A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devicesCitation formats

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A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices. / Alqurashi, Ahmed; Selvakumar, C.R.

In: Superlattices and microstructures, Vol. 118, 01.06.2018, p. 308-318.

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Alqurashi, Ahmed ; Selvakumar, C.R. / A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices. In: Superlattices and microstructures. 2018 ; Vol. 118. pp. 308-318.

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@article{9d50fcff67054bd38e314c800839e2be,
title = "A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices",
abstract = "There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.",
author = "Ahmed Alqurashi and C.R. Selvakumar",
year = "2018",
month = jun,
day = "1",
doi = "10.1016/j.spmi.2018.03.072",
language = "English",
volume = "118",
pages = "308--318",
journal = "Superlattices and microstructures",
issn = "0749-6036",
publisher = "Elsevier BV",

}

RIS

TY - JOUR

T1 - A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices

AU - Alqurashi, Ahmed

AU - Selvakumar, C.R.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

AB - There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

U2 - 10.1016/j.spmi.2018.03.072

DO - 10.1016/j.spmi.2018.03.072

M3 - Article

VL - 118

SP - 308

EP - 318

JO - Superlattices and microstructures

JF - Superlattices and microstructures

SN - 0749-6036

ER -