Computational methods for semiclassical and quantum transport in semiconductor devices

The progressive miniaturization of semiconductor devices, and the use of bulk materials other than silicon, necessitates the use of a wide variety of models in semiconductor device simulation. These include classical and semiclassical models, such as the Boltzmann equation and the hydrodynamic system, as well as quantum transport models such as the quantum Boltzmann equation and the quantum hydrodynamic system. This paper gives an overview of recently developed numerical methods for these systems. The focus is on Galerkin methods for the semiclassical and quantum kinetic systems and on difference methods for the classical and quantum hydrodynamic systems. The stability and convergence properties of these methods and their relation to the analytical properties of the continuous systems are discussed.