Rational Chebyshev approximation for the Fermi-Dirac integral ℱ-3/2(x)

A. Trellakis, A. J. Galick, U. Ravaioli

Research output: Contribution to journalArticlepeer-review


The solution of the nonlinear Schrödinger-Poisson system of equations for one-dimensional states in a quantum structure (e.g. quantum wire) requires an efficient evaluation of the Fermi-Dirac integral ℱ-3/2(x) at each iteration step if a Newton approach is used. A computationally efficient rational Chebyshev approximation is given here for the complete Fermi-Dirac integral of order -3/2, which limits the maximum relative error well below 10-13. Accurate approximations of different order Fermi-Dirac integrals are achievable with the same algorithm.

Original languageEnglish (US)
Pages (from-to)771-773
Number of pages3
JournalSolid-State Electronics
Issue number5
StatePublished - May 1997

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Electrical and Electronic Engineering
  • Materials Chemistry


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