Diffusion, Nucleation and Recombination in Confined Geometries

In this work we address several problems of surface physics which are all based on the transport mechanism of diffusion. Essential parts consider systems in which particles interact upon meeting, either by reaction or by nucleation. For the astrophysical problem of hydrogen recombination on interstellar dust, the previous analytical treatment is substantially improved upon: The parameter responsible for reaction is defined consistently, and in its calculation, we account for the nature of two-dimensional diffusion. Within several models that are also compared with each other, one obtains explicit results that excellently agree with Monte Carlo simulations. Special attention is given to the influence of the confined geometry, which is analytically examined and explained for a minimal model. We also deal with the role of disorder in the surface structure. A further section presents the closely related problem of nucleation at island edges, which, however, proves to be no longer tractable analytically even under moderate assumptions. Step growth under the effect of codeposited impurities is a technologically relevant process, which is examined in a one-dimensional random walk model. Using microscopic models for the resulting disorder on the surface, one finds interesting results that also bear implications for simulations. Those results concern the general influence on the speed and stability of step growth as well as the nature of boundary conditions in the corresponding continuum model. In the last part we thoroughly analyze a model to describe the diffusion field in desorption experiments, which can be made directly visible on a large scale and with real time resolution. The model agrees well with experimental data and hence constitutes an important step in understanding the fundamental processes involved. Based on this understanding, one can draw direct conclusions from the observation of a surface of complex morphology on its microscopic properties