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A perturbation‐theoretical treatment of the time‐dependent Boltzmann equation for crystal electrons in a strong electric field
Author(s) -
Henneberger K.,
Röseler J.
Publication year - 1972
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220490237
Subject(s) - eigenfunction , eigenvalues and eigenvectors , perturbation (astronomy) , zener diode , boltzmann equation , physics , electric field , electron , boltzmann constant , distribution function , perturbation theory (quantum mechanics) , quantum electrodynamics , classical mechanics , mathematical analysis , quantum mechanics , mathematics , voltage , resistor
The properties of the time‐dependent distribution function, particularly the possibility of formation of Zener oscillations, are investigated. Hereby the Boltzmann equation is reduced to an eigenvalue problem. In addition to general investigations, a perturbation‐theoretical method for the calculation of the eigenfunctions and the eigenvalues in the strong‐field limit is given. The restriction to the first terms of the perturbation‐theoretical expansion is allowed, if and only if Zener oscillations exist relatively unperturbed. This is possible for electric field strengths which satisfy the rough condition\documentclass{article}\pagestyle{empty}\begin{document}$$\frac{{\Omega_0 }}{{\left({2\pi} \right)^3}}\int\limits_{1.{\rm BZ}} {{\rm d}^3 \bf {k}\,{\rm d}^3 \bf {k}'} \,Q(\bf {k},\bf {k}')\ll \frac{a}{2}|F|$$\end{document}Using an exactly solvable but nontrivial model, the results found by general considerations can finally be confirmed and completed.