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Theory of the potential of a donor ion in silicon
Author(s) -
Csavinszky P.,
Morrow R. A.
Publication year - 1981
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.560190522
Subject(s) - ion , impurity , scattering , electron , silicon , poisson's equation , dielectric , point (geometry) , ionization , variable (mathematics) , poisson distribution , atomic physics , chemistry , physics , quantum mechanics , mathematics , mathematical analysis , geometry , statistics , organic chemistry
Abstract In this paper a variational principle has been formulated for obtaining an approximate solution of Poisson's equation for the potential of a donor ion embedded in Si. A comparison of a two parameter approximate analytical potential with the exact numerical potential shows excellent agreement for several electron concentrations. It is also found that the present theory, using the concept of a “spatially variable dielectric constant,” leads to a donor‐ion potential which deviates significantly from the potential of Dingle, which has been the traditional starting point of calculations of electron mobility limited by ionized‐impurity scattering.