Microelectronics is one of the most rapidly changing scientific fields today. The tendency to shrink devices as far as possible to increase the performance and maximize the number of transistors per chip results in extremely small devices which can no longer be described using simple analytical models. In the beginnings of microelectronics, devices where mainly analyzed by applying drift-diffusion theory to simplified device geometries and doping profiles to obtain more or less complex analytical descriptions. To account for two-dimensionality and space-charge effects tools were developed which solved the coupled drift-diffusion equations and Poisson's equation numerically. The results obtained by this approach were very satisfying until approximately a decade ago when it was realized that hot-carrier and quantum effects became increasingly important. More accurate models were developed and existing approaches refined to meet the needs of the semiconductor industry. The evolution of transport modeling from the very beginnings to the highly sophisticated models proposed for modern structures is covered in the chapter by A. Abramo. It becomes apparent that the balance between an accurate description of the various phenomena occurring in state-of-the-art MOS transistors and reasonable simulation times is increasingly difficult to find.

After this overview various of the mentioned simulation approaches are covered in more detail. In the second chapter, H. Kosina and M. Nedjalkov give a detailed overview of particle models for device simulation, commonly known as Monte Carlo methods. In contrast to the macroscopic drift-diffusion and hydrodynamic models, where only statistical averages are considered, particle models follow the...