Maximum entropy principle for hydrodynamic transport in semiconductor devices

A hydrodynamic (HD) transport approach based on a closed system of balance equations is developed from the maximum entropy principle. By considering a nonlinear expansion with respect to a local thermodynamic equilibrium, we determine an analytic expression for the distribution function as a function of macroscopic quantities such as density, velocity, energy, deviatoric stress, heat flux associated with charge carriers. From the determined distribution function and considering the collision interactions of carriers with phonons, all the constitutive functions appearing in the fluxes and collisional productions of the balance equations are explicitly calculated. The analytical closure so obtained is applied to the case of some n⁺nn⁺ submicron Si structures. Numerical HD calculations are found to compare well with those obtained by an ensemble Monte Carlo simulator thus validating the approach developed here. © 1999 American Institute of Physics.