Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices Articles uri icon

publication date

  • julio 2016

issue

  • 7

volume

  • 18

international standard serial number (ISSN)

  • 1099-4300

abstract

  • Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the system of equations for the moments but its accuracy or range of validity are not always clear. In this paper, we compare numerical solutions of balance equations for nonlinear electron transport in semiconductor superlattices. The equations have been obtained from Boltzmann-Poisson kinetic equations very far from equilibrium for strong fields, either by the maximum entropy principle or by a systematic Chapman-Enskog perturbation procedure. Both approaches produce the same current-voltage characteristic curve for uniform fields. When the superlattices are DC voltage biased in a region where there are stable time periodic solutions corresponding to recycling and motion of electric field pulses, the differences between the numerical solutions produced by numerically solving both types of balance equations are smaller than the expansion parameter used in the perturbation procedure. These results and possible new research venues are discussed.

keywords

  • maximum entropy principle
    chapman-enskog method
    boltzmann-poisson kinetic equation
    balance equation
    semiconductor superlattices
    moment equations
    charge-transport
    principle
    model