Due to the rapid progress of Si technology and the introduction of new device types and materials, it is a challenging task to develop and improve models for TCAD device simulation. During this development process it is important to compare the results of TCAD simulations to those obtained by more fundamental methods. Here the Monte Carlo approach, in which the movement of electrons and holes within a device is sampled over a simulation time period, proves to be very successful. There are two approaches to represent the band structure of a material in a Monte Carlo simulator: namely, analytical expressions, such as the parabolic or non-parabolic approximations, or a fullband structure. In the latter case the band structure is calculated for a representable part of the first Brillouin zone — the so-called irreducible wedge — and then passed to the Monte Carlo simulator in the form of a three-dimensional mesh. Especially fullband Monte Carlo proved to be the tool of choice to obtain material properties under arbitrary stress/strain conditions, because the variations of the band structure are treated in a rather fundamental way and are accurately reproduced even for high-strain conditions. Apart from simulations in the field of strain engineering — which is a key feature for actual MOSFET device design — fullband Monte Carlo is generally applicable for hot carrier problems, because an accurate representation of the band structure at higher energies is essential here. In contrast to hot electrons, cold electrons are located in a small area around the valley minima most of the time. To obtain accurate results in the combined low-temperature - low-field regime, a refined unstructured mesh with high resolution around the valley minima is used. With the refined mesh we are able to simulate devices which operate below 10K, such as blocked impurity band photo detectors used for space observation.