Maximum-entropy principle for static and dynamic high-field transport in semiconductors

Abstract

Within the maximum entropy principle we present a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport under electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. The theoretical approach is applied to $n\text{\ensuremath{-}}\mathrm{Si}$ at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with experimental data.