2009 Workshop on Kinetic Theory Inst. of Math., Academia Sinica, Taipei The hierarchy of models for semiconductors

Several kinds of models are proposed to analyze the electron flow through semicon-ductor devices. Especially a hydrodynamic, an energy transport and a drift-diffusion models are frequently utilized for the simulation with the suitable choice according to the purpose of use of real devices. Hence, mathematical analysis on solvability of these models globally in time and their model hierarchy are important problems not only in mathematics but also in engineering. The hierarchy is formally understood by the limit procedure to make a momentum relaxation time and/or an energy relaxation time tend to zero. The main purpose of this talk is to discuss the solvability of the models and justify the relaxation limit procedures rigorously