The ongoing trend for high-frequency (HF) applications drives the development of high-speed devices. Therefore, trustworthy device simulations are inevitable for understanding and designing future HF devices. During the last decade, the predictive capabilities of Drift-Diffusion (DD) and Hydrodynamic (HD) transport models turned out to be insufficient for state-of-the-art high-frequency transistors. Consequently, a more physics based transport model helps to counter these issues and thus, the Boltzmann transport equation (BTE) comes into focus. In this thesis, a deterministic solution method for the BTE is pursued. First, physical fundamentals and mathematical preconsiderations for the treatment of the BTE are reviewed. This covers the calculation of band structures/dispersion relations, an overview of scattering mechanisms and a detailed description of the coordinate transformations required for analyzing prominent semiconducting materials, such as Silicon-Germanium and III-V compounds, like Indium-Phosphide. The second part focuses on the numerical treatment of the BTE. Besides the employed normalization strategy, the discretization of the BULK BTE is described in detail. Based on the latter, the extensions for the device BTE are specified. A method for the direct calculation of stationary BTE solutions - for the BULK and device case - is introduced and an overview of the WENO method is outlined. The third part is dedicated to the applications of the deterministic solution method and simulation results of the BTE. Recipes for calculating the most important quantities, like current/electron densities, are given. Simulation results for the BULK case and for hetero-junction bipolar transistors are presented and analyzed. Here, the focus is put on both Silicon/Silicon-Germanium and Indium-Phosphide/Indium-Gallium-Arsenide material systems. The part is concluded by a critical review on the current field of application. A summary and an outlook on future extensions concludes the thesis. Besides pointing out the achievements of this work, the last section also gives a short motivation for adapting the method to 1D semiconductors, like carbon nanotubes.