Hydrodynamical model of charge transport in GaAs based on the maximum entropy principle

A hydrodynamical model based on the maximum entropy principle is formulated for GaAs semiconductors. Explicit closure relations for the moment equations of the electron density, energy, velocity and energy-flux are obtained by using the Kane dispersion approximation for the description of the conduction bands. All the relevant scattering mechanisms are included: interaction of electrons with acoustic, polar and non-polar optical phonons, impurities. Application to the bulk case reveal s that the model describes with accuracy the effect of negative differential conductivity, typical of GaAs, as well as the velocity overshoot and saturation.