LOGISTIC FUNCTION PROFILE FIT: A least-squares program for fitting interface profiles to an extended logistic function

Journal Article · Sat Sep 15 00:00:00 EDT 2012 · Journal of Vacuum Science and Technology. A, Vacuum, Surfaces and Films

DOI:https://doi.org/10.1116/1.4736865· OSTI ID:22098975

Kirchhoff, William H. ^[1]

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1. Surface and Microanalysis Science Division, National Institute of Standards and Technology, 100 Bureau Drive, Stop 8370, Gaithersburg, Maryland 20899-8370 (United States)

The extended logistic function provides a physically reasonable description of interfaces such as depth profiles or line scans of surface topological or compositional features. It describes these interfaces with the minimum number of parameters, namely, position, width, and asymmetry. Logistic Function Profile Fit (LFPF) is a robust, least-squares fitting program in which the nonlinear extended logistic function is linearized by a Taylor series expansion (equivalent to a Newton-Raphson approach) with no apparent introduction of bias in the analysis. The program provides reliable confidence limits for the parameters when systematic errors are minimal and provides a display of the residuals from the fit for the detection of systematic errors. The program will aid researchers in applying ASTM E1636-10, 'Standard practice for analytically describing sputter-depth-profile and linescan-profile data by an extended logistic function,' and may also prove useful in applying ISO 18516: 2006, 'Surface chemical analysis-Auger electron spectroscopy and x-ray photoelectron spectroscopy-determination of lateral resolution.' Examples are given of LFPF fits to a secondary ion mass spectrometry depth profile, an Auger surface line scan, and synthetic data generated to exhibit known systematic errors for examining the significance of such errors to the extrapolation of partial profiles.

• OSTI ID: 22098975
• Journal Information: Journal of Vacuum Science and Technology. A, Vacuum, Surfaces and Films, Vol. 30, Issue 5; Other Information: (c) 2012 American Vacuum Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0734-2101
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY
AUGER ELECTRON SPECTROSCOPY
CHEMICAL ANALYSIS
DEPTH
ERRORS
EXTRAPOLATION
FUNCTIONS
ISO
LEAST SQUARE FIT
MASS SPECTROSCOPY
NONLINEAR PROBLEMS
SERIES EXPANSION
SPUTTERING
STANDARDS
TOPOLOGY
X-RAY PHOTOELECTRON SPECTROSCOPY