Comparison of Non‐Parabolic Hydrodynamic ModelsBased On Different Band Structure Models

This paper presents two non-parabolic hydrodynamic model formulations suitable for thesimulation of inhomogeneous semiconductor devices. The first formulation uses the Kanedispersion relationship, (ℏk)2/2m = W(1+αW). The second formulation makes use of a power law, (ℏk)2/2m = xWy, for the dispersion relation. The non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation is limited. The power law formulation produces closed form coefficients similar to those under the parabolic band approximationbut the carrier concentration can deviate. An extended power law dispersion relationis proposed to account for band structure effects, (ℏk)2/2m = xW1+yW. This dispersion relation closely matches the calculated band structure over a wide energy range and may lead toclosed form coefficients for the hydrodynamic model