Closure relations for macroscopic transport models

In this paper, the higher-order transport models in semiconducting devices including the energy-balance model, the hydrodynamic model and a six-moment model have been proposed to overcome some limitations of the classic drift-diffusion model. A vast number of models exist and there is a considerable amount of confusion as to their relation to each other. The main differences between these models are shown to the assumptions used for the closure relations. The common simplifications for the investigation of some moments of the distribution function are also presented.