The Regions Property Page

 

Quantification of XPS spectra is performed using the information prepared on the Regions Property Page of the Quantification Parameters dialog window.

 

Regions can be created using:

 

 

Figure 1: Regions Property Page

 

Integration regions define the parameters used to identify the signal associated with a peak in the spectrum. These parameters are tabulated on the Regions Property Page in columns where each item in a column is either an editable input or a read-only value determined from the data. Editable items, when selected with the left mouse button, become text entry fields and may be altered using keyboard entry. These include

 

Name

The name used to identify the region in quantification tables.

RSF

Relative Sensitivity Factor for a transition.

Start

Start energy for the integration region.

End

End energy for the integration region.

BG Type

Background type used as a lower bound to the peak.

Av Width

Determines the number of points used to tie the background to the data. Actual number of points averaged = 2 * Av Width + 1.

Start Offset

Percentage offset applied to the start of the background after the initial tie point is determined from the Av Width.

End Offset

Percentage offset applied to the end of the background after the initial tie point is determined from the Av Width.

Cross-section

Parameters used to determine the background. Meaning depends on the chosen background type.

Tag

A string used to identify the region for computational purposes.

Table 1: Editable items available on the Regions Property Page.

 

BG Type

 

Figure 2 shows the list of background types on offer in CasaXPS. The dialog window in Figure 2 is invoked by holding the Control Key down at the same time as selecting the BG Type field within a Region. The BG Type text-field is updated from the selected background when the OK pushbutton is pressed. The region is updated with the chosen background once the Return Key is pressed on the Regions Property Page.

 

The read-backs include:

 

Area

 

The reported area is determined from the background-subtracted data after normalisation with respect to the total acquisition time (dwell-time times number of sweeps), energy step size and is also adjusted for transmission correction using the Intensity Calibrations fields marked in Figure 1. If the VAMAS file contains transmission correction and the Automatic checkbox is ticked, then the reported area includes the transmission adjustment. There is also an energy dependent exponent text-field for compensating for mean-free-path and analyser variations. The measured area is multiplied by the kinetic energy of the ejected electron raised to the power of the value entered in this text-field. The energy dependent adjustments are typically required when Scofield cross-sections are used to compensate for the relative transition probabilities for the measure photoelectric lines and, for many instruments, a value of –0.5 would be typical (however this value is not necessarily universally applicable).

 

St Dev Area

 

The standard deviation in the Area parameter read-back is zero unless the Calculate Error Bars pushbutton (Figure 1) is pressed following any adjustments to the regions parameters. The standard deviation in the area is computed for each region defined on a spectrum using a Monte Carlo procedure for determining the error distribution for each of the computed areas. If the standard deviation in the Area is calculated, the standard deviation for the percentage concentration is also reported in the Standard Reports generated by the Report Spec Property Page also on the Quantification Parameters dialog window.

 

The Monte Carlo error analysis assumes noise in the data is consistent with the expected noise in XPS data. This requires raw counts within the original data file coupled with total acquisition time. The procedure estimates the error in the recorded peak intensities with respect to the measurement process and is therefore a measure of the precision with which the values are measured and is not a measure for the accuracy in a given concentration value.

 

 

 

 

Figure 2: Background Types offered on the Regions Property Page. To invoke this dialog window, hold the Control Key down when selecting the BG Type field.

 

Spline Backgrounds

 

CasaXPS 2.1.8 offers backgrounds based upon the existing CasaXPS background types Shirley, Linear, Tougaard and (so called) None, but where the curve is decided by a set of cubic spline polynomials rather than the underlying functional forms. These new background types “Spline Linear” (abbreviation “sl”), Spline Shirley (“ss”), Spline Tougaard (“st”) and Spline None (“sn”) are flexible backgrounds and can be adjusted under mouse control or optimised as part of a synthetic peak model.

 

A spline is a mechanical device used by draftsman to draw aesthetically pleasing curves using pen and paper: the draftsman fixes a set of points (knots) on the drawing, then bends a flexible strip of plastic or wood (the spline) around the knots and traces the shape onto the paper. Spline interpolation is the mathematical equivalent of this process and is achieved using a piece-wise cubic polynomial approximation to replace the mechanical spline. The smooth curve is achieved by requiring that adjacent cubic polynomials take on the value of the knots and that the first derivatives of these polynomials at the knots are equal. These conditions together with two end point conditions, such as assuming the second derivative at the two extreme knots is zero, allow a unique solution for the set of cubic polynomials for a given set of knots.

 

CasaXPS uses six knots to define five cubic polynomials cross a region, which determine the background shape for that region. The knots are evenly spaced between the start and end points of the region, while the intensity at a knot may be adjusted under mouse control. This is achieved on the Components Property Page, where selecting a point on the background and dragging the mouse to a new position repositions the nearest knot and therefore adjusts the shape of the spline background. If the knot is an internal knot then the spline is bent to a new shape, while if the knot corresponds to the end-points, the start and end offset region-parameters are adjusted resulting in the background gradient altering.

 

A new option on the Components Property Page allows the internal knots within a spline background to be optimised. Please note, the chi-square goodness-of-fit knows nothing about the physical world and therefore optimising a background, while improving the goodness-of-fit will probably have nothing to do with the true mechanisms unless the model optimised is perfectly defined and there is no noise in the data. Well-defined rigid models are the only models worth optimising. Backgrounds are the least-well understood shapes in XPS and as such optimisation is not recommended. The inclusion of the spline background type in CasaXPS is intended for use where all else fails: for example a peak positioned on a strong plasmon loss feature is not open to a Shirley background approximation, however a Spline Linear with a few judicious modifications may allow an analysis to proceed.

 

While optimisation of peaks and background is not recommended, optimising a background for a region without peaks does have a useful benefit. The spline background, for a well-chosen interval, will create a smooth approximation to the signal and so provides a means of estimating the noise in the data. The estimate for the noise will appear along with the residual trace in the form of the standard deviation in the normalised residual. If Poisson statistics are at work, then the value for the noise should be close to unity. With knowledge of this statistic for a given piece of data the target value for a peak-fit can be established.