A variational treatment of the potential of impurity ions in semiconductors with spatially variable dielectric constants

✍ Scribed by P. Csavinszky

• Publisher: John Wiley and Sons
• Year: 1978
• Tongue: English
• Weight: 258 KB
• Volume: 13
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560130207

✦ Synopsis

Abstract

The primary purpose of the present paper consists in obtaining a correction to Dingle's potential for a (point) impurity ion (embedded) in Si or Ge. This goal is accomplished by making use of a variational principle in taking into account the effect of the spatial variation of the dielectric constant in the respective medium. It is found that the resulting impurity‐ion potential can be represented as the product of Dingle's potential and a factor which, with increasing distance from the charged impurity, approaches unity. The secondary purpose of the present paper consists in suggesting a way for the modification of an impurity‐ion potential that has been obtained previously with a boundary condition, that, in retrospect, is open to criticism. It is shown that the modified impurity‐ion potential can be represented as the product of the author's previous potential and a factor which, with increasing distance from the charged impurity, approaches unity.