@phdthesis{Herrmann2016,
  author    = {Herrmann, Oliver},
  title     = {Graphene-based single-electron and hybrid devices, their lithography, and their transport properties},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-146924},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {This work explores three different aspects of graphene, a single-layer of carbon atoms arranged in a hexagonal lattice, with regards to its usage in future electronic devices; for instance in the context of quantum information processing. For a long time graphene was believed to be thermodynamically unstable. The discovery of this strictly two-dimensional material completed the family of carbon based structures, which had already been subject of intensive research with focus on zero-dimensional fullerenes and one-dimensional carbon nanotubes. Within only a few years of its discovery, the field of graphene related research has grown into one of today's most diverse and prolific areas in condensed matter physics, highlighted by the award of the 2010 Nobel Prize in Physics to A.K. Geim and K. Noveselov for "their groundbreaking experiments regarding the two-dimensional material graphene". From the point of view of an experimental physicist interested in the electronic properties of a material system, the most intriguing characteristic of graphene is found in the Dirac-like nature of its charge carriers, a peculiar fact that distinguishes graphene from all other known standard semiconductors. The dynamics of charge carriers close to zero energy are described by a linear energy dispersion relation, as opposed to a parabolic one, which can be understood as a result of the underlying lattice symmetry causing them to behave like massless relativistic particles. This fundamentally different behavior can be expected to lead to the observation of completely new phenomena or the occurrence of deviations in well-known effects. Following a brief introduction of the material system in chapter 2, we present our work studying the effect of induced superconductivity in mesoscopic graphene Josephson junctions by proximity to superconducting contacts in chapter 3. We explore the use of Nb as the superconducting material driven by the lack of high critical temperature and high critical magnetic field superconductor technology in graphene devices at that time. Characterization of sputter-deposited Nb films yield a critical transition temperature of \(T_{C}\sim 8{\rm \,mK}\). A prerequisite for successful device operation is a high interface quality between graphene and the superconductor. In this context we identify the use of an Ti as interfacial layer and incorporate its use by default in our lithography process. Overall we are able to increase the interface transparency to values as high as \(85\\%\). With the prospect of interesting effects in the ballistic regime we try to enhance the electronic quality of our Josephson junction devices by substrate engineering, yet with limited success. We achieve moderate charge carrier mobilities of up to \(7000{\rm \,cm^2/Vs}\) on a graphene/Boron-nitride heterostructure (fabrication details are covered in chapter 5) putting the junction in the diffusive regime (\(L_{device}<L_{\rm{mfp}}\)). We speculate that either inhomogeneities in the graphene channel or lithography residues are responsible for this observation. Furthermore we study the Josephson effect and Andreev reflection related physics in this device by low-temperature transport measurements. The junction carries a bipolar supercurrent which remains finite at the charge neutrality point. The genuine Josephson character is confirmed by the modulation of the supercurrent as a function of an out-of-plane magnetic field resembling that of a Fraunhofer-like pattern. This is further supported by the response of the junction to microwave radiation in the form of Shaprio steps. Surprisingly we find a strongly reduced superconducting energy gap of approximately \(\Delta = 400{\rm \,\mu eV}\) by quantitatively analyzing data of multiple Andreev reflections. We show this result to be consistent by careful analysis of the device parameters and comparison of these to a theoretical model. More experiments will be needed to determine the origin of this reduction and if the presence of the Ti interfacial layer plays an important role in that. With regards to possible usability of superconducting contacts in more complex hybrid structures we can conclude that our work establishes the necessary preconditions while still leaving room for improvements; especially in terms of device quality. In the second part of this work we are primarily interested in electrical transport properties of graphene nanodevices and their application in graphene-superconductor hybrid structures. The fact that graphene is mechanically stable down to a few tens of nanometers in width while exhibiting a finite conductance makes it an appealing choice as host for single-electron devices, also known as quantum dots. Our work on this topic is covered in chapter 4 where we first develop a high-resolution lithography process for the fabrication of single electron devices with critical feature sizes of roughly \(50{\rm \,nm}\). To this end we use a resist etch mask in combination with a reactive-ion etch process for device patterning. Carrier confinement in graphene is known to be hindered by the Klein tunneling phenomenon, a challenge that can be overcome by using all-graphene nano-constrictions to decouple the source and drain contacts from the central island. The traditionally used constriction design is comprised of long and narrow connections. We argue that a design with very short and narrow constrictions could be beneficial for the quantum dot performance as the length merely affects the overall conductance and requires extended side-gates to control their transmission. We confirm the functionality of two different devices in low-temperature measurements, which differ in the size of their central island with \(d=250{\rm \,nm}\) for device no. 1 and \(d=400{\rm \,nm}\) for device no. 2. Coulomb blockade measurements conducted at \(20{\rm \,mK}\) on both devices reveal clear sequences of Coulomb peaks with amplitudes of up to \(0.8\rm{\,e}^2/\rm{h}\), a value significantly larger than what is commonly reported for similar devices. We interpret this as an indication of rather homogeneous constrictions, resulting from the modified design. Coulomb diamond measurements display the behavior expected for a lithographically designed single quantum dot revealing no features related to the presence of an additional dot. Using the stability diagram we determine the addition energies of the two dots and find them to be in good agreement with values reported in the literature for devices of similar size. Using the normalized Coulomb peak spacing as a figure of merit for the device quality we find that device no. 1 quantitatively compares well with a similar device fabricated on a superior hexagonal boron-nitride substrate. This result underlines the importance of non-substrate related extrinsic disorder sources and emphasizes the cleanliness of our lithography process. Superconductor-graphene quantum dot hybrid structures employing Nb and Al electrodes were successfully fabricated from a lithography point of view, yet no evidence of any superconducting related effect was found in transport measurements. We assign the missing observation to interface issues that require careful analysis and likely a revision of the fabrication process. A property equally important in graphene Josephson Junctions and quantum dots is the electronic quality of the device, as has been addressed in the previous paragraphs. It turns out that the \(\rm{SiO}_{2}\;\) substrate and lithography residues constitute the two major sources of disorder in graphene. In chapter 5 we present an approach based on the original work of Dean et al. who utilize hexagonal-Boron nitride as a replacement substrate for \(\rm{SiO}_{2}\). This idea was then extended by Wang et al. who also used this material as a shield to protect the graphene surface from contaminations during the lithography process. These structures are commonly referred to as van der Waals heterostructures and are assembled by stacking individual crystals on top of each other. For this purpose we build a mechanical transfer system based on an optical microscope equipped with an additional micro-manipulator stage allowing precise alignment of two micrometer sized crystals with high precision. We demonstrate the functionality of this setup on the basis of successfully fabricated heterostructures. Furthermore a variation on the traditional method for single graphene/boron nitride structures is presented. Based on a reversed stacking order this method yields large areas of homogeneous graphene, however it comes with the drawback of limited yields. A common type of problem accompanying the fabrication of encapsulated graphene structures is the formation of contamination spots (also referred to as bubbles in the literature) at the interfaces between BN and graphene. We experience similar issues which we are unable to prevent and thus pose a limit to the maximum available device size. In the next step we develop a full lithography paradigm including high-resolution device patterning by electron beam lithography combined with reactive ion etching and two different ways to establish electrical contact to the encapsulated graphene flake. In this context we explore the use of three different types of etch masks and find a double layer of PMMA/HSQ best suited for our purposes. Our low power plasma etch process utilizes a combination of \(\rm{O}_{2}\;\) and \(\rm{CHF}_{3}\;\) and is optimized to show reproducible etch results. A widely used method for electrical contacts relies on one-dimensional edge contacts whose functionality crucially depends on the use of Cr as the interface layer. For compatibility reasons with superconducting materials, e.g. Nb, we develop a self-aligned contact process that instead of only Cr is also compatible with Ti. We achieve this by modifying the plasma etch parameters such that the etch process exhibits extremely low graphene etch rates while keeping a high etch rate for h-BN. This allows clearing of a narrow stripe of graphene at the edge of the structure by using a thick PMMA layer as etch mask as replacement of the PMMA/HSQ combination. The purpose of this PMMA mask is two-fold since it also serves as lift-off mask during metalization. The quality of the edge contacts fabricated with either method is excellent as determined from transport measurements at room and cryogenic temperatures. With typical contact resistances of a few hundred \({\rm \,}\Omega\mu{\rm m}\) and a record low of \(100{\rm \,}\Omega\mu{\rm m}\) the contacts can be considered to be state-of-the-art. The positive effect of encapsulation on the electronic quality is confirmed on a device exhibiting charge carrier mobilities exceeding \(10^5{\rm \,cm^2/Vs}\), one magnitude larger than what is commonly achieved on \(\rm{SiO}_{2}\). The investigation of induced superconductivity in graphene Josephson Junctions, quantum dots, and high mobility heterostructures underlines the versatility of this material system, while covering only a tiny fraction of its prospects. Combination of the acquired knowledge regarding the physical effects and the developed lithography processes lay the foundation towards the fabrication and study of novel graphene hybrid devices.},
  subject      = {Graphen},
  language  = {en}
}
@phdthesis{Pfaff2016,
  author    = {Pfaff, Florian Georg},
  title     = {Spektroskopie und hochaufl{\"o}sende Mikroskopie zur Analyse der Grenzfl{\"a}cheneigenschaften in SrTiO\(_3\)-basierten Heterostrukturen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-145023},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {> In oxidischen Heterostrukturen kann es zur Ausbildung unerwarteter elektronischer und magnetischer Phasen kommen. Ein bekanntes Beispiel ist das Heterostruktursystem LaAlO\(_3\)/SrTiO\(_3\), an dessen Grenzfl{\"a}che ein zweidimensionalen Elektronensystem (2DES) entsteht, sofern die LaAlO\(_3\)-Filmdicke einen kritischen Wert von mindestens vier Einheitszellen aufweist. {\"A}hnliches Verhalten konnte an der Heterostruktur γ-Al\(_2\)O\(_3\)/SrTiO\(_3\) beobachtet werden. Die gemessenen Elektronenbeweglichkeiten und Fl{\"a}chenladungstr{\"a}gerdichten {\"u}bertreffen hierbei die in LaAlO\(_3\)/SrTiO\(_3\) um mehr als eine Gr{\"o}ßenordnung. Die vorliegende Arbeit besch{\"a}ftigt sich mit der Herstellung sowie der Analyse dieser beiden Heterostruktursysteme. Die Hauptaspekte sind dabei die Untersuchung der physikalischen Eigenschaften an der Grenzfl{\"a}che sowie das Verst{\"a}ndnis der zugrundeliegenden Mechanismen. > > Im Hinblick auf das Wachstum wird demonstriert, dass die f{\"u}r LaAlO\(_3\)/SrTiO\(_3\) etablierte Wachstumsroutine der gepulsten Laserablation sowie die zur {\"U}berwachung des Schichtwachstums verwendete Methode der Beugung hochenergetischer Elektronen in Reflexion (RHEED) f{\"u}r das γ-Al\(_2\)O\(_3\)-Wachstum modifiziert werden m{\"u}ssen. So kann gezeigt werden, dass durch eine geeignete Variation der Wachstumsgeometrie die Resonanz von Oberfl{\"a}chenwellen, welche im Falle des γ-Al\(_2\)O\(_3\)-Wachstums die Beobachtung von RHEED-Oszillationen erschwert, vermieden werden kann und somit auch hier die {\"U}berwachung des heteroepitaktischen Schichtwachstum mittels Elektronenbeugung m{\"o}glich wird. > > F{\"u}r die Ausbildung des 2DES in LaAlO\(_3\)/SrTiO\(_3\) wird das Szenario der elektronischen Rekonstruktion als m{\"o}gliche Ursache diskutiert, wonach das divergierende Potential innerhalb des polaren LaAlO\(_3\)-Films durch einen Ladungstransfer von der Probenoberfl{\"a}che in die obersten Atomlagen des unpolaren SrTiO\(_3\)-Substrats kompensiert wird. Zudem sind die Eigenschaften der Heterostruktur von den Wachstumsparametern abh{\"a}ngig. So wird in der vorliegenden Arbeit eine deutliche Zunahme der Ladungstr{\"a}gerkonzentration und der r{\"a}umliche Ausdehnung der leitf{\"a}higen Schicht insbesondere f{\"u}r Proben, welche bei sehr niedrigen Sauerstoffhintergrunddr{\"u}cken gewachsen wurden, gezeigt und auf die Erzeugung von Sauerstofffehlstellen innerhalb des Substrats zur{\"u}ckgef{\"u}hrt. Dar{\"u}ber hinaus wird erstmalig die Herstellung atomar scharfer Grenzfl{\"a}chen mit sehr geringer Defektdichte selbst bei sehr niedrigen Wachstumsdr{\"u}cken belegt und erstmals auch direkt elektronenmikroskopisch nachgewiesen. Es werden allenfalls vernachl{\"a}ssigbare Effekte der Sauerstoffkonzentration auf charakteristische, strukturelle Merkmale der Probe beobachtet. Desweiteren zeigt diese Arbeit erstmalig eine von den Wachstumsbedingungen abh{\"a}ngige Gitterverzerrung des Films, was in {\"U}bereinstimmung mit Rechnungen auf Basis der Dichtefunktionaltheorie einen Hinweis auf ein komplexes Zusammenspiel von elektronischer Rekonstruktion, Sauerstofffehlstellen an der LaAlO\(_3\)-Oberfl{\"a}che und einer Verzerrung der Kristallstruktur als Ursache f{\"u}r die Entstehung des 2DES in LaAlO\(_3\)/SrTiO\(_3\) liefert. > > Neben der mikroskopischen Analyse des 2DES in LaAlO\(_3\)/SrTiO\(_3\) wird die elektronische Struktur dieses Systems zudem mithilfe der resonanten inelastischen R{\"o}ntgenstreuung charakterisiert. Die vorliegende Dissertation zeigt dabei, neben dem Nachweis lokalisierter Ladungstr{\"a}ger vor dem Einsetzen metallischen Verhaltens ab einer kritischen Schichtdicke von vier Einheitszellen, die Existenz eines Raman- und eines fluoreszenzartigen Signals in Abh{\"a}ngigkeit der verwendeten Photonenenergie, was wiederum auf einen unterschiedlichen elektronischen Charakter im Zwischenzustand zur{\"u}ckgef{\"u}hrt werden kann. Gest{\"u}tzt wird diese Interpretation durch vergleichbare Messungen an γ- Al\(_2\)O\(_3\)/SrTiO\(_3\). In diesem System finden sich zudem ebenfalls Anzeichen lokalisierter Ladungstr{\"a}ger unterhalb der kritischen Schichtdicke f{\"u}r metallisches Verhalten, was ein Hinweis auf einen mit LaAlO\(_3\)/SrTiO\(_3\) vergleichbaren Grundzustand sein k{\"o}nnte. > > Weitere Messungen mithilfe der resonanten Photoelektronenspektroskopie erm{\"o}glichen zudem eine direkte Beobachtung und Analyse der Ti 3d-Valenzelektronen. Messungen an LaAlO\(_3\)/SrTiO\(_3\) und γ-Al\(_2\)O\(_3\)/SrTiO\(_3\) liefern dabei Hinweise auf verschiedene elektronische Ti 3d-artige Zust{\"a}nde. Diese werden zum einen den mobilen Ladungstr{\"a}gern des 2DES zugeschrieben, zum anderen als lokalisierte Elektronen in der N{\"a}he von Sauerstofffehlstellen identifiziert. Eine Analyse des Resonanzverhaltens sowie der spektralen Form der beobachteten Signale zeigt quantitative Unterschiede, was auf einen unterschiedlichen treibenden Mechanismus in beiden Systemen hindeutet und im Hin- blick auf den Einfluss von Sauerstofffehlstellen auf das System diskutiert wird. Zudem zeigen impulsaufgel{\"o}ste Messungen der Zust{\"a}nde am chemischen Potential eine unterschiedliche Intensit{\"a}tsverteilung im k -Raum. Dies wird im Zusammenhang mit Matrixelementeffekten diskutiert und kann vermutlich auf Photoelektronendiffraktion bedingt durch die unterschiedliche Kristallstruktur des Filmmaterials, zur{\"u}ckgef{\"u}hrt werden.},
  subject      = {{\"U}bergangsmetalloxide},
  language  = {de}
}