Si and GaAs mobility derived from a a hydrodynamical model for semiconductors based on the maximum entropy principle

Consistent hydrodynamical models for electron transport in Si and GaAs semiconductors, free of any fitting parameter, have been formulated in (Cont. Mech. Thermodyn. 11 (1999) 307; Contemp. Mech. Thermodyn. 12 (1999) 31; Contemp. Mech. Thermodyn. 14 (2002) 405; COMPEL (to appear)) on the basis of the maximum entropy principle (MEP), by describing the valleys in the energy conduction band by means of the Kane dispersion relation. Explicit constitutive functions for fluxes and production terms appearing in the macroscopic balance equations of density, crystal momentum, energy and energy-flux have been obtained. Scatterings of electrons with polar (in the case of GaAs) and non-polar optical phonons, both for intervalley and intravalley interactions, and with acoustic phonons and impurities have been taken into account. Here we derive from the previous hydrodynamical models both low- and high-field mobilities. The results are compared with those given by the Caughey-Thomas formula and eventually the validity of the Einstein relation is investigated.