Investigation of the convergence of an expansion of the screening-charge density for impurity ions in semiconductors

✍ Scribed by P. Csavinszky

• Book ID: 104579094
• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 344 KB
• Volume: 12
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560120210

✦ Synopsis

Abstract

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.