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

A. Trellakis; A. J. Galick; U. Ravaioli

doi:10.1016/S0038-1101(96)00261-4

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

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

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	771-773
Number of pages	3
Journal	Solid-State Electronics
Volume	41
Issue number	5
DOIs	https://doi.org/10.1016/S0038-1101(96)00261-4
State	Published - May 1997

ASJC Scopus subject areas

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

Online availability

10.1016/S0038-1101(96)00261-4

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Cite this

@article{7b1819e89ba84f7f8a01607f9608cd66,

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

abstract = "The solution of the nonlinear Schr{\"o}dinger-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.",

author = "A. Trellakis and Galick, {A. J.} and U. Ravaioli",

note = "Funding Information: This work was supported by the National Science Foundationg rantE CS 95-09715a ndECD 89-431 66a, ndby a graduatef ellowshipo f the ComputationaSl ciencea nd Engineeringp rogrammea t the Universityo f Illinois.",

year = "1997",

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doi = "10.1016/S0038-1101(96)00261-4",

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AU - Trellakis, A.

AU - Galick, A. J.

AU - Ravaioli, U.

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