Relaxation-time approximations of quasi-hydrodynamic type in semiconductor device modelling

We analyse mathematical models for the description of carrier transport in semiconductors as a hierarchy of models constructed on the basis of the the relaxation-time concept. In this hierarchy we focus on a reasonable compromise between drift-diffusion, hydrodynamic, and kinetic models, This compromise is provided by non-local quasi-hydrodynamic mathematical models describing non-equilibrium physical processes in semiconductor devices. Details of the normalization procedure for the quasi-hydrodynamic system will be given along with a transformation of the energy-balance equations to provide computationally convenient forms.