Notes on Fermi-Dirac Integrals

TL;DR

This paper compiles essential properties of Fermi-Dirac integrals, provides Matlab scripts for their calculation, and introduces a new table-based method that improves accuracy and speed for semiconductor applications.

Contribution

It offers a comprehensive collection of properties and multiple Matlab implementations, including a novel table-based script that enhances accuracy and computational efficiency.

Findings

Provides Matlab scripts for calculating Fermi-Dirac integrals.

Introduces a new table-based Matlab script with improved accuracy.

Includes accessible code and resources for practical applications.

Abstract

Fermi-Dirac integrals appear frequently in semiconductor problems, so a basic understanding of their properties is essential. The purpose of these notes is to collect in one place, some basic information about Fermi-Dirac integrals and their properties. We also present Matlab scripts that calculate Fermi-Dirac integrals (the "script F" defined by Dingle (1957)) in three different ways. The codes are available in Appendix and at the following website: "Notes on Fermi-Dirac Integrals (4th Edition)" by Raseong Kim, Xufeng Wang, and Mark Lundstrom at http://nanohub.org/resources/5475 In the 4th edition, we also provide a new table-based Matlab script (download available at https://github.com/wang159/FDIntegral_Table) that is less likely to give large errors in a wide range of input while still much faster than the rigorous numerical integration.