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An error analysis for numerically evaluating random uncertainties in x-ray photoelectron spectroscopy has been implemented in version 2003 of the spectra treatment and analysis software UNIFIT in order to improve the understanding of the statistical basis and the reliability of the model parameters for photoelectron spectra. The theoretical basis as well as two approaches to obtain error limits of the fit parameters have been considered. Several test spectra have been analysed and discussed. A representative example has been chosen to demonstrate the relevance of the error estimation for practical surface analysis. Suggestions for the minimization of errors in the peak-fitting procedures are presented.

A comparative study for the fitting of X-ray photoelectron spectra (XPS) using different model functions is presented. Synthetically generated test spectra using Gaussian/Lorentzian convolution and a real measured spectrum are fitted with the three commonly used models: product, sum and Gaussian/Lorentzian convolution functions. In these limited tests, it was found that the sum function is superior to the product function, particularly for low-noise spectra. Copyright  2007 John Wiley & Sons, Ltd. KEYWORDS: photoelectron spectroscopy; peak fit; Gaussian and Lorentzian functions; product function; sum function; Voigt profile INTRODUCTIONPeak-fit programs for the modelling of X-ray photoelectron spectra (XPS) generally use a combination of a Lorentzian (or in case of asymmetric lines the Doniach-Sunjic function 1 ) and a Gaussian function. 2 The applied model depends on the program code of the employed software 3 (Table 1). Available options give the operator the possibility to select a different model function in their analysis of the spectra. But recommendations for choosing the optimal model function for fitting XPS spectra are mostly not given.The intensity distribution of photoelectron spectra may be modelled mathematically by a convolution of independent Lorentzian and Gaussian functions giving the so-called Voigt profile. In order to simplify the expensive convolution procedure, the product or, alternatively, the sum of the Lorentzian and Gaussian function designed with the same parameter set were proposed to approximate the Voigt profile of a real spectrum.The question to be answered here is: what is the better alternative to the Voigt function, the product or the sum function? The significant difference in the product and Voigt profiles has already been demonstrated. 4 In order to study this problem, four synthetic test spectra were generated with the software package MICROCAL ORIGIN. The result of their analysis using the sum-type, the product-type and the Voigt-model functions applying the program UNIFIT 2006 5 are discussed and compared. Finally, the three different methods were tested on a Cu 3p spectrum of a reference sample. THEORETICAL BACKGROUND Quantities for peak-fit evaluation and optimizationGenerally, the analysis of XPS spectra is performed by comparing the experimentally recorded spectral intensity distribution with a theoretical model curve. The particular peak model parameters, e.g. peak position and intensity, are determined iteratively by a non-linear parameter estimation routine. The Marquardt-Levenberg algorithm 6 has been chosen very often in order to minimize the reduced chisquare 2Ł (Eqn (1)). 7 The final set of peak parameters, characterized by the parameter vector E p, are taken from the minimum of 2Ł E p , determined by the expressionwith the measured spectrum M i recorded at N energy values corresponding to channel i, the synthesized model curve S i, E p and P independent parameters of the model function. Another quantitative measure for discovering correlations in the residu...