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Investigation of the convergence of an expansion of the screening‐charge density for impurity ions in semiconductors
Author(s) -
Csavinszky P.
Publication year - 1977
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560120210
Subject(s) - impurity , convergence (economics) , semiconductor , series (stratigraphy) , degeneracy (biology) , ion , charge (physics) , condensed matter physics , poisson's equation , physics , dirac (video compression format) , quantum mechanics , nonlinear system , point (geometry) , mathematics , bioinformatics , geometry , neutrino , economics , biology , economic growth , paleontology
In theories of the potential of an impurity ion in semiconductors, the common starting point is an expansion of the Fermi–Dirac integral ℱ 1/2 appearing in the screening‐charge density. In the present paper, a formal test of the convergence of the series for ℱ 1/2 is carried out. The results show that, in the physically important limits of complete degeneracy and complete nondegeneracy, respectively, the series for ℱ 1/2 do converge. This establishes the validity of nonlinear Poisson equations for the impurity‐ion potential, which can be solved approximately by making use of a variational principle.