Multi-dimensional modeling and simulation of semiconductor nanophotonic devices

Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources

On the convexity of the entropy along entropic interpolations

Convexity properties of the entropy along displacement interpolations are crucial in the Lott-Sturm-Villani theory of lower bounded curvature of geodesic measure spaces. As discrete spaces fail to be geodesic, an alternate analogous theory is necessary in the discrete setting. Replacing displacement interpolations by entropic ones allows for developing a rigorous calculus, in contrast with Otto's informal calculus. When the underlying state space is a Riemannian manifold, we show that the first and second derivatives of the entropy as a function of time along entropic interpolations are expressed in terms of the standard Bakry-\'Emery operators $\Gamma$ and $\Gamma_2$. On the other hand, in the discrete setting new operators appear. Our approach is probabilistic; it relies on the Markov property and time reversal. We illustrate these calculations by means of Brownian diffusions on manifolds and random walks on graphs. We also give a new unified proof, covering both the manifold and graph cases, of a logarithmic Sobolev inequality in connection with convergence to equilibrium

Controlled merging and annihilation of localized dissipative structures in an AC-driven damped nonlinear Schrödinger system

We report studies of controlled interactions of localized dissipative structures in a system described by the AC-driven damped nonlinear Schrödinger equation (equivalent to the Lugiato-Lefever model). Extensive numerical simulations reveal a variety of interaction scenarios that are governed by the properties of the system driver, notably its gradients. In our experiments, performed with a nonlinear optical bre (Kerr) resonator, the phase prole of the driver is used to induce interactions of the dissipative structures on demand. We observe both merging and annihilation of localized structures, i.e. interactions governed by the dissipative, out of-equilibrium nature of the system. These interactions fundamentally dier from those typically found for conventional conservative solitons

How good is the generalized Langevin equation to describe the dynamics of photo-induced electron transfer in fluid solution?

The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium. An accurate description of these reactions requires knowing the free energy surface (FES) and the friction felt by the reactants. Most of theories start from the Langevin equation to derive the dynamics, but there are few examples comparing it with experiments. Here we explore the applicability of a Generalized Langevin Equation (GLE) with an arbitrary potential and a non-markovian friction. To this end we have performed broadband fluorescence measurements with sub-picosecond time resolution of a covalently linked organic electron donor-acceptor system in solvents of changing viscosity and dielectric permittivity. In order to establish the FES of the reaction we resort to stationary electronic spectroscopy. On the other hand, the dynamics of a non-reacting substance, Coumarin 153, provide the calibrating tool for the friction over the FES, which is assumed to be solute independent. A simpler and computationally faster approach uses the Generalized Smoluchowski Equation (GSE), which can be derived from the GLE for pure harmonic potentials. Both approaches reproduce the measurements in most of the solvents reasonably well. At long times, some differences arise from the errors inherited from the analysis of the stationary solvatochromism and at short times from the excess excitation energy. However, whenever the dynamics become slow the GSE shows larger deviations than the GLE, the results of which always agree qualitatively with the measured dynamics, regardless of the solvent viscosity or dielectric properties. The here applied method can be used to predict the dynamics of any other reacting system, given the FES parameters and solvent dynamics are provided. Thus no fitting parameters enter the GLE simulations, within the applicability limits found for the model in this work.Comment: 30 pages, 22 figures, 5 tables, 97 reference

Quantum Chemical Investigation of the Interaction of Hydrogen with Solid Surfaces

In dieser Arbeit werden die Wechselwirkungen von Wasserstoff mit festen Materialien und Oberflächen untersucht. Zunächst wird der Kontext unserer Untersuchung durch eine kurze Einordnung in die Geschichte der Naturwissenschaften im Allgemeinen, und der Oberflächenforschung im Speziellen, hergestellt. Anschließend wird der quanten- mechanische Apparat, welcher nötig ist um die betrachteten Systeme zu beschreiben, eingeführt um dann detailliert die Potentialhyperfläche der Entstehung von Wasser durch Adsoprtion von Wasserstoff auf einer teilweise oxidierten Ruthenium(0001) Metalloberfläche zu studieren. Zudem wird das gleiche System betrachtet, wenn die Metalloberfläche zusätzlich von einer biatomaren, kristallinen Lage Siliziumdioxid (SiO2 ) bedeckt ist, wodurch eine räumliche Beengung eintritt. Wir verwenden unsere Ergebnisse zusammen mit experimentellen Beobachtungen und mathematischen Metho- den um ein vollständig theoretisches Modell zu entwerfen und das System grundlegend verstehen zu können. In einem weiteren Schritt werden die chemischen Änderungen der Siliziumdioxid Doppellage untersucht, wenn das System Wasserstoffplasma ausgesetzt wird. Es werden diverse mögliche Defektstrukturen diskutiert und mithilfe experi- menteller Befunde die wahrscheinlichste Struktur isoliert. Im letzten Kapitel werden die typischen Näherungen untersucht, welche notwendig sind um quantenmechanische Methoden mit Hilfe von Computern durchführbar zu machen. Wir verwenden den sogenannten embedded-fragment Ansatz um die Diffusionsbarriere von Wasserstoff auf Aluminiumoxid mit chemischer Genauigkeit zu berechnen. Unsere Ergebnisse auf dem coupled-cluster with singles, doubles and perturbative triples (CCSD(T))- Niveau können sowohl als Referenz für experimentelle Untersuchungen, als auch für andere quantenmechanische Methoden wie z.B. die Dichtefunktionaltheorie, angesehen werden.The present thesis aims at investigating the interactions of hydrogen with solid surfaces and materials. We first offer a brief historical context for surface science, as well as quantum mechanics and science is general, before deriving the mathematical appa- ratus necessary to investigate our systems of interest. We then move on to explore the potential energy surface of the water-formation-reaction on a partially oxidized ruthenium(0001) surface when confined under a two-atom thick sheet of silica (SiO2 ). We further employ our findings in conjunction with experimental observations and mathematical modeling to set up a fully theoretical model of the system in order to explain its behavior. In the second chapter we investigate the chemical alteration of the ultra-thin silica bilayer by means of exposing it to hydrogen plasma. We elucidate possible defects formed during the process and pin-point the most likely structure found. In the last chapter, we investigate the possible error sources that are inherent in quantum mechanical modeling and employ the so called embedded fragment approach to lift the approximations up to the coupled cluster singles and doubles with perturba- tive triples (CCSD(T)) level of theory. We then apply this methodology to the diffusion of hydrogen on aluminum oxide to obtain a diffusion barrier of chemical accuracy that may both be used to benchmark other approaches such as density functional theory, as well as experimental findings

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time