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A variational principle for the potential of impurity ions in semiconductors with spatially variable dielectric constants
Author(s) -
Csavinszky P.
Publication year - 2009
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.560100834
Subject(s) - dielectric , semiconductor , coulomb , impurity , ion , poisson's equation , variable (mathematics) , variational principle , poisson distribution , condensed matter physics , constant (computer programming) , physics , quantum mechanics , chemistry , mathematical analysis , electron , mathematics , statistics , computer science , programming language
Abstract Dingle's theory of the screening of (point) impurity ions in semiconductors (with standard energy surfaces) is generalized to semiconductors with spatially variable dielectric constants. With the analytical approximations to the spatial dielectric functions of Si and Ge, obtained for these materials by Azuma and Shindo and by Okuro and Azuma, Poisson's equation for the potential of an impurity ion assumes a specific form. The asymptotic form of this differential equation is solved approximately by an equivalent variational principle. The result is a linear combination of two exponentially screened Coulomb potentials (with different screening lengths) scaled by the static dielectric constant of the medium.