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Holotomography is an extension of computed tomography where samples with low X-ray absorption can be investigated with higher contrast. In order to achieve this, the imaging system must yield an optical resolution of a few micrometers or less, which reduces the measurement area (field of view = FOV) to a few mm at most. If the sample size, however, exceeds the field of view (called local tomography or region of interest = ROI CT), filter problems arise during the CT reconstruction and phase retrieval in holotomography. In this paper, we will first investigate the practical impact of these filter problems and discuss approximate solutions. Secondly, we will investigate the effectiveness of a technique we call “multiscalar holotomography”, where, in addition to the ROI CT, a lower resolution non-ROI CT measurement is recorded. This is used to avoid the filter problems while simultaneously reconstructing a larger part of the sample, albeit with a lower resolution in the additional area.
In this work, high-energy observables arising during different phases of SN explosions are studied with respect to their potential for allowing conclusions on suggested explosion scenarios and physical mechanisms that are thought to influence the evolution of SNe in a major way. The focus on selected observables at keV and MeV energies is motivated by the appearance of large degeneracies that can even be found for disparate scenarios in many wavelength regimes. Since the discussed emission in the high-energy regime is directly linked to nuclear processes being usually very distinct for different suggested physical models, the signatures at keV and MeV energies allow for meaningful comparisons of simulations with observations.
The focus of this work is studying recombination mechanisms occurring in organic solar cells, as well as their impact on one of their most important parameters — the open circuit voltage Voc.
Firstly, the relationship between Voc and the respective charge carrier density n in the active layer under open circuit conditions is analyzed. Therefor, a model after Shockley for the open circuit voltage is used, whose validity is proven with the aid of fits to the measured data. Thereby, it is emphasized that the equation is only valid under special conditions. In the used reference system P3HT:PC61BM the fits are in agreement with the measurement data only in the range of high temperatures (150 - 300 K), where Voc increases linearly with decreasing temperature. At lower temperatures (50 – 150 K), the experiment shows a saturation of Voc. This saturation cannot be explained with the model by the measured falling charge carrier density with decreasing temperatures. In this temperature range Voc is not directly related to the intrinsic properties of the active layer. Voc saturation is due to injection energy barriers at the contacts, which is ascertained by macroscopic simulations. Furthermore, it is observed that Voc in the case of saturation is equivalent to the so-called built-in potential. The difference between the built-in potential and the energy gap corresponds thereby to the sum of the energy barriers at both contacts.
With the knowledge of the Voc(n) dependency for not contact limited solar cells, it is possible to investigate the recombination mechanisms of charge carriers in the active layer. For Langevin recombination the recombination rate is Rn2 (recombination order RO = 2), for Shockley-Read-Hall (SRH) Rn1 (RO=1); in various publications RO higher than two is reported with two main explanations.
1: Trap states for charge carriers exist in the respective separated phases, i.e. electrons in the acceptor phase and holes in the donor phase, which leads to a delayed recombination of the charge carriers at the interface of both phases and finally to an apparent recombination order higher than 2.
2: The enhanced R(n) dependency is attributed to the so called recombination prefactor, which again is dependent from n dependent mobility µ.
It is shown that for the system P3HT:PC61BM at room temperature the µ(n) dependency does nearly completely explain the higher RO but not at lower temperatures which in this case supports the first explanation. In the material system PTB7:PC71BM the increased RO cannot be explained by the µ(n) dependency even at room temperature.
To support the importance of trap states in combination with a phase separation for the explanation of the enhanced RO, additional trap states were incorporated in the solar cells to investigate their influence on the recombination mechanisms. To achieve this, P3HT:PC61BM solar cells were exposed to synthetic air (in the dark and under illumination) or TCNQ was added in small concentrations to the active layer which act as electron traps. For the oxygen degraded solar cell the recombination order is determined by a combination of open Voc-transients and Voc(n) measurements. Thereby, a continuous increase of the recombination order from 2.4 to more than 5 is observed with higher degradation times. By the evaluation of the ideality factor it can be shown that the impact of SRH recombination is increasing with higher trap concentration in relation to Langevin recombination. A similar picture is revealed for solar cells with TCNQ as extrinsic trap states.
Finally, a phenomenon called s-shaped IV-curves is investigated, which can sometimes occur for solar cells under illumination. As course of this a reduced surface recombination velocity can be found. Experimentally, the solar cells were fabricated using a special plasma treatment of the ITO contact. The measured IV-curves of such solar cells are reproduced by macroscopic simulations, where the surface recombination velocity is reduced. Hereby, it has to be distinguished between the surface recombination of majority and minority charge carriers at the respective contacts. The theory can be experimentally confirmed by illumination level dependent IV-curves as well as short circuit current density and open circuit voltage transients.
The discovery of the Giant Magneto Resistance (GMR) effect in 1988 by Albert Fert [Baib 88] and Peter Grünberg [Bina 89] led to a rapid development of the field of spintronics and progress in the information technology. Semiconductor based spintronics, which appeared later, offered a possibility to combine storage and processing in a single monolithic device. A direct result is reduced heat dissipation. The observation of the spin Seebeck effect by Ushida [Uchi 08] in 2008 launched an increased interest and encouraged research in the field of spin caloritronics. Spintronics is about the coupling of charge and spin transport. Spin caloritronics studies the interaction between heat and spin currents. In contrast to spintronics and its variety of applications, a particular spin-caloritronic device has not yet been demonstrated. However, many of the novel phenomena in spin caloritronics can be detected in most spintronic devices. Moreover, thermoelectric effects might have a significant influence on spintronic device operation. This will be of particular interest for this work. Additional knowledge on the principle of coupling between heat and spin currents uncovers an alternative way to control heat dissipation and promises new device functionalities.
This thesis aims to further extend the knowledge on thermoelectrics in materials with strong spin-orbit coupling, in this case the prototypical ferromagnetic semiconductor (Ga,Mn)As. The study is focused on the thermoelectric / thermomagnetic effects at the interface between a normal metal and the ferromagnetic (Ga,Mn)As. In such systems, the different interfaces provide a condition for minimal phonon drag contribution to the thermal effects. This suggests that only band contributions (a diffusion transport regime) to these effects will be measured.
Chapter 2 begins with an introduction on the properties of the studied material system, and basics on thermoelectrics and spin caloritronics. The characteristic anisotropies of the (Ga,Mn)As density of states (DOS) and the corresponding magnetic properties are described. The DOS and magnetic anisotropies have an impact on the transport prop- erties of the material and that results in effects like tunneling anisotropic magnetores- istance (TAMR) [Goul 04]. Some of these effects will be used later as a reference to the results from thermoelectric / thermomagnetic measurements. The Fingerprint tech- nique [Papp 07a] is also described. The method gives an opportunity to easily study the anisotropies of materials in different device geometries.
Chapter 3 continues with the experimental observation of the diffusion thermopower of (Ga,Mn)As / Si-doped GaAs tunnel junction. A device geometry for measuring the diffusion thermopower is proposed. It consists of a Si - doped GaAs heating channel with a Low Temperature (LT) GaAs / (Ga,Mn)As contact (junction) in the middle of the channel. A single Ti / Au contact is fabricated on the top of the junction. For transport characterization, the device is immersed in liquid He. A heating current technique is used to create a temperature difference by local heating of the electron system on the Si:GaAs side. An AC current at low frequency is sent through the channel and it heats the electron population in it, while the junction remains at liquid He temperature (experimentally con- firmed). A temperature difference arises between the heating channel and the (Ga,Mn)As contact. As a result, a thermal (Seebeck) voltage develops across the junction, which we call tunnelling anisotropic magneto thermopower (TAMT), similar to TAMR. TAMT is detected by means of a standard lock-in technique at double the heating current frequency (at 2f ). The Seebeck voltage is found to be linear with the temperature difference. That dependence suggests a diffusion transport regime. Lattice (phonon drag) contribution to the thermovoltage, which is usually highly nonlinear with temperature, is not observed.
The value of the Seebeck coefficient of the junction at 4.2 K is estimated to be 0.5 µV/K.
It is about three orders of magnitude smaller than the previously reported one [Pu 06]. Subsequently, the thermal voltage is studied in external magnetic fields. It is found that the thermopower is anisotropic with the magnetization direction. The anisotropy is explained with the anisotropies of the (Ga,Mn)As contact. Further, switching events are detected in the thermopower when the magnetic field is swept from negative to positive fields. The switchings remind of a spin valve signal and is similar to the results from previous experiments on spin injection using a (Ga,Mn)As contacts in a non-local detection scheme. That shows the importance of the thermoelectric effects and their possible contribution to the spin injection measurements. A polar plot of the collected switching fields for different magnetization angles reveals a biaxial anisotropy and resembles earlier TAMR measurements of (Ga,Mn)As tunnel junction. A simple cartoon model is introduced to describe and estimate the expected thermopower of the studied junction. The model yields a Fermi level inside of the (Ga,Mn)As valence band. Moreover, the model is found to be in good agreement with the experimental results.
The Nernst effect of a (Ga,Mn)As / GaAs tunnel junction is studied in Chapter 4. A modified device geometry is introduced for this purpose. Instead of a single contact on the top of the square junction, four small contacts are fabricated to detect the Nernst signal. A temperature difference is maintained by means of a heating current technique described in Chapter 3. A magnetic field is applied parallel to the device plane. A voltage drop across two opposite contacts is detected at 2f. It appears that a simple cosine function with a parameter the angle between the magnetization and the [100] crystal direction in the (Ga,Mn)As layer manages to describe this signal which is attributed to the anomalous Nernst effect (ANE) of the ferromagnetic contact. Its symmetry is different than the Seebeck effect of the junction. For the temperature range of the thermopower measurements the ANE coefficient has a linear dependence on the temperature difference (∆T). For higher ∆T, a nonlinear dependence is observed for the coefficient. The ANE coefficient is found to be several orders of magnitude smaller than any Nernst coefficient in the literature. Both the temperature difference and the size of the ANE coefficient require further studies and analysis. Switching events are present in the measured Nernst signal when the magnetic field is swept from positive to negative values. These switchings are related to the switching fields in the ferromagnetic (Ga,Mn)As. Usually, there are two states which are present in TAMR or AMR measurements - low and high resistance. Instead of that, the Nernst signal appears to have three states - high, middle and low thermomagnetic voltage. That behaviour is governed not only by the magnetization, but also by the characteristic of the Nernst geometry.
Chapter 5 summarizes the main observations of this thesis and contains ideas for future work and experiments.
In this work, three different material systems comprising carbon were researched: (i) Organic polymers and small molecules, in conjunction with fullerene molecules for applications in organic photovoltaics (OPV), (ii) single walled semiconducting carbon nanotubes and (iii) silicon carbide (SiC), whose defect color centers are recently in the limelight as candidates for quantum applications. All systems were analyzed using the optically detected magnetic resonance (ODMR) spectroscopy.
In the OPV chapter, first the intrinsic parameters and orientations of high spin excitons were analyzed in the materials P3HT, PTB7 and DIP. Specifically the influence of ordering in these organic systems was adressed. The second part of the OPV chapter is concerned with triplet generation by electron back transfer in the high-efficiency OPV material combination PTB7:PC71BM.
The carbon nanotube chapter first shows the way to the first unambiguous proof of the existence of triplet excitons in semiconducting (6,5) single-walled carbon nanotubes (SWNT) by ODMR spectroscopy. A model for exciton kinetics, and also orientation and intrinsic parameters were propoesed.
The last part of this work is devoted to spin centers in silicon carbide (SiC). After a brief introduction, the spin multiplicity of the V2 and V3 silicon vacancies, and also of a Frenkel pair and an unassigned defect UD in 6H SiC, and of the V2 vacancy and the Frenkel pair in 4H SiC, was shown to be S=3/2. The spin polarized pumping of the 3/2 manifold of the quartet ground state of the silicon vacancies allows stimulated microwave emission. Furthermore, in 6H SiC, the UD and Frenkel pair were shown to have a large dependence of their intrinsic zero field interaction parameters on the temperature, while the vacancies are temperature independent. The application of the UD and Frenkel pair as temperature sensor, and of the vacancies as a vector magnetic field sensor is discussed.
Light amplification by stimulated emission of radiation, well-known for revolutionising photonic science, has been realised primarily in fermionic systems including widely applied diode lasers. The prerequisite for fermionic lasing is the inversion of electronic population, which governs the lasing threshold. More recently, bosonic lasers have also been developed based on Bose-Einstein condensates of exciton-polaritons in semiconductor microcavities. These electrically neutral bosons coexist with charged electrons and holes. In the presence of magnetic fields, the charged particles are bound to their cyclotron orbits, while the neutral exciton-polaritons move freely. We demonstrate how magnetic fields affect dramatically the phase diagram of mixed Bose-Fermi systems, switching between fermionic lasing, incoherent emission and bosonic lasing regimes in planar and pillar microcavities with optical and electrical pumping. We collected and analyzed the data taken on pillar and planar microcavity structures at continuous wave and pulsed optical excitation as well as injecting electrons and holes electronically. Our results evidence the transition from a Bose gas to a Fermi liquid mediated by magnetic fields and light-matter coupling.
One rarely finds practical guidelines for the implementation of complex optical setups. Here, we aim to provide technical details on the decision making of building and revising a custom sensor-based adaptive optics (AO) direct stochastic optical reconstruction microscope (dSTORM) to provide practical assistance in setting up or troubleshooting similar devices.
The foundation of this report is an instrument constructed as part of a master's thesis in 2021, which was built for deep tissue imaging. The setup is presented in the following way: (1) An optical and mechanical overview of the system at the beginning of this internship is given. (2) The optical components are described in detail in the order at which the light passes through, highlighting their working principle and implementation in the system. The optical component include (2A) a focus on even sample illumination, (2B) restoring telecentricity when working with commercial microscope bodies, (2C) the AO elements, namely the deformable mirror (DM) and the wavefront sensor, and their integration, and (2D) the separation of wavefront and image capture using fluorescent beads and a dichroic mirror. After addressing the limitations of the existing setup, modification options are derived. The modifications include the implementation of adjustment only light paths to improve system stability and revise the degrees of freedom of the components and changes in lens choices to meet the specifications of the AO components. Last, the capabilities of the modified setup are presented and discussed: (1) First, we enable epifluorescence imaging of bead samples through 180 µm unstained murine hippocampal tissue with wavefront error correction of ~ 90 %. Point spread function, wavefront shape and Zernike decomposition of bead samples are presented. (2) Second, we move from epifluorescent to dSTORM imaging of tubulin stained primary mouse hippocampal cells, which are imaged through up to 180 µm of unstained murine hippocampal tissue. We show that full width at half maximum (FWHM) of prominent features can be reduced in size by nearly a magnitude from uncorrected epiflourescence images to dSTORM images corrected by the adaptive optics. We present dSTORM localization count and FWHM of prominent features as as a function of imaging depth.
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement and uncertainty relations. No additional randomness is added by hand and no assumptions about a priori probabilities are made, instead measure concentration results are used to justify the methods of Statistical Physics. The approach explains the applicability of the microcanonical and canonical ensemble and the tendency to equilibrate in a natural way. This work contains a pedagogical review of the existing literature and some new results. The most important of which are: i) A measure theoretic justification for the microcanonical ensemble. ii) Bounds on the subsystem equilibration time. iii) A proof that a generic weak interaction causes decoherence in the energy eigenbasis. iv) A proof of a quantum H-Theorem. v) New estimates of the average effective dimension for initial product states and states from the mean energy ensemble. vi) A proof that time and ensemble averages of observables are typically close to each other. vii) A bound on the fluctuations of the purity of a system coupled to a bath.
This thesis presents the detailed development of the fabrication process and the first observations of artificial magnetic atoms from the II-VI diluted magnetic semiconductor alloy (Zn,Cd,Be,Mn)Se. In order to manufacture the vertical quantum dot device which exhibits artificial atom behavior a number of development steps are conducted. First, the II-VI heterostructure is adjusted for the linear transport regime. Second, state of the art vertical quantum dot fabrication techniques in the III-V material system are investigated regarding their portability to the II-VI heterostructure. And third, new approaches to the fabrication process are developed, taking into account the complexity of the heterostructure and its physical properties. Finally a multi-step fabrication process is presented, which is built up from electron beam and optical lithography, dry and wet etching and insulator deposition. This process allows for the processing of pillars with diameters down to 200 nm with an insulating dielectric and gate. Preliminary transport data on the fabricated vertical quantum dots are presendted confirming the magnetic nature of the resulting artificial atoms.
Recently a new state of matter was discovered in which the bulk insulating state in a material is accompanied by conducting surface or edge states. This new state of matter can be distinguished from a conventional insulator phase by the topological properties of its band structure which led to the name "topological insulators". Experimentally, topological insulator states are mostly found in systems characterized by a band inversion compared to conventional systems. In most topological insulator systems, this is caused by a combination of energetically close bands and spin orbit coupling. Such properties are found in systems with heavy elements like Hg and Bi. And indeed, the first experimental discovery of a topological insulator succeeded in HgTe quantum wells and later also in BiSb bulk systems.
Topological insulators are of large interest due to their unique properties: In 2-dimensional topological insulators one dimensional edge states form without the need of an external magnetic field (in contrast to the quantum Hall effect). These edge states feature a linear band dispersion, a so called Dirac dispersion. The quantum spin Hall states are helical edge states, which means they consist of counterpropagating oppositely spin polarized edge channels. They are therefore of great potential for spintronic applications as well as building blocks for new more exotic states like Majorana Fermions. 3-dimensional topological insulators feature 2-dimensional surface states with only one Dirac band (also called Dirac cone) on each surface and an interesting spin texture where spin and momentum are locked perpendicular to each other in the surface plane. This unique surface band structure is predicted to be able to host several exotic states like e.g. Majorana Fermions (in combination with superconductors) and magnetic monopole like excitations.
This PhD thesis will summarize the discovery of topological insulators and highlights the developments on their experimental observations. The work focuses on HgTe which is up to now the only topological insulator material where the expected properties are unambiguously demonstrated in transport experiments. In HgTe, the topological insulator properties arise from the inversion of the Gamma_6 and Gamma_8 bands. The band inversion in HgTe is due to a combination of a high spin orbit splitting in Te and large energy corrections (due to the mass-velocity term) to the energy levels in Hg. Bulk HgTe, however, is a semimetal, which means for the conversion into a topological insulator a band gap has to be opened. In two dimensions (HgTe quantum well structures) this is achieved via quantum confinement, which opens a band gap between the quantum well subbands. In three dimensions, strain is used to lift the degeneracy of the semimetallic Gamma_8 bands opening up a band gap.
The thesis is structured as follows:
- The first chapter of this thesis will give a brief overview on discoveries in the field of topological insulators. It focuses on works relevant to experimental results presented in the following chapters. This includes a short outline of the early predictions and a summary of important results concerning 2-dimensional topological insulators while the final section discusses observations concerning 3-dimensional topological insulators.
- The discovery of the quantum spin Hall effect in HgTe marked the first experimental observation of a topological insulator. Chapter 2 will focus on HgTe quantum wells and the quantum spin Hall effect.
Above a critical thickness, HgTe quantum wells are predicted to host the quantum spin Hall state, the signature of a 2-dimensional topological insulator. HgTe quantum wells exhibiting low carrier concentrations and at the same time high carrier mobilities are required to be able to measure the quantum spin Hall effect. The growth of such high quality HgTe quantum wells was one of the major goals for this work. Continuous optimization of the substrate preparation and growth conditions resulted in controlled carrier densities down to a few 10^10 cm^-2. At the same time, carrier mobilities exceeding 1 x 10^6 cm^2/Vs have been achieved, which provides mean free paths of several micrometers in the material. Thus the first experimental evidence for the existence of the quantum spin Hall edge states succeeded in transport experiments on microstructures: When the Fermi energy was located in the bulk band gap a residual quantized resistance of 2e^2/h was found. Further experiments focused on investigating the nature of transport in this regime. By non-local measurements the edge state character could be established. The measured non-local resistances corresponded well with predictions from the Landauer-Büttiker theory applied to transport in helical edge channels.
In a final set of experiments the spin polarization of the edge channels was investigated. Here, we could make use of the advantage that HgTe quantum well structures exhibit a large Rashba spin orbit splitting. In systems with a large Rashba spin orbit splitting a spin accumulation is expected to occur at the edge of the sample perpendicular to a current flow. This so-called spin Hall effect was then used as a spin injector and detector. Using split gate devices it was possible to bring spin Hall and quantum spin Hall state into direct contact, which enabled an all electrical detection of the spin polarization of the quantum spin Hall edge channels.
- HgTe as a 3-dimensional topological insulator will be presented in chapter 3. Straining the HgTe layer enables the observation of topological insulator behavior. It was found that strain can be easily implemented during growth by using CdTe substrates. CdTe has a slightly larger lattice constant than HgTe and therefore leads to tensile strain in the HgTe layer as long as the growth is pseudomorphic. Magnetotransport studies showed the emergence of quantum Hall transport with characteristic signatures of a Dirac type bandstructure. Thus, this result marks the first observation of the quantum Hall effect in the surface states of a 3-dimensional topological insulator.
Transport experiments on samples fitted with a top gate enabled the identification of contributions from individual surfaces. Furthermore, the surface state quantum Hall effect was found to be surprisingly stable, perturbations due to additional bulk transport could not be found, even at high carrier densities of the system.
- Chapters 4 - 6 serve as in depth overviews of selected works: Chapter 4 presents a detailed overview on the all electrical detection of the spin Hall effect in HgTe quantum wells. The detection of the spin polarization of the quantum spin Hall effect is shown in chapter 5 and chapter 6 gives a detailed overview on the quantum Hall effect originating from the topological surface state in strained bulk HgTe.
The investigations discussed in this thesis pioneered the experimental work on the transport properties of topological insulator systems. The understanding of the fundamental properties of topological insulators enables new experiments in which e.g. the inclusion of magnetic dopants or the interplay between topological insulator and superconductors can be investigated in detail.