Twenty analyts used a variety of data analysis programs and a variety of curve-fitting approaches to determining peak binding energies. Results indicate that data analysis of doublet spectra may be problematic, since up to 50% of the XPS-STD doublets were assigned incorrectly as singlets. For spectra that were correctly identified as doublets, bias and random error in peak binding energies depended on the amount of separation between component peaks and on their relative intensities. Biases ranged from -0.055 eV to 0.34 eV while random errors ranged from 0.012 eV to 0.13 eV. Use of the Gaussian-Lorentzian function fitted to spectra resulted in smaller biases than the use of a Gaussian function alone.

For a complete discussion of the XPS-STD pilot study, see Surface and Interface Analysis, vol. 26, 939-956 (1998). Below are a few tables and figures from that article.

Table 1. Data Analysis Performed by Analysts: Software Program and Least-Squares-Fitting Procedure Used

Analyst	Software	Least-Squares Fitting Procedure
1	Program by R.W.M. Kwok, Dept. of Chemistry, Chinese University of Hong Kong, Shatin, Hong Kong.	Two Gaussian-Lorentzian (G-L) functions fit to single peak in reference spectrum. G-L ratio for larger component function 0.90:0.10; G-L ratio for smaller component function 0.40:0.60. Binding energy (BE) of smaller component = BE of larger component + 0.68 eV. Height of smaller component = 0.11 x height of larger component. Full width at half-maximum intensity (FWHM) = 0.85 eV for both components. Each identified STD peak was fitted with two-component G-L function.
2	Program by R.W.M. Kwok, Dept. of Chemistry, Chinese University of Hong Kong, Shatin, Hong Kong.	Two G-L functions fit to single peak in reference spectrum. G-L ratio for larger component function 0.90:0.10; G-L ratio for smaller component function 0.31:0.69. BE of smaller component = BE of larger component + 0.5 eV. Height of smaller component = 0.288 x height of larger component. FWHM = 0.81 eV for larger component; 0.85 eV for smaller component. Each identified STD peak was fitted with two-component G-L function.
3	Logafit 6/9/89 (program by A. Proctor, Quantegy Inc., Opelika, AL)*	Symmetric G-L function used with asymmetric tailing as option.
4	S-probe ESCA Software v. 1.36.00 (for SSI Instruments)*	Voigt function used with G-L ratio 0.85:0.15. Symmetric function used for most spectra; 10% asymmetric function used for some spectra. FWHM: 0.7-1.3 eV
5	Kratos Vision v. 1.4.0*	Two G-L functions fit to single peak in reference spectrum. G-L ratio for larger component function, 0.70:0.30; G-L ratio for smaller component function, 0.20:0.80. BE of smaller component = BE of larger component + 0.5 eV. Height of smaller component = 0.25 x height of larger component. FWHM = 0.93 eV for both components. Each identified STD peak was fitted with two-component G-L function.
6	EscaTools v. 4.2 with Matlab*	G-L function used with 0.75:0.25 ratio.
7	EscaTools v. 4.607 with Matlab 4.2c.1*	G-L function used with 0.8:0.2 ratio. Average FWHM = 0.87 eV; minimum FWHM = 0.6 eV; maximum FWHM = 1.3 eV for test spectra.
8	EscaTools v. 4.5*	Asymmetric Gaussian function used with asymmetry factor = -0.051 obtained from fit to reference spectrum. Nelder-Mead fitting routine used. FWHM = 0.92± 0.05 eV for test spectra.
9	Written by analyst	Two G-L functions fit to single peak in reference spectrum. BE of smaller component function = BE of larger component function + 0.68 eV. Intensity of smaller component = 0.28 x intensity of larger component. FWHM = 0.766 eV (0.661 eV Gaussian, 0.105 eV Lorentzian) for both components. Singlets fitted with either two-component function or a single G-L function. Doublets fitted with two-component function and a single G-L function. Levenberg-Marquardt fitting algorithm used.
10	ANEW for data analysis excluding curve fitting. GAMNEW for curve fitting.	G-L product function used with 0.45:0.55 ratio; FWHM = 0.95 eV from reference spectra. Test spectra fit with one or two functions with fixed G-L ratio and fixed FWHM.
11	EscaTools v. 4.2*	G-L function used with 0.75:0.25 ratio. Nelder-Mead fitting algorithm used.
12	ESCA 1.36.04 for use with SSI SSX-101 M-probe*	Asymmetric G-L function used with fixed 0.90:0.10 ratio. Asymmetry parameters variable.
13	AIDA 7.01*	Gaussian function.
14	Common Data Processing System v.3.1; PeakFit v.1.5A*	Asymmetric G-L product function used with 0.64:0.35 ratio; FWHM = 0.92 eV; asymmetry parameter = 0.15 from fit to reference spectrum. Different values for function parameters used for test spectra. Levenberg-Marquardt fitting algorithm used.
15	WaveMatrics, Igor Pro v.2.0*	G-L function used with 0.80:0.20 ratio.
16	MicroCal Origin v.3.77*	Gaussian function used.
17	Kaleida Graph 3.0.5J*	Function used with two Gaussian components and one linear component (for background).
18	Written by analyst	G-L function used.
19	MAC SCIENCE Data Processing for X-ray Diffraction, Japan 1990.5*	Asymmetric Voigt function used. Variable ratio of Gaussian to Lorentzian contributions in Voigt function. FWHM = 0.931 eV for reference spectrum. FWHM = 0.931"0.087 eV for test spectra.
20	MicroCal Origin, v. 3.0*	Gaussian function used.

* Certain commercial products are identified here to specify the means of data acquisition. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the product identified is necessarily the best available for the purpose.

Table 2. Data Analysis Performed by Analysts: Criteria for Choosing the Number of Peaks, Analysis Choices and Criteria for Fit.

Analyst	Criteria for choosing 1 or 2 peaks	Smoothing and background subtraction procedures	Placement of endpoints for curve fitting	Criteria for non-linear least-squares fit
1	Visual inspection of fit and minimization of sum of squared residuals. If difference in binding energies after curvefitting for doublet was minimal, then 1 peak was assigned.	Shirley background removed before curvefitting.	Placed in middle of noisy regions on either side of peak. In some cases, endpoints were averages of several points.	Minimization of sum of squared residuals (Chi-squared).
2	Visual inspection of fit and minimization of sum of squared residuals. If difference in binding energies after curvefitting for doublet was minimal, then 1 peak was assigned.	Shirley background removed before curvefitting.	Placed in middle of noisy regions on either side of peak. In some cases, endpoints were averages of several points.	Minimization of Chi-squared.
3	Compared FWHM for test spectra with FWHM for reference spectrum.	After curvefitting, background of each peak calculated individually, in proportion to peak area, to give integral background overall.	At 281.45 eV and either 289.0 eV or 290.0 eV.	Minimization of Chi-squared and visual examination of residuals.
4	Visual inspection.	50% of spectra smoothed with 7- or 9-point weighted average. Shirley background.	Placed approximately 0.5 eV beyond where peak could not be distinguished from baseline.	Minimization of Chi-squared and visual examination of residuals.
5	Visual inspection of overall peak shape and peak asymmetry, and FWHM ratio of test spectra to reference spectrum. If FWHM ratio< 1.05, then 1 peak was assigned; if FWHM ratio.1.15 and no valley apparent, then 2 peaks assigned.	Shirley background.	Placed outside of peak envelope. Endpoints averaged over 10 data points.	Visual inspection of fit and residuals.
6	Visual inspection and FWHM.	Shirley background.	Placed away from peaks.	N.I.*
7	Visual inspection.	Shirley background.	At 282 eV and 290 eV for most test spectra.	Visual inspection of fit and minimization of residuals.
8	Visual inspection for asymmetry. If FWHM for test spectra >10% wider than FWHM for reference spectrum, then 2 peaks were assigned.	Shirley background.	Placed by visual inspection.	Visual inspection and minimization of Chi-squared.
9	N.I.	N.I.	N.I.	N.I.
10	Visual inspection of first and second derivative spectra.	Shirley background.	Variable.	Minimization of Chi-squared.
11	Peak asymmetry and minimization of sum of squared residuals.	Shirley background.	Placed at approximately 3 eV away from peak maximum.	Minimization of Chi-squared.
12	Visual inspection. If FWHM > 1.0 eV, then 2 peaks were assigned.	Shirley background.	Placed by visual inspection.	Visual inspection and minimization of Chi-squared.
13	Inspection of fit residuals for one peak and second derivative spectrum.	Linear background.	N.I.	Visual inspection and minimization of Chi-squared.
14	Peak asymmetry and FWHM for test spectrum compared to those for reference spectrum. If FWHM for test spectra >20% wider that FWHM for reference spectrum, then 2 peaks were assigned.	Tougaard background subtracted prior to curvefitting.	At 281.45 eV and 288.45 eV	Minimization of residuals.
15	Visual inspection.	Linear background.	N.I.	Inspection of standard deviations for each fit parameter.
16	N.I.	Linear background.	N.I.	N.I.
17	Visual inspection and comparison of fit parameters for test spectra and reference spectrum.	Linear background.	N.I.	Minimization of residuals.
18	Peak asymmetry.	Shirley background.	Placed far from peak maximum. Endpoints were averages of multiple points.	Minimization of Chi-squared.
19	N.I.	Savitzky-Golay smoothing with a 9-point filter.	N.I.	N.I.
20	Inspection of derivative spectra after smoothing.	Linear background.	Visual inspection.	Visual inspection.

* No information supplied by analyst.

Figure 1. Percentage of incorrect assignments of one peak for doublet spectra or two peaks for singlet spectra.

Figure 2. Box plots of bias estimates for the larger peak in doublet spectra and for the singlet spectra. Boxes enclose inter-quartile ranges, end caps indicate 10th and 90th percentiles and center lines indicate medians for 11 participants who analyzed >2 replicate data sets. Solid circles are the medians for the four data sets of participants who analyzed all 10 replicate sets with random-normal residuals from the ANOVA.

Figure 3. Box plots of random errors for the larger peak in doublet spectra and for the singlet spectra. Center lines are median values for 11 participants who analyzed >2 replicate data sets. Solid circles are the median values for four data sets of participants who analyzed all 10 replicate spectral sets with random-normal residuals from the ANOVA.