The Calculator: Subtracting Spectra

The subjects covered in this section include:

1. The user interface for the Calculator property page on the Spectrum Processing dialog window.
2. Issues with XPS background subtraction.
3. Quantification of narrow scan spectra.

A specific example is used to illustrate features in CasaXPS.

Motivation for the Analysis

The first step in any quantification is to define backgrounds to spectral features. The most commonly used backgrounds are linear, Shirley or Tougaard, all of which owe their popularity to ease-of-use rather than the ability of these shapes to adequately describe the background beneath a photoelectric peak. Nevertheless, despite their failings, the desire of most analysts is to apply these algorithm to all peaks used for quantification in a consistent manner and gain virtue by producing repeatable results. Further, the choice of background is often coupled with a particular set of sensitivity factors, so there is a strong desire to reduce all data to an appropriate state in which the preferred background is easily deployed.

The example chosen to examine the Calculator in CasaXPS contains a small Cr 2p doublet located on a loss structure resulting from a large O 1s peak. In the absence of the O 1s peak, most analysts might choose to use a Shirley background as a means of defining the intensity from the Cr 2p doublet; however the energy loss structure from the O 1s results in the Cr 2p doublet being tilted with respect to the appearance of these two peaks in the absence of oxygen and further, the O 1s loss structure contains minor loss peaks lying within the limits of the Cr 2p doublet (Figure 1). These minor loss peaks are of significant size compared to the chromium doublet. The spectra shown in Figure 1 are acquired from modified and unmodified surfaces, where the Cr 2p doublet appears in the spectra following the modification of the material. The hope is therefore to remove the contribution from the O 1s loss structure from the Cr 2p peaks in the modified material using the unmodified O 1s loss structure, before applying a standard Shirley background to define the intensity of the chromium signal.

Figure 1: Comparison of the Cr 2p energy interval for both the modified and unmodified materials.

Solution

The intention is to quantify a set of samples for which silicon, carbon, oxygen and chromium are quantified using narrow scan spectra. The O 1s peaks shown in Figure 2 illustrate the nature of the problem. The lower trace is the data taken from the unmodified material and, although the count rates are similar, the data from the modified material differs potentially in magnitude and relative position of the spectral features. Before attempting to remove the distortions from the Cr 2p doublet due to the O 1s loss structure by subtracting the unmodified data from the modified data, the two sets of data must be calibrated in energy and scaled in intensity in such a way as to retain the essential quantification information.

The Experiment Frame in Figure 1 displays a zoomed section of the O 1s traces displayed in Figure 2, however the to traces in Figure 1 are visualised using a display option which normalises the displayed data at a point (indicated in Figure 1 by the black vertical line). The spectra as displayed in Figure 1 look reasonably well matched, however the choice for the normalisation point required an element of trial and error before settling on the position seen in Figure 1. While visually acceptable, the same procedure for scaling the data is far less acceptable when the difference of the scaled data is intended for use in quantification against other intensities. When quantification is involved, the method for scaling and shifting the data should be as systematic as possible.

Normalising the display of overlaid spectra: The Normalise Display option on the Y Axis property page of Tile Display Parameters dialog window allows the scaling of two or more spectra, for display purposes only; the spectra are displayed using the same axes determined for the active spectrum in the active tile. The data is scaled using the intensities from a single data bin within each spectrum, where the position of the data bin is determined by the location of a vertical line cursor. To adjust the position of the vertical cursor the Shift Key must be held down while the left-mouse-button is click at a point on the active tile. The state of the Normalise Display option can be toggled using the toolbar button.

Figure 2: Experiment Frame showing the VAMAS blocks from the modified (top row) and unmodified (bottom row) samples.

Normalising the Data

The procedure for normalising a data-set in preparation for use with the Calculator is performed on the Calibration property page of the Spectrum Processing dialog window (Figure 3). The Calibration property page in Figure 3 is defined ready for the data set shown in Figure 2, where the Si 2p spectra in each data set are about to be used to compute the necessary adjustments to both intensity and energy. The idea is that the two samples are essential equivalent in terms of the Si 2p spectra and that any differences in position and intensity of these two independently acquired Si 2p spectra can be accounted for within the acquisition process. That is to say, if each spectrum within a data set is energy calibrated and intensity scaled using a normalisation constant determined from the Si 2p peak, then provided the same procedure is applied to both data sets, the background characteristics on the Cr 2p data can be accommodated by subtracting the two sets of scaled spectra. Further more, making these same adjustments to each spectrum in the data based on the counts per second intensity from the Si 2p data will leave the quantification table invariant with respect to the transformation. The steps to perform these transformations are as follows:

1. Define a quantification region on each of the Si 2p spectra.
2. Enter the position for the Si 2p peak in the True text-field on the Calibration property page.
3. Since regions are defined on the Si 2p spectra as part of this procedure, the tick-boxes in the section labelled Adjust for both regions and components should be ticked.
4. Ensure the tick-box labelled Use Reference Intensity is also ticked.
5. Ensure only the Si 2p VAMAS blocks are selected in the right-hand-side of the Experiment Frame.
6. Finally, press the button labelled Apply By Row (1^st Region)

The consequence of these steps is the creation of a new Experiment Frame in which each data set now appears as energy calibrated and intensity adjusted spectra. The Si 2p region defined on the original data set have been used to compute the measured position of the Si 2p peak and also the intensity of the peak in counts per sec electron Volts. These computed values for the two Si 2p spectra are used to shift each of the spectra on a row by row basis and the intensity of each spectrum is scaled so that the area of the Si 2p peaks in the new Experiment Frame is equal to the arbitrary value entered in the Reference text-field. All peaks in a row are scaled by this same value resulting rows of data from different samples all scaled so the intensities are directly comparable. The data is now ready for the Calculator.

Figure 3: Calibration Property Page where the parameters are set-up ready to scale and energy calibrate a data set.

The new Experiment Frame generated by the calibration step is assigned the same name as the original VAMAS file, but with the string _Norm concatenated with the base name of the VAMAS file (see the title bar for the CasaXPS main window in Figure 4). The data in the normalised file is scaled in intensity measured in CPSeV, therefore the dwell-time and number of scans fields in the original file are no longer meaningful and so are set to unity in the normalised VAMAS blocks. A further point worth noting is that the area field reported for the Si 2p spectra on the Regions property page of the Quantification Parameters dialog window is equal to the requested scale value, which means that transmission and escape depth corrections are also accounted for during the intensity scaling procedure. The transmission and escape depth parameter are transferred to the new file of scaled spectra so quantification can proceed in an identical fashion to the equivalent computation performed on the original file.

Figure 4: Calculator Property Page

The intensity calibration might equally well be performed based on a synthetic component rather than a quantification region. If the intensity for the normalisation is determined from a synthetic component, it may be a surprise to observe the area parameter from the synthetic component, following the normalisation, is not necessarily equal to the reference intensity, which was the case for normalisation based on regions. Indeed, if transmission and/or escape depth corrections are included in the calculation, the area parameter for the synthetic component used to normalise the spectra will not equal the reference value. This is because the area value seen on the Components property page of the Quantification Parameters dialog window is a parameter for a peak model and is therefore an input value. The values used in a quantification report are output parameters and according to the rules used in CasaXPS, only output values are adjusted for transmission and escape depth, therefore the area reported for a component in a quantification report will agree with the reference intensity used to normalise the spectra. In the case of the quantification region, the area is computed from the data and therefore an output; hence the transmission and escape depth corrections are already included area as determined from the region.

Subtracting the Spectra

The Calculator property page on the Spectrum Processing dialog window (Figure 4) offers a range of options for performing arithmetic on spectra. The calculator is structured so that a spectrum is loading into a temporary location associated with the Calculator property page and from this temporary location the data is applied to any number of spectra indicated via the browser, where the result of the operation is passed into the processed data for each of the spectra included in the browser selection.

The data shown in Figure 4 are displayed using a zoomed section of the O 1s regions from both the modified and unmodified materials following the energy calibration and intensity normalisation procedure described above. After normalisation, the unmodified background lies above the Cr 2p doublet peaks, although the data is scaled appropriately. The calculator requires the data from the unmodified sample to be loaded into the temporary location and the trace in the temporary location positioned below the Cr 2p doublet by an offset operation. Once prepared, the temporary data can be subtracted from the Cr 2p data to yield a spectrum for which a Shirley background is applicable. Using the normalised Experiment Frame, the steps within CasaXPS are as follows:

1. Display the O 1s spectrum from the unmodified sample in the active tile and press the Set Operand button on the Calculator property page. The trace associated with the temporary location on the Calculator property page is displayed over the top of the data in the active tile and will continue to be displayed for as long as the Calculator property page is the top page on the Spectrum Processing dialog window.
2. Double-click the Cr 2p narrow scan spectrum VAMAS block from the modified material. The Cr 2p spectrum will display in the active tile and, provided the calculator page is active, the calculator operand (temporary location data) will appear also in the active tile.
3. Press the Offset Adjust button (Figure 4). The action associated with the Offset Adjust button causes a negative offset to be applied to each data channel of the temporary calculator operand. For XPS spectra, this ensures each data from the calculator operand is below the target spectrum; in this case the Cr 2p data.
4. Select the Cr 2p VAMAS block in the right-hand-side of the Experiment Frame. Only those spectra selected in the browser will be operated upon by the calculator. Further more, if the same operation is required for a set of Cr 2p spectra taken from different samples, say, then selecting all the Cr 2p spectra at the same time permits the action to be applied on bulk.
5. Select the type of arithmetic operation required. In this example the radio button for subtraction should be chosen.
6. Press the button labelled Apply to Browser Selection. The current processed data in the Cr 2p spectrum is replaced by the section of the O 1s spectrum subtracted from the Cr 2p data.

The exercise is completed by defining appropriate quantification regions for the four narrow scan spectra (C 1s, Si 2p, O 1s and the computed Cr 2p data) and the creating a quantification table either using the Quantification property page on the Annotation dialog window or the Report Spec property page of the Quantification Parameters dialog window.

The result of the quantification based on the normalised data and the use of the calculator is superior to a quantification performed on the original data. Apart from eliminating the general trend of the O 1s loss background, a first order correction for the resonant loss feature clearly visible in Figure 4 is also possible (Figure 5). For small Cr 2p peaks, the background due to scattering of the O 1s transition would certainly result in an over estimate for the intensity of the Cr 2p signal if the procedure described above were not followed.

A note of caution however, is that any manipulation of the data resulting in intensity adjustments invalidates the use of Monte Carlo error analysis. Uncertainties determined from quantification regions or synthetic peaks require the data to obey Poisson statistics; any scaling of the data will remove the information needed to analyse the errors and therefore error bars can not be computed for data modified by the calculator.

Figure 5: Quantification based on the narrow scan spectra selected in the right-hand-side of the Experiment Frame. The insert tile displays the Cr 2p after the O 1s background has been removed using the calculator.

The Calculator User Interface

The following is a general review of the Calculator user-interface.

The Calculator section of the Calculator property page seen in Figure 4 represents those options associated with the definition and manipulation of the temporary VAMAS block information referred to as the operand.

The operand is set from the active spectrum (first VAMAS block selected and displayed in the active tile). On pressing the Set Operand button, the current temporary VAMAS block maintained by the Calculator property page is replaced by the VAMAS block for the active spectrum in the active tile. A trace from the operand is displayed in the active tile whenever the Calculator property page is active.

The operand is combined as a right operand with the current browser selection using the operator selected from these radio buttons. The operator must be chosen before the Apply to Browser Selection button is pressed.

The data from the current operand is used as the right-operand for the chosen operation and is applied to each left-operand corresponding to the VAMAS blocks selected in the right-hand-side of the Experiment Frame. The result of the operation is stored in the process data for the selected VAMAS block. Resetting the processing operations using the Processing History property will restore the raw data, thus undoing the action of the calculator.

The data held within the operand may be adjusted relative to the spectrum displayed in the active tile. These adjustments can take the form of button actions or mouse controlled offsets, shifts and scaling. When adjusting the operand using the mouse, the Shift-Key must be held down. If the mouse is left-clicked at a point in the active tile whilst holding down the Shift-Key, the operand is offset in order to position the operand trace through the point at which the mouse click was performed. To scale and shift the operand the mouse should be dragged whilst at the same time the Shift-Key is held down. The vertical size of the resulting box determines the scaling applied to the operand data and the horizontal dimension produces a shift in the energy position. Pointing to a data channel on the operand with the Shift-Key held down and then dragging the mouse to the comparable position on the active spectrum will move the operand over the top of the active spectrum.

The action of the Reset Operand is to scale the data in the operand to match the ordinate range for the active spectrum in the active tile. That is to say, the operand data is force to be visible within the active tile and therefore in a state where the mouse actions can be used to position the operand relative to the active spectrum.

Pressing the CPS Adjust button alters the dwell-time and number of scans within the operand to match the VAMAS block corresponding active spectrum.

Adjusts the data in the operand to ensure all the ordinate values are non-positive. See the above discussion for the application of the offset adjust button.

Once an operand has been adjusted appropriately, the VAMAS block maintained by the Calculator property page can be saved to an Experiment Frame using the Save Operand button.

The remainder of the options on the Calculator property page act directly on the active spectrum or indicated VAMAS blocks. For some operations, the result of the operation is a new Experiment Frame containing VAMAS block generate by the action of a button, however for most the processed data in the active spectrum is altered by the operation.

The ordinates within the active spectrum are scaled and offset using the values entered into the Factor and Offset text-fields on the Calculator property page. A quantification region must be defined on the spectrum. The background subtracted data is scaled by the value entered in the Factor text-field and added to the background plus the value entered in the Offset text-field.

Analogous to the Scale option, however the data is normalise to the area of the first region defined on the spectrum before scaling is performed. The background is removed from the data and the offset value added to the normalised scaled ordinates.

Normalisation based on a data bin within a spectrum is performed using this button. The action of the button is modified by the tick box. If the tick-box is deselected, the normalisation is performed using the data channel with maximum intensity, however when ticked, the normalisation is performed using a datum indicated by a mouse action. To define the desired position at which the normalization is to be performed, hold the Shift Key down and left-click on the spectrum. The feedback text on the Calculator property page will indicate the value for the energy determined by the Shift-Left-Click action. Each datum in the spectrum is divided by the intensity at the selected bin, where the intensity is measured in counts per second.

Normalisation based on the maximum intensity in a spectrum, where the intensity is measured in counts.

The Calculate Noise option offers a means of visualising the noise in a spectrum. The procedure repeatedly applies a linear least squares fit to a linear polynomial over localised sections of the spectra with the view to minimising the information content at a local level. The difference between the spectrum and the smoothed curve replaces the processed data in the VAMAS block. The procedure is most effective away from peaks.

Two spectra overlaid in the active tile are used to generate a sequence of VAMAS blocks, where the new VAMAS blocks contain data derived from linear interpolation between the two original spectra. Linear combinations of the two spectra are generated where the percentage step size for the interpolating parameter is entered in the Factor text-field on the Calculator property page. The original spectra are assign experimental variables of zero and one hundred, so for example, if the Factor text-field is set to “1”, then the number of interpolated spectra will be one hundred and one. A new Experiment Frame is created containing the interpolated spectra.

An arbitrary arithmetic expression including the data from VAMAS blocks from a given Experiment Frame is used to create a new VAMAS block within a new Experiment Frame. Each VAMAS block within a VAMAS file is assigned an index number starting with zero. The individual VAMAS blocks are referenced, when included in an expression, using the VAMAS block index in the format vb0, vb1, vb2, etc. and combined using constants and brackets as seen in the VAMAS Block Expression dialog window shown in Figure 6. Once an expression is entered into the text-field and the OK button pressed, a new VAMAS block is created in a new Experiment Frame; the VAMAS block comment contains an entry indicating the name of the original VAMAS file and the expression used to create the data within the new VAMAS block.

Displaying the VAMAS block index: Figure 6 shows four tiles each displaying a single spectrum. At the top of each axes box a string displays information about the source for the data shown in the tile, namely, the VAMAS block index and the index for the corresponding variable. The index for the corresponding variable on display is typically index zero, while the vb# depends on which VAMAS block is drawn in the display tile. The option for displaying the spectrum index information is located on the Display property page of the Tile Display Parameters dialog window.

Figure 6