High speed numerical integration of Fermi Dirac integrals
Thompson, Jeremy Stewart.
Luscombe, James H.
Walters, Donald Lee
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In this thesis we present an algorithm for the precise determination of Fermi-Dirac (FD) integral functions, for arbitrary values of the parameter and the argument. The FD integrals are a class of functions that are used extensively in the modeling of semiconductor devices, e.g., when the charge carriers are in a strongly quantum, degenerate regime, such as in heavily doped semiconductors. The determination of FD integrals has a long history. Our approach to evaluating these functions is two-fold. First, we develop exact power series expansions of the integral. These series, however, converge too slowly to be a practical means of evaluating the integral. The second aspect of our approach is to apply numerical series acceleration methods to improve significantly the rate of convergence of these series expansions. The result is a computer program that provides efficient, accurate values of the FD integral.
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