Hydrodynamic Models of SemiconductorElectron Transport at High Fields

Hydrodynamic or continuum descriptions of electron transport have long been used for modeling and simulatingsemiconductor devices. In this paper, we use classical field theory ideas to discuss the physical foundations of suchdescriptions as applied specifically to high-field transport regimes. The classical field theory development of thesetypes of models is of interest because it differs significantly from and may be viewed as complementary toconventional derivations based on the Boltzmann equation: After outlining the general field theoretic principlesupon which our development of fluid-based high-field transport descriptions is based, we study several specificmodels both analytically and using numerical simulation. These models provide an overall framework forunderstanding and extending various theories which have appeared in the literature. Most importantly, theyemphasize the importance of including memory or history effects and viscosity in describing high-field transport.In all of this our aim is a unified and synoptic view unencumbered with microscopic details. Obtaining quantitativeagreement with specific experiments and/or microscopic simulations is only of secondary importance. We sharethe view that continuum approaches can provide succinct and computationally-efficient models needed for currentand future semiconductor device analysis and engineering. At the same time, we believe that these models neednot be phenomenological but can be given solid physical foundation in macroscopic principles