A terapia com prótons está presente em 16 países e até 2015 tratou mais de 130 mil pacientes. No entanto, no Brasil essa terapia ainda não está presente por diversos motivos, sendo o principal o alto custo. Antes de realizar tratamentos, é necessário fazer alguns testes para verificação da entrega de energia dos feixes de prótons. Como as medidas de microdosimetria são muito caras, a principal alternativa é a realização de simulações em programas computacionais, como o GEANT4 e SRIM. O GEANT4 é um programa que permite simular geometrias complexas, enquanto que o SRIM realiza simulações mais simples e ambas trabalham com o método de Monte Carlo. Neste trabalho foram utilizadas estas duas ferramentas para realizar simulações de feixes de prótons em fantomas com três diferentes composições (água, água e tecido ósseo, tecido ósseo e cerebral). Para realizar a análise da entrega de energia dos feixes de prótons ao longo destes fantomas, tornou-se necessário criar um programa denominada “Programa de Processamento de Dados em Próton Terapia Simulada”, que proporcionou criar matrizes, além dos cálculos dos picos de Bragg para avaliação da interação. Além disso, foi analisada a homogeneidade da interação de um feixe de prótons em um detector, em que foi verificado que as simulações em GEANT4 são homogêneas, não tendo uma tendência do feixe em se localizar em uma determinada região, assim como as energias depositadas são iguais nas regiões do fantoma. Também foram avaliados os valores do alcance de profundidade dos picos de Bragg em fantomas cilíndricos com três diferentes densidades: 1,03 g/cm³, 1,53 g/cm³ e 2,03 g/cm³, sendo a primeira, a densidade fornecida pelo GEANT4 para tecido cerebral. Foi verificado que as distâncias do alcance de profundidade dos picos de Bragg são iguais nestas três diferentes densidades. / Proton therapy is present in 16 countries and by 2015 has treated more than 130,000 Patients. However, in Brazil this therapy is not yet present for several reasons, Being the main the high cost. Before performing treatments, it is necessary to do some tests to verify the energy delivery of the proton bundles. As the Microdosimetry are very expensive, the main alternative is to carry out simulations in Programs such as GEANT4 and SRIM. GEANT4 is a program that Allows you to simulate complex geometries, while SRIM performs more complex simulations. Simple and both work with the Monte Carlo method. On this work were used these twain tools to perform a proton beam simulation in phantom with three different compositions (water, bones and water, brain and bones). To perform the energy delivery analysis of the proton beams along these phantoms, has become necessary create a program denominated “Data Processing Program Proton Therapy Simulated”, which allowed to create matrices, beyond the calculations of the Bragg peaks for interaction evaluation. Besides that, it was analyzing the homogeneity of the integration of a proton beam into a detector, in which it was verified that the simulations on GEANT4 are homogeneous, not having a tendency of the beam in locating in a certain region, just as the energies deposited are equal. The value of the depth range of the Bragg peaks were also evaluated in cylindrical phantoms with three different densities: 1,03 g/cm³, 1,53g/cm³ and 2,03 g/cm³, the first being the density provided by GEANT4 for brain tissue. It has been found that the depth range distances of the Bragg peaks are the same at these three different densities.

A terapia com prótons está presente em 16 países e até 2015 tratou mais de 130 mil pacientes. No entanto, no Brasil essa terapia ainda não está presente por diversos motivos, sendo o principal o alto custo. Antes de realizar tratamentos, é necessário fazer alguns testes para verificação da entrega de energia dos feixes de prótons. Como as medidas de microdosimetria são muito caras, a principal alternativa é a realização de simulações em programas computacionais, como o GEANT4 e SRIM. O GEANT4 é um programa que permite simular geometrias complexas, enquanto que o SRIM realiza simulações mais simples e ambas trabalham com o método de Monte Carlo. Neste trabalho foram utilizadas estas duas ferramentas para realizar simulações de feixes de prótons em fantomas com três diferentes composições (água, água e tecido ósseo, tecido ósseo e cerebral). Para realizar a análise da entrega de energia dos feixes de prótons ao longo destes fantomas, tornou-se necessário criar um programa denominada “Programa de Processamento de Dados em Próton Terapia Simulada”, que proporcionou criar matrizes, além dos cálculos dos picos de Bragg para avaliação da interação. Além disso, foi analisada a homogeneidade da interação de um feixe de prótons em um detector, em que foi verificado que as simulações em GEANT4 são homogêneas, não tendo uma tendência do feixe em se localizar em uma determinada região, assim como as energias depositadas são iguais nas regiões do fantoma. Também foram avaliados os valores do alcance de profundidade dos picos de Bragg em fantomas cilíndricos com três diferentes densidades: 1,03 g/cm³, 1,53 g/cm³ e 2,03 g/cm³, sendo a primeira, a densidade fornecida pelo GEANT4 para tecido cerebral. Foi verificado que as distâncias do alcance de profundidade dos picos de Bragg são iguais nestas três diferentes densidades. / Proton therapy is present in 16 countries and by 2015 has treated more than 130,000 Patients. However, in Brazil this therapy is not yet present for several reasons, Being the main the high cost. Before performing treatments, it is necessary to do some tests to verify the energy delivery of the proton bundles. As the Microdosimetry are very expensive, the main alternative is to carry out simulations in Programs such as GEANT4 and SRIM. GEANT4 is a program that Allows you to simulate complex geometries, while SRIM performs more complex simulations. Simple and both work with the Monte Carlo method. On this work were used these twain tools to perform a proton beam simulation in phantom with three different compositions (water, bones and water, brain and bones). To perform the energy delivery analysis of the proton beams along these phantoms, has become necessary create a program denominated “Data Processing Program Proton Therapy Simulated”, which allowed to create matrices, beyond the calculations of the Bragg peaks for interaction evaluation. Besides that, it was analyzing the homogeneity of the integration of a proton beam into a detector, in which it was verified that the simulations on GEANT4 are homogeneous, not having a tendency of the beam in locating in a certain region, just as the energies deposited are equal. The value of the depth range of the Bragg peaks were also evaluated in cylindrical phantoms with three different densities: 1,03 g/cm³, 1,53g/cm³ and 2,03 g/cm³, the first being the density provided by GEANT4 for brain tissue. It has been found that the depth range distances of the Bragg peaks are the same at these three different densities.

The work is concerning forms of persecution to members of Seventh-Day Adventist Church in communist Czechoslovakia. Theoretical part describes possible forms of persecution from communist party to this Church and its members. Research part contains testimonies of interviews with addressed respondents with the author, including their experiences of such a persecution in that time. Most respondents were imprisoned during their military service, part of them lost the decree for chaplain work at certain region. Two respondents also experienced persecution in special military units.

Cette thèse est composée de deux parties indépendantes : la première partie traite des équations différentielles stochastiques dans le cadre de la G-espérance, tandis que la deuxième partie présente les résultats obtenus pour les équations différentielles stochastiques du seconde ordre. Dans un premier temps, on considère les intégrales stochastiques par rapport à un processus croissant, et on donne une extension de la formule d'Itô dans le cadre de la G-espérance. Ensuite, on étudie une classe d'équations différentielles stochastiques réfléchies unidimensionnelles dirigées par un G-mouvement brownien. Dans la suite, en utilisant une méthode de localisation, on prouve l'existence et l'unicité de solutions pour les équations différentielles stochastiques dirigées par un G-mouvement brownien, dont les coefficients sont localement lipschitziens. Enfin, dans le même cadre, on discute des problèmes de réflexion multidimensionnelle et on fournit quelques résultats de convergence. Dans un deuxième temps, on étudie une classe d'équations différentielles stochastiques rétrogrades du seconde ordre à croissance quadratique. Le but de ce travail est de généraliser le résultat obtenu par Possamaï et Zhou en 2012. On montre aussi l'existence et l'unicité des solutions pour ces équations, mais sous des hypothèses plus faibles. De plus, ce résultat théorique est appliqué aux problèmes de maximisation robuste de l'utilité du portefeuille en finance. / This thesis consists of two relatively independent parts : the first part concerns stochastic differential equations in the framework of the G-expectation, while the second part deals with a class of second order backward stochastic differential equations. In the first part, we first consider stochastic integrals with respect to an increasing process and give an extension of Itô's formula in the G-framework. Then, we study a class of scalar valued reflected stochastic differential equations driven by G-Brownian motion. Subsequently, we prove the existence and the uniqueness of solutions for some locally Lipschitz stochastic differential equations driven by G-Brownian motion. At the end of this part, we consider multidimensional reflected problems in the G-framework, and some convergence results are obtained. In the second part, we study the wellposedness of a class of second order backward stochastic differential equations (2BSDEs) under a quadratic growth condition on their coefficients. The aim of this part is to generalize a wellposedness result for quadratic 2BSDEs by Possamaï and Zhou in 2012. In this thesis, we work under some usual assumptions and deduce the existence and uniqueness theorem as well. Moreover, this theoretical result for quadratic 2BSDEs is applied to solve some robust utility maximization problems in finance.

L'utilisation de protons dans le traitement du cancer est largement reconnue grâce au parcours fini des protons dans la matière. Pour la planification du traitement par protons, l'incertitude dans la détermination de la longueur du parcours des protons provient principalement de l'inexactitude dans la conversion des unités Hounsfield (obtenues à partir de tomographie rayons X) en pouvoir d'arrêt des protons. La tomographie proton (pCT) est une solution attrayante car cette modalité reconstruit directement la carte du pouvoir d'arrêt relatif à l'eau (RSP) de l'objet. La technique pCT classique est basée sur la mesure de la perte d'énergie des protons pour reconstruire la carte du RSP de l'objet. En plus de la perte d'énergie, les protons subissent également des diffusions coulombiennes multiples et des interactions nucléaires qui pourraient révéler d'autres propriétés intéressantes des matériaux non visibles avec les cartes de RSP. Ce travail de thèse a consisté à étudier les interactions de protons au travers de simulations Monte Carlo par le logiciel GATE et d'utiliser ces informations pour reconstruire une carte de l'objet par rétroprojection filtrée le long des chemins les plus vraisemblables des protons. Mise à part la méthode pCT conventionnelle par perte d'énergie, deux modalités de pCT ont été étudiées et mises en œuvre. La première est la pCT par atténuation qui est réalisée en utilisant l'atténuation des protons pour reconstruire le coefficient d'atténuation linéique des interactions nucléaires de l'objet. La deuxième modalité pCT est appelée pCT par diffusion qui est effectuée en mesurant la variation angulaire due à la diffusion coulombienne pour reconstruire la carte de pouvoir de diffusion, liée à la longueur de radiation du matériau. L'exactitude, la précision et la résolution spatiale des images reconstruites à partir des deux modalités de pCT ont été évaluées qualitativement et quantitativement et comparées à la pCT conventionnelle par perte d'énergie. Alors que la pCT par perte d'énergie fournit déjà les informations nécessaires pour calculer la longueur du parcours des protons pour la planification du traitement, la pCT par atténuation et par diffusion donnent des informations complémentaires sur l'objet. D'une part, les images pCT par diffusion et par atténuation fournissent une information supplémentaire intrinsèque aux matériaux de l'objet. D'autre part, dans certains des cas étudiés, les images pCT par atténuation démontrent une meilleure résolution spatiale dont l'information fournie compléterait celle de la pCT par perte d'énergie. / The use of protons in cancer treatment has been widely recognized thanks to the precise stopping range of protons in matter. In proton therapy treatment planning, the uncertainty in determining the range mainly stems from the inaccuracy in the conversion of the Hounsfield units obtained from x-ray computed tomography to proton stopping power. Proton CT (pCT) has been an attractive solution as this modality directly reconstructs the relative stopping power (RSP) map of the object. The conventional pCT technique is based on measurements of the energy loss of protons to reconstruct the RSP map of the object. In addition to energy loss, protons also undergo multiple Coulomb scattering and nuclear interactions which could reveal other interesting properties of the materials not visible with the RSP maps. This PhD work is to investigate proton interactions through Monte Carlo simulations in GATE and to use this information to reconstruct a map of the object through filtered back-projection along the most likely proton paths. Aside from the conventional energy-loss pCT, two pCT modalities have been investigated and implemented. The first one is called attenuation pCT which is carried out by using the attenuation of protons to reconstruct the linear inelastic nuclear cross-section map of the object. The second pCT modality is called scattering pCT which is performed by utilizing proton scattering by measuring the angular variance to reconstruct the relative scattering power map which is related to the radiation length of the material. The accuracy, precision and spatial resolution of the images reconstructed from the two pCT modalities were evaluated qualitatively and quantitatively and compared with the conventional energy-loss pCT. While energy-loss pCT already provides the information needed to calculate the proton range for treatment planning, attenuation pCT and scattering pCT give complementary information about the object. For one, scattering pCT and attenuation pCT images provide an additional information intrinsic to the materials in the object. Another is that, in some studied cases, attenuation pCT images demonstrate a better spatial resolution and showed features that would supplement energy-loss pCT reconstructions.

This thesis is concerned with several issues of a posteriori error estimates for linear problems. In its first part error estimates for the heat conduction equation discretized by the backward Euler method in time and discontinuous Galerkin method in space are derived. In the second part guaranteed and locally efficient error estimates involving algebraic error for Poisson equation discretized by the discontinuous Galerkin method are derived. The technique is based on the flux reconstruction where meshes with hanging nodes and variable polynomial degree are allowed. An adaptive strategy combining both adaptive mesh refinement and stopping criteria for iterative algebraic solvers is proposed. In the last part a numerical method for computing guaranteed lower and upper bounds of principal eigenvalues of symmetric linear elliptic differential operators is presented. 1

Neste trabalho apresentamos a construção e teste de um sistema experimental que nos permite produzir um fluxo intenso de átomos lentos. Discutimos o desenho e construção do solenóide que compensa o efeito Doppler que surge durante o processo de desaceleração, as câmaras de vácuo, o forno que gera o feixe atômico e o sistema ótico utilizado. Estudamos a técnica de desaceleração de átomos pelo ajuste Zeeman. Uma nova técnica de observação que consiste no acompanhamento da fluorescência do feixe ao longo do caminho de desaceleração é usada, o que nos permite uma observação direta do processo. / This work presents the development and test of an experimental set-up which allows to produce a very strong slow motion atomic beam. We discuss the calculation and construction of the solenoid to compensate the Doppler effect arising during the deceleration process, vacuum chambers, the oven which produces the atomic beam and the optical system used. We have studied the Zeeman-tuned technique to slow an atomic beam of sodium atoms. A new technique to study the deceleration which Consist in monitoring the fluorescence along the deceleration path is used, which allow us a direct observation of the process.

Neste trabalho apresentamos a construção e teste de um sistema experimental que nos permite produzir um fluxo intenso de átomos lentos. Discutimos o desenho e construção do solenóide que compensa o efeito Doppler que surge durante o processo de desaceleração, as câmaras de vácuo, o forno que gera o feixe atômico e o sistema ótico utilizado. Estudamos a técnica de desaceleração de átomos pelo ajuste Zeeman. Uma nova técnica de observação que consiste no acompanhamento da fluorescência do feixe ao longo do caminho de desaceleração é usada, o que nos permite uma observação direta do processo. / This work presents the development and test of an experimental set-up which allows to produce a very strong slow motion atomic beam. We discuss the calculation and construction of the solenoid to compensate the Doppler effect arising during the deceleration process, vacuum chambers, the oven which produces the atomic beam and the optical system used. We have studied the Zeeman-tuned technique to slow an atomic beam of sodium atoms. A new technique to study the deceleration which Consist in monitoring the fluorescence along the deceleration path is used, which allow us a direct observation of the process.

In der vorliegenden Arbeit wird erstmals das QQDS-Magnetspektrometer für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Helmholtz-Zentrum Dresden-Rossendorf umfassend vorgestellt. Zusätzlich werden sowohl alle auf die Analytik Einfluss nehmenden Parameter untersucht als auch Methoden und Modelle vorgestellt, wie deren Einfluss vermieden oder rechnerisch kompensiert werden kann. Die Schwerpunkte dieser Arbeit gliedern sich in fünf Bereiche. Der Erste ist der Aufbau und die Inbetriebnahme des QQDS-Magnetspektrometers, der zugehörige Streukammer mit allen Peripheriegeräten und des eigens für die höchstauflösende elastische Rückstoßanalyse entwickelten Detektors. Sowohl das umgebaute Spektrometer als auch der im Rahmen dieser Arbeit gebaute Detektor wurden speziell an experimentelle Bedingungen für die höchstauflösende Ionenstrahlanalytik leichter Elemente angepasst und erstmalig auf einen routinemäßigen Einsatz hin getestet. Der Detektor besteht aus zwei Komponenten. Zum einen befindet sich am hinteren Ende des Detektors eine Bragg-Ionisationskammer, die zur Teilchenidentifikation genutzt wird. Zum anderen dient ein Proportionalzähler, der eine Hochwiderstandsanode besitzt und direkt hinter dem Eintrittsfenster montiert ist, zur Teilchenpositionsbestimmung im Detektor. Die folgenden zwei Schwerpunkte beinhalten grundlegende Untersuchungen zur Ionen-Festkörper-Wechselwirkung. Durch die Verwendung eines Magnetspektrometers ist die Messung der Ladungszustandsverteilung der herausgestreuten Teilchen direkt nach einem binären Stoß sowohl möglich als auch für die Analyse notwendig. Aus diesem Grund werden zum einen die Ladungszustände gemessen und zum anderen mit existierenden Modellen verglichen. Außerdem wird ein eigens entwickeltes Modell vorgestellt und erstmals im Rahmen dieser Arbeit angewendet, welches den ladungszustandsabhängigen Energieverlust bei der Tiefenprofilierung berücksichtigt. Es wird gezeigt, dass ohne die Anwendung dieses Modells die Tiefenprofile nicht mit den quantitativen Messungen mittels konventioneller Ionenstrahlanalytikmethoden und mit der Dickenmessung mittels Transmissionselektronenmikroskopie übereinstimmen, und damit falsche Werte liefern würden. Der zweite für die Thematik wesentliche Aspekt der Ionen-Festkörper-Wechselwirkung, sind die Probenschäden und -modifikationen, die während einer Schwerionen-bestrahlung auftreten. Dabei wird gezeigt, dass bei den hier verwendeten Energien sowohl elektronisches Sputtern als auch elektronisch verursachtes Grenzflächendurchmischen eintreten. Das elektronische Sputtern kann durch geeignete Strahlparameter für die meisten Proben ausreichend minimiert werden. Dagegen ist der Einfluss der Grenzflächendurchmischung meist signifikant, so dass dieser analysiert und in der Auswertung berücksichtigt werden muss. Schlussfolgernd aus diesen Untersuchungen ergibt sich für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Rossendorfer 5-MV Tandembeschleuniger, dass die geeignetsten Primärionen Chlor mit einer Energie von 20 MeV sind. In Einzelfällen, wie zum Beispiel der Analyse von Bor, muss die Energie jedoch auf 6,5 MeV reduziert werden, um das elektronische Sputtern bei der notwendigen Fluenz unterhalb der Nachweisgrenze zu halten. Der vierte Schwerpunkt ist die Untersuchung von sowohl qualitativen als auch quantitativen Einflüssen bestimmter Probeneigenschaften, wie beispielsweise Oberflächenrauheit, auf die Form des gemessenen Energiespektrums beziehungsweise auf das analysierte Tiefenprofil. Die Kenntnis der Rauheit einer Probe an der Oberfläche und an den Grenzflächen ist für die Analytik unabdingbar. Als Resultat der genannten Betrachtungen werden die Einflüsse von Probeneigenschaften und Ionen-Festkörper-Wechselwirkungen auf die Energie- beziehungsweise Tiefenauflösung des Gesamtsystems beschrieben, berechnet und mit der konventionellen Ionenstrahlanalytik verglichen. Die Möglichkeiten der höchstauflösenden Ionenstrahlanalytik werden zudem mit den von anderen Gruppen veröffentlichten Komplementärmethoden gegenübergestellt. Der fünfte und letzte Schwerpunkt ist die Analytik leichter Elemente in ultradünnen Schichten unter Berücksichtigung aller in dieser Arbeit vorgestellten Modelle, wie die Reduzierung des Einflusses von Strahlschäden oder die Quantifizierung der Elemente im dynamischen Ladungszustandsnichtgleichgewicht. Es wird die Tiefenprofilierung von Mehrschichtsystemen, bestehend aus SiO2-Si3N4Ox-SiO2 auf Silizium, von Ultra-Shallow-Junction Bor-Implantationsprofilen und von ultradünnen Oxidschichten, wie zum Beispiel High-k-Materialien, demonstriert. / In this thesis the QQDS magnetic spectrometer that is used for high resolution ion beam analysis (IBA) of light elements at the Helmholtz-Zentrum Dresden-Rossendorf is presented for the first time. In addition all parameters are investigated that influence the analysis. Methods and models are presented with which the effects can be minimised or calculated. There are five focal points of this thesis. The first point is the construction and commissioning of the QQDS magnetic spectrometer, the corresponding scattering chamber with all the peripherals and the detector, which is specially developed for high resolution elastic recoil detection. Both the reconstructed spectrometer and the detector were adapted to the specific experimental conditions needed for high-resolution Ion beam analysis of light elements and tested for routine practice. The detector consists of two compo-nents. At the back end of the detector a Bragg ionization chamber is mounted, which is used for the particle identification. At the front end, directly behind the entrance window a proportional counter is mounted. This proportional counter includes a high-resistance anode. Thus, the position of the particles is determined in the detector. The following two points concern fundamental studies of ion-solid interaction. By using a magnetic spectrometer the charge state distribution of the particles scattered from the sample after a binary collision is both possible and necessary for the analysis. For this reason the charge states are measured and compared with existing models. In addition, a model is developed that takes into account the charge state dependent energy loss. It is shown that without the application of this model the depth profiles do not correspond with the quantitative measurements by conventional IBA methods and with the thickness obtained by transmission electron microscopy. The second fundamental ion-solid interaction is the damage and the modification of the sample that occurs during heavy ion irradiation. It is shown that the used energies occur both electronic sputtering and electronically induced interface mixing. Electronic sputtering is minimised by using optimised beam parameters. For most samples the effect is below the detection limit for a fluence sufficient for the analysis. However, the influence of interface mixing is so strong that it has to be included in the analysis of the layers of the depth profiles. It is concluded from these studies that at the Rossendorf 5 MV tandem accelerator chlorine ions with an energy of 20 MeV deliver the best results. In some cases, such as the analysis of boron, the energy must be reduced to 6.5 MeV in order to retain the electronic sputtering below the detection limit. The fourth focus is the study of the influence of specific sample properties, such as surface roughness, on the shape of a measured energy spectra and respectively on the analysed depth profile. It is shown that knowledge of the roughness of a sample at the surface and at the interfaces for the analysis is needed. In addition, the contribution parameters limiting the depth resolution are calculated and compared with the conventional ion beam analysis. Finally, a comparison is made between the high-resolution ion beam analysis and complementary methods published by other research groups. The fifth and last focus is the analysis of light elements in ultra thin layers. All models presented in this thesis to reduce the influence of beam damage are taken into account. The dynamic non-equilibrium charge state is also included for the quantification of elements. Depth profiling of multilayer systems is demonstrated for systems consisting of SiO2-Si3N4Ox-SiO2 on silicon, boron implantation profiles for ultra shallow junctions and ultra thin oxide layers, such as used as high-k materials.

In der vorliegenden Arbeit wird erstmals das QQDS-Magnetspektrometer für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Helmholtz-Zentrum Dresden-Rossendorf umfassend vorgestellt. Zusätzlich werden sowohl alle auf die Analytik Einfluss nehmenden Parameter untersucht als auch Methoden und Modelle vorgestellt, wie deren Einfluss vermieden oder rechnerisch kompensiert werden kann. Die Schwerpunkte dieser Arbeit gliedern sich in fünf Bereiche. Der Erste ist der Aufbau und die Inbetriebnahme des QQDS-Magnetspektrometers, der zugehörige Streukammer mit allen Peripheriegeräten und des eigens für die höchstauflösende elastische Rückstoßanalyse entwickelten Detektors. Sowohl das umgebaute Spektrometer als auch der im Rahmen dieser Arbeit gebaute Detektor wurden speziell an experimentelle Bedingungen für die höchstauflösende Ionenstrahlanalytik leichter Elemente angepasst und erstmalig auf einen routinemäßigen Einsatz hin getestet. Der Detektor besteht aus zwei Komponenten. Zum einen befindet sich am hinteren Ende des Detektors eine Bragg-Ionisationskammer, die zur Teilchenidentifikation genutzt wird. Zum anderen dient ein Proportionalzähler, der eine Hochwiderstandsanode besitzt und direkt hinter dem Eintrittsfenster montiert ist, zur Teilchenpositionsbestimmung im Detektor. Die folgenden zwei Schwerpunkte beinhalten grundlegende Untersuchungen zur Ionen-Festkörper-Wechselwirkung. Durch die Verwendung eines Magnetspektrometers ist die Messung der Ladungszustandsverteilung der herausgestreuten Teilchen direkt nach einem binären Stoß sowohl möglich als auch für die Analyse notwendig. Aus diesem Grund werden zum einen die Ladungszustände gemessen und zum anderen mit existierenden Modellen verglichen. Außerdem wird ein eigens entwickeltes Modell vorgestellt und erstmals im Rahmen dieser Arbeit angewendet, welches den ladungszustandsabhängigen Energieverlust bei der Tiefenprofilierung berücksichtigt. Es wird gezeigt, dass ohne die Anwendung dieses Modells die Tiefenprofile nicht mit den quantitativen Messungen mittels konventioneller Ionenstrahlanalytikmethoden und mit der Dickenmessung mittels Transmissionselektronenmikroskopie übereinstimmen, und damit falsche Werte liefern würden. Der zweite für die Thematik wesentliche Aspekt der Ionen-Festkörper-Wechselwirkung, sind die Probenschäden und -modifikationen, die während einer Schwerionen-bestrahlung auftreten. Dabei wird gezeigt, dass bei den hier verwendeten Energien sowohl elektronisches Sputtern als auch elektronisch verursachtes Grenzflächendurchmischen eintreten. Das elektronische Sputtern kann durch geeignete Strahlparameter für die meisten Proben ausreichend minimiert werden. Dagegen ist der Einfluss der Grenzflächendurchmischung meist signifikant, so dass dieser analysiert und in der Auswertung berücksichtigt werden muss. Schlussfolgernd aus diesen Untersuchungen ergibt sich für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Rossendorfer 5-MV Tandembeschleuniger, dass die geeignetsten Primärionen Chlor mit einer Energie von 20 MeV sind. In Einzelfällen, wie zum Beispiel der Analyse von Bor, muss die Energie jedoch auf 6,5 MeV reduziert werden, um das elektronische Sputtern bei der notwendigen Fluenz unterhalb der Nachweisgrenze zu halten. Der vierte Schwerpunkt ist die Untersuchung von sowohl qualitativen als auch quantitativen Einflüssen bestimmter Probeneigenschaften, wie beispielsweise Oberflächenrauheit, auf die Form des gemessenen Energiespektrums beziehungsweise auf das analysierte Tiefenprofil. Die Kenntnis der Rauheit einer Probe an der Oberfläche und an den Grenzflächen ist für die Analytik unabdingbar. Als Resultat der genannten Betrachtungen werden die Einflüsse von Probeneigenschaften und Ionen-Festkörper-Wechselwirkungen auf die Energie- beziehungsweise Tiefenauflösung des Gesamtsystems beschrieben, berechnet und mit der konventionellen Ionenstrahlanalytik verglichen. Die Möglichkeiten der höchstauflösenden Ionenstrahlanalytik werden zudem mit den von anderen Gruppen veröffentlichten Komplementärmethoden gegenübergestellt. Der fünfte und letzte Schwerpunkt ist die Analytik leichter Elemente in ultradünnen Schichten unter Berücksichtigung aller in dieser Arbeit vorgestellten Modelle, wie die Reduzierung des Einflusses von Strahlschäden oder die Quantifizierung der Elemente im dynamischen Ladungszustandsnichtgleichgewicht. Es wird die Tiefenprofilierung von Mehrschichtsystemen, bestehend aus SiO2-Si3N4Ox-SiO2 auf Silizium, von Ultra-Shallow-Junction Bor-Implantationsprofilen und von ultradünnen Oxidschichten, wie zum Beispiel High-k-Materialien, demonstriert. / In this thesis the QQDS magnetic spectrometer that is used for high resolution ion beam analysis (IBA) of light elements at the Helmholtz-Zentrum Dresden-Rossendorf is presented for the first time. In addition all parameters are investigated that influence the analysis. Methods and models are presented with which the effects can be minimised or calculated. There are five focal points of this thesis. The first point is the construction and commissioning of the QQDS magnetic spectrometer, the corresponding scattering chamber with all the peripherals and the detector, which is specially developed for high resolution elastic recoil detection. Both the reconstructed spectrometer and the detector were adapted to the specific experimental conditions needed for high-resolution Ion beam analysis of light elements and tested for routine practice. The detector consists of two compo-nents. At the back end of the detector a Bragg ionization chamber is mounted, which is used for the particle identification. At the front end, directly behind the entrance window a proportional counter is mounted. This proportional counter includes a high-resistance anode. Thus, the position of the particles is determined in the detector. The following two points concern fundamental studies of ion-solid interaction. By using a magnetic spectrometer the charge state distribution of the particles scattered from the sample after a binary collision is both possible and necessary for the analysis. For this reason the charge states are measured and compared with existing models. In addition, a model is developed that takes into account the charge state dependent energy loss. It is shown that without the application of this model the depth profiles do not correspond with the quantitative measurements by conventional IBA methods and with the thickness obtained by transmission electron microscopy. The second fundamental ion-solid interaction is the damage and the modification of the sample that occurs during heavy ion irradiation. It is shown that the used energies occur both electronic sputtering and electronically induced interface mixing. Electronic sputtering is minimised by using optimised beam parameters. For most samples the effect is below the detection limit for a fluence sufficient for the analysis. However, the influence of interface mixing is so strong that it has to be included in the analysis of the layers of the depth profiles. It is concluded from these studies that at the Rossendorf 5 MV tandem accelerator chlorine ions with an energy of 20 MeV deliver the best results. In some cases, such as the analysis of boron, the energy must be reduced to 6.5 MeV in order to retain the electronic sputtering below the detection limit. The fourth focus is the study of the influence of specific sample properties, such as surface roughness, on the shape of a measured energy spectra and respectively on the analysed depth profile. It is shown that knowledge of the roughness of a sample at the surface and at the interfaces for the analysis is needed. In addition, the contribution parameters limiting the depth resolution are calculated and compared with the conventional ion beam analysis. Finally, a comparison is made between the high-resolution ion beam analysis and complementary methods published by other research groups. The fifth and last focus is the analysis of light elements in ultra thin layers. All models presented in this thesis to reduce the influence of beam damage are taken into account. The dynamic non-equilibrium charge state is also included for the quantification of elements. Depth profiling of multilayer systems is demonstrated for systems consisting of SiO2-Si3N4Ox-SiO2 on silicon, boron implantation profiles for ultra shallow junctions and ultra thin oxide layers, such as used as high-k materials.