Uncertainty estimation (standard deviation) of XPS peaks in CasaXPS?

Estimating the uncertainty (standard deviation) of XPS peaks in CasaXPS involves several steps, focusing on the precision of the peak fitting process. CasaXPS provides tools to quantify the uncertainty associated with the peak parameters, which can be utilized to estimate the standard deviation of XPS peaks. Here is a detailed procedure to achieve this:

Step-by-Step Procedure:

Load the XPS Data:Open CasaXPS and load your XPS data file.

Background Subtraction:Perform background subtraction on your spectrum. This is typically done using a Shirley or Tougaard background, depending on your specific requirements.

Peak Fitting:Define the peaks to be fitted. This involves selecting the appropriate peak models (e.g., Gaussian, Lorentzian, or a combination) and initial parameters (position, height, width). Fit the peaks to the data. This is done by selecting the regions of interest and performing a nonlinear least-squares fitting.

Accessing the Peak Parameters:Once the peaks are fitted, CasaXPS provides the parameters of the fitted peaks, such as position, area, and full width at half maximum (FWHM). Ensure that the fit is acceptable by checking the residuals and the quality of the fit visually.

Uncertainty Estimation:CasaXPS provides the capability to calculate the uncertainty of the peak parameters. This is typically done using the covariance matrix of the fit parameters, which can be accessed within the software. The covariance matrix contains information about the variances and covariances of the fitted parameters. The square root of the diagonal elements of the covariance matrix gives the standard deviation (uncertainty) of each parameter.

Calculating the Standard Deviation: To calculate the standard deviation of a specific peak parameter (e.g., peak position, area, or FWHM), use the following approach:Open the peak fit results and locate the covariance matrix. Identify the relevant diagonal element corresponding to the parameter of interest. The standard deviation (σ) is the square root of this diagonal element.

Practical Example:

Perform the Fit:Fit the peaks in your spectrum using CasaXPS.

Access the Covariance Matrix:After the fit, go to the results section where the peak parameters are listed. CasaXPS typically provides an option to view the detailed fit statistics, which includes the covariance matrix.

Extract the Standard Deviation: For example, if you are interested in the uncertainty of the peak position:Locate the diagonal element of the covariance matrix corresponding to the peak position. If this element is C_position, then the standard deviation σ_position is given by: σposition=Cposition\sigma_{\text{position}} = \sqrt{C_{\text{position}}}σposition=Cposition

Additional Considerations:

Goodness of Fit:Ensure that the fit is statistically acceptable. Poor fits can lead to incorrect uncertainty estimates. Evaluate the goodness of fit using chi-squared (χ²) statistics and residual analysis.
Parameter Correlation:Be aware of the correlation between fit parameters. Highly correlated parameters can affect the accuracy of the uncertainty estimation.

Conclusion:

By following these steps, you can estimate the uncertainty (standard deviation) of XPS peaks in CasaXPS. Accurate uncertainty estimation is crucial for reliable interpretation of XPS data and understanding the precision of your measurements. Always ensure that the fitting procedure is robust and the results are critically evaluated for consistency and reliability.

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