
Accession Number : ADA311805
Title : High Speed Numerical Integration of Fermi Dirac Integrals.
Descriptive Note : Master's thesis,
Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA
Personal Author(s) : Thompson, Jeremy S.
PDF Url : ADA311805
Report Date : JUN 1996
Pagination or Media Count : 54
Abstract : In this thesis we present an algorithm for the precise determination of FermiDirac (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 twofold. 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.
Descriptors : *MATHEMATICAL MODELS, *NUMERICAL INTEGRATION, COMPUTER PROGRAMS, ALGORITHMS, PARAMETERS, ELECTRON DENSITY, PROBABILITY DISTRIBUTION FUNCTIONS, INTEGRALS, ACCURACY, THESES, INPUT OUTPUT PROCESSING, CHARGE CARRIERS, SEMICONDUCTOR DEVICES, MATHEMATICAL PROGRAMMING, ELECTRON ENERGY, APPROXIMATION(MATHEMATICS), ERROR ANALYSIS, INTERPOLATION, CONVERGENCE, QUANTUM ELECTRONICS, CHARGE DENSITY, SUBROUTINES, APPLIED MATHEMATICS, BOLTZMANN EQUATION, POWER SERIES, HYPERGEOMETRIC FUNCTIONS.
Subject Categories : Operations Research
Electricity and Magnetism
Distribution Statement : APPROVED FOR PUBLIC RELEASE