| An introductory overview of the background, current state, and future trend on semiconductor device modeling from the physical, mathematical, and numerical perspectives will be given. These perspectives are described in the view point of our research interests, which is by no means a general view in the vast research community on this subject. The mathematical models include Botzmann transport (BT) equation, drift-diffusion (DD) equations, simplified energy-balance (SEB) model, simpler hydrodynamic (SHD) model, and hydrodynamic (HD) model. Application of the models will be exclusively restricted to N-MOSFET devices. A monotone iterative method for numerical solutions of the DD model will also be briefly described. Numerical simulations on the devices under various biasing conditions, doping profiles, and effective channels will be presented. |