@phdthesis{Schmitt2022,
  author    = {Schmitt, Fabian Bernhard},
  title     = {Transport properties of the three-dimensional topological insulator mercury telluride},
  doi       = {10.25972/OPUS-29173},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-291731},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {The subject of this thesis is the investigation of the transport properties of topological and massive surface states in the three-dimensional topological insulator Hg(Mn)Te. These surface states give rise to a variety of extraordinary transport phenomena, making this material system of great interest for research and technological applications. In this connection, many physical properties of the topological insulator Hg(Mn)Te still require in-depth exploration. The overall aim of this thesis is to analyze the quantum transport of HgTe-based devices ranging from hundreds of micrometers (macroscopic) down to a few micrometers in size (microscopic) in order to extend the overall understanding of surface states and the possibilities of their manipulation. In order to exploit the full potential of our high-quality heterostructures, it was necessary to revise and improve the existing lithographic fabrication process of macroscopic three-dimensional Hg(Mn)Te samples. A novel lithographic standard recipe for the fabrication of the HgTe-based macrostructures was developed. This recipe includes the use of an optimized Hall bar design and wet etching instead of etching with high-energy \(\mathrm{{Ar^{+}}}\)-ions, which can damage the samples. Further, a hafnium oxide insulator is applied replacing the SiO\(_{2}\)/Si\(_{3}\)N\(_{4}\) dielectric in order to reduce thermal load. Moreover, the devices are metallized under an alternating angle to avoid discontinuities of the metal layers over the mesa edges. It was revealed that the application of gate-dielectric and top-gate metals results in n-type doping of the devices. This phenomenon could be attributed to quasi-free electrons tunneling from the trap states, which form at the interface cap layer/insulator, through the cap into the active layer. This finding led to the development of a new procedure to characterize wafer materials. It was found that the optimized lithographic processing steps do not unintentionally react chemically with our heterostructures, thus avoiding a degradation of the quality of the Hg(Mn)Te layer. The implementation of new contact structures Ti/Au, In/Ti/Au, and Al/Ti/Au did not result in any improvement compared to the standard structure AuGe/Au. However, a novel sample recipe could be developed, resulting in an intermixing of the contact metals (AuGe and Au) and fingering of metal into the mesa. The extent of the quality of the ohmic contacts obtained through this process has yet to be fully established. This thesis further deals with the lithographic realization of three-dimensional HgTe-based microstructures measuring only a few micrometer in size. Thus, these structures are in the order of the mean free path and the spin relaxation length of topological surface state electrons. A lithographic process was developed enabling the fabrication of nearly any desired microscopic device structure. In this context, two techniques suitable for etching microscopic samples were realized, namely wet etching and the newly established inductively coupled plasma etching. While wet etching was found to preserve the crystal quality of the active layer best, inductively coupled plasma etching is characterized by high reproducibility and excellent structural fidelity. Hence, the etching technique employed depends on the envisaged type of experiment. Magneto-transport measurements were carried out on the macroscopic HgTe-based devices fabricated by means of improved lithographic processing with respect to the transport properties of topological and massive surface states. It was revealed that due to the low charge carrier density present in the leads to the ohmic contacts, these regions can exhibit an insulating behavior at high magnetic fields and extremely low temperatures. As soon as the filling factor of the lowest Landau levels dropped below a critical value (\(\nu_{\mathrm{{c}}}\approx0.8\)), the conductance of the leads decreased significantly. It was demonstrated that the carrier density in the leads can be increased by the growth of modulation doping layers, a back-gate-electrode, light-emitting diode illumination, and by the application of an overlapping top-gate layout. This overlapping top-gate and a back-gate made it possible to manipulate the carrier density of the surface states on both sides of the Hg(Mn)Te layer independently. With this setup, it was identified that topological and massive surface states contribute to transport simultaneously in 3D Hg(Mn)Te. A model could be developed allowing the charge carrier systems populated in the sample to be determined unambiguously. Based on this model, the process of the re-entrant quantum Hall effect observed for the first time in three-dimensional topological insulators could be explained by an interplay of n-type topological and p-type massive surface states. A well-pronounced \(\nu=-1\rightarrow\nu=-2\rightarrow\nu=-1\) sequence of quantum Hall plateaus was found in manganese-doped HgTe-based samples. It is postulated that this is the condensed-matter realization of the parity anomaly in three-dimensional topological insulators. The actual nature of this phenomenon can be the subject of further research. In addition, the measurements have shown that inter-scattering occurs between counter-propagating quantum Hall edge states. The good quantization of the Hall conductance despite this inter-scattering indicates that only the unpaired edge states determine the transport properties of the system as a whole. The underlying inter-scattering mechanism is the topic of a publication in preparation. Furthermore, three-dimensional HgTe-based microstructures shaped like the capital letter "H" were investigated regarding spin transport phenomena. The non-local voltage signals occurring in the measurements could be attributed to a current-induced spin polarization of the topological surface states due to electrons obeying spin-momentum locking. It was shown that the strength of this non-local signal is directly connected to the magnitude of the spin polarization and can be manipulated by the applied top-gate voltage. It was found that in these microstructures, the massive surface and bulk states, unlike the topological surface states, cannot contribute to this spin-associated phenomenon. On the contrary, it was demonstrated that the population of massive states results in a reduction of the spin polarization, either due to the possible inter-scattering of massive and topological surface states or due to the addition of an unpolarized electron background. The evidence of spin transport controllable by a top-gate-electrode makes the three-dimensional material system mercury telluride a promising candidate for further research in the field of spintronics.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Strunz2022,
  author    = {Strunz, Jonas},
  title     = {Quantum point contacts in HgTe quantum wells},
  doi       = {10.25972/OPUS-27459},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-274594},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {Quantenpunktkontakte (englisch: quantum point contacts, QPCs) sind eindimensionale Engstellen in einem ansonsten zweidimensionalen Elektronen- oder Lochsystem. Seit der erstmaligen Realisierung in GaAs-basierten zweidimensionalen Elektronengasen sind QPCs sukzessive zu einem Grundbestandteil mesoskopischer Physik geworden und erfahren in einer Vielzahl von Experimenten Anwendung. Jedoch ist es bis zur Anfertigung der vorliegenden Arbeit nicht gelungen, QPCs in der neuen Materialklasse der zweidimensionalen topologischen Isolatoren zu realisieren. In diesen Materialien tritt der sogenannte Quanten-Spin-Hall-Effekt (QSH-Effekt) auf, welcher sich durch die Ausbildung von leitf{\"a}higen, eindimensionalen sowie gleichermaßen spinpolarisierten Zust{\"a}nden an der Bauteilkante auszeichnet, w{\"a}hrend die restlichen Bereiche der Probe isolierend sind. Ein in einem zweidimensionalen topologischen Isolator realisierter QPC kann demgem{\"a}ß daf{\"u}r benutzt werden, die sich stets an der Bauteilkante befindlichen QSH-Randkan{\"a}le einander r{\"a}umlich anzun{\"a}hern, was beispielsweise die Untersuchung potentieller Wechselwirkungseffekte zwischen ebenjenen Randkan{\"a}len erm{\"o}glicht. Die vorliegende Arbeit beschreibt die erstmalig erfolgreich durchgef{\"u}hrte Implementierung einer QPC-Technologie in einem QSH-System. {\"U}berdies werden die neuartigen Bauteile experimentell charakterisiert sowie analysiert. Nach einer in Kapitel 1 erfolgten Einleitung der Arbeit besch{\"a}ftigt sich das nachfolgende Kapitel 2 zun{\"a}chst mit der besonderen Bandstruktur von HgTe. In diesem Kontext wird die Ausbildung der QSH-Phase f{\"u}r HgTe-Quantentr{\"o}ge mit einer invertierten Bandstruktur erl{\"a}utert, welche f{\"u}r deren Auftreten eine Mindesttrogdicke von d_QW > d_c = 6.3 nm aufweisen m{\"u}ssen. Im Anschluss wird das Konzept eines QPCs allgemein eingef{\"u}hrt sowie das zugeh{\"o}rige Transportverhalten analytisch beschrieben. {\"U}berdies werden die Einschr{\"a}nkungen und Randbedingungen diskutiert, welche bei der Realisierung eines QPCs in einem QSH-System Ber{\"u}cksichtigung finden m{\"u}ssen. Darauf folgt die Pr{\"a}sentation des eigens zur QPC-Herstellung entwickelten Lithographieprozesses, welcher auf einer mehrstufigen Anwendung eines f{\"u}r HgTe-Quantentrogstrukturen geeigneten nasschemischen {\"A}tzverfahrens beruht. Die im Nachgang diskutierten Transportmessungen exemplarischer Proben zeigen die erwartete Leitwertquantisierung in Schritten von ΔG ≈ 2e^2/h im Bereich des Leitungsbandes -- sowohl f{\"u}r eine topologische als auch f{\"u}r eine triviale (d_QW < d_c) QPC-Probe. Mit dem Erreichen der Bandl{\"u}cke saturiert der Leitwert f{\"u}r den topologischen QPC um G_QSH ≈ 2e^2/h, wohingegen ebenjener f{\"u}r den Fall des trivialen Bauteils auf G ≈ 0 abf{\"a}llt. Dar{\"u}ber hinaus belegen durchgef{\"u}hrte Messungen des differentiellen Leitwertes einer invertierten QPC-Probe in Abh{\"a}ngigkeit einer Biasspannung die stabile Koexistenz von topologischen und trivialen Transportmoden. Gegenstand von Kapitel 3 ist die Beschreibung der Ausbildung eines QSH-Interferometers in QPCs mit geringer Weite, welche unter Verwendung von Quantentr{\"o}gen mit einer Trogdicke von d_QW = 7 nm hergestellt werden. Die Diskussion von Bandstrukturrechnungen legt dar, dass die r{\"a}umliche Ausdehnung der Randkan{\"a}le von der jeweiligen Position der Fermi-Energie im Bereich der Bandl{\"u}cke abh{\"a}ngt. Hieraus resultiert eine Transportsituation, in welcher -- unter bestimmten Voraussetzungen -- Reservoir-Elektronen mit randomisiertem Spin an beide QSH-Randkan{\"a}le mit gleicher Wahrscheinlichkeit koppeln, was in der Ausbildung eines QSH-Rings resultiert. Diese Ringbildung wird im Rahmen eines durch Plausibilit{\"a}ts{\"u}berpr{\"u}fung getesteten Modells erkl{\"a}rt und spezifiziert. Danach erfolgt eine theoretische Einf{\"u}hrung von drei relevanten Quantenphasen, deren Akkumulation in der Folge f{\"u}r mehrere geeignete QPC-Proben nachgewiesen wird. Es handelt sich hierbei um die Aharonov-Bohm-Phase, um die dynamische Aharonov-Casher-Phase sowie um eine Spin-Bahn-Berry-Phase mit einem Wert von π. Diese experimentellen Ergebnisse stehen dar{\"u}ber hinaus im Einklang mit analytischen Modellbetrachtungen. Das anschließende Kapitel 4 stellt den letzten Teil der Arbeit dar und besch{\"a}ftigt sich mit der Beobachtung einer anomalen Leitwertsignatur, welche f{\"u}r QPC-Proben basierend auf einer Quantentrogdicke von d_QW = 10.5 nm auftritt. Diese Proben zeigen neben der durch die QSH-Phase bedingten Leitwertquantisierung von G_QSH ≈ 2e^2/h ein weiteres Leitwertplateau mit einem Wert von G ≈ e^2/h = 0.5 x G_QSH. Diese sogenannte 0.5-Anomalie ist nur f{\"u}r ein kleines Intervall von QPC-Weiten beobachtbar und wird mit zunehmender Bauteilweite abgeschw{\"a}cht. Weiterf{\"u}hrende Untersuchungen in Abh{\"a}ngigkeit der Temperatur sowie einer angelegten Biasspannung deuten dar{\"u}ber hinaus darauf hin, dass das Auftreten der 0.5-Anomalie mit einem modifizierten topologischen Zustand einhergeht. {\"U}berdies wird eine zus{\"a}tzliche sowie vervollst{\"a}ndigende Charakterisierung dieses Transportregimes durch die Realisierung eines neuartigen Bauteilkonzeptes m{\"o}glich, welches einen QPC in eine standardisierte Hall-Bar-Geometrie integriert. Das Ergebnis der experimentellen Analyse einer solchen Probe verkn{\"u}pft das Auftreten der 0.5-Anomalie mit der R{\"u}ckstreuung eines QSH-Randkanals. Demgem{\"a}ß wird aus Sicht des Einteilchenbildes geschlussfolgert, dass im Kontext der 0.5-Anomalie lediglich ein Randkanal transmittiert wird. Zudem werden zwei theoretische Modelle basierend auf Elektron-Elektron-Wechselwirkungen diskutiert, welche beide jeweils als urs{\"a}chlicher Mechanismus f{\"u}r das Auftreten der 0.5-Anomalie in Frage kommen. Abschließend ist zu deduzieren, dass die Implementierung einer QPC-Technologie in einem QSH-System eine bedeutende Entwicklung im Bereich der Erforschung von zweidimensionalen topologischen Isolatoren darstellt, welche eine Vielzahl zuk{\"u}nftiger Experimente erm{\"o}glicht. So existieren beispielsweise theoretische Vorhersagen, dass QPCs in einem QSH-System die Detektion von Majorana- sowie Para-Fermionen erm{\"o}glichen. {\"U}berdies ist die nachgewiesene Ausbildung eines QSH-Interferometers in geeigneten QPC-Proben eine Beobachtung von großer Folgewirkung. So erm{\"o}glicht die beobachtete dynamische Aharonov-Casher-Phase im QSH-Regime die kontrollierbare Modulation des topologischen Leitwertes, was die konzeptionelle Grundlage eines topologischen Transistors darstellt. Eine weitere Anwendungsm{\"o}glichkeit wird durch die Widerstandsf{\"a}higkeit geometrischer Phasen gegen{\"u}ber Dephasierung er{\"o}ffnet, wodurch die nachgewiesene Spin-Bahn-Berry-Phase mit einem Wert von π im Kontext potentieller Quantencomputerkonzepte von Interesse ist. Dar{\"u}ber hinaus ist die Transmission von nur einem QSH-Randkanal im Zuge des Auftretens der 0.5-Anomalie {\"a}quivalent zu 100 \% Spinpolarisierung, was einen Faktor essentieller Relevanz f{\"u}r die Realisierung spintronischer Anwendungen darstellt. Demgem{\"a}ß beinhaltet die vorliegende Arbeit den experimentellen Nachweis von drei unterschiedlichen Effekten, von welchen jedem einzelnen eine fundamentale Rolle im Rahmen der Entwicklung neuer Generationen logischer Bauelemente zukommen kann -- erm{\"o}glicht durch die Realisierung von QPCs in topologischen HgTe-Quantentr{\"o}gen.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Mueller2022,
  author    = {M{\"u}ller, Valentin Leander},
  title     = {Transport signatures of topological and trivial states in the three-dimensional topological insulator HgTe},
  doi       = {10.25972/OPUS-25952},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-259521},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {The thesis at hand is concerned with improving our understanding of and our control over transport properties of the three-dimensional topological insulator HgTe. Topological insulators are characterized by an insulating bulk and symmetry-protected metallic surface states. These topological surface states hold great promise for research and technology; at the same time, many properties of experimentally accessible topological insulator materials still need to be explored thoroughly. The overall aim of this thesis was to experimentally investigate micrometer-sized HgTe transport devices to observe the ballistic transport regime as well as intercarrier scattering and possibly identify special properties of the topological surface states. Part I of the thesis presents lithographic developments concerned with etching small HgTe devices. The aim was to replace existing processes which relied on dry etching with high-energy \(\text{Ar}^+\) ions and an organic etch mask. This etching method is known to degrade the HgTe crystal quality. In addition, the etch mask turned out to be not durable for long etching processes and difficult to remove completely after etching. First, \(\text{BaF}_2\) was introduced as a new etch mask for dry etching to replace the organic etch mask. With common surface characterization techniques like SEM and XPS it was shown that \(\text{BaF}_2\) etch masks are easy to deposit, highly durable in common dry etching processes for \(\text{Hg}_{1-x}\text{Cd}_x\text{Te}\), and easy to remove in deionized water. Transport results of HgTe devices fabricated with the new etch mask are comparable to results obtained with the old process. At the same time, the new etch mask can withstand longer etching times and does not cause problems due to incomplete removal. Second, a new inductively coupled plasma dry etching process based on \(\text{CH}_4\) and Ar was introduced. This etching process is compatible with \(\text{BaF}_2\) etch masks and yields highly reproducible results. Transport results indicate that the new etching process does not degrade the crystal quality and is suitable to produce high-quality transport devices even in the micrometer range. A comparison with wet-etched samples shows that inductively coupled plasma etching introduces a pronounced edge roughness. This - usually undesirable - property is actually beneficial for some of the experiments in this study and mostly irrelevant for others. Therefore, most samples appearing in this thesis were fabricated with the new process. Part II of the thesis details the advancements made in identifying topological and trivial states which contribute to transport in HgTe three-dimensional topological insulators. To this end, macroscopic Hall bar samples were fabricated from high-quality tensilely strained HgTe layers by means of the improved lithographic processes. All samples were equipped with a top gate electrode, and some also with a modulation doping layer or a back gate electrode to modify the carrier density of the surface states on both sides of the HgTe layer. Due to the high sample quality, Landau levels could be well-resolved in standard transport measurements down to magnetic fields of less than 0.5T. High-resolution measurements of the Landau level dispersion with gate voltage and magnetic field allowed disentangling different transport channels. The main result here is that the upper (electron) branches of the two topological surface states contribute to transport in all experimentally relevant density regimes, while the hole branch is not accessible. Far in n-regime bulk conduction band states give a minor contribution to transport. More importantly, trivial bulk valence band holes come into play close to the charge neutrality point. Further in p-regime, the strong applied gate voltage leads to the formation of two-dimensional, massive hole states at the HgTe surface. The interplay of different states gives rise to rich physics: Top gate-back gate maps revealed that an anticrossing of Landau levels from the two topological surface states occurs at equal filling. A possible explanation for this effect is a weak hybridization of the surface states; however, future studies need to further clarify this point. Furthermore, the superposition of n-type topological and p-type trivial surface states leads to an intriguing Landau level dispersion. The good quantization of the Hall conductance in this situation indicates that the counterpropagating edge states interact with each other. The nature of this interaction will be the topic of further research. Part III of the thesis is focused on HgTe microstructures. These "channel samples" have a typical width of 0.5 to 4µm and a typical length of 5 to 80µm. The quality of these devices benefits particularly from the improved lithographic processes. As a result, the impurity mean free path of the topological surface state electrons is on the order of the device width and transport becomes semiballistic. This was verified by measuring the channel resistance in small magnetic fields in n-regime. The deflection of carriers towards the dissipative channel walls results in a pronounced peak in the magnetoresistance, which scales in a predictable manner with the channel width. To investigate transport effects due to mutual scattering of charge carriers, the differential resistance of channel samples was measured as a function of carrier temperature. Selective heating of the charge carriers - but not the lattice - was achieved by passing a heating current through the channel. Increasing the carrier temperature has two pronounced effects when the Fermi level is situated in proximity to the bulk valence band maximum where the density of states is large. First, when both topological surface state electrons and bulk holes are present, electron-hole scattering leads to a pronounced increase in resistance with increasing carrier temperature. Second, a thermally induced increase of the electron and hole carrier densities reduces the resistance again at higher temperatures. A model considering these two effects was developed, which can well reproduce the experimental results. Current heating experiments in zero-gap HgTe quantum wells and compressively strained HgTe layers are consistent with this model. These observations raise the question as to how electron-hole scattering may affect other transport properties of HgTe-based three-dimensional topological insulators, which is briefly discussed in the outlook.},
  subject      = {Topologischer Isolator},
  language  = {en}
}
@phdthesis{Zusan2014,
  author    = {Zusan, Andreas},
  title     = {The Effect of Morphology on the Photocurrent Generation in Organic Solar Cells},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-117852},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2014},
  abstract  = {Organic solar cells have great potential to become a low-cost and clean alternative to conventional photovoltaic technologies based on the inorganic bulk material silicon. As a highly promising concept in the field of organic photovoltaics, bulk heterojunction (BHJ) solar cells consist of a mixture of an electron donating and an electron withdrawing component. Their degree of intermixing crucially affects the generation of photocurrent. In this work, the effect of an altered blend morphology on polaron pair dissociation, charge carrier transport, and nongeminate recombination is analyzed by the charge extraction techniques time delayed collection field (TDCF) and open circuit corrected transient charge extraction (OTRACE). Different comparative studies cover a broad range of material systems, including polymer and small-molecule donors in combination with different fullerene acceptors. The field dependence of polaron pair dissociation is analyzed in blends based on the polymer pBTTT-C16, allowing a systematic tuning of the blend morphology by varying the acceptor type and fraction. The effect of both excess photon energy and intercalated phases are minor compared to the influence of excess fullerene, which reduces the field dependence of photogeneration. The study demonstrates that the presence of neat fullerene domains is the major driving force for efficient polaron pair dissociation that is linked to the delocalization of charge carriers. Furthermore, the influence of the processing additive diiodooctane (DIO) is analyzed using the photovoltaic blends PBDTTT-C:PC71BM and PTB7:PC71BM. The study reveals amulti-tiered alteration of the blend morphology of PBDTTT-C based blends upon a systematic increase of the amount of DIO. Domains on the hundred nanometers length scale in the DIO-free blend are identified as neat fullerene agglomerates embedded in an intermixed matrix. With the addition of the additive, 0.6\% and 1\% DIO already substantially reduces the size of these domains until reaching the optimum 3\% DIO mixture, where a 7.1\% power conversion efficiency is obtained. It is brought into connection with the formation of interpenetrating polymer and fullerene phases. Similar to PBDTTT-C, the morphology of DIO-free PTB7:PC71BM blends is characterized by large fullerene domains being decreased in size upon the addition of 3\% DIO. OTRACE measurements reveal a reduced Langevin-type, super-second order recombination in both blends. It is demonstrated that the deviation from bimolecular recombination kinetics cannot be fully attributed to the carrier density dependence of the mobility but is rather related to trapping in segregated PC71BM domains. Finally, with regard to small-molecule donors, a higher yield of photogeneration and balanced transport properties are identified as the dominant factors enhancing the efficiency of vacuum deposited MD376:C60 relative to its solution processed counterpart MD376:PC61BM. The finding is explained by a higher degree of dimerization of the merocyanine dye MD376 and a stronger donor-acceptor interaction at the interface in the case of the vacuum deposited blend.},
  subject      = {Organische Solarzelle},
  language  = {en}
}