### Abstract

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 language | English (US) |
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Pages (from-to) | 771-773 |

Number of pages | 3 |

Journal | Solid-State Electronics |

Volume | 41 |

Issue number | 5 |

DOIs | |

State | Published - May 1997 |

### ASJC Scopus subject areas

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

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## Cite this

Trellakis, A., Galick, A. J., & Ravaioli, U. (1997). Rational Chebyshev approximation for the Fermi-Dirac integral ℱ

_{-3/2}(x).*Solid-State Electronics*,*41*(5), 771-773. https://doi.org/10.1016/S0038-1101(96)00261-4