Two new series for the Fermi–Dirac integral

Mohankumar, N.

doi:10.1016/j.cpc.2007.03.002

Cited by 9 publications

(6 citation statements)

References 19 publications

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“…The present series of Mamedov given in Eqs. (7)-(8) as well as the series indicated in [4] belong to the third group. They have the merit of being exact analytical representations which may be possibly useful in some scenario to interpret physical phenomenon.…”

Section: The De Quadrature Methods and The Comparison Of Computationalmentioning

confidence: 99%

“…A variety of methods exists in the literature which normally come under one of the following three categories, namely, series expansion, asymptotics and numerical integration. For a brief summary of the existing methods, the reader is referred to Mohankumar [4]. The expressions for the electron density and energy density in HEMT device involve the following integral which is a variant of F r (η):…”

Section: Methods Of Mamedovmentioning

confidence: 99%

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Comments on the accurate evaluation of integrals arising from the bulk electron densities in quantum wells

Mohankumar

2008

Computer Physics Communications

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Section: The De Quadrature Methods and The Comparison Of Computationalmentioning

confidence: 99%

Section: Methods Of Mamedovmentioning

confidence: 99%

Comments on the accurate evaluation of integrals arising from the bulk electron densities in quantum wells

Mohankumar

2008

Computer Physics Communications

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“…(9) of this article. N. Mohankumar [11] has derived a very interesting equation which makes use of the complementary Error function. The results of his article may help to further develop the numerical properties of Eq.…”

Section: Discussionmentioning

confidence: 99%

“…The scientific literature, spanning about a century, is replete with papers devoted the study of FermiDirac integrals. Many attempts have been made to find more accurate analytical solutions, [6][7][8][9][10][11] and there have been numerous papers dedicated to their accurate numerical calculation [12][13][14][15]. The number of articles written on this subject could probably fill a large tome.…”

Section: Introductionmentioning

confidence: 99%

The Open Mathematics Journal

Selvaggi¹

2012

TOMATJ

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This paper presents a derivation for analytically evaluating the half-order Fermi-Dirac integrals. A complete analytical derivation of the Fermi-Dirac integral of order 1 2 is developed and then generalized to yield each half-order Femi-Dirac function. The most important step in evaluating the Fermi-Dirac integral is to rewrite the integral in terms of two convergent real convolution integrals. Once this done, the Fermi-Dirac integral can put into a form in which a proper contour of integration can be chosen in the complex plane. The application of the theorem of residues reduces the FermiDirac integral into one which becomes analytically tractable. The final solution is written in terms of the complementary and imaginary Error functions.

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“…Using (8), (9), (10) and (11) as well as ( [12], [13], [14]) we finally arrive at an approximate 2D solution of (3) which is given as:…”

Section: Semi-analytical Solution To 2-dimensional Nonlinear Poimentioning

confidence: 99%

Semi-analytical solutions to the Schroedinger-Poisson Model of electron states

Barrett

Souza

Cirstea

2010

2010 12th International Conference on Optimization of Electrical and Electronic Equipment

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Semi-analytical solutions of the non-linear Schrodinger -Poisson Model for simulation of electronic states in semiconductor devices are investigated in both two and three dimensions. Solutions of the electrostatic potential are found from solving Poisson's equation in the complex space, and subsequently used to solve Schrodinger equation. The wavefunctions and energy levels are calculated using the Evans function technique.

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Two new series for the Fermi–Dirac integral

Cited by 9 publications

References 19 publications

Comments on the accurate evaluation of integrals arising from the bulk electron densities in quantum wells

Comments on the accurate evaluation of integrals arising from the bulk electron densities in quantum wells

The Open Mathematics Journal

Semi-analytical solutions to the Schroedinger-Poisson Model of electron states

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