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This thesis presents an experimental study of the thermoelectrical properties of semiconductor quantum dots (QD). The measurements give information about the interplay between first order tunneling and macroscopic quantum tunneling transport effects in the presence of thermal gradients by the direct comparison of the thermoelectric response and the energy spectrum of the QD. The aim of the thesis is to contribute to the understanding of the charge and spin transport in few-electron quantum dots with respect to potential applications in future quantum computing devices. It also gives new insight into the field of low temperature thermoelectricity. The investigated QDs were defined electrostatically in a two dimensional electron gas (2DEG) formed with a GaAs/(Al,Ga)As heterostructure by means of metallic gate electrodes on top of the heterostructure. Negative voltages with respect to the potential of the 2DEG applied to the gate electrodes were used to deplete the electron gas below them and to form an isolated island of electron gas in the 2DEG which contains a few ten electrons. This QD was electrically connected to the 2DEG via two tunneling barriers. A special electron heating technique was used to create a temperature difference between the two connecting reservoirs across the QD. The resulting thermoelectric voltage was used to study the charge and spin transport processes with respect to the discrete energy spectrum and the magnetic properties of the QD. Such a two dimensional island usually exhibits a discrete energy spectrum, which is comparable to that of atoms. At temperatures below a few degrees Kelvin, the electrostatic charging energy of the QDs exceeds the thermal activation energy of the electrons in the leads, and the transport of electrons through the QD is dominated by electron-electron interaction effects. The measurements clarify the overall line shape of thermopower oscillations and the observed fine structure as well as additional spin effects in the thermoelectrical transport. The observations demonstrate that it is possible to control and optimize the strength and direction of the electronic heat flow on the scale of a single impurity and create spin-correlated thermoelectric transport in nanostructures, where the experimenter has a close control of the exact transport conditions. The results support the assumption that the performance of thermoelectric devices can be enhanced by the adjustment of the QD energy levels and by exploiting the properties of the spin-correlated charge transport via localized, spin-degenerate impurity states. Within this context, spin entropy has been identified as a driving force for the thermoelectric transport in the spin-correlated transport regime in addition to the kinetic contributions. Fundamental considerations, which are based on simple model assumptions, suggest that spin entropy plays an important role in the presence of charge valence fluctuations in the QD. The presented model gives an adequate starting point for future quantitative analysis of the thermoelectricity in the spin-correlated transport regime. These future studies might cover the physics in the limit of single electron QDs or the physics of more complex structures such as QD molecules as well as QD chains. In particular, it should be noted that the experimental investigations of the thermopower of few-electron QDs address questions concerning the entropy transport and entropy production with respect to single-bit information processing operations. These questions are of fundamental physical interest due to their close connection to the problem of minimal energy requirements in communication, and thus ultimately to the so called "Maxwell's demon" with respect to the second law of thermodynamics.
Semiconductor Quantum Dots (QDs) have been attracting immense interest over the last decade from both basic and application-orientated research because of their envisioned use as fundamental building blocks in non-classical device architectures. Their presumable ease of integration into existing semiconductor technology has bought them the reputation of being cost-efficiently scalable and renders them a place among the top candidates in a wide range of proposed quantum logic and quantum information processing schemes. These include the highly acclaimed use of QD as triggered sources of single pairs of entangled photons, which is a key ingredient of most of the intensivly investigated optical quantum cryptography operations. A big obstacle towards these goals are the pronounced asymmetries that are intrinsically present in all currently availabe semiconductor QD systems. They are a natural by-product that stems from the employed self-assembled growth methods and manifest in various forms such as shape-asymmetry, inhomogeneous strain distribution within the QD and concomittant piezo-elecric fields. These asymmetries in return give rise to distinct anisotropies in the optical properties of QDs, which in fact render their optical response classic. For device oriented research these anisotropies are therefore typically considered unwanted and actively researched to be controlled. They are, however, interesting from a fundamental point of view, as anisotropic QDs basically provide a testbed system for fundamental atom-like quantum physics with non-centrosymmetric potentials. As shall be shown in the current work, this gives rise to novel and interesting physics in its own right. Employing photoluminescence spectroscopy (PL) we investigate the optical anisotropy of the radiative recombination of excitons confined to CdSe/ZnSe QDs. This is done by angle-dependent polarization-resolved PL. We demonstrate experimentally that the electron-hole exchange interaction in asymmetric QDs gives rise to an effective conversion of the optical polarization from linear to circular and vice versa. The experiment is succesfully modeled in the frame of an exciton pseudospin-formalism that is based on the exchange induced finestructure splitting of the radiative excitonic states and unambiguously proves that the observed polarization conversion is the continuous-wave equivalent to quantum beats between the exchange split states in the time domain. These results indicate that QDs may offer extended functionality beyond non-classical light sources in highly integrated all-optical device schemes, such as polarization converters or modulators. In a further extension we apply the exciton pseudospin-formalism to optical alignment studies and demonstrate how these can be used to directly measure the otherwise hidden symmetry distribution over an ensemble of QDs. This kind of measurement may be used on future optical studies in order to link optical data more directly to structural investigations, as it yields valuable information on capped QDs that cannot be looked at directly by topological methods. In the last part of this work we study the influence of an in-plane magnetic field on the optical anisotropy. We find that the optical axis of the linear polarization component of the photoluminescence signal either rotates in the opposite direction to that of the magnetic field or remains fixed to a given crystalline direction. A qualitative theoretical analysis based on the exciton pseudospin Hamiltonian unambiguously demonstrates that these effects are induced by isotropic and anisotropic contributions to the heavy-hole Zeeman term, respectively. The latter is shown to be compensated by a built-in uniaxial anisotropy in a magnetic field B=0.4 T, resulting in an optical response that would be expected for highly symmetric QDs. For a comprehensive quantitative analysis the full heavy-hole exciton k.p-Hamiltonian is numerically calculated and the resulting optical polarization is modeled. The model is able to quantitatively describe all experimental results using a single set of parameters. From this model it is explicitly seen that a optical response characteristic for high symmetry QDs may be obtained from an ensemble of asymmetric QDs without a crossing of the zero-field bright exciton states, which was required for application of QDs in non-classical light sources. It is clearly demonstrated that any scheme using in-plane magnetic fields to symmetrize the optical response has to take into account at least four optically active states instead of the two observed in the absence of magnetic fields. These findings may explain some of the major disagreement on recent entanglement studies in asymmetric QDs, as models that do not take the above result into account cannot be a priori expected to provide reliable results on excitonic Bell states.
Due to their potential application for quantum computation, quantum dots have attracted a lot of interest in recent years. In these devices single electrons can be captured, whose spin can be used to define a quantum bit (qubit). However, the information stored in these quantum bits is fragile due to the interaction of the electron spin with its environment. While many of the resulting problems have already been solved, even on the experimental side, the hyperfine interaction between the nuclear spins of the host material and the electron spin in their center remains as one of the major obstacles. As a consequence, the reduction of the number of nuclear spins is a promising way to minimize this effect. However, most quantum dots have a fixed number of nuclear spins due to the presence of group III and V elements of the periodic table in the host material. In contrast, group IV elements such as carbon allow for a variable size of the nuclear spin environment through isotopic purification. Motivated by this possibility, we theoretically investigate the physics of the central spin model in carbon based quantum dots. In particular, we focus on the consequences of a variable number of nuclear spins on the decoherence of the electron spin in graphene quantum dots.
Since our models are, in many aspects, based upon actual experimental setups, we provide an overview of the most important achievements of spin qubits in quantum dots in the first part of this Thesis. To this end, we discuss the spin interactions in semiconductors on a rather general ground. Subsequently, we elaborate on their effect in GaAs and graphene, which can be considered as prototype materials. Moreover, we also explain how the central spin model can be described in terms of open and closed quantum systems and which theoretical tools are suited to analyze such models.
Based on these prerequisites, we then investigate the physics of the electron spin using analytical and numerical methods. We find an intriguing thermal flip of the electron spin using standard statistical physics. Subsequently, we analyze the dynamics of the electron spin under influence of a variable number of nuclear spins. The limit of a large nuclear spin environment is investigated using the Nakajima-Zwanzig quantum master equation, which reveals a decoherence of the electron spin with a power-law decay on short timescales. Interestingly, we find a dependence of the details of this decay on the orientation of an external magnetic field with respect to the graphene plane. By restricting to a small number of nuclear spins, we are able to analyze the dynamics of the electron spin by exact diagonalization, which provides us with more insight into the microscopic details of the decoherence. In particular, we find a fast initial decay of the electron spin, which asymptotically reaches a regime governed by small fluctuations around a finite long-time average value. Finally, we analytically predict upper bounds on the size of these fluctuations in the framework of quantum thermodynamics.
Within the framework of this thesis the mechanisms of growth and reorganisation of surfaces within the first few layers were investigated that are the basis for the fabrication of high quality thin films and interfaces. Two model systems, PTCDA/Ag(111) and CdSe/ZnSe quantum dots (QD), were chosen to study such processes in detail and to demonstrate the power and improvements of the aberration corrected spectromicroscope SMART [1] simultaneously. The measurements benefit especially from the enhanced transmission of the microscope and also from its improved resolution. SMART, the first double–aberration corrected instrument of its kind [2], provided comprehensive methods (LEEM/PEEM, μ–LEED, μ–XPS) to study in–situ and in real time the surface reorganisation and to determine morphology, local structure and local chemical composition of the resulting thin film. Complementarily, a commercial AFM [3] was used ex–situ. XPEEM and μ–XPS measurements were made possible by attaching SMART to the high flux density beamline of the soft–X–ray source BESSY–II [4]. PTCDA/Ag(111) – Growth and structure of the first two layers Although PTCDA/Ag(111) is one of the most intensely studied model systems for the growth of organic semiconductor thin films, it still offers new insights into a complex growth behaviour. This study enlightens the temperature dependant influence of morphological features as small as monatomic Ag steps on the growth process of the first two layers. At low temperatures, single Ag steps act as diffusion barriers. But interdiffusion was observed already for the 2nd layer whereas domain boundaries in the 1st PTCDA–layer persist for crystallite growth in the 2nd layer. 1st layer islands are more compact and the more dendritic development of the 2nd layer indicates reduced interaction strength between 2nd and 1st layer. These findings were explained by a model consisting of structural and potential barriers. The second part of the PTCDA study reveals a variety of phases that appears only if at least two layers are deposited. Besides the six known rotational domains of the interface system PTCDA/Ag(111) [5], a further manifold of structures was discovered. It does not only show a surprising striped image contrast, but the 2nd layer also grows in an elongated way along these so–called ’ripples’. The latter show a rather large period and were found in a wide temperature range. Additionally the μ-LEED pattern of such a domain shows a new super–superstructure as well. This phase is explained by a structural model that introduces a rotated, more relaxed domain in the 2nd layer that does not exist in the first layer. Its structural parameters are similar to those of the bulk unitcells of PTCDA. The model is confirmed by the observation of two different rotational domains that grow on top of one single ’substrate’ domain in the 1st layer. The orientations of the ripple phases fit as well to the predictions of the model. The growth direction along the ripples corresponds to the short diagonal of the super–superstructure unitcell with diamond–like shape. CdSe/ZnSe – Inverse structuring by sublimation of an α-Te cap With the second model system the formation of CdSe quantum dots (QD) from strained epi-layers was investigated. In this case the structures do not form during deposition, but rather during sublimation of the so–called ‘ignition cap’. For these pilot experiments not only the process of QD formation itself was of interest, but also the portability of the preparation and the prevention of contaminations. It was found that the α-Se is well suited for capping and the last step of the QD preparation, the sublimation of the α-Te cap, needs a sufficiently high rate in rise of temperature. Subsequently the cap, the process of desorption and the final surface with the quantum structures were investigated in detail. The cap was deposited by the MBE-group in Würzburg as an amorphous Te layer but was found to contain a variety of structures. Holes, cracks, and micro–crystallites within an α-Te matrix were identified. Sublimation of the “ignition cap” was observed in real–time. Thus the discovered cap-structures could be correlated with the newly formed features as, e.g., QDs on the bare CdSe surface. Since CdSe/ZnSe QDs prefer to form in the neighbourhood of the Te μ–crystallites, Te was found to play a major role in their formation process. Different explanations as the impact of Te as a surfactant, an enhanced mobility of adatoms or as stressor nuclei are discussed. The spectromicroscopic characterisation of the CdSe surface with QDs revealed the crystallographic directions. An increased Cd signal of the film was found at positions of former holes. Several possibilities as segregation or surface termination are reviewed, that might explain this slight Cd variation. Therewith, an important step to a detailed understanding of the complex reorganisation process in coating systems could be achieved.
This thesis treats the thermopower and other thermal effects in single quantum dots (QD) and quantum dot systems. It contributes new experimental results to the broad and active field of research on thermoelectrics in low dimensional systems. The thermopower experiments discussed in this work focus on QDs which exhibit a net spin and on tunnel-coupled double QDs (DQD). Furthermore, experiments are presented which address the realization of a QD device which extracts thermal energy from a heat reservoir and converts it into a directed charge current in a novel way.
The samples used for these investigations have been fabricated from GaAs/AlGaAs heterostructures which contain a two dimensional electron gas. Using optical and electron beam lithography, the devices have been realized by means of the top-gate technology. All experiments have been performed at low temperature. In order to create a controllable temperature difference in the samples the current heating technique has been used. These experimental basics as well as fundamentals of electric and thermoelectric transport are introduced in Part I of this thesis.
The experiments on the thermopower of a single QD are described in Part II. Essentially, they deal with the problem of how a single spin situated on a QD influences the thermoelectric properties of the system. In this context, the Kondo-effect plays a crucial role. Generally, the Kondo effect is the result of a many-body state which arises from an antiferromagnetic coupling of a magnetic impurity with the surrounding conduction electrons. Here, the magnetic impurity is represented by a QD which is occupied with an odd number of electrons so that it exhibits a net spin. For the first time the thermopower of a Kondo-QD has been studied systematically as a function of two parameters, namely the QD coupling energy and the sample temperature. Both parameters are crucial quantities for Kondo-physics to be observed. Based on these data, it is shown that the thermopower line shape as a function of QD energy is mainly determined by two competing contributions: On the one hand by the enhanced density of states around the Fermi level due to Kondo-correlations and on the other hand by thermopower contributions from the Coulomb resonances. Furthermore, the experiments confirm theoretical predictions which claim that the spectral DOS arising from Kondo-correlations shifts away from the Fermi level for those QD level configurations which are not electron-hole symmetric. Comparison with model calculations by T. Costi and V. Zlatic [Phys. Rev. B 81, 235127 (2010)] shows qualitative and partly even quantitative agreement. A finite thermovoltage at the center of the Kondo-region, which occurred in previous investigations, is also observed in the experiments presented here. It is not covered by the current theory of the Kondo effect. The dependence of this signal on temperature, coupling energy and magnetic field, which differ from non-Kondo regions, is analyzed. In order to clarify the physics behind this phenomenon further studies are desirable.
Furthermore, it is shown by variation of the QD coupling energy over a wide range that Kondo-correlations can be detected in the thermopower even in the regime of very weak coupling. In contrast, no Kondo signatures are visible in the conductance in this energy range. It is found that in the limit of weak coupling the Kondo effect causes the thermopower to exhibit a diminished amplitude in close vicinity of a conductance resonance. Subsequent filling of spin-degenerate states then leads to a thermopower amplitude modulation (odd-even-effect). Although this effect had been observed in previous studies, no connection to Kondo physics had been established in order to explain the observations.
Hence, the experiments on a single QD presented in this thesis provide unique insight into the complex interplay of different transport mechanisms in a spin-correlated QD. Moreover, the results confirm the potential of thermopower measurements as a highly sensitive tool to probe Kondo-correlations.
In Part III thermal effects are investigated in systems which contain two coupled QDs.
Such QD-systems are particularly interesting with respect to thermoelectric applications: Many proposals utilize the extremely sharp energy filtering properties of such coupled QDs and also different kinds of inter dot coupling to construct novel and highly efficient thermoelectric devices. In the present work, thermopower characterizations are performed on a tunnel-coupled DQD for the first time. The key result of these investigations is the thermopower stability diagram. Here it is found, that in such a system maximal thermopower is generated in the vicinity of the so-called triple points (TP) at which three charge states of the DQD are degenerate. Along the axis of total energy, which connects two adjacent TP, a typical thermopower line shape is observed. It is explained and modeled within an intuitive picture that assumes two transport channels across the DQD, representing the TP. For those regions which are far away from the TP, the thermopower turns out to be very sensitive to the relative configuration of the QD energies. The conductance and thermopower data are well reproduced within a model that assumes transport via molecular states. Integration of both models into one then allows model calculations for a complete stability cell in conductance and thermopower to be done.
Furthermore, experiments on two capacitively coupled QDs are presented. In these studies the focus lies on testing the feasibility of such systems for the manipulation and generation of charge currents from thermal energy. In a series of experiments it is shown that such a system of QDs can be utilized to increase or decrease a current flowing between two electron reservoirs by varying the temperature in a third reservoir. This effect is based on the cross-correlation of occupation fluctuations of the individual QDs. These are positive for certain QD energy level configurations and negative for others, which increases or decreases the charge current in the experiments, respectively. In the stability diagram this is manifested in a characteristic clover leaf shaped structure of positive and negative current changes in vicinity of the TP. All main experimental results are reproduced qualitatively in simple model calculations. Due to the close analogy between electrical and thermal conductance of a QD, this effect of thermal switching can, in principle, also be used to built a thermal transistor.
Finally, it is shown that a system consisting of two Coulomb-coupled QDs, which couple a hot electron reservoir electrostatically to two cold electron reservoirs, can be utilized as a novel device which extracts heat from its environment and converts it into a directed charge current. The idea of this heat-to-current converter (HCC) was first proposed by R. Sánchez and M. Büttiker [Phys. Rev. B 83, 085428 (2011)]. It is not only characterized by the novelty of its working principle but also by the fact, that it decouples the directions of charge current and energy flow. In the experiments presented here, such HCC-currents are identified unambiguously: For certain QD-level configurations an electric current between the two cold reservoirs is observed if the temperature in the third reservoir is increased. The direction of this current is shown to be independent of an external voltage. In contrast, the direction of the current exhibits a characteristic dependence on the tunneling coefficients of the QDs, as predicted by theory: By adjusting the thickness and the shape of the respective tunnel junctions, a charge current can be generated between two cold reservoirs, and it can even be inverted. The experimental observations are quantitatively reproduced by model calculations by R. Sánchez and B. Sothmann. Thus, the results represent direct evidence for the existence of HCC-currents. Due to the novelty of the working principle of the HCC and its relevance from a fundamental scientific point of view, the results presented here are an important step towards energy harvesting devices at the nano scale.
Graphene-based single-electron and hybrid devices, their lithography, and their transport properties
(2016)
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.
Albeit of high technological import, epitaxial self-assembly of CdSe/ZnSe QDs is non-trivial and still not clearly understood. The origin and attributes of these QDs are significantly different from those of their III-V and group-IV counterparts. For III-V and group-IV heterosystems, QD-formation is assigned to the Stranski Krastanow (SK) transition, wherein elastic relaxation of misfit strain leads to the formation of coherent three-dimensional (3D) islands, from a supercritically strained two-dimensional (2D) epilayer. Unfortunately, this phenomenon is inconspicuous for the CdSe/ZnSe heterosystem. Well-defined 3D islands are not readily formed in conventional molecular beam epitaxial (MBE) growth of CdSe on ZnSe. Consequently, several alternative approaches have been adopted to induce/enhance formation of QDs. This thesis systematically investigates three such alternative approaches, along with conventional MBE, with emphasis on the formation-mechanism of QDs, and optimization of their morphological and optical attributes. It is shown here that no distinct 3D islands are formed in MBE growth of CdSe on ZnSe. The surface of the CdSe layer represents a rough 2D layer, characterized by a dense array of shallow (<1nm) abutting mounds. In capped samples, the CdSe deposit forms an inhomogeneous CdZnSe quantum well (QW)-like structure. This ternary QW consists of local Cd-rich inclusions, which confine excitons three-dimensionally, and act as QDs. The density of such QDs is very high (~ 1012 cm-2). The QDs defined by the composition inhomogeneities of the CdZnSe QW presumably originate from the shallow mounds of the uncapped CdSe surface. By a technique wherein a CdSe layer is grown at a low temperature (TG = 230 °C) and subsequently annealed at a significantly higher temperature (TA =310 °C), tiny but distinct 3D islands are formed. In this work, the mechanism underlying the formation of these islands is reported. While the CdSe deposit forms a quasi-two-dimensional (quasi-2D) layer at TG = 230 °C, subsequent annealing at TA = 310 °C results in a thermally activated “up-climb” of adatoms onto two-dimensional clusters (or precursors) and concomitant nucleation of 3D islands. The areal density of QDs, achieved by this technique, is at least a decade lower than that typical for conventional MBE growth. It is demonstrated that further reduction is possible by delaying the temperature ramp-up to TA. In the second technique, formation of distinct islands is demonstrated by deposition of amorphous selenium (a-Se) onto a 2D CdSe epilayer at room temperature and its subsequent desorption at a higher temperature (TD = 230 °C). Albeit the self-assembled islands are large, they are severely truncated during subsequent capping with ZnSe, presumably due to segregation of Cd and Zn-alloying of the islands. The segregation phenomenon is analyzed in this work and correlated to the optical properties of the QDs. Additionally, very distinct vertical correlation of QDs in QD-superlattices, wherein the first QD-layer is grown by this technique and the subsequent ones by migration enhanced epitaxy (MEE), is reported. The process steps of the third variant technique, developed in course of this work, are very similar to those of the previous one-the only alteration being the substitution of selenium with tellurium as the cap-forming-material. This leads not only to large alteration of the morphological and optical attributes of the QDs, but also to formation of unique self-assembled island-patterns. Oriented dashes, straight and buckled chains of islands, and aligned island-pairs are formed, depending on the thickness of the Te-cap layer. The islands are partially alloyed with Te and emit luminescence at very low energies (down to 1.7 eV at room temperature). The Te cap layer undergoes (poly)crystallization during temperature ramp-up (from room temperature to TD) for desorption. Here, it is shown that the self-assembled patterns of the island-ensembles are determined by the pattern of the grain boundaries of the polycrystalline Te layer. Based on an understanding of the mechanism of pattern formation, a simple and “clean” method for controlled positioning of individual QDs and QD-based extended nanostructures, is proposed in this work. The studies carried out in the framework of this thesis provide not only a deeper insight into the microscopic processes governing the heteroepitaxial self-assembly of CdSe/ZnSe(001) QDs, but also concrete approaches to achieve, optimize, and control several technologically-important features of QD-ensembles. Reduction and control of QD-areal-density, pronounced vertical correlation of distinctly-defined QDs in QD-superlattices, and self-assembly of QD-based extended structures, as demonstrated in this work, might turn out to be beneficial for envisioned applications in information-, and communication-technologies.
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.
Metal nanostructures have been known for a long time to exhibit optical resonances via localized surface plasmons. The high electric fields in close proximity to the metal surface have prospects to dramatically change the dynamics of electronic transitions, such as an enhanced spontaneous decay rate of a single emitter. However, there have been two major issues which impede advances in the experimental realization of enhanced light-matter interaction. (i) The fabrication of high-quality resonant structures requires state-of-the-art patterning techniques in combination with superior materials. (ii) The tiny extension of the optical near-field requires precise control of the single emitter with respect to the nanostructure. This work demonstrates a solution to these problems by combining scanning probe and optical confocal microscopy. Here, a novel type of scanning probe is introduced which features a tip composed of the edge of a single crystalline gold sheet. The patterning via focused ion beam milling makes it possible to introduce a plasmonic nanoresonator directly at the apex of the tip. Numerical simulations demonstrate that the optical properties of this kind of scanning probe are ideal to analyze light-matter interaction. Detailed experimental studies investigate the coupling mechanism between a localized plasmon and single colloidal quantum dots by dynamically changing coupling strength via their spatial separation. The results have shown that weak interaction affects the shape of the fluorescence spectrum as well as the polarization. For the best probes it has been found that it is possible to reach the strong coupling regime at the single emitter level at room temperature. The resulting analysis of the experimental data and the proposed theoretical models has revealed the differences between the established far-field coupling and near-field coupling. It has been found that the broad bandwidth of plasmonic resonances are able to establish coherent coupling to multiple transitions simultaneously giving rise to an enhanced effective coupling strength. It has also been found that the current model to numerically calculate the effective mode volume is inaccurate in case of mesoscopic emitters and strong coupling. Finally, light-matter interaction is investigated by the means of a quantum-dot-decorated microtubule which is traversing a localized nearfield by gliding on kinesin proteins. This biological transport mechanism allows the parallel probing of a meta-surface with nm-precision. The results that have been put forward throughout this work have shed new light on the understanding of plasmonic light-matter interaction and might trigger ideas on how to more efficiently combine the power of localized electric fields and novel excitonic materials.