Shower approach in the simulation of ion scattering from solids

An efficient approach for the simulation of ion scattering from solids is proposed. For every encountered atom, we take multiple samples of its thermal displacements among those which result in scattering with high probability to finally reach the detector. As a result, the detector is illuminated by intensive “showers,” where each event of detection must be weighted according to the actual probability of the atom displacement. The computational cost of such simulation is orders of magnitude lower than in the direct approach, and a comprehensive analysis of multiple and plural scattering effects becomes possible. We use this method for two purposes. First, the accuracy of the approximate approaches, developed mainly for ion-beam structural analysis, is verified. Second, the possibility to reproduce a wide class of experimental conditions is used to analyze some basic features of ion-solid collisions: the role of double violent collisions in low-energy ion scattering; the origin of the “surface peak” in scattering from amorphous samples; the low-energy tail in the energy spectra of scattered medium-energy ions due to plural scattering; and the degradation of blocking patterns in two-dimensional angular distributions with increasing depth of scattering. As an example of simulation for ions of MeV energies, we verify the time reversibility for channeling and blocking of 1-MeV protons in a W crystal. The possibilities of analysis that our approach offers may be very useful for various applications, in particular, for structural analysis with atomic resolution.

Time-multiscale methods for the simulation of slow transport problems in atomistic systems

En esta tesis presentamos una teoría adaptada a la simulación de fenómenos lentos de transporte en sistemas atomísticos. En primer lugar, desarrollamos el marco teórico para modelizar colectividades estadísticas de equilibrio. A continuación, lo adaptamos para construir modelos de colectividades estadísticas fuera de equilibrio. Esta teoría reposa sobre los principios de la mecánica estadística, en particular el principio de máxima entropía de Jaynes, utilizado tanto para sistemas en equilibrio como fuera de equilibrio, y la teoría de las aproximaciones del campo medio. Expresamos matemáticamente el problema como un principio variacional en el que maximizamos una entropía libre, en lugar de una energía libre. La formulación propuesta permite definir equivalentes atomísticos de variables macroscópicas como la temperatura y la fracción molar. De esta forma podemos considerar campos macroscópicos no uniformes. Completamos el marco teórico con reglas de cuadratura de Monte Carlo, gracias a las cuales obtenemos modelos computables. A continuación, desarrollamos el conjunto completo de ecuaciones que gobiernan procesos de transporte. Deducimos la desigualdad de disipación entrópica a partir de fuerzas y flujos termodinámicos discretos. Esta desigualdad nos permite identificar la estructura que deben cumplir los potenciales cinéticos discretos. Dichos potenciales acoplan las tasas de variación en el tiempo de las variables microscópicas con las fuerzas correspondientes. Estos potenciales cinéticos deben ser completados con una relación fenomenológica, del tipo definido por la teoría de Onsanger. Por último, aportamos validaciones numéricas. Con ellas ilustramos la capacidad de la teoría presentada para simular propiedades de equilibrio y segregación superficial en aleaciones metálicas. Primero, simulamos propiedades termodinámicas de equilibrio en el sistema atomístico. A continuación evaluamos la habilidad del modelo para reproducir procesos de transporte en sistemas complejos que duran tiempos largos con respecto a los tiempos característicos a escala atómica. ABSTRACT In this work, we formulate a theory to address simulations of slow time transport effects in atomic systems. We first develop this theoretical framework in the context of equilibrium of atomic ensembles, based on statistical mechanics. We then adapt it to model ensembles away from equilibrium. The theory stands on Jaynes' maximum entropy principle, valid for the treatment of both, systems in equilibrium and away from equilibrium and on meanfield approximation theory. It is expressed in the entropy formulation as a variational principle. We interpret atomistic equivalents of macroscopic variables such as the temperature and the molar fractions, wich are not required to be uniform, but can vary from particle to particle. We complement this theory with Monte Carlo summation rules for further approximation. In addition, we provide a framework for studying transport processes with the full set of equations driving the evolution of the system. We first derive a dissipation inequality for the entropic production involving discrete thermodynamic forces and fluxes. This discrete dissipation inequality identifies the adequate structure for discrete kinetic potentials which couple the microscopic field rates to the corresponding driving forces. Those kinetic potentials must finally be expressed as a phenomenological rule of the Onsanger Type. We present several validation cases, illustrating equilibrium properties and surface segregation of metallic alloys. We first assess the ability of a simple meanfield model to reproduce thermodynamic equilibrium properties in systems with atomic resolution. Then, we evaluate the ability of the model to reproduce a long-term transport process in complex systems.

Impact of N on the atomic-scale Sb distribution in quaternary GaAsSbN-capped InAs quantum dots

The use of GaAsSbN capping layers on InAs/GaAs quantum dots (QDs) has recently been proposed for micro- and optoelectronic applications for their ability to independently tailor electron and hole confinement potentials. However, there is a lack of knowledge about the structural and compositional changes associated with the process of simultaneous Sb and N incorporation. In the present work, we have characterized using transmission electron microscopy techniques the effects of adding N in the GaAsSb/InAs/GaAs QD system. Firstly, strain maps of the regions away from the InAs QDs had revealed a huge reduction of the strain fields with the N incorporation but a higher inhomogeneity, which points to a composition modulation enhancement with the presence of Sb-rich and Sb-poor regions in the range of a few nanometers. On the other hand, the average strain in the QDs and surroundings is also similar in both cases. It could be explained by the accumulation of Sb above the QDs, compensating the tensile strain induced by the N incorporation together with an In-Ga intermixing inhibition. Indeed, compositional maps of column resolution from aberration-corrected Z-contrast images confirmed that the addition of N enhances the preferential deposition of Sb above the InAs QD, giving rise to an undulation of the growth front. As an outcome, the strong redshift in the photoluminescence spectrum of the GaAsSbN sample cannot be attributed only to the N-related reduction of the conduction band offset but also to an enhancement of the effect of Sb on the QD band structure.