A non parabolic hydrodynamical subband model for semiconductors based on the maximum entropy principle

A hydrodynamic subband model for semiconductors is formulated by closing the moment system derived from the Schrödinger–Poisson–Boltzmann equations on the basis of the maximum entropy principle, by taking into account non parabolic energy bands of Kane’s type. Explicit closure relations for fluxes and production terms are obtained, including scattering of electrons with acoustic and non polar optical phonons and surface scattering. Numerical simulations of a quantum diode show the feasibility of the model. The importance of the non parabolicity is assessed.