Systematic multi-configuration calculations on structures and properties of complex atoms

Die relativistische Multikonfigurations Dirac-Fock (MCDF) Methode ist gegenwärtig eines der am häufigsten benutzten Verfahren zur Berechnung der elektronischen Struktur und der Eigenschaften freier Atome. In diesem Verfahren werden die Wellenfunktionen ausgewählter atomarer Zustände als eine Linearkombination von sogenannten Konfigurationszuständen (CSF - Configuration State Functions) konstruiert, die in einem Teilraum des N-Elektronen Hilbert-Raumes eine (Vielteilchen-)Basis aufspannen. Die konkrete Konstruktion dieser Basis entscheidet letzlich über die Güte der Wellenfunktionen, die üblicherweise mit Hilfe einer Variation des Erwartungswertes zum no-pair Dirac-Coulomb Hamiltonoperators gewonnen werden. Mit Hilfe von MCDF Wellenfunktionen können die dominanten relativistischen und Korrelationseffekte in freien Atomen allgemein recht gut erfaßt und verstanden werden. Außer der instantanen Coulombabstoßung zwischen allen Elektronenpaaren werden dabei auch die relativistischen Korrekturen zur Elektron-Elektron Wechselwirkung, d.h. die magnetischen und Retardierungsbeiträge in der Wechselwirkung der Elektronen untereinander, die Ankopplung der Elektronen an das Strahlungsfeld sowie der Einfluß eines ausgedehnten Kernmodells erfaßt. Im Vergleich mit früheren MCDF Rechnungen werden in den in dieser Arbeit diskutierten Fallstudien Wellenfunktionsentwicklungen verwendet, die um 1-2 Größenordnungen aufwendiger sind und daher systematische Untersuchungen inzwischen auch an Atomen mit offenen d- und f-Schalen erlauben. Eine spontane Emission oder Absorption von Photonen kann bei freien Atomen theoretisch am einfachsten mit Hilfe von Übergangswahrscheinlichkeiten erfaßt werden. Solche Daten werden heute in vielen Forschungsbereichen benötigt, wobei neben den traditionellen Gebieten der Fusionsforschung und Astrophysik zunehmend auch neue Forschungsrichtungen (z.B. Nanostrukturforschung und Röntgenlithographie) zunehmend ins Blickfeld rücken. Um die Zuverlässigkeit unserer theoretischen Vorhersagen zu erhöhen, wurde in dieser Arbeit insbesondere die Relaxation der gebundenen Elektronendichte, die rechentechnisch einen deutlich größeren Aufwand erfordert, detailliert untersucht. Eine Berücksichtigung dieser Relaxationseffekte führt oftmals auch zu einer deutlich besseren Übereinstimmung mit experimentellen Werten, insbesondere für dn=1 Übergänge sowie für schwache und Interkombinationslinien, die innerhalb einer Hauptschale (dn=0) vorkommen. Unsere in den vergangenen Jahren verbesserten Rechnungen zu den Wellenfunktionen und Übergangswahrscheinlichkeiten zeigen deutlich den Fortschritt bei der Behandlung komplexer Atome. Gleichzeitig kann dieses neue Herangehen künftig aber auch auf (i) kompliziertere Schalensstrukturen, (ii) die Untersuchung von Zwei-Elektronen-ein-Photon (TEOP) Übergängen sowie (iii) auf eine Reihe weiterer atomarer Eigenschaften übertragen werden, die bekanntermaßen empflindlich von der Relaxation der Elektronendichte abhängen. Dies sind bspw. Augerzerfälle, die atomare Photoionisation oder auch strahlende und dielektronische Rekombinationsprozesse, die theoretisch bisher nur selten überhaupt in der Dirac-Fock Näherung betrachtet wurden.

Interatomic potential structures in highly ionized scattering systems

The interatomic potential of the ion-atom scattering system I^N+-I at small intermediate internuclear distances is calculated for different charge states N from atomic Dirac-Focker-Slater (DFS) electron densities within a statistical model. The behaviour of the potential structures, due to ionized electronic shells, is studied by calculations of classical elastic differential scattering cross-sections.

Two-photon decay of the 1s2s ^1S_0 state in _36Kr^34+ produced by resonant transfer and excitation

The doubly excited 2s2p ^1P_1 level of Kr^{34+} populated via resonant transfer and excitation (RTE) feeds selectively the metastable ls2s ^1 S_0 state which can only decay via simultaneous emission of two photons to the ground state 1s^2 ^1 S_0. X-ray/X-ray coincidence measurements in heavy ionatom collisions enable the direct measurement of the spectral distribution of the two-photon decay in He-like ions. In addition, we observe strong photon cascades indueed by radiative electron capture.

Conceptual structures represented by conceptual graphs and formal concept analysis

Conceptual Graphs and Formal Concept Analysis have in common basic concerns: the focus on conceptual structures, the use of diagrams for supporting communication, the orientation by Peirce's Pragmatism, and the aim of representing and processing knowledge. These concerns open rich possibilities of interplay and integration. We discuss the philosophical foundations of both disciplines, and analyze their specific qualities. Based on this analysis, we discuss some possible approaches of interplay and integration.

Synthesis and Characterization of Novel Spiro-Starburst-Structures as Blue Light Emitters and Zeolites

Spiro-starburst-structures with symmetric globular structures in forms of first and second generations that readily form stable amorphous glasses have been synthesized and then characterised in this work. During the synthesis of these materials, possibilities of the extension of the chains of the phenyl rings in 2,2’,7 and 7’-positions of the central core of the spirobifluorene as well as the 2’,7 and 7’-positions of the terminal spirobifluorene units of the spiro-starburst-structures have been investigated so that solubilities and morphologies of the compounds are not negatively influenced. Their morphological properties have been explored by recording their decomposition temperature and glass transition temperature. These compounds possessing two perpendicular arrangement of the two molecular halves show high glass transition temperature (Tg), which is one of the most important parameter indicating the stability of the amorphous state of the material for optoelectronic devices like organic light emitting diodes. Within the species of second generation compounds, for example, 4-spiro3 shows the highest Tg (330 °C) and the highest branching degree. When one [4B(SBF)SBF-SBF 84] or two [4SBFSBF-SBF 79] terminal spirobifluorene units are removed, the Tg decreases to 318 °C and 307 °C respectively. Photo absorption and fluorescence spectra and cyclic voltammetry measurements are taken in account to characterize the optoelectronic properties of the compounds. Spiro-starburst-structures emit radiation in the blue region of the visible spectrum. The peak maxima of absorption and emission spectra are observed to be at higher wavelength in the molecules with longer chromophore chains than in the molecules with shorter chromophore chains. Excitation spectra are monitored with their emission peak maxima. The increasing absorbing species in molecule leads to increasing molar extinction coefficient. In the case of 4B(TP)SBF-SBF 53 and 4B(SBF)SBF-SBF 84, the greater values of the molar extinction coefficients (43*104 and 44*104 L mol-1 cm-1 respectively) are the evidences of the presence of four times octiphenyl conjugation rings and eight times terminal fluorene units respectively. The optical properties of solid states of these compounds in the form of thin film indicate that the intermolecular interaction and aggregation of individual molecules in neat amorphous films are effectively hindered by their sterically demanding structures. Accordingly, in solid state, they behave like isolated molecules in highly dilute solution. Cyclic voltammetry measurements of these compounds show electrochemically reversibility and stability. Furthermore, the zeolitic nature (host-guest) of the molecular sieve of the synthesized spiro-starburst-structures has been analysed by thermogravimetric analysis method.

Development of directly modulated high speed telecommunication lasers based on surface defined feedback gratings

High-speed semiconductor lasers are an integral part in the implemen- tation of high-bit-rate optical communications systems. They are com- pact, rugged, reliable, long-lived, and relatively inexpensive sources of coherent light. Due to the very low attenuation window that exists in the silica based optical fiber at 1.55 μm and the zero dispersion point at 1.3 μm, they have become the mainstay of optical fiber com- munication systems. For the fabrication of lasers with gratings such as, distributed bragg reflector or distributed feedback lasers, etching is the most critical step. Etching defines the lateral dimmensions of the structure which determines the performance of optoelectronic devices. In this thesis studies and experiments were carried out about the exist- ing etching processes for InP and a novel dry etching process was de- veloped. The newly developed process was based on Cl2/CH4/H2/Ar chemistry and resulted in very smooth surfaces and vertical side walls. With this process the grating definition was significantly improved as compared to other technological developments in the respective field. A surface defined grating definition approach is used in this thesis work which does not require any re-growth steps and makes the whole fabrication process simpler and cost effective. Moreover, this grating fabrication process is fully compatible with nano-imprint lithography and can be used for high throughput low-cost manufacturing. With usual etching techniques reported before it is not possible to etch very deep because of aspect ratio dependent etching phenomenon where with increasing etch depth the etch rate slows down resulting in non-vertical side walls and footing effects. Although with our de- veloped process quite vertical side walls were achieved but footing was still a problem. To overcome the challenges related to grating defini- tion and deep etching, a completely new three step gas chopping dry etching process was developed. This was the very first time that a time multiplexed etching process for an InP based material system was demonstrated. The developed gas chopping process showed extra ordinary results including high mask selectivity of 15, moderate etch- ing rate, very vertical side walls and a record high aspect ratio of 41. Both the developed etching processes are completely compatible with nano imprint lithography and can be used for low-cost high-throughput fabrication. A large number of broad area laser, ridge waveguide laser, distributed feedback laser, distributed bragg reflector laser and coupled cavity in- jection grating lasers were fabricated using the developed one step etch- ing process. Very extensive characterization was done to optimize all the important design and fabrication parameters. The devices devel- oped have shown excellent performance with a very high side mode suppression ratio of more than 52 dB, an output power of 17 mW per facet, high efficiency of 0.15 W/A, stable operation over temperature and injected currents and a threshold current as low as 30 mA for almost 1 mm long device. A record high modulation bandwidth of 15 GHz with electron-photon resonance and open eye diagrams for 10 Gbps data transmission were also shown.

1.55 µm High-Speed QDs Lasers for Optical Telecommunication Applications

In this work investigation of the QDs formation and the fabrication of QD based semiconductor lasers for telecom applications are presented. InAs QDs grown on AlGaInAs lattice matched to InP substrates are used to fabricate lasers operating at 1.55 µm, which is the central wavelength for far distance data transmission. This wavelength is used due to its minimum attenuation in standard glass fibers. The incorporation of QDs in this material system is more complicated in comparison to InAs QDs in the GaAs system. Due to smaller lattice mismatch the formation of circular QDs, elongated QDs and quantum wires is possible. The influence of the different growth conditions, such as the growth temperature, beam equivalent pressure, amount of deposited material on the formation of the QDs is investigated. It was already demonstrated that the formation process of QDs can be changed by the arsenic species. The formation of more round shaped QDs was observed during the growth of QDs with As2, while for As4 dash-like QDs. In this work only As2 was used for the QD growth. Different growth parameters were investigated to optimize the optical properties, like photoluminescence linewidth, and to implement those QD ensembles into laser structures as active medium. By the implementation of those QDs into laser structures a full width at half maximum (FWHM) of 30 meV was achieved. Another part of the research includes the investigation of the influence of the layer design of lasers on its lasing properties. QD lasers were demonstrated with a modal gain of more than 10 cm-1 per QD layer. Another achievement is the large signal modulation with a maximum data rate of 15 Gbit/s. The implementation of optimized QDs in the laser structure allows to increase the modal gain up to 12 cm-1 per QD layer. A reduction of the waveguide layer thickness leads to a shorter transport time of the carriers into the active region and as a result a data rate up to 22 Gbit/s was achieved, which is so far the highest digital modulation rate obtained with any 1.55 µm QD laser. The implementation of etch stop layers into the laser structure provide the possibility to fabricate feedback gratings with well defined geometries for the realization of DFB lasers. These DFB lasers were fabricated by using a combination of dry and wet etching. Single mode operation at 1.55 µm with a high side mode suppression ratio of 50 dB was achieved.

Asymptotic model for shape resonance control of diatomics by intense non-resonant light

We derive a universal model for atom pairs interacting with non-resonant light via the polarizability anisotropy, based on the long range properties of the scattering. The corresponding dynamics can be obtained using a nodal line technique to solve the asymptotic Schrödinger equation. It consists of imposing physical boundary conditions at long range and vanishing the wavefunction at a position separating the inner zone and the asymptotic region. We show that nodal lines which depend on the intensity of the non-resonant light can satisfactorily account for the effect of the polarizability at short range. The approach allows to determine the resonance structure, energy, width, channel mixing and hybridization even for narrow resonances.

Asymptotic model for shape resonance control of diatomics by intense non-resonant light: universality in the single-channel approximation

Non-resonant light interacting with diatomics via the polarizability anisotropy couples different rotational states and may lead to strong hybridization of the motion. The modification of shape resonances and low-energy scattering states due to this interaction can be fully captured by an asymptotic model, based on the long-range properties of the scattering (Crubellier et al 2015 New J. Phys. 17 045020). Remarkably, the properties of the field-dressed shape resonances in this asymptotic multi-channel description are found to be approximately linear in the field intensity up to fairly large intensity. This suggests a perturbative single-channel approach to be sufficient to study the control of such resonances by the non-resonant field. The multi-channel results furthermore indicate the dependence on field intensity to present, at least approximately, universal characteristics. Here we combine the nodal line technique to solve the asymptotic Schrödinger equation with perturbation theory. Comparing our single channel results to those obtained with the full interaction potential, we find nodal lines depending only on the field-free scattering length of the diatom to yield an approximate but universal description of the field-dressed molecule, confirming universal behavior.

Meshing highly regular structures: The case of super carbon nanotubes of arbitrary order

Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.