Multi-scan Peak Fitting

 

The follow example illustrates some of the issues associated with peak-fitting a unified model across a set of related high-resolution spectra. A summary of the steps involved is detailed below, as too is a description of how to copy and fit these models to other groups of spectra.

 

Spectra from a blend of Poly(methyl methacrylate) PMMA and Poly(styrene) PS was recorded on the SSI (SSX 100/206) with a monochromatic Al Ka X-ray line, a pass energy of 50 eV and an analyzed area of about 1.4 mm2 (Figure 1).

 

 

Figure 1: Blend of PMMA and PS recorded at CIFA [1].

 

Spectra from pure PMMA and PS [2] show that only PMMA has a contribution to the O 1s line seen in Figure 1. The PMMA C 1s and O 1s peaks can be decomposed in respectively four [C-(C,H), C-C=O, C-O and O-C=O) and two [O==, O-] components the areas of which follow the 2:1:1:1:1:1 ratio. The C 1s [C-(C,H] peak of PS appears at the same binding energy as the dominant C-(C,H) component in PMMA C 1s line.

 

The traditional method for analyzing the high-resolution spectra from such a material is to construct two separate peak models for the C 1s and O 1s spectra and then optimize the peak parameters without reference to the required relationship between C1s and O 1s peaks components. The final peak fits are then judged by comparisons between the intensities for the two sets of peaks optimized separately. Alternatively, a PMMA peak model could be constructed for both the C 1s and O 1s lines as well as the PS C 1s line(s), which is then optimized as a unit. The outcome of such an optimization can differ from that of optimizing the peak fits separately.

 

Figure 2: Separate peak-fits for the C 1s and O 1s high-resolution from the PMMA+PS blend.

 

Figure 2 and the corresponding quantification reported in Table 1 show the results of optimizing the C 1s and O 1s synthetic peaks based upon each to the separate spectral regions. The constraints shown in Table 1 do not include any information about the relationship between the PMMA C 1s and O 1s lines. Although the residuals displayed in Figure 2 are reasonable, the Atomic Concentrations in Table 1 deviate from the expected stoichiometry for the PMMA polymer.

 

Table 1

Name

Energy

% Conc.

Pos Const

FWHM Const

Area Const

Const Id

C 1s-1

284.744

22.37

297.51 , 277.51

0.3433 , 8.582

E * 2

A

C 1s-2

284.744

18.38

A - 0

A * 1

4.0 , 10000000.0

B

C 1s-3

285.675

11.19

297.51 , 277.51

A * 1

E * 1

C

C 1s-4

286.72

11.2

297.51 , 277.51

A * 1

E * 1

D

C 1s-5

288.872

11.21

297.51 , 277.51

0.2227 , 5.568

4.0 , 10000000.0

E

O 1s

532.031

12.82

543.51 , 523.51

0.5929 , 14.82

4.0 , 10000000.0

A

O 1s

533.628

12.84

543.51 , 523.51

0.2376 , 5.94

A * 1

B

 

Figure 3 on the other-hand has been fitted using additional constraints linking the areas for the PMMA C 1s lines to the O 1s lines shown in Table 2. The optimization is performed on the C 1s spectrum at the same time as the O 1s data and as a result the relative intensity for the saturated carbon peaks has altered between the models defined by Table 1 and Table 2. Without imposing the additional constraints between the C 1s and the O 1s PMMA lines in Table 2, it is difficult to visually determine how the C 1s envelope should be fitted in order to achieve the correct stoichiometry for the PMMA component. Obviously, individually optimized spectra will not have the necessary input to ensure the known relationships and therefore fitting the spectra as a unit has clear advantages.

 

Figure 3

 

Table 2

Name

Energy

% Conc.

Pos Const

FWHM Const

Area Const

Const Id

C 1s-1

284.711

25.02

297.51 , 277.51

0.3433 , 8.582

E * 2

A

C 1s-2

284.711

12.43

A - 0

A * 1

4.0 , 10000000.0

B

C 1s-3

285.499

12.51

297.51 , 277.51

A * 1

E * 1

C

C 1s-4

286.639

12.51

297.51 , 277.51

A * 1

E * 1

D

C 1s-5

288.866

12.51

297.51 , 277.51

0.2227 , 5.568

4.0 , 10000000.0

E

O 1s

532.032

12.51

543.51 , 523.51

0.5929 , 14.82

E * 2.93

F

O 1s

533.623

12.51

543.51 , 523.51

0.2376 , 5.94

E * 2.93

G

 

Performing a Multiple Region Optimization

Optimization across spectral regions is achieved by overlaying the spectra concerned in a single tile, creating all the components required as part of the model and pressing the “Fit Components” pushbutton on the Components property page. When more than one spectra appears in the active tile, performing a fit (by pressing the Fit Components button) causes CasaXPS to prompt the user with a dialog window asking whether the fit should be achieved using multiple spectra. If the Yes button is pressed on the dialog window, the optimization will use the components defined on the active spectrum in the active tile and then apply these components to each of the spectra displayed in the active tile. If the No button is pressed then only those components corresponding to the active spectrum will be optimized; the Marquardt optimization method will leave components with zero intensity inside the data region unchanged.

 

 

Constructing a Model Spanning Multiple Spectral Regions

 

CasaXPS allows synthetic components to be defined on a single spectrum where the location of a synthetic component does not have to belong to the energy range for the data in that spectrum. Thus both the C 1s and O 1s synthetic components can be defined on the same spectrum. If both spectra to be fitted are overlaid in a tile and the Components property page on the Quantification dialog window is visible, then creating components for both the C1s and the O 1s will assign these components to the active spectrum in the active tile. When multiple spectra are overlaid, the active spectrum is the spectrum whose name appears in the top text-field of the Components property page. It is useful to note which spectrum is the active spectrum out of the set of spectra ultimately used in the optimization.

 

As a rule, when a new component is created CasaXPS attempts to find a reasonable set of parameters based upon the residual for the active spectrum. The active spectrum cannot be used to define peak parameters for components outside the range of the data and so an alternative strategy must be used for creating these out-of-range components. In order to create the basis components for the model, each of the individual spectral regions may be used to initially create the appropriate peaks. Once the peaks have been created on the individual spectra, the “Copy All” button on the Components property page allows these peaks to be moved from one spectrum to another. After assembling the entire set of peaks on the active spectrum, the appropriate constraints can be imposed.

 

Viewing the Components and their Residual

 

The normal mode of display shows each spectrum together with components and corresponding residual over the energy range for that spectrum. When peaks are defined on a single spectrum corresponding to other related spectra then an alternative display mode is required. An option on the Display property page on the Tile Parameters dialog window allows the components displayed to be switched to only those on the active spectrum. Once this switch is set, the components and residuals from the active spectrum of the active tile are plotted against each of the spectra displayed in the active tile. Figure 4 shows the Tile Parameter dialog window where the “Display Comps from First Spectrum” option is ticked. Note that without this display option ticked, the components outside the energy range of the active spectrum will not be visible, even though the overlaid spectra are displayed. If this option is not ticked, any residual plots will relate to the individual spectra and their specific components (if any) rather than the common set of components on the active spectrum.

 

Figure 4: Display Comps form First Spectrum

 

Issues associated with common peak models

 

 

Once a set of peaks for the C 1s and O 1s spectra are defined, the problem of relating intensities must be addressed. The raw spectra for the two regions differ with respect to the relative sensitivity for the elements, variation in the transmission efficiency of the instrument and mean-free-path adjustments. In the case of an SSI instrument the mean-free-path energy dependency is entered into the VAMAS file created by CasaXPS as a second corresponding variable. The transmission variation is then accounted for within the RSF values. Generally, however, to compare data from different elements and/or acquired over different energy intervals requires the raw spectra to be corrected for transmission as well as adjustments made to any area constraints included in the combined model using RSF information.

 

Figure 5 shows the Components property page, where the peak in column A represents the C-(C,H) saturated hydrocarbon component from PMMA while column B is fixed with respect to column A in terms of position and FWHM. Column B represents the PS C-(C,H) line. Column C is a second PMMA C 1s line and each of the C 1s lines from PMMA are related in area to the C 1s line in Column E. All these C 1s peaks have identical RSF values and are measured over approximately the same energy range. This however is not true for the PMMA O 1s lines and although the energy-dependence variation can be removed by applying the Intensity Calib option, the RSF differences must be added to the model in the form of constraints. Note that in Table 2 the area constraints for the O 1s lines are set to the ratio of RSF value for the O 1s lines to the C 1s lines. The peak parameters for the area are relative to the active spectrum and so the O 1s areas must be scaled by the RSF values as well as the stoichiometry for the molecule. Stoichiometry dictates that the area for the O 1s lines should be the same and also equal to the area of the C 1s line in Column E (Table 2).

 

 

 

Figure 5: Components Property Page.

 

Summary

 

Steps required when peak-fitting across multiple high-resolution spectra:

 

 

 

Automatic Fitting of Peaks Across Multiple Spectral Regions

 

Once a peak fit has been performed on a single tile containing multiple spectral regions, the set of peaks can be copied and auto-fitted to other overlaid spectra. This requires each set of spectra, for which an auto-fit is required, to appear in separate tiles in the scrolled list on the left-hand-side of the Experiment-frame. The scrolled list in the left-hand-side can be loaded with overlaid spectra by selecting the spectra using the right-hand-side browser view and then pressing the  toolbar button. The result of pressing the toolbar button is to create a set of tiles (one per row selected in the right-hand-side) in which the selected spectra are overlaid on a row basis. Figure 6 shows a depth profile where three rows in the right-hand-side are selected and subsequently displayed using the  toolbar button. Spectra displayed in this format may be fitted to a synthetic model by pressing the Copy and Fit button on the Components property page. Note that only components will be copied by this operation, so background regions must be defined prior to the button being pressed.

 

 

Figure 6: Each row selected in the right-hand-side of the experiment frame is displayed as overlaid spectra in the left-hand-side once the  toolbar button is pressed.

 

[1] Michel Genet (private communication)

[2] Beamson G. and Briggs D., “The XPS of Polymers Database” Surface Spectra Ltd (2000)