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Estimation of depth profiles from inelastic backgrounds in XPS. I. General relationships
Author(s) -
Aminov Kamil L.,
Jørgensen Jørgen S.,
Pedersen J. Boiden
Publication year - 1995
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.740231104
Subject(s) - simple (philosophy) , resolution (logic) , x ray photoelectron spectroscopy , spectral line , mathematics , statistical physics , distribution (mathematics) , computational physics , mathematical analysis , computer science , physics , quantum mechanics , nuclear magnetic resonance , artificial intelligence , philosophy , epistemology
The accuracy by which an unknown concentration profile can be found by analysis of XPS spectra is investigated theoretically by analytical and numerical techniques. The problem of determining the profile is reformulated as an optimization problem. By use of analytical techniques we obtain qualitative statements about the depth resolution and we derive fundamental relationships between the different parameters that indicate their relative importance. In order to illustrate the various dependencies of the variability of the model parameters, we derive analytical expressions for the standard errors of the model parameters for two simple models: a dalta layer and an exponentially decreasing profile. Furthermore, the complete probability distribution of the model parameters for a rectangular model is investigated numerically.