[en] Leakage currents are one of the major bottlenecks impeding the downscaling efforts of the semiconductor industry. Two core devices of integrated circuits, the transistor and, especially, the DRAM storage capacitor, suffer from the increasing loss currents. In this perspective a fundamental understanding of the physical origin of these leakage currents is highly desirable. However, the complexity of the involved transport phenomena so far has prevented the development of microscopic models. Instead, the analysis of transport through the ultra-thin layers of high-permittivity (high-k) dielectrics, which are employed as insulating layers, was carried out at an empirical level using simple compact models. Unfortunately, these offer only limited insight into the physics involved on the microscale. In this context the present work was initialized in order to establish a framework of microscopic physical models that allow a fundamental description of the transport processes relevant in high-k thin films. A simulation tool that makes use of kinetic Monte Carlo techniques was developed for this purpose embedding the above models in an environment that allows qualitative and quantitative analyses of the electronic transport in such films. Existing continuum approaches, which tend to conceal the important physics behind phenomenological fitting parameters, were replaced by three-dimensional transport simulations at the level of single charge carriers. Spatially localized phenomena, such as percolation of charge carriers across pointlike defects, being subject to structural relaxation processes, or electrode roughness effects, could be investigated in this simulation scheme. Stepwise a self-consistent, closed transport model for the TiN/ZrO₂ material system, which is of outmost importance for the semiconductor industry, was developed. Based on this model viable strategies for the optimization of TiN/ZrO₂/TiN capacitor structures were suggested and problem areas that may arise in the future could be timely identified. Clearly, such a simulation environment should also be of use for the study of follow-up material systems which, already in the front-end research, show very promising performance, however, combined with great challenges especially in gaining control of the leakage currents.