Maximum entropy principle within a total energy scheme: Application to hot-carrier transport in semiconductors

Abstract

The maximum entropy principle is applied to a conducting band with energy wave vector dispersion of general form and to an arbitrary number of generalized kinetic fields. By considering a linear expansion around a local Maxwellian, within a total average energy scheme, we obtain a closed system of hydrodynamic equations for a full band model in which all the unknown constitutive functions are completely determined. With this approach, under spatially homogeneous conditions we present a systematic study of the small-signal analysis for the most important response functions of the electron system in the general framework of the moments theory. The case of a ${n}^{+}{\mathrm{nn}}^{+}$ nonhomogeneous structure is also considered. Numerical hydrodynamic calculations are validated by a comparison with Monte Carlo simulations performed for the case of n-type Si at 300 K.