Diffusive semiconductor moment equations using Fermi-Dirac statistics

作者：Juengel Ansgar; Krause Stefan; Pietra Paola

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2011, 62(4): 623-639.

DOI：10.1007/s00033-010-0106-z

• Semiconductor Boltzmann equation
• Moment method
• Fermi-Dirac statistics
• Entropy maximization
• Drift-diffusion equations
• Energy-transport equations

Diffusive moment equations with an arbitrary number of moments are formally derived from the semiconductor Boltzmann equation employing a moment method and a Chapman-Enskog expansion. The moment equations are closed by employing a generalized Fermi-Dirac distribution function obtained from entropy maximization. The current densities allow for a drift-diffusion-type formulation or a "symmetrized" formulation, using dual-entropy variables from nonequilibrium thermodynamics. Furthermore, drift-diffusion and new energy-transport equations based on Fermi-Dirac statistics are obtained and their degeneracy limit is studied.

• 出版日期2011-8