In this work we provide several improvements in the study of phase transitions of interacting particle systems: - We determine a quantitative relation between non-extremality of the limiting Gibbs measure of a tree-based spin system, and the temporal mixing of the Glauber Dynamics over its finite projections. We define the concept of 'sensitivity' of a reconstruction scheme to establish such a relation. In particular, we focus on the independent sets model, determining a phase transition for the mixing time of the Glauber dynamics at the same location of the extremality threshold of the simple invariant Gibbs version of the model. - We develop the technical analysis of the so-called spatial mixing conditions for interacting particle systems to account for the connectivity structure of the underlying graph. This analysis leads to improvements regarding the location of the uniqueness/non-uniqueness phase transition for the independent sets model over amenable graphs; among them, the elusive hard-square model in lattice statistics, which has received attention since Baxter's solution of the analogous hard-hexagon in 1980. - We build on the work of Montanari and Gerschenfeld to determine the existence of correlations for the coloring model in sparse random graphs. In particular, we prove that correlations exist above the 'clustering' threshold of such a model; thus providing further evidence for the conjectural algorithmic 'hardness' occurring at such a point.

In this work, atomic scale investigation of pressure-induced transformations in the solid state have been carried out. A series of compounds including GaN, ZnO, CaF2, and AgI, in addition to elemental phosphorus have been studied. The corresponding transition mechanisms have been elucidated with a clear description of atomic displacements and intermediate structures involved therein. In the first group of compounds, the long standing debate on the transition path of the wurtzite(WZ)-to-rocksalt(RS) transition in semiconductors, GaN and ZnO was resolved using geometrical modeling combined with molecular dynamics (MD) simulations conducted in the frame of transition path sampling (TPS) method. In GaN, a two-step mechanism through a metastable intermediate phase with a tetragonal structure iT has been revealed from simulations. In ZnO, the tetragonal intermediate structure was kinetically less stable, although still part of the real transition mechanism. It appeared at the interface between WZ and RS as consequence of a layers shearing. The transition regime in ZnO was characterized by a competition between iT structure and another hexagonal intermediate with hexagonal symmetry iH. Although possible, the latter is not functional for the transition. In both cases, GaN and ZnO, two points of agreement with experiments have been revealed. The tilting of structures after transition, and the phonon mode softening associated with atomic displacements leading to the tetragonal structure iT In the second group of compounds, the investigation of transitions in superionic conductors, CaF2 and AgI, demonstrated a different and particular behavior of atomic motion under pressure. The solid-solid reconstruction of CaF2 structure was shown to be initiated and precedented by high disorder of the anionic sublattice. The percolation of fluoride ions through voids in the fluorite structure created a thin interface of liquid like state. The sparce regions caused by the departure of anions facilitates the cation sublattice reconstruction. In AgI, ion diffusion during the wurtzite/zincnlende(ZB)$rocksalt transition was more pronounced due to the extended stacking disorder WZ/ZB. The Ag+ ions profited not only from the structure of the interface but used the combination of interstitial voids offered by both phases, WZ and ZB, to achieve long diffusion paths and cause the cation sublattice to melt. Clearly, a proper account for such phenomena cannot be provided by geometry-designed mechanisms based on symmetry arguments. In phosphorus, the question of how the stereochemically active lone pairs are reorganized during the orthorhombic (PI) to trigonal (PV) structural transition was answered by means of simulations. Computation was performed at different levels theory. First, the mechanism of the transition was obtained from TPS MD simulations. MD runs were performed within density functional tight binding method (DFTB). The analysis of atomic displacements along the real transformation path indicated a fast bond switching mechanism. In a second step, the nature of the interplay between orbitals of phosphorus during the bond switching was investigated. A simultaneous deformation of lone pair and P−P bond showed a mutual switching of roles during the transformation. This interplay caused a low dimensional polymerization of phosphorus under pressure. The corresponding structure formed as zigzag linear chain of fourfold coordinated phosphorus atoms (· · ·(P(P2))n · · ·) at the interface between PI and PV phases. A further result of this work was the development of a simulation strategy to incorporate defects and chemical doping to structural transformations. On top of the transition path sampling iterations, a Monte Carlo like procedure is added to stepwise substitute atoms in the transforming system. Introducing a chemically different dopant to a pure system represents a perturbation to the energy landscape where the walk between different phases is performed. Therefore, any change in the transition regime reflects the kinetic preference of a given structural motif at times of phase formation. This method was applied to the elucidation of WZ-RS transition mechanism in the series of semiconducting compounds AlN, GaN, and InN. Simulations showed that In atoms adopt the same transformation mechanism as in GaN and favor it, while Al atoms demonstrated a significant reluctance to the path going through tetragonal intermediate iT. The difference between transition regime in mixed systems InxGa1−xN and AlxGa1−xN is in agreement with experiments on high pressure behavior of AlN, GaN, and InN. While transitions in GaN and InN are reversible down to ambient conditions, AlN is stable. The work presented in this thesis constitutes the seed of new perspectives in the understanding of pressure-induced phase transformations in the solid state, where the physics and the chemistry are brought together by means of computer simulations.

The relentless commercial drive for smaller, faster, and cheaper semi-conductor devices has pushed the existing patterning technologies to their limits. Photolithography, one of the crucial processes that determine the feature size in a microchip, is currently facing this challenge. The immaturity of next generation lithography (NGL) technology, particularly EUV, forces the semiconductor industry to explore new processing technologies that can extend the use of the existing lithographic method (i.e. ArF lithography) to enable production beyond the 32 nm node. Two new resolution enhancement techniques, double exposure lithography (DEL) and pitch division lithography (PDL), were proposed that could extend the resolution capability of the current lithography tools. This thesis describes the material and process development for these two techniques. DEL technique requires two exposure passes in a single lithographic cycle. The first exposure is performed with a mask that has a relaxed pitch, and the mask is then shifted by half pitch and re-used for the second exposure. The resolution of the resulting pattern on the wafer is doubled with respect to the features on the mask. This technique can be enabled with a type of material that functions as optical threshold layer (OTL). The key requirements for materials to be useful for OTL are a photoinduced isothermal phase transition and permeance modulation with reverse capabilities. A number of materials were designed and tested based on long alkyl side chain crystalline polymers that bear azobenzene pendant groups on the main chain. The target copolymers were synthesized and fully characterized. A proof-of-concept for the OTL design was successfully demonstrated with a series of customized analytical techniques. PDL technique doubles the line density of a grating mask with only a single exposure and is fully compatible with current lithography tools. Thus, this technique is capable of extending the resolution limit of the current ArF lithography without increasing the cost-of-ownership. Pitch division with a single exposure is accomplished by a dual-tone photoresist. This thesis presents a novel method to enable a dual-tone behavior by addition of a photobase generator (PBG) into a conventional resist formulation. The PBG was optimized to function as an exposure-dependent base quencher, which mainly neutralizes the acid generated in high dose regions but has only a minor influence in low dose regions. The resulting acid concentration profile is a parabola-like function of exposure dose, and only the medium exposure dose produces a sufficient amount of acid to switch the resist solubility. This acid response is exploited to produce pitch division patterns by creating a set of negative-tone lines in the overexposed regions in addition to the conventional positive-tone lines. A number of PBGs were synthesized and characterized, and their decomposition rate constants were studied using various techniques. Simulations were carried out to assess the feasibility of pitch division lithography. It was concluded that pitch division lithography is advantageous when the process aggressiveness factor k₁ is below 0.27. Finally, lithography evaluations of these dual-tone resists demonstrated a proof-of-concept for pitch division lithography with 45 nm pitch divided line and space patterns for a k₁ of 0.13. / text

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This work makes significant contributions in the field of sufficient schedulability tests for rate-monotonic scheduling (RMS) and their application to partitioned RMS. Goal is the maximization of possible utilization in worst or average case under a given number of processors. This scenario is more realistic than the dual case of minimizing the number of necessary processors for a given task set since the hardware is normally fixed. Sufficient schedulability tests are useful for quick estimates of task set schedulability in automatic system-synthesis tools and in online scheduling where exact schedulability tests are too slow. Especially, the approach of Accelerated Simply Periodic Task Sets (ASPTSs) and the concept of circular period similarity are cornerstones of improvements in the success ratio of such schedulability tests. To the best of the author's knowledge, this is the first application of circular statistics in real-time scheduling. Finally, the thesis discusses the use of sharp total utilization thresholds for partitioned EDF. A constant-time admission control is enabled with a controlled residual risk. / Diese Arbeit liefert entscheidende Beiträge im Bereich der hinreichenden Planbarkeitstests für ratenmonotones Scheduling (RMS) und deren Anwendung auf partitioniertes RMS. Ziel ist die Maximierung der möglichen Last im Worst Case und im Average Case bei einer gegebenen Zahl von Prozessoren. Dieses Szenario ist realistischer als der duale Fall der Minimierung der Anzahl der notwendigen Prozessoren für eine gegebene Taskmenge, da die Hardware normalerweise fixiert ist. Hinreichende Planbarkeitstests sind für schnelle Schätzungen der Planbarkeit von Taskmengen in automatischen Werkzeugen zur Systemsynthese und im Online-Scheduling sinnvoll, wo exakte Einplanungstests zu langsam sind. Insbesondere der Ansatz der beschleunigten einfach-periodischen Taskmengen und das Konzept der zirkulären Periodenähnlichkeit sind Eckpfeiler für Verbesserungen in der Erfolgsrate solcher Einplanungstests. Nach bestem Wissen ist das die erste Anwendung zirkulärer Statistik im Echtzeit-Scheduling. Schließlich diskutiert die Arbeit plötzliche Phasenübergänge der Gesamtlast für partitioniertes EDF. Eine Zugangskontrolle konstanter Zeitkomplexität mit einem kontrollierten Restrisiko wird ermöglicht.

Nous avons investigué, via les simulations de Monte Carlo, les propriétés non-perturbatives du modèle de Higgs abélien en 2+1 dimensions sans et avec le terme de Chern-Simons dans la phase de symétrie brisée, en termes de ses excitations topologiques: vortex et anti-vortex. Le but du présent travail est de rechercher les phases possibles du système dans ce secteur et d'étudier l'effet du terme de Chern-Simons sur le potentiel de confinement induit par les charges externes trouvé par Samuel. Nous avons formulé une description sur réseau du modèle effectif en utilisant une tesselation tétraédrique de l'espace tridimensionnel Euclidien pour générer des boucles de vortex fermées. En présence du terme de Chern-Simons, dans une configuration donnée, nous avons formulé et calculé le nombre d'enlacement entre les différentes boucles de vortex fermées. Nous avons analysé les propriétés du vide et calculé les valeurs moyennes de la boucle de Wilson, de la boucle de Polyakov à différentes températures et de la boucle de 't Hooft en présence du terme de Chern-Simons. En absence du terme de Chern-Simons, en variant la masse des boucles de vortex, nous avons trouvé deux phases distinctes dans le secteur de la symétrie brisée, la phase de Higgs habituelle et une autre phase caractérisée par l'apparition de boucles infinies. D'autre part, nous avons trouvé que la force entre les charges externes est écrantée correpondant à la loi périmètre pour la boucle de Wilson impliquant qu'il n'y a pas de confinement. Cependant, après la transition, nous avons trouvé qu'il existe toujours une portion de charges externes écrantée, mais qu'après une charge critique, l'énergie libre diverge. En présence du terme de Chern-Simons, et dans la limite de constante de couplage faible de Chern-Simons nous avons trouvé que les comportements de la boucle de Wilson et de la boucle de 't Hooft ne changent pas correspondants à une loi périmètre, impliquant qu'il n'y a pas de confinement. De plus, le terme de Chern-Simons ne contribue pas à la boucle de Wilson. / We investigate, via Monte Carlo simulations, non-perturbative properties of a 2+1 dimensional Abelian Higgs model without and with the Chern-Simons term in the symmetry broken phase in terms of its topological excitations: vortices and anti-vortices. The aim of the present work is to understand what phases exist for the system in that sector and the effect of the Chern-Simons term on the confining potential induced between external charges found by Samuel. We formulate a lattice description of the effective model starting from a tetrahedral tessellation of Euclidean three space to generate non-intersecting closed vortex loops. In the presence of the Chern-Simons term, for a given configuration, we formulate and compute the linking number between different closed vortex loops. We analyse properties of the vacuum and compute the expectation value of Wilson loop operator, Polyakov loop operator at different temperatures and the 't Hooft loop operator in the presence of the Chern-Simons term. In the absence of a Chern-Simons term, as we vary the mass of the vortex loops, we find two distinct phases in the symmetry broken sector, the usual Higgs phase and a novel phase which is heralded by the appearance of the so-called infinite loops. On the other hand, we find that the force between all external charges is screened, corresponding to a perimeter law for the Wilson loop implying no confinement. However, after the transition, we find that small external charges are still screened, but after a critical value of the external charge, free energy diverges. In the presence of Chern-Simons term, and in the limit where the coupling constant is low for Chern-Simons we find that the behavior of Wilson loop does not change: it is still a perimeter law, implying no confinement. Moreover, the Chern-Simons term does not contribute to the Wilson loop. 'tHooft loop behaves like a perimeter law too.

Le mécanisme menant à des déformations structurales suivant le bombardement d'échantillons de a-Si d'un faisceau d'ions lourds et rapides est sujet de controverses. Nous nous sommes penchés sur l'hypothèse de la formation d'une zone liquide causée par la déposition d'énergie des ions incidents dans le contexte de la théorie du pic thermique. Des échantillons de silicium amorphe furent préparés dans le but d'observer les indices d'une transition de phase l-Si/a-Si suivant la déposition locale d'énergie sur le parcours d'un ion lourd énergétique dans le a-Si. Les échantillons furent implantés d'impuretés de Cu ou d'Ag avant d'être exposés à un faisceau d'ions Ag12+ de 70 MeV. L'utilisation de l'analyse GISAXS est projetée afin d'observer une concentration locale d'impuretés suivant leur ségrégation sur la trace de l'ion. Des masques d'implantation nanométriques d'oxide d'aluminium ont été fabriqués afin d'augmenter la sensibilité de l'analyse GISAXS et une méthode d'alignement de ces masques selon la direction du faisceau fut développée. Le bombardement d'échantillons au travers de ces masques a donné lieu à un réseau de sites d'impacts isolés presque équidistants. / The machanisms underlying structural deformations following swift heavy ion beam a-Si irradiation are subject of debate. We investigated the hypothesis of the presence of a liquid phase in the wake of the energetic ions in the thermal spike framework. a-Si samples were prepared in order to track a transient liquid phase by implanting Cu or Ag on the a-Si surface and exposing the sample to a 70 MeV Ag12+ beam. Cu and Ag are both very sensitive to segregation in Si and are therefore thought to be capable of keeping track of a molten transient state by concentrating on the ion track. Samples are to be investigated with GISAXS. Nanoscale implantation masks were developed from nanoporous alumina membranes in order to impose a pattern on the ion impact sites and thus improve GISAXS sensitivitity. An alignment method is also developed for the positioning of pores parallel to the ion beam direction. A nearly equidistant impact sites pattern was achieved by irradiating fused silica through these implantation masks.