Physics-based solutions to carrier distribution functions in extreme non-equilibrium situations

The previously developed hydrokinetic concept combining transport informati on at the hydrodynamic and kinetic levels is applied to educe transport app roaches at various temporal and spatial scales. The hydrokinetic approaches are derived from the evolution process of the hydrodynamic parameters and kinetic distribution function (DF) influenced by scattering and variations in field. The DF resulting from this physics-based approach is described by a chosen finite set of moments (hydrodynamic parameters) whose characteris tic scales therefore determine the evolution scale of the hydrokinetic DF. Formulation of the hydrokinetic approach at the momentum characteristic sca le is presented. The approach is applied to the investigation of the electr on DFs in silicon at 100 K and 300 K subjected to drastic changes in field. Monte Carlo (MC) simulations are used to examine the validity of the propo sed hydrokinetic approaches. Major assumptions for the hydrokinetic approac h at the momentum characteristic scale are verified numerically. Results sh ow that, when properly incorporating influences of energy and velocity rela xation into the hydrokinetic DF, the approach can account for highly non-Ma xwellian and ballistic behaviours of electrons in fast-transient situations . The proposed model is fairly simple and efficient, and results are in goo d agreement with those derived from the MC simulations in ultra-fast-transi ent situations.