The success of TCAD depends on the reliability and efficency of the computer models used. Due to the rapid progress of Si technology and the introduction of new device types and materials, known models are continously being improved and new models are being developed. 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 (MC) approach, in which the movement of electrons or holes within a material of interest is sampled over a simulation time period, proves to be very successful. As computational power increases, MC methods can even be used in combination with TCAD device simulations, helping to solve hot carrier and short channel problems. Basically there are two representations of the band structure of a material in an MC simulator: namely, analytical expressions, as the parabolic or non-parabolic approximations, or a full band structure. In the latter case the band structure is calculated for a representable part of the first Brillouin zone and then passed to the MC simulator in the form of a three-dimensional mesh. Despite the higher computational costs, it is necessary to use the full-band approach for hot carrier problems, because an accurate representation of the band structure at higher energies is essential here. It has been shown that these computational costs can be kept sufficiently low when using tetrahedra as elementary mesh elements and isotropic scattering models which only depend on the density-of-states (DOS). Since the density of states is given by an integral over an equi-energy surface in the Brillouin zone, and this surface is a plane area within a tetrahedron, fast calculation of the DOS and fast determination of the carrier state after a scattering process are obtained. Cold electrons are located in a small area around the valley minima most of the time. The use of a refined unstructured mesh with high resolution around the valley minima provides accurate results even in the combined low temperature - low field regime. So far, the VMC Full-Band Simulator can handle both strained and unstrained silicon and germanium and its alloys.
Currently the expansion of the Vienna Monte Carlo Simulator (VMC) to a full-band simulator is in progress, with the further goal of integrating this simulator with Minimos-NT, which then will provide the feature of self-consistent two- or three-dimensional combined TCAD/MC device simulations.