . . . . . . . 33 3.3.2 Waveguides and Cryostats . . . . . . . . . . . . . . . . . 34 3.4 Development of the Resonant Cavity Setup . . . . . . . . . . . 35 3.4.1 Mode Propagation . . . . . . . . . . . . . . . . . . . . . 38 3.4.2 Resonant CavityModes . . . . . . . . . . . . . . . . . . 40 3.4.3 Resonant Cavity Design . . . . . . . . . . . . . . . . . . 41 3.4.4 Resonant Cavity Sample Stick . . . . . . . . . . . . . . . 45 3.4.5 Experimental Characterization . . . . . . . . . . . . . . 47 3.4.6 Performing an ESR Experiment . . . . . . . . . . . . . . 53 II Quasi One-Dimensional Spin-Chains 57 4 Motivation 59 5 Quasi One-Dimensional Systems 61 5.1 Magnetic Order and Excitations . . . . . . . . . . . . . . . . . . 63 5.2 Competing Interactions . . . . . . . . . . . . . . . . . . . . . . . 64 5.3 Haldane Spin Chain . . . . . . . . . . . . . . . . . . . . . . . . . 66 6 Linarite 69 6.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6.2 Magnetization and ESR . . . . . . . . . . . . . . . . . . . . . . . 71 6.3 NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.4 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . 81 6.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7 The Ni-hybrid NiCl3C6H5CH2CH2NH3 83 7.1 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7.2 Susceptibility andMagnetization . . . . . . . . . . . . . . . . . 85 7.3 ESR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 7.4 Further Investigations . . . . . . . . . . . . . . . . . . . . . . . . 95 7.5 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . 96 8 Summary 99 III SiGe Nanostructures 101 9 Motivation 103 10 SiGe Semiconductor Nanostructures 107 10.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 10.1.1 Silicon and Germanium . . . . . . . . . . . . . . . . . . 107 10.1.2 Epitaxial Growth of SiGe Heterostructures . . . . . . . 109 10.1.3 Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 10.1.4 Band Deformation . . . . . . . . . . . . . . . . . . . . . 112 10.2 Sample Structure and Characterization . . . . . . . . . . . . . 114 11 Modelling of SiGe/Si Heterostructures 119 11.1 Program Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 120 11.2 Implementation of Si/Ge System . . . . . . . . . . . . . . . . . 121 11.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 11.3.1 Single Quantum Dot . . . . . . . . . . . . . . . . . . . . 123 11.3.2 Multiple Quantum Dots . . . . . . . . . . . . . . . . . . 127 11.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 11.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 12 ESR Experiments on Si/SiGe Quantum Dots 135 12.1 ESR on Si Structures . . . . . . . . . . . . . . . . . . . . . . . . . 135 12.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 137 12.2.1 Samples grown at 600◦C . . . . . . . . . . . . . . . . . . 138 12.2.2 Samples grown at 700◦C . . . . . . . . . . . . . . . . . . 139 12.2.3 T1-Relaxation Time . . . . . . . . . . . . . . . . . . . . . 143 12.2.4 Effect of Illumination . . . . . . . . . . . . . . . . . . . . 145 12.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 12.3.1 Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . 149 12.3.2 Assignment of ESR Lines . . . . . . . . . . . . . . . . . . 150 12.3.3 Relaxation Times . . . . . . . . . . . . . . . . . . . . . . 153 12.3.4 Donors in Heterostructures . . . . . . . . . . . . . . . . 153 12.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 13 Summary and Outlook 157 Bibliography 163 Acknowledgements 176

Sources of single and polarization-entangled photons are an essential component in a variety of potential quantum information applications. Suitable emitters need to generate photons deterministically and at fast repetition rates, with highest degrees of single-photon purity, entanglement and indistinguishability. Semiconductor quantum dots are among the leading candidates for this task, offering entangled-photon pair emission on-demand, challenging current state-of-the-art sources based on the probabilistic spontaneous parametric down-conversion (SPDC). Unfortunately, their susceptibility to perturbations from the solid-state environment significantly affects the photon coherence and entanglement degree. Furthermore, most quantum dot types suffer from poor wavelength control and emitter yield, due to a random growth process. This thesis investigates the emerging family of GaAs/AlGaAs quantum dots obtained by in-situ Al droplet etching and nanohole infilling. Particular focus is laid on the interplay of growth parameters, quantum dot morphology and optical properties. An unprecedented emission wavelength control with distributions as narrow as ± 1 nm is achieved, using four independent growth parameters: The GaAs infilling amount, the deposition sequence, the migration time and the Al concentration in the barrier material. This enables the generation of large emitter ensembles tailored to match the optical transitions of rubidium, a leading quantum memory candidate. The photon coherence is enhanced by an optimized As flux during the growth process using the GaAs surface reconstruction. With these improvements, we demonstrate for the first time two-photon interference from separate, frequency-stabilized quantum dots using a rubidium-based Faraday filter as frequency reference. Two-photon resonant excitation of the biexciton state is employed for the coherent and deterministic generation of photon pairs with negligible multi-photon emission probability. The GaAs/AlGaAs quantum dots exhibit a very small average fine structure of (4.8 ±2.4) µeV and short average radiative lifetimes of 200 ps, enabling entanglement fidelities up to F = 0.94, which are among the highest reported for any entangled-photon source to date. Furthermore, almost all fabricated emitters on a single wafer exhibit fidelities beyond the classical limit - without any post-growth tuning. By embedding the quantum dots into a broadband-optical antenna we enhance the photon collection efficiency significantly without impairing the high degrees of entanglement. Thus, for the first time, quantum dots are able to compete with SPDC sources, paving the way towards the realization of a semiconductor-based quantum repeater - among many other key enabling quantum photonic elements.:Contents List of Figures ix List of Tables xiii 1 Introduction 1 1.1 Researchmotivation ...................1 1.1.1 Structure of this thesis ................. 3 1.2 Applications based on entangled photons ............. 4 1.2.1 Quantum bits ...................4 1.2.2 Quantum key distribution ................ 5 1.2.3 Qubit teleportation .................. 7 1.2.4 Teleportation of entanglement ..............9 1.2.5 The photonic quantumrepeater .............. 10 1.3 Generation of entangled photons ...............12 1.3.1 The ideal entangled-photon source ............. 12 1.3.2 Non-deterministic photon sources ............. 13 1.3.3 Deterministic photon sources ..............14 2 Fundamentals 17 2.1 Semiconductor quantumdots ................17 2.1.1 Introduction to semiconductor quantum dots .......... 17 2.1.2 Formation of confined excitonic states ............ 19 2.1.3 Energy hierarchy of excitonic states ............. 21 2.2 Entangled photons from semiconductor quantumdots ......... 22 2.2.1 The concept of entanglement ............... 22 2.2.2 Polarization-entangled photon pairs fromthe biexciton radiative decay .. 23 2.2.3 Origin and impact of the exciton fine structure splitting ....... 25 2.2.4 Impact of spin-scattering, dephasing and background photons on the degree of entanglement ..................29 2.3 Quantum dot entangled-photon sources - State of the art ........32 2.4 Exciton radiative lifetime .................. 34 2.4.1 The concept of radiative lifetime .............. 34 2.4.2 Measurement of the radiative lifetime ............35 2.5 Single-photon purity ...................37 2.5.1 Photon number distributions ............... 37 2.5.2 Second-order correlation function .............38 2.5.3 Measurement of the second-order correlation function ....... 40 2.6 Measurement of entanglement ................42 2.6.1 Quantum state tomography ...............43 2.7 Photon coherence and spectral linewidth .............46 2.7.1 The concept of coherence ................ 46 2.7.2 First-order coherence ................. 46 2.7.3 Relation between coherence and spectral linewidth ........ 49 2.7.4 homogeneous vs. inhomogeneous broadening in single quantumdots ..50 2.8 Photon indistinguishability .................51 2.8.1 Hong-Ou-Mandel interference ..............51 2.8.2 Hong-Ou-Mandel interference between photons fromseparate sources .. 52 2.8.3 The Bell state measurement with linear optics .......... 53 3 Experimentalmethods 55 3.1 The GaAs and AlAs material system ............... 55 3.2 Molecular beam epitaxy ..................56 3.2.1 The Concept of molecular beam epitaxy ...........56 3.2.2 Layout and components of the III-V Omicron MBE ........58 3.2.3 Growth parameters .................. 59 3.2.4 Reflection high-energy electron diffraction (RHEED) ........ 60 3.2.5 Growth rate determination using RHEED oscillations .......61 3.3 Optical setups .....................63 4 Results 67 4.1 Growth of GaAs/AlGaAs quantum dots by in-situ Al droplet etching .....68 4.1.1 Motivation for the study of GaAs / AlGaAs quantum dots ......68 4.1.2 GaAs / AlGaAs quantum dot growth process ..........69 4.1.3 Interplay between growth parameters, quantumdot morphology and optical properties ................. 71 4.1.4 Nanohole morphology and quantumdot formation ........ 73 4.1.5 Optical characterization ................75 4.1.6 Deterministic wavelength control .............77 4.1.7 Photon coherence and radiative lifetime ...........84 4.1.8 Decoherence processes in semiconductor quantum dots ......86 4.1.9 Chamber conditioning and growth process optimization ......87 4.1.10 Arsenic flux calibration using the GaAs surface reconstruction ..... 88 4.1.11 Enhanced photon coherence after growth process adjustments ....92 4.2 Two-photon interference from frequency-stabilized GaAs/AlGaAs quantum dots .................94 4.2.1 Frequency tuning of semiconductor quantumdots ........95 4.2.2 Experimental setup .................. 95 4.2.3 Optical characterization of the separate GaAs/AlGaAs quantum dots ... 98 4.2.4 Faraday anomalous dispersion optical filter and frequency feedback ... 99 4.2.5 Two-photon interference between remote, frequency-stabilized quantum dots 100 4.3 Solid-state ensemble of highly entangled photon sources at rubidiumatomic transitions ........................102 4.3.1 Fine-structure splitting ................103 4.3.2 Resonant excitation of the biexciton state ...........105 4.3.3 Single photon purity and radiative lifetime ........... 107 4.3.4 Radiative lifetime of GaAs/AlGaAs quantumdots - comparison to other quantumdot types ...................108 4.3.5 Degree of entanglement ................109 4.3.6 Highly-efficient extraction of the obtained entangled photons ..... 116 5 Conclusions 119 5.1 Summary ....................... 119 5.2 Discussion and outlook ..................122 Bibliography 127 Publications and scientific presentations 150 Acknowledgments 154 Selbstständigkeitserklärung 157 Curriculum vitae 157