Details

Autor(en) / Beteiligte

• Jüngel, Ansgar

Titel

Energy-Transport Equations

Ist Teil von

• Transport Equations for Semiconductors, p.1-27

Ort / Verlag

Berlin, Heidelberg: Springer Berlin Heidelberg

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The drift-diffusion equations are derived by the moment method by employing only the zeroth-order moment \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\langle M\rangle = \int_B M\mathrm{d}k/4\pi^3$\end{document}, where the Maxwellian M describes the equilibrium state. As explained in Sect. 2.4, we obtain more general diffusion equations by taking into account higher-order moments. The energy-transport equations are derived by choosing the moments \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n=\langle M\rangle$\end{document}(particle density) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ne=\langle E(k)M\rangle$\end{document}(energy density), where\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$E(k)$\end{document}is the energy band. The results of Sect. 2.4 are valid only for a simple BGK collision operator. In this chapter, we will assume more realistic scattering terms including elastic, carrier–carrier, and inelastic collision processes. In the following we proceed as in [1] and [2].