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Regularization: A stable and accurate method for generating depth profiles from angle‐dependent XPS data
Author(s) -
Tyler B. J.,
Castner D. G.,
Ratner B. D.
Publication year - 1989
Publication title -
surface and interface analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 90
eISSN - 1096-9918
pISSN - 0142-2421
DOI - 10.1002/sia.740140804
Subject(s) - smoothing , regularization (linguistics) , singular value decomposition , algorithm , tikhonov regularization , x ray photoelectron spectroscopy , data point , mathematics , computer science , statistics , inverse problem , physics , mathematical analysis , nuclear magnetic resonance , artificial intelligence
An algorithm for generating depth profiles from angle‐dependent XPS data has been developed. The algorithm uses the regularization method with non‐negativity constraints. Four criteria for determining the optimal amount of solution smoothing have been investigated. A criterion that uses the least‐squared error in the regenerated data set proved most effective for selecting the optimal smoothing. Simulated data for a two‐layer sample were used to investigate the effects of the number of data points, where each data point consisted of the spectra acquired at a take‐off angle. Simulated data were also used to investigate the effect of random error on the calculated depth profiles. Increasing the number of data points improved the resolution at the interface. Greater than 10% error could be added to the data without affecting the stability of the algorithm. The algorithm has also been tested on actual angle‐dependent XPS data sets from a thin polyurethane film on gold, a thin silicon oxide film on silicon, and a thick polyetherurethane film on glass. Performance of the regularization algorithm has been compared to an algorithm that uses a singular value decomposition of angle‐dependent XPS data to generate depth profiles. The regularization algorithm demonstrates significantly improved stability and accuracy with roughly equal computational difficulty. Using the regularization algorithm, a quantitative estimate of the depth profile in the upper 100 Å region of a sample can be calculated using data with > 10% error and using as few as three data points.