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Maximum entropy: A new approach to non‐destructive deconvolution of depth profiles from angle‐dependent XPS
Author(s) -
Smith G. C.,
Livesey A. K.
Publication year - 1992
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.740190134
Subject(s) - deconvolution , principle of maximum entropy , x ray photoelectron spectroscopy , inverse , entropy (arrow of time) , data set , experimental data , mathematics , algorithm , statistical physics , computational physics , statistics , physics , geometry , thermodynamics , nuclear magnetic resonance
The application of the maximum entropy method to non‐destructive depth profiling by angle‐dependent XPS is described. The algorithm gives the set of depth profiles that has maximum Skilling‐Jaynes entropy, subject to the condition that the calculated data agree with the measured data within the experimental precision. The method does not require an inverse transform, is robust to experimental noise and is not restricted to small numbers of components. The programme can determine which of a set of prior estimates for the depth profiles is most probable; however, the reconstruction near the surface is virtually independent of this choice. Further, the method also estimates the accuracy of the reconstruction from a single data set. It is illustrated using model data and by a re‐analysis of angle‐resolved XPS data sets available in the literature.