Encoding of stoichiometric constraints in the composition depth profile reconstruction from angle resolved X-ray photoelectron spectroscopy data

The inversion of angle resolved XPS data is a difficult problem, due to mathematical complexity of accurate model of electron transport, sensitivity to noise and small number of measured points limiting the depth resolution and the accuracy of the calculated depth profiles. Extended maximum entropy model for the calculation of apparent compositions (measured intensity ratios) is presented which allows to encode linear relationship between element concentrations. These can be used to calculate a solution with additional stoichiometric relationships and analyze, simultaneously, signals from several synthetic peak components. The synthetic peak components used in the model can represent various core level energy shifts, which are otherwise difficult to determine unambiguously from the measured signal. Element concentrations linked with stoichiometric relationships are used to identify compound materials with known density and inelastic scattering properties. The new model, thus allows self-consistent recovery of depth profiles using maximum entropy method without the assumption of homogeneous density. The improved accuracy of the recovered depth profiles is demonstrated on the analysis of HfON/SiON overlayers. Various artefacts in the depth profiles obtained with standard maximum entropy model, which assumes constants density are identified. Copyright (C) 2011 John Wiley & Sons, Ltd.