No description available.

Ultradünne Filme der 3d-Metalle auf einem magnetischen Substrat können durch die magnetische Kopplung ebenfalls eine Magnetisierung erfahren. Im allgemeinen ist die Art und Stärke der induzierten magnetischen Momente von der Dicke und der Struktur dieser Filme abhängig. In dieser Arbeit wurden speziell die Wachstumseigenschaften von Fe, Cr, Mn und V auf einem Fe(100)-Substrat bezüglich ihrer Morphologie und der Grenzflächeninter-diffusion sowie die magnetische Kopplung der Filme zum Substrat untersucht. Bei diesen Studien kam primär die streifende Oberflächenstreuung schneller Ionen (H+, He+, Ar+) mit Primärenergien von bis zu 25keV unter typischen Einfallswinkeln von 1..2° zur Oberfläche zum Einsatz. Bei einer solchen Streuung können die Projektile nicht in die Oberfläche eindringen, sondern werden von dieser reflektiert. Insbesondere die Aufnahme der spekularen Streuintensität und die Halbwertsbreite der resultierenden Streuverteilung erlaubten die Beobachtung des Wachstums-pro-zesses in Echtzeit sowie die quantitative Bestimmung von Stufendichten, kritischen Keim-größen, den Füllungsgrad atomarer Filmlagen, Aktivierungsenergien der lateralen Diffusion, die Änderung der Austrittsarbeit, sowie die Größe der thermischen Auslenkungen der Oberflächenatome. Die Anregung von Auger-Elektronen an der Oberfläche bei der streifenden Streuung von Protonen erlaubte in Verbindung mit der konventionellen Auger-Spektroskopie nach Anregung durch steil einfallende Elektronen die Bestimmung der Konzentra-tionsprofile an der Grenzfläche des Films zum Substrat bei unterschiedlich starker Grenzflächeninterdiffusion. Die Charakterisierung der magnetischen Oberflächenmomente des Fe(100) und der darauf gewachsenen 3d-Metallfilme erfolgte indirekt aus der Polarisation des Fluo-res-zenzlichts aus dem Zerfall des HeI3³P-Zustandes nach der Streuung, der durch den Einfang der polarisierten Elektronen von der Oberfläche entsprechend der dort vorhandenen Zustandsdichte besetzt wird. Grundlegende Zusammenhänge zwischen der Spin-Polarisation des HeI3³P-Zustandes und der Magnetisierung der streuenden Oberfläche wurden am Fe(100) studiert. Mittels einfacher Modelle konnte in diesen Studien die extreme Oberflächen-empfindlichkeit der angewendeten Meßmethode wie auch die qualitative Abhängigkeit der Spin-Polarisation von der elektronischen Zustandsdichte der Festkörper-Oberfläche nachgewiesen werden. Für die Interpretation der Polarisationsdaten beim heteroepitaktischen Filmwachstum war es notwendig, das Wachstum möglichst realitätsnah in einem Modell abzubilden. Dazu wurde ein bereits bestehendes Modell zur Beschreibung des homoepitakti-schen Filmwachstums auf niedrigindizierten Oberflächen weiterentwickelt, so daß auch die zeitliche Entwicklung der Interdiffusion bei heteroepitaktischem Wachstum beschrieben werden kann. Die Eichung des Modells erfolgte mit den Ergebnissen aus der Untersuchung des Wachstums mit der streifenden Ionenstreuung und der Auger-Spektroskopie. Damit wurde es erstmals möglich, die Magnetisierung der heteroepitaktisch gewachsenen 3d-Metallfilme bei nicht idealem Filmwachstum und deutlicher Grenz-flächeninterdiffusion anhand experimenteller Ergebnisse von ein und derselben Probe zu beschreiben sowie den Zusammenhang zwischen Struktur, Interdiffusion und Magnetisierung nachzuweisen. / Ultrathin films of 3d-metals on a magnetic substrate can experience a magnetization due to magnetic coupling. Commonly the induced magnetic moments depend on the thickness and the structure of these films. This work is focussed on the growth properties of Fe, Cr, Mn, and V on the Fe(100) surface with respect to the morphology and the interdiffusion at the interface as well as the magnetic coupling of the film to the substrate. In the experiments mainly the grazing surface scattering of fast ions (H+, He+, Ar+) was applied with primary energies up to 25keV and typical incidence angles of 1..2° to the surface. Using this grazing scattering geometry the projectiles cannot penetrate into but are reflected from the surface. Especially the monitoring of the specular intensity and halfwidth of the resulting scattering distribution enabled the observation of growth processes in real time as well as the quantitative determination of step density, critical growth nuclei, filling of atomic layers, activation energy of lateral diffusion on the surface, change of workfunction, and the size of thermal vibrational amplitudes of the surface atoms. The excitation of Auger electrons at the surface on one hand side by grazing scattering of protons and on the other hand side by electrons at large incidence angles was used to determine the concentration profile at the interface between film and substrate at different degrees of interdiffusion. The magnetic moments of the Fe(100) surface and the 3d-metal films grown on it was indirectly characterized by the polarization of fluorescence light from the deexcitation of HeI3³P-state after the scattering. This atomic state was filled by spin polarized electrons from the surface corresponding to the surface state densities. Basic relations between the spin polarization of the HeI3³P-state and the magnetization of the scattering surface was tested at the Fe(100) surface. Applying simple models an extreme surface sensitivity of the method used here as well as the qualitative dependence of the spin polarization from electron density of states of the surface layer was observed. For the interpretation of the polarization data recorded during heteroepitactical film growth it was necessary to model the growth realistically. Therefore an existing model for homoepitactical film growth on low index surfaces was further developed in order to describe the history of interdiffusion during heteroepitactical film growth. The parameters in the model were adjusted by means of the results from the growth studies with grazing surface scattering and Auger spectroscopy. So for the first time the description of the magnetization of heteroepitactically grown 3d-metal films with nonideal layer growth and interdiffusion both related to experimental results at the same specimen was made possible. Furthermore the interaction between film structure, interdiffusion and magnetization was shown.

The exploitation of the soft x-ray/extreme ultra-violet (EUV) region of the electromagnetic spectrum is possible mainly due to the development of multilayer (ML) mirrors. This region of the electromagnetic spectrum offers great opportunities in both science and technology. The shorter wavelength allows one to see smaller features in microscopy and write finer features in lithography. High reflectivity with moderate spectral bandwidth at normal/near-normal incidence can be achieved in soft x-ray/ EUV spectral range using these ML mirrors, where natural crystals with the required large periodicity are not available. These MLs are generally artificial Bragg’s reflectors, which consist of alternative high and low density materials with periodicity in the nanometer range. The main advantages of ML optics stem from the tunability of layer thickness, composition, lateral gradient, and the gradient along the normal to the substrate; these can be tailored according to the desired wavelength regime. They have the great advantage of being adaptable to figured surfaces, enabling their use as reflective optics in these spectral regions, for focusing and imaging applications. Broadband reflectivity and wavelength tunability are also possible by using MLs with normal and lateral gradient, respectively. However, fabrication of these ML mirrors requires the capability to deposit uniform, ultra-thin (a few angstroms-thick) films of different materials with thickness control on the atomic scale. Thus, one requires a proper understanding of substrate surfaces, individual layers, chemical reactivity at interfaces and, finally, of the ML structures required for particular applications. The performance of these MLs is limited by (the lack of) contrast in optical constants of the two materials, interfacial roughness, the chemical reactivity of two materials and, finally, errors in the thickness of individual layers. Soft x-ray/extreme ultra-violet ML mirrors have found a wide range of applications in synchrotron radiation beam lines, materials science, astronomy, x-ray microscopy, x-ray laser, x-ray lithography, polarizers, and plasma diagnostics. The Indus–1 synchrotron radiation (SR) source is an operational 450 MeV machine, which produces radiation up to soft x-rays. Indus-2 is a 2.5 GeV machine, which has been commissioned recently to produce hard x-rays (E > 25 keV). The combination of Indus-1 and Indus-2 will cover a broad energy spectrum from IR to hard x-rays. Therefore, there is a significant need and opportunity to study MLs of different pairs of materials, with different parameters such as periodicity and optimum thickness of individual layers. The goal of the present thesis is to fabricate MLs for soft x-ray optics and to study their physics for application as polarizers in the wavelength range from 67 Å to 160 Å on the Indus-1 synchrotron source. To accomplish this task, a UHV electron beam evaporation system has been developed indigenously for the fabrication of MLs. Three different ML systems viz., Mo/Si, Fe/B4C and Mo/Y have been fabricated, and their surfaces and interfaces were investigated thoroughly for the polarizer application. X-ray reflectivity (XRR) has been used extensively in the investigations of these MLs. This is because XRR is a highly sensitive non-destructive technique for the characterization of buried interfaces, and gives microscopic information (at atomic resolution) over a macroscopic length scale (a few microns). Numerical analysis of XRR data has been carried out using computer programs. Depth-graded x-ray photoelectron spectroscopy (XPS) has been used for compositional analysis at interfaces for some of the ML structures, as a technique complementary to XRR. The performance of some of these MLs has been tested in the soft x-ray region, using the Indus-1 synchrotron radiation (SR) source. Prior to studying the MLs, a detailed study of the surfaces and interfaces of thin films, bi-layers, and tri-layers was carried out using XRR and the glancing incidence fluorescence technique. The discontinuous-to-continuous transition and the mode of film growth, which are vital to the optimization of layer thickness (basically for the high-atomic number or high-Z layer) in the ML structures, were also investigated using in situ sheet resistance measurement method. Indus-1 is a soft x-ray SR source that covers atomic absorption edges of many low-Z materials. The present work demonstrates the possibilities of characterizing low-Z thin films and multilayers using soft x-ray resonant reflectivity. In one case, we have shown for first time that soft x-ray resonant reflectivity can be employed as a non-destructive technique for the determination of interlayer composition. In a second study using the Indus-1 SR source, we have shown, by observing the effect of the anomalous optical constant on reflectivity pattern when photon energy is tuned across the atomic absorption edge of the constituent low-Z element, that soft x-ray resonant reflectivity is an element-specific technique. This thesis is organized into 7 chapters. A brief summary of individual chapters is presented below. Chapter 1 gives a brief general introduction to x-ray ML optics. This is followed by a discussion of the importance of the soft x-ray region of electromagnetic radiation. The optical properties of x-rays are reviewed and optical constants are calculated for some of the important materials used for x-ray MLs. The refractive index in the x-ray region being less than unity (except absorption edges), the consequent limitation of conventional transmission lenses is discussed. The limitation of glancing angle incidence optics is presented, motivating the need for ML optics, which is discussed along with a theoretically calculated reflectivity profile. The procedure for materials for the MLs for application in different spectral regions is discussed, along with a survey of literature related to the present thesis. The importance of the quality of surfaces and interfaces on the performance of ML structures has been shown through simulations. The applications of soft x-ray MLs are discussed with emphasis on polarization. This is followed by a review of different modes of growth of thin films. Finally, the scope of the present work is highlighted. Chapter 2 provides brief descriptions of the experimental techniques used in the present investigations and of the numerical methods employed for quantitative data analysis. The XRR technique is discussed elaborately because it has been used extensively. Detailed calculations of x-ray reflectivity from single surfaces, thin films and bi-layers are presented, along with simulated values. The effect of critical angle and Brewster’s angle is also discussed. Data analysis methods for computing x-ray reflectivity from multilayer structures, based on dynamical and kinematical models, have been discussed. The effect of roughness on XRR has been discussed based on the recursion formalism of dynamical theory. Simulations of XRR and experimental XRR data fitting are carried out using computer programs. The XRR experimental set up is also outlined. A theoretical background is given for the electrical measurements on thin films. This is followed by a brief overview of x-ray photoelectron spectroscopy (XPS) and interpretation of spectra. Finally, the glancing incidence x-ray fluorescence (GIXRF) technique is outlined. Chapter 3 describes in detail the ultra-high vacuum electron beam evaporation system developed in house especially for the fabrication of thin films and x-ray multilayer optics. At the outset, a brief overview of different deposition techniques commonly used for the fabrication of x-ray optical elements is presented. Design, fabrication, and assembly of different accessories are discussed. The control of thickness and uniformity of the films deposited has been checked through the experiments, whose results are provided. The results obtained for ML test structures are presented to show the capability of system in carrying out fabrication of high quality x-ray ML structures. Finally, the versatility of evaporation system incorporating in situ characterization facilities such as -situ electrical measurements for different substrate temperatures is illustrated. Chapter 4 presents a study of the growth of ultra-thin Mo films at different substrate temperatures using in situ sheet resistance measurements. First, a theoretical background is given on the different stages of island growth and on factors affecting thin film growth, followed by a discussion of the possible electrical conduction phenomena in continuous and discontinuous metal films. The nature of thin film growth and a detailed microscopic picture at different growth stages are derived from a modeling of sheet resistance data obtained in situ. The various conduction mechanisms have been identified in different stages of growth. In the island growth stage, the isotropic and anisotropic growth of Mo islands is identified from the model. In the insulator-metal transition region, experimentally determined values of critical exponent of conductivity agrees well with theoretically predicted values for a two-dimensional (2D) percolating system, revealing that Mo films on float glass substrate is predominantly a 2D structure. The minimum thickness for which Mo films becomes continuous is obtained as 1.8 nm and 2.2 nm for Mo deposited at substrate temperatures 300 K and 100 K, respectively. An amorphous-to- crystalline transition is also observed, and discussed. Chapter 5 covers the detailed study of the surfaces and interfaces studies in three different ML structures viz., Mo/Si, Fe/B4C and Mo/Y, meant for the polarizer application in the wavelength range of 67 Å to 160 Å. Multilayers with varying periodicity, varying number of layer pairs, and different ratios of high-Z layer thickness to the period, were fabricated using the electron beam system. Initially, a brief overview of the design aspects of ML structures is given, along with the theoretically calculated reflectivity at Brewster’s angle from the best material combinations. In Mo/Si MLs, the interlayer formed at the interfaces due to interdiffusion of the two elements is asymmetric in thickness, i.e., Mo-on-Si interlayer is thicker than the Si-on-Mo interlayer. To take account of these interlayers in XRR data fitting, a four layer model is considered. The effect of interlayers on reflectivity pattern was studied using simulations, and differences with respect to roughness are also discussed. The mechanism of formation of asymmetric interlayers is also discussed. The interlayer composition has determined using depth-graded XPS. The results reveal the formation of the MoSi2 composition at both the interfaces. The experimental results agree well with theoretical calculations based on solid-state amorphization reaction, which is a result of large heat of mixing. The effective heat of formation model reveals the formation of MoSi2 as the first phase. The soft x-ray reflectivity performance of the Mo/Si ML structure at Brewster’s angle is tested using Indus-1 synchrotron radiation (SR). Using XRR and GIXFR, a study of the surfaces and interfaces of bilayers of B4C-on-Fe and Fe-on- B4C, and tri-layers of Fe-B4C-Fe was carried out, with a systematic variation of Fe and B4C layer thicknesses. A sharp interface was observed in Fe-on-B4C, whereas a low density (w.r.t. Fe) interlayer is observed at the B4C-on-Fe interface. The interlayer properties fluctuates w.r.t. the bottom Fe layer thickness and is independent of the top B4C layer thickness. The nature of fluctuations has been discussed in detail. A study of the surfaces and interfaces of Fe/B4C MLs is described. Finally, a study of the surfaces and interfaces of bilayers, tri-layers, and MLs of the Mo/Y system is discussed in detail. Chapter 6 describes the application of soft x-ray resonant reflectivity for the characterization of low-Z thin films and interfaces in multilayer structures. Initially, a discussion of the energy dependence of atomic scattering factors and hence of optical constants is provided with simulations, with emphasis on the atomic absorption edge. Then, a brief overview of synchrotron radiation, with particular emphasis on the parameters of the Indus-1 synchrotron source is given. The possibilities of determining the composition of the buried interlayer with sub-nanometer scale sensitivity using soft x-ray resonant reflectivity are discussed. The methodology has been applied to study the Mo/Si interface both by simulations and by experiments on the Indus-1 SR, by tuning the photon energy to the Si L-absorption edge. Finally, direct evidence of elemental specificity of soft x-ray resonant reflectivity through the observation of the effect of anomalous optical constants on the reflectivity pattern is discussed. We demonstrate the method through simulations and experiments on the B4C material in B4C thin films and Fe/ B4C bi-layers, using Indus-1 SR tuned to the boron Kedge. Chapter 7 summarizes the main findings of the present work, and provides an outlook for further investigations in the field.

A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work. / In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben.

Das wesentliche Ziel dieser Doktorarbeit ist es, die Zusammenhänge zwischen der Struktur von kleinen organischen Molekülen, deren Anordnung in der Dünnschicht und der Effizienz organischer Solarzellen zu beleuchten. Die Kombination der komplementären Methoden spektroskopischer Ellipsometrie (VASE) und Röntgenstreuung, vor allem der unter streifendem Einfall (GIXRD), hat sich als sehr effiient für die Strukturuntersuchungen organischer Dünnschichten erwiesen. Zusammen geben sie einen detailreichen Einblick in die intermolekulare Anordnung, die Kristallinität, die molekulare Orientierung, die optischen Konstanten n und k und die Phasenseparation von organischen Schichten. Zusätzlich wird die Topografie der organischen Dünnschicht mit Rasterkraftmikroskopie untersucht. Der erste Fokus liegt auf der Analyse des Dünnschichtwachstums von Zink-Phthalocyanin (ZnPc) Einzelschichten. Für alle untersuchten Schichtdicken (5, 10, 25, 50 nm) und Substrattemperaturen (Tsub=30°C, 60°C, 90°C) zeigt ZnPc ein kristallines Schichtwachstum mit aufrecht stehenden ZnPc Molekülen. Um effiziente organische Solarzellen herzustellen, werden Donor- und Akzeptormoleküle üblicherweise koverdampft. Bei der Mischung von Donor- und Akzeptormolekülen bildet sich eine gewisse Phasenseparation aus, deren Form wesentlich für die Ladungsträgerextraktion entlang der Perkolationpfade ist. Der Ursprung dieser Phasenseparation wird innerhalb dieser Arbeit experimentell für ZnPc:C60 Absorber-Mischschichten untersucht. Um die Ausprägung der Phasenseparation zu variieren, werden verschiedene Tsub (30°C, 100°C, 140°C) und Mischverhältnisse (6:1, 3:1, 2:1, 1:1, 1:2, 1:3, 1:6) bei der Koverdampfung von ZnPc und C60 angewendet. GIXRD Messungen zeigen, dass hier der bevorzugte Kristallisationsprozess von C60 Molekülen die treibende Kraft für eine effiziente Phasenseparation ist. Solarzellen, die ZnPc:C60 Mischschichten mit verbesserter Phasenseparation enthalten (Tsub=140°C, 1:1), zeigen eine verbesserte Ladungsträgerextraktion und somit eine höhere Effizienz von 3,0% im Vergleich zu 2,5% für die entsprechende Referenzsolarzelle (Tsub=30°C, 1:1). Im zweiten Teil der Arbeit wird der Einfluss der Molekülorientierung auf die Dünnschichtabsorption beispielhaft an ZnPc und Diindenoperylen (DIP) untersucht. DIP und ZnPc Moleküle, die auf schwach wechselwirkenden Substraten wie Glas, SiO2, amorphen organischen Transportschichten oder C60 aufgedampft sind, zeigen eine eher stehende Orientierung innerhalb der Dünnschicht in Bezug zur Substratoberfläche. Im Gegensatz dazu führt die Abscheidung auf stark wechselwirkenden Substraten, wie z.B. einer Gold- oder Silberschicht oder 0.5 nm bis 2 nm dünnen PTCDA (3,4,9,10-Perylentetracarbonsäuredianhydrid) Templatschichten laut GIXRD und VASE Messungen dazu, dass sich die ZnPc und DIP Moleküle eher flach liegend orientieren. Dies führt zu einer wesentlich besseren Dünnschichtabsorption da das molekulare Übergangsdipolmoment jeweils innerhalb der Ebene des ZnPc und des DIP Moleküls liegt. Ein Einbetten von Gold- oder Silberzwischenschichten in organischen Solarzellen führt leider zu keinen klaren Abhängigkeiten, da die verbesserte Absorption durch die flach liegenden Moleküle von Mikrokavitäts- und plasmonischen Effekten überlagert wird. Ebenso wenig führte das Einfügen einer PTCDA-Zwischenschicht in organischen Solarzellen zum Erfolg, da hier Transportbarrieren den Effekt der verbesserten Absorption überlagern. Das letzte Kapitel konzentriert sich auf den Einfluss der Molekülstruktur auf das Dünnschichtwachstum am Beispiel von DIP und dessen Derivaten Ph4-DIP und P4-Ph4-DIP, Isoviolanthron und Bis-nFl-NTCDI (N,N-Bis(fluorene-2-yl)-naphthalenetetra-carboxylic Diimid) Derivaten. GIXRD Messungen belegen deutlich, dass die sterischen Behinderungen, hervorgerufen durch die Phenylringe (für Ph4-DIP und P4-Ph4-DIP) und Seitenketten (für Bis-nFl-NTCDI), ein amorphes Schichtwachstum induzieren. Im Vergleich sind die Dünnschichten von DIP und Bis-HFl-NTCDI kristallin. Bezüglich der Molekülorientierung und folglich der Absorption von DIP und dessen Derivaten kann ein starker Einfluss des Schichtwachstums beobachtet werden. In Solarzellen verhindert die Präsenz der Phenylringe eine effiziente Phasenseparation der Mischschichten aus (P4-)Ph4-DIP:C60, was zu einer verschlechterten Ladungsträgerextraktion und damit zu einem reduzierten Füllfaktor (FF) von 52% im Vergleich zu dem entsprechender DIP:C60 Solarzellen mit FF=62% führt Die Untersuchungen an der Bis-nFl-NTICDI Serie zeigen ein ähnliches Ergebnis: Auch hier zeichnen sich die amorphen Schichten aus Bis-nFl-NTCDI Molekülen mit Seitenketten durch schlechtere Transporteigenschaften aus als nanokristalline Bis-HFl-NTCDI Schichten. / The aim of this thesis is to demonstrate correlations between the molecular structure of small organic molecules, their arrangement in thin films, and the solar cell performance. For structure analysis of the organic thin films, the combination of variable angle spectroscopic ellipsometry (VASE) and grazing incidence X-ray diffraction (GIXRD) as complementary methods turned out to be a powerful combination. Using both methods, it is possible to obtain information about the crystallinity, crystallite size, intermolecular arrangement, mean molecular orientation, optical constants n and k, and phase separation within thin films. In addition, the topography of thin films is analyzed by atomic force microscopy. First, the thin film morphology of pristine zinc-phthalocyanine (ZnPc) films deposited at different substrate temperatures (Tsub=30°C, 60°C, 90°C) and for varying film thicknesses (5, 10, 25, 50 nm) is investigated. The ZnPc films grow highly crystalline with an upright standing molecular orientation with respect to the substrate surface for all investigated Tsub and all film thicknesses. In effcient organic solar cells, donor and acceptor molecules are commonly co-deposited to form a blend absorber film. This is usually accompanied by a certain phase separation between donor and acceptor molecules leads to a formation of percolation paths necessary to extract electrons and holes towards the electrodes. For ZnPc:C60 blends the origin of this phase separation process is analyzed by investigating different degrees of phase separation induced by film deposition at different Tsub (30°C, 100°C, 140°C) and for different blend ratios (6:1, ... , 1:6 (vol%)). GIXRD measurements indicate that the preferred crystallization of C60 is the driving force for good phase separation. Solar cells with improved phase separation of ZnPc:C60 blends (Tsub=140°C, 1:1) reveal a better charge carrier extraction and thus enhanced effciencies of 3.0% in comparison to 2.5% for the reference device (Tsub=30°C, 1:1). In the second part, the impact of molecular orientation within the absorber thin films on light harvesting is examined for pristine ZnPc and diindenoperylene (DIP) films. For film deposition on weakly interacting substrates like glass, SiO2, amorphous organic transport films, or C60, the orientation of DIP and ZnPc molecules is found to be upright standing. In contrast, GIXRD and VASE measurements show that films deposited onto strongly interacting substrates like Au and Ag, as well as on thin PTCDA templating layers lead to nearly flat-lying ZnPc and DIP molecules. Since the molecular transition dipole moment is oriented in the plane of the DIP and ZnPc molecules, the light absorption in films with flat-lying molecules is strongly improved. Unfortunately, an implementation of Au or Ag sublayers in organic solar cells does not result in reliable dependencies since the enhanced absorption by an improved molecular orientation is superimposed by different effects like microcavity and plasmonic effects. The implementation of PTCDA interlayers leads to transport barriers making the solar cell data interpretation difficult. In the last part, the influence of molecular structure on thin film growth is studied for DIP and its derivatives Ph4-DIP and P4-Ph4-DIP, isoviolanthrone, and Bis-nFl-NTCDI derivatives. GIXRD measurements reveal that steric hindrance is induced by the addition of side chains (for Bis-nFl-NTCDI) and phenyl rings (for Ph4-DIP and P4-Ph4-DIP) (N,N-Bis(fluorene-2-yl)-naphthalenetetra-carboxylic diimide) leading to an amorphous thin film growth. In contrast, DIP films and Bis-HFl-NTCDI films are found to be crystalline. The mean molecular orientation and hence the absorption is strongly affected by the different growth modes of DIP and its derivatives. In OSC, the presence of the phenyl rings prevents an effcient phase separation for (P4-)Ph4-DIP:C60 blends which causes diminished charge extraction in comparison to the crystalline DIP:C60 blends. For the Bis-nFl-NTCDI series, the transport properties are significantly worse in the amorphous films composed of Bis-nFl-NTCDI derivatives with alkyl chains in comparison to the nanocrystalline films made of the bare Bis-HFl-NTCDI.

System on Chip (SoC) and System in Package (SiP) are two electronic technologies that involve integrating multiple functionalities onto a single platform. When the platform is a single wafer, as in SOC, it requires the ability to deposit various materials that enable the different functions on to an underlying substrate that can host the electronic circuitry. Transition metal oxides which have a wide range of properties are ideal candidates for the functional material. Si wafer on which micro-electronics technology is widely commercialized is the ideal host platform. Integrating oxides with Si, generally in the form of thin films as required by microelectronics technology, is however a challenge. It starts with the fact that the properties of crystalline oxides to be exploited in performing various functions are direction dependent. Thus, thin films of these oxides need to be deposited on Si in certain crystallographic orientations. Even if a suitably oriented Si wafer surface were available, it does not always provide for epitaxial growth a critical requirement for controlling the crystalline orientation of thin films. This is because Si surface is covered by an amorphous oxide of Si (SiOx). Thus, during growth of the functional oxide, an ambience in which the Si itself will not oxidize needs to be provided. In addition, during thin film growth on either Si or SiOx surface stresses are generated from various sources. Stress and its relaxation are also associated with the formation and evolution of defects. Both, stress and defects need to be managed in order to harness their beneficial effects and prevent detrimental ones. Given the requirement of SoC technology and the problem associated, the research work reported in this thesis was hence concerned with the precise controlling the stress and microstructure in oxide thin films deposited on Si substrates. In order to do so a versatile, ultra high vacuum (UHV) thin film with a base pressure of 10-9 Torr was designed and built as part of this study. The chamber is capable of depositing films by both sputtering (RF & DC) and pulsed laser ablation (PLD). The system has been designed to include an optical curvature measurement tool that enabled real-time stress measurement during growth. Doped zirconia, ZrO2, was chosen as the first oxide to be deposited, as it is among the few oxides that is more stable than SiOx. It is hence used as a buffer layer. It is shown in this thesis that a change in the growth rate at nucleation can lead to (100) or (111) textured films. These two are among the most commonly preferred orientation. Following nucleation a change in growth rate does not affect orientation but affects stress. Thus, independent selection of texture and stress is demonstrated in YSZ thin films on Si. A quantitative model based on the adatom motion on the growth surface and the anisotropic growth rates of the two orientations is used to explain these observations. This study was then subsequent extended to the growth on platinized Si another commonly used Si platform.. A knowledge of the stress and microstructure tailoring in cubic zirconia on Si was then extended to look at the effect of stress on electrical properties of zirconia on germanium for high-k dielectric applications. Ge channels are expected to play a key role in next generation n-MOS technology. Development of high-k dielectrics for channel control is hence essential. Interesting stress and property relations were analyzed in ZrO2/Ge. Stress and texture in pulsed laser deposited (PLD) oxides on silicon and SrTiO3 were studied. It is shown in this thesis that stress tuning is critical to achieve the highest possible dielectric constant. The effect of stress on dielectric constant is due to two reasons. The first one is an indirect effect involving the effect of stress on phase stability. The second one is the direct effect involving interatomic distance. By stress control an equivalent oxide thickness (EOT) of 0.8 nm was achieved in sputter deposited ZrO2/Ge films at 5 nm thickness. This is among the best reported till date. Finally, the effect of growth parameters and deposition geometry on the microstructural and stress evolution during deposition of SrTiO3 on Si and BaTiO3 on SrTiO3 by pulsed laser deposition is the same chamber is described.

Inexhaustible solar energy, which provides a clean, economic and green energy, seems to be an alternative solution, for current and future energy demands. Harvesting solar energy presents a challenge in using eco-friendly, earth abundant and inexpensive materials. Although present CdTe and Cu (In, Ga)Se2 (CIGS) technologies, provide light-to-electricity comparable to silicon technology, toxicity of Cd and scarcity of In limits the widespread utilization. Future tera-watt level module capacity would then be feasible by the low-cost technologies. The chalcogenide thin film technology would therefore provide the exceptional utilization in the large-area module monolithic integrations benefitting from the low material consumption owing to the direct band gap. The current thesis presents the results obtained from the quest of other thin film materials and their utilization to an unconventional Cd-free buffer layer. The films suitability for the future applications was assessed through photovoltaics device studies in a comparative manner. Chapter-1 deals with the motivation for the solar energy and the importance of thin film photovoltaics. Alternative materials which are abundantly available would help to reach the future tera watt level production, where the conventional silicon technology alone cannot satisfy the global energy demand. The utilization of non-conventional thin film based solar cells and their working principles were elucidated. The histories of the copper based alternative materials were introduced. Chapter-2 deals with the versatile thin film growth technique that has been designed fabricated and installed further which can handle the growth of the absorber and the top TCO layers with insitu sulphurisation. The methodology of the absorber deposition was discussed in detail. The experimental details for the co-sputtering of CuInAl alloy were presented. A novel selenization method, assisted by the combination of inert gases was developed for the annealing of CuInAl alloyed precursor films. Chapter-3 deals with the presentation of the results obtained on buffer and window layers. Chemical Bath deposition technique was employed for the growth and optimization of the conventional CdS and non-toxic buffer ZnS buffer layers. A) Cadmium sulphide thin films suitable for the utilization of high efficiency solar cells were optimized. Optimization of the buffer involved the effects of cadmium precursors, ammonia concentration and buffer capsule effect. A green route was presented so as to consume the precursors to the maximum extent possible. B) The alternative non-toxic buffer Zinc Sulphide (ZnS) thin films were successfully grown using the above optimized conditions. Moreover the window layer was also optimized for better device partner. Zinc Oxide was used as a n-type partner for the p-type CIS films. The ZnO films were grown by the RF-sputtering from the single cathode exhibited good crystallinity with Zincite structure (hexagonal ZnS, a= 3.249A0 and c= 5.205A0). All the grown films showed high resistivity. Al: ZnO thin films were optimized in two methods 1) by dc co-sputtering from the elemental cathodes, Zinc and Aluminum, 2) dc-sputtering from the single 2% Al-doped ZnO cathode. Low resistivity Al:ZnO thin films were deposited in both the cases. Effect of Aluminum doping into ZnO crystal lattice upon the optical and electrical properties were discussed. Chapter-4 deals with the synthesis of various absorber materials, characterizations and some properties. Briefly the A) Optimization of the CuIn1-xAlxSe2 phase with better adhesion and better crystallinity. Aluminum doping into the crystal lattice of CuInSe2 aided the wide band gap tuning of CIAS thin films. Morphological investigations were carried out for the different set of thin films before and after selenization. Effects of copper and Aluminum concentrations on the lattice parameter of the selenized thin films were addressed. The present chapter deals with the A) electrical properties of CIAS films and its heterojunction partners. Resistivity measurements and effects of Cu/In ratio and the effect of Al doping were described in detail. The CIAS/ZnO heterostructure, CIAS/Al:ZnO heterostructure junction properties as a function of different sun illuminations were discussed. B) The alternative earth abundant, eco-friendly, non-toxic elements Cu2ZnSnS4, absorber thin films synthesis and characterizations. Photo conductive photo measurements showed CZTS a potential candidate for near infra-red photodectection. C) Cu2CoSnS4 (CCTS) nanostructures and quantum dots were synthesized via simple chemical routes. CCTS quantum dots were tuned to exhibit the red edge effect and cold white phosphors. D) Cu3BiS3 nano rods were synthesized and characterized structurally and optically. The transport properties of Cu3BiS3 nanorods were tailored for showing the metallic to semiconducting transitions. Chapter-5 Discusses the A) Efforts made in understanding the CIAS based solar cells through interfaces such as CIAS/ZnO, Mo/CIAS, CIAS/CdS/i-ZnO/Al:ZnO and improving the open circuit voltage VOC upon a rotating substrate, involving the inline and in situ processes, for fabricating the cell/ module were discussed. The device statistics for various set of cells were analyzed. B) Solar cells of CTS absorber with the non-toxic buffer ZnS were fabricated and device properties were analyzed. C) CCTS quantum dots embedded in the polymer matrix were utilized for making the inverted hybrid solar devices in combination of ITO/AZnO bilayered contact replacing the acidic PEDOT: PSS. D) The solar cells made of CCTS hollow spheres by spin coating the absorber in the configuration SLG/Mo/CCTS/CdS/ iZno-AZnO/Ni-Al-Al showed a lower efficiency of 0.02%. Chapter-6 concludes with the summary of present investigations and the scope for future work.

Das wesentliche Ziel dieser Doktorarbeit ist es, die Zusammenhänge zwischen der Struktur von kleinen organischen Molekülen, deren Anordnung in der Dünnschicht und der Effizienz organischer Solarzellen zu beleuchten. Die Kombination der komplementären Methoden spektroskopischer Ellipsometrie (VASE) und Röntgenstreuung, vor allem der unter streifendem Einfall (GIXRD), hat sich als sehr effiient für die Strukturuntersuchungen organischer Dünnschichten erwiesen. Zusammen geben sie einen detailreichen Einblick in die intermolekulare Anordnung, die Kristallinität, die molekulare Orientierung, die optischen Konstanten n und k und die Phasenseparation von organischen Schichten. Zusätzlich wird die Topografie der organischen Dünnschicht mit Rasterkraftmikroskopie untersucht. Der erste Fokus liegt auf der Analyse des Dünnschichtwachstums von Zink-Phthalocyanin (ZnPc) Einzelschichten. Für alle untersuchten Schichtdicken (5, 10, 25, 50 nm) und Substrattemperaturen (Tsub=30°C, 60°C, 90°C) zeigt ZnPc ein kristallines Schichtwachstum mit aufrecht stehenden ZnPc Molekülen. Um effiziente organische Solarzellen herzustellen, werden Donor- und Akzeptormoleküle üblicherweise koverdampft. Bei der Mischung von Donor- und Akzeptormolekülen bildet sich eine gewisse Phasenseparation aus, deren Form wesentlich für die Ladungsträgerextraktion entlang der Perkolationpfade ist. Der Ursprung dieser Phasenseparation wird innerhalb dieser Arbeit experimentell für ZnPc:C60 Absorber-Mischschichten untersucht. Um die Ausprägung der Phasenseparation zu variieren, werden verschiedene Tsub (30°C, 100°C, 140°C) und Mischverhältnisse (6:1, 3:1, 2:1, 1:1, 1:2, 1:3, 1:6) bei der Koverdampfung von ZnPc und C60 angewendet. GIXRD Messungen zeigen, dass hier der bevorzugte Kristallisationsprozess von C60 Molekülen die treibende Kraft für eine effiziente Phasenseparation ist. Solarzellen, die ZnPc:C60 Mischschichten mit verbesserter Phasenseparation enthalten (Tsub=140°C, 1:1), zeigen eine verbesserte Ladungsträgerextraktion und somit eine höhere Effizienz von 3,0% im Vergleich zu 2,5% für die entsprechende Referenzsolarzelle (Tsub=30°C, 1:1). Im zweiten Teil der Arbeit wird der Einfluss der Molekülorientierung auf die Dünnschichtabsorption beispielhaft an ZnPc und Diindenoperylen (DIP) untersucht. DIP und ZnPc Moleküle, die auf schwach wechselwirkenden Substraten wie Glas, SiO2, amorphen organischen Transportschichten oder C60 aufgedampft sind, zeigen eine eher stehende Orientierung innerhalb der Dünnschicht in Bezug zur Substratoberfläche. Im Gegensatz dazu führt die Abscheidung auf stark wechselwirkenden Substraten, wie z.B. einer Gold- oder Silberschicht oder 0.5 nm bis 2 nm dünnen PTCDA (3,4,9,10-Perylentetracarbonsäuredianhydrid) Templatschichten laut GIXRD und VASE Messungen dazu, dass sich die ZnPc und DIP Moleküle eher flach liegend orientieren. Dies führt zu einer wesentlich besseren Dünnschichtabsorption da das molekulare Übergangsdipolmoment jeweils innerhalb der Ebene des ZnPc und des DIP Moleküls liegt. Ein Einbetten von Gold- oder Silberzwischenschichten in organischen Solarzellen führt leider zu keinen klaren Abhängigkeiten, da die verbesserte Absorption durch die flach liegenden Moleküle von Mikrokavitäts- und plasmonischen Effekten überlagert wird. Ebenso wenig führte das Einfügen einer PTCDA-Zwischenschicht in organischen Solarzellen zum Erfolg, da hier Transportbarrieren den Effekt der verbesserten Absorption überlagern. Das letzte Kapitel konzentriert sich auf den Einfluss der Molekülstruktur auf das Dünnschichtwachstum am Beispiel von DIP und dessen Derivaten Ph4-DIP und P4-Ph4-DIP, Isoviolanthron und Bis-nFl-NTCDI (N,N-Bis(fluorene-2-yl)-naphthalenetetra-carboxylic Diimid) Derivaten. GIXRD Messungen belegen deutlich, dass die sterischen Behinderungen, hervorgerufen durch die Phenylringe (für Ph4-DIP und P4-Ph4-DIP) und Seitenketten (für Bis-nFl-NTCDI), ein amorphes Schichtwachstum induzieren. Im Vergleich sind die Dünnschichten von DIP und Bis-HFl-NTCDI kristallin. Bezüglich der Molekülorientierung und folglich der Absorption von DIP und dessen Derivaten kann ein starker Einfluss des Schichtwachstums beobachtet werden. In Solarzellen verhindert die Präsenz der Phenylringe eine effiziente Phasenseparation der Mischschichten aus (P4-)Ph4-DIP:C60, was zu einer verschlechterten Ladungsträgerextraktion und damit zu einem reduzierten Füllfaktor (FF) von 52% im Vergleich zu dem entsprechender DIP:C60 Solarzellen mit FF=62% führt Die Untersuchungen an der Bis-nFl-NTICDI Serie zeigen ein ähnliches Ergebnis: Auch hier zeichnen sich die amorphen Schichten aus Bis-nFl-NTCDI Molekülen mit Seitenketten durch schlechtere Transporteigenschaften aus als nanokristalline Bis-HFl-NTCDI Schichten. / The aim of this thesis is to demonstrate correlations between the molecular structure of small organic molecules, their arrangement in thin films, and the solar cell performance. For structure analysis of the organic thin films, the combination of variable angle spectroscopic ellipsometry (VASE) and grazing incidence X-ray diffraction (GIXRD) as complementary methods turned out to be a powerful combination. Using both methods, it is possible to obtain information about the crystallinity, crystallite size, intermolecular arrangement, mean molecular orientation, optical constants n and k, and phase separation within thin films. In addition, the topography of thin films is analyzed by atomic force microscopy. First, the thin film morphology of pristine zinc-phthalocyanine (ZnPc) films deposited at different substrate temperatures (Tsub=30°C, 60°C, 90°C) and for varying film thicknesses (5, 10, 25, 50 nm) is investigated. The ZnPc films grow highly crystalline with an upright standing molecular orientation with respect to the substrate surface for all investigated Tsub and all film thicknesses. In effcient organic solar cells, donor and acceptor molecules are commonly co-deposited to form a blend absorber film. This is usually accompanied by a certain phase separation between donor and acceptor molecules leads to a formation of percolation paths necessary to extract electrons and holes towards the electrodes. For ZnPc:C60 blends the origin of this phase separation process is analyzed by investigating different degrees of phase separation induced by film deposition at different Tsub (30°C, 100°C, 140°C) and for different blend ratios (6:1, ... , 1:6 (vol%)). GIXRD measurements indicate that the preferred crystallization of C60 is the driving force for good phase separation. Solar cells with improved phase separation of ZnPc:C60 blends (Tsub=140°C, 1:1) reveal a better charge carrier extraction and thus enhanced effciencies of 3.0% in comparison to 2.5% for the reference device (Tsub=30°C, 1:1). In the second part, the impact of molecular orientation within the absorber thin films on light harvesting is examined for pristine ZnPc and diindenoperylene (DIP) films. For film deposition on weakly interacting substrates like glass, SiO2, amorphous organic transport films, or C60, the orientation of DIP and ZnPc molecules is found to be upright standing. In contrast, GIXRD and VASE measurements show that films deposited onto strongly interacting substrates like Au and Ag, as well as on thin PTCDA templating layers lead to nearly flat-lying ZnPc and DIP molecules. Since the molecular transition dipole moment is oriented in the plane of the DIP and ZnPc molecules, the light absorption in films with flat-lying molecules is strongly improved. Unfortunately, an implementation of Au or Ag sublayers in organic solar cells does not result in reliable dependencies since the enhanced absorption by an improved molecular orientation is superimposed by different effects like microcavity and plasmonic effects. The implementation of PTCDA interlayers leads to transport barriers making the solar cell data interpretation difficult. In the last part, the influence of molecular structure on thin film growth is studied for DIP and its derivatives Ph4-DIP and P4-Ph4-DIP, isoviolanthrone, and Bis-nFl-NTCDI derivatives. GIXRD measurements reveal that steric hindrance is induced by the addition of side chains (for Bis-nFl-NTCDI) and phenyl rings (for Ph4-DIP and P4-Ph4-DIP) (N,N-Bis(fluorene-2-yl)-naphthalenetetra-carboxylic diimide) leading to an amorphous thin film growth. In contrast, DIP films and Bis-HFl-NTCDI films are found to be crystalline. The mean molecular orientation and hence the absorption is strongly affected by the different growth modes of DIP and its derivatives. In OSC, the presence of the phenyl rings prevents an effcient phase separation for (P4-)Ph4-DIP:C60 blends which causes diminished charge extraction in comparison to the crystalline DIP:C60 blends. For the Bis-nFl-NTCDI series, the transport properties are significantly worse in the amorphous films composed of Bis-nFl-NTCDI derivatives with alkyl chains in comparison to the nanocrystalline films made of the bare Bis-HFl-NTCDI.

A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work. / In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben.

No description available.