Particle and energy fluxes in semiconductors: Full-band hydrodynamic equations and the thermodynamic limit

The hydrodynamic model for semiconductors includes equations of continuity for the carrier number, average energy, average velocity, and average energy flux. The last two equations can be recast as generalized drift-diffusion expressions, which are formally similar to those of the particle and energy fluxes provided by classical thermodynamics based upon entropy production. The derivation of the hydrodynamic model is reexamined, and the entropy principle is derived from the definition of fermion entropy. It is shown that the thermodynamic expressions are included as a limiting case of the hydrodynamic expressions and, in particular, that the hydrodynamic definitions of the momentum-relaxation time and energy-flux relaxation time provide the correct thermodynamic limit by fulfilling the Onsager relation. [S0163-1829(99)02840-4].