XPS Quantification and Related Subjects

The subjects covered in this section are:

The basic concepts of quantification regions and synthetic components.
Relative Sensitivity Factors and instrument transmission.
The Element Library mechanism in CasaXPS.
Report generation.

The CasaXPS interface for preparing a quantification report is the Quantification Parameters Dialog Window (Figure 1), available under the Quantify menu item on the Options Menu.

Figure 1: Quantification Parameters Dialog Window

Quantification Regions

The intensity of a peak in an XPS spectrum is measured by integrating the recorded counts per second minus a computed background over an energy interval delimiting the peak. For the purposes of quantifying a sample, the integrated intensity must be adjusted for both relative sensitivity of the various photoelectric lines and energy dependent instrumental/measurement artefacts before computing the elemental composition for a surface. The primary purpose of quantification regions as defined in CasaXPS is to provide the information required for this calculation.

Synthetic Components

When photoelectric peaks overlap, the tool most often used to partition the contributions from the individual transitions to the recorded envelope is optimisation using predefined line-shapes for modelling the underlying transitions. The intensity for a peak is determined by fitting a set of synthetic components to the data by minimising the sum of squares residual, where the intensity for a peak is extracted as one of the optimisation parameters. A synthetic component is therefore analogous to a quantification region; however quantities such as position, area and full-width-half-maximum (FWHM) are determined from an optimization procedure using a given line-shape rather than, in the case of quantification regions, being computed directly from the data.

Quantification Items and Reports

Since quantification regions and a synthetic components both result in characteristic quantities for XPS peaks, in CasaXPS both are referred to as quantification items. Quantification reports are constructed from the characteristic values determined from these quantification items.

A quantification report may be either a Standard Report or a Custom Report. The Standard Report option allows a tabulation of quantification items, grouped by experimental variable, where values taken from each quantification item appear as a line in the final report. Various options are available for Standard Reports to permit the user to define the format for each row of information, however each quantification item, if included, appears as a row in the table of results. Custom Reports, on the other hand are column orientated and one or more quantification items can contribute to the values reported in a column. Essentially, a column in a Custom Report is defined in terms of arithmetic expressions involving the name fields given to the quantification items and are aimed at extracting trends within a data set defined by the variation of quantification items with respect to the experimental variable.

Quantification of Spectra

The following is a set of examples illustrating the various methods for preparing a quantification report. First, however, an overview to the possible analysis scenarios is presented before the mechanics of performing the tasks is detailed.

Quantification of a Survey Spectrum

The most common and basic analysis of a sample is probably the elemental quantification using quantification regions on a low resolution survey spectrum. Figure 2 shows a survey spectrum acquired from a PMMA sample using a Kratos Axis 165 operating in Hybrid mode at a pass-energy of 160 eV, where the elemental quantification in the form of an atomic concentration table appears as annotation on the tile displaying the data.

In CasaXPS, the method for creating the quantification table may follow several paths:

Automatic peak identification leading directly to annotating the display with a region quantification table.
Manual peak identification followed by manual labelling of peaks leading to region creation based on the annotation labels.
Region creation using the Element Library entries.
Direct region creation using the Regions Property page.

Quantification tables based on regions can be displayed over the data, as seen in Figure 2, or alternatively separate quantification table text files are created from the information derived from the quantification regions. The route taken leading to the quantification table depends on the nature of the spectrum under analysis and also personal preference.

Figure 2: Quantification of a Survey Spectrum

The easiest method, when it works, is the automatic peak identification and region creation route. The regions shown in Figure 2 were created using this procedure. The spectrum in Figure 2 is a very simple PMMA spectrum and therefore lends itself to automatic analysis because of the good signal to noise and the peaks are within the expected energy position for the various photoelectric lines; automatic peak identification generally works provided the peaks can be distinguished from the noise and the spectrum is calibrated with respect to energy. The steps to perform an automatic quantification are as follows:

Display the survey spectrum in the Active Tile.
Calibrate the energy scale using the Processing dialog window.
Invoke the Element Library dialog window.
Press the Find Peaks button on either the Element Table property page or from the Periodic Table property page. Both buttons perform the same task.
Use the Periodic Table buttons to add or remove elements from those identified in the previous step until the set of element markers match the peaks in the data.
While still displaying the element markers, press the Create Regions pushbutton located on the Element Library dialog window. A set of quantification regions are created and the corresponding quantification table is displayed over the spectrum.
At this point it is worth checking the background start and end positions for each region and, if required, creating any additional regions. The need to manually create regions is sometimes required because the automatic creation procedure will only create a region when a peak can be distinguished from the background and occasionally minor peaks may be ignored by this process.

Visually reviewing regions: A quick means of checking the energy limits for a set of regions is to press the Reset toolbar button. The Reset toolbar button loads a set of energy intervals on to the zoom list determined from the current set of quantification regions. Once the zoom list is loaded in this way, pressing the Zoom Out toolbar button causes the display to step through the quantification regions.

The regions created via the Element Library dialog window are chosen from those elements identified using the Find Peaks button and subsequently adjusted using either the Element Table Scrolled List or the Periodic Table property pages on the Element Library dialog window to add or remove elements from those originally identified. For any given element, the transition with the largest RSF is selected when the quantification regions are created. There may be good reasons why the default transition is not appropriate and depending on whether the choice is specific to a given sample or preferred in general, the regions can be either modified manually or the default transition overridden using a configuration file. An example of an element for which the default transition is rarely used during quantification is aluminium. The Al 2p transition is generally preferred to the Al 2s when quantifying a sample, presumably due to the complex background structures resulting from metallic aluminium, and since the RSF for the Al 2s transition is larger than the Al 2p transition, it becomes necessary to force the creation mechanism to choose the Al 2p transition when automatic region creation is performed. A configuration file CasaXPS_quant.lib located in the same directory as the CasaXPS.exe executable file is used to override the default creation choice. The entries in the file CasaXPS_quant.lib are formatted identically to the standard CasaXPS element library, therefore to override a given transition simply copy the corresponding entry from the element library file into the configuration file CasaXPS_quant.lib. The significant information in the CasaXPS_quant.lib file is the species and transition columns; all other values in this file are ignored, but nevertheless must be included.

The second means of creating quantification regions is based on annotating the peaks prior to creating the regions. A typical spectrum will require the labelling of peaks for presentation purposes and so as part of the labelling process quantification regions can be created en route to labelling the spectrum. Peak labels themselves are created in conjunction with the Element Library dialog window and since one problem associated with the quantification process is the correct extraction of the relative sensitivity factors for the peak in question, this link between the peak label and the element library is helpful when creating regions. The methodology is as follows:

First annotate the peaks used to quantify the sample. The Peak Labels property page on the Annotation dialog window offers those lines for which the Element Library has been used to display element markers and when created via the Peak Label property page, the labels are assigned the text used in the Element Library.
Once the peaks intended for use in the quantification are labelled using the text from the Element Library, the Regions property page is used to create the quantification regions. That is to say, the Create from Label pushbutton causes the creation of a quantification region for each peak label.
The remaining peak labels for those peaks not used in the quantification can now be created using the same mechanism as that used in step 1.

A survey spectrum VAMAS block does not initially contain information identifying peaks in the data, hence the importance of linking the Element Library text strings with quantification region creation via the annotation peak labels. A further means of specifying the transition associated with a peak, but without the need to create peak label annotation, is via the Element Table scrolled-list (Figure 3). The creation of quantification regions is performed by selecting the Regions property page on the Quantification Parameters dialog window and, on the Element Library dialog window, ticking the two tick-boxes below the scrolled list in Figure 3 labelled, Zoom When Line Selected and Create When Line Selected followed by selecting a line via the name field in the scrolled list. These tick boxes modify the behaviour of the scrolled list on the Element Table property page. The Zoom When Line Selected tick-box causes the action of picking a transition in the Element Table to zoom the display so that the energy scale visible in the Active Tile matches a small interval around the line indicated via the name field of the scrolled-list. The Create When Line Selected tick box similarly modifies the same action by creating a quantification region using the energy interval currently used to display the spectrum. The act of creating a quantification region by selecting a line in the Element Table ensures the correct relative sensitivity factor is used in the newly created region.

Figure 3: Element Library Property Page

The fourth method for creating a quantification region is to simply press the Create button on the Region property page of the Quantification Parameters dialog window. The current zoom state determines the start and end energies for the new created region, however all other parameters are merely a repeat of the parameters previously used to create a quantification region. If the species/transition fields are consistent with an entry in the Element Library, then the relative sensitivity factor is retrieved from the library and used in the quantification region. For survey spectra, owing to the lack of species/transition information, the basic creation mechanism is of little use, however if narrow scan spectra are involved, the species/transition fields should be correctly assigned, in which case the Create pushbutton will indeed result in the correct assignment for the relative sensitivity of the line.

Although the Create pushbutton, when applied to a survey spectrum, creates a region without retrieving the RSF from the library, the RSF from the library can be entered using the name field for the region. The default name field in the created region will not match any element library entry, however if the region name is re-entered using a name from the library preceded by the # character, then on pressing the return key the name field will be entered without the # character and the element library field matching the string is used to update the RSF in the region.

In the case of a survey spectrum, an atomic concentration table may be displayed over the spectrum as seen in Figure 2 or alternatively a quantification report is generated using the Report Spec property page on the Quantification Parameters dialog window. When using the Report Spec property page, the VAMAS block containing the survey spectrum must be selected in the right-hand-side of the Experiment Frame prior to pressing the button used to generate the report table.

Quantification of High Resolution Spectra

The mechanisms described for the creation of quantification regions on a survey spectrum are also applicable to high resolution data from a sample typically recorded as a sequence of narrow scan spectra. The key difference is that each narrow scan spectrum is assigned one or more quantification regions and since more than one spectrum is included when quantifying a sample, the quantification table generated from these separate narrow scan spectra requires the use of the browser in the right-hand-side of the Experiment Frame to perform the task. Those spectra for which a quantification report is desired must be selected in the right-hand-side of the Experiment Frame. Further more, quantification using multiple acquisition regions for a given sample requires all corresponding VAMAS blocks used in the quantification to appear in the same row of the browser pane in the right-hand-side of the Experiment Frame. If the VAMAS file does not result in the correct alignment of the VAMAS blocks in the right-hand-side, then the values for the species/transition and the experimental variable must be adjusted until those VAMAS blocks containing the spectra and quantification regions for each sample all appear in a single row. A quantification report is generated from only those quantification regions for which the VAMAS blocks are selected in the right-hand-side and a separate row will appear in the quantification table for each quantification item in the row of selected VAMAS blocks in the right-hand-side.

Quantification with Tags

A problem when quantifying samples, particularly for older instruments, is the variation of an analyser’s transmission characteristic with pass energy, lens modes and any other acquisition variables. A consequence of these operating mode dependent variations in the measured peak areas is that, without transmission correction, quantification must be performed using the same acquisition settings. Transmission correction usually takes the form of, so called, transmission functions and in modern instruments these are typically saved along with the spectra for use during quantification. Older instruments rarely include transmission correction so, when more than one operating mode is used, an alternative strategy is offered in CasaXPS for quantification.

Quantification using TAGS is designed to allow for the situations where elemental concentrations determined from the survey operating mode are combined with high resolution data to reveal chemical state information unavailable in the lower resolution survey spectrum. Peak models determined from the high resolution spectra are associated with quantification regions defined on the survey spectrum and the relative intensity of the synthetic peaks from the high resolution spectrum are used to proportion the elemental concentration from the survey data. Thus, the chemical state information present in the high resolution spectra is referenced back to the survey spectrum. The result is a combined quantification report in which the transmission variations are eliminated from the quantification report.

Both quantification regions and synthetic components include as part of their definition a TAG field. These TAG fields are text strings, which when the same string is used for both a region and a corresponding synthetic component, the region intensity is further tabulated using the relative intensities of synthetic peaks with the same string in the TAG fields as the string entered for TAG field in the region. Quantification using TAG fields is one of the options on the Report Spec property page of the Quantification Parameters dialog window.

Quantification of Depth Profiles

The general philosophy in CasaXPS is to handle larger data sets by identical mechanisms to those used for smaller set of data. The same quantification items used to quantify survey and narrow scan regions are used to reduce XPS depth profiles to traces for each chemical state monitored as a function of depth.

The structure of a profile experiment is essentially a sequence of survey or narrow scan spectra recorded following an etch cycle or stage tilt; thus the VAMAS blocks appear in columns corresponding to the assignments for the species/transition where each row is aligned with respect to a common etch time or angle. The route to tabulating a set of intensities as a function of experimental variable is via defining regions and/or synthetic variables for a spectrum and then propagating these quantification items to spectra with similar requirements. There is no requirement to propagate the quantification items through an entire set of spectra; rather the propagation is performed only on those VAMAS blocks selected in the right-hand-side of an Experiment Frame. Thus, a peak model, for example, can be adjusted at intervals during a depth profile in order to account for new or absent peaks resulting from a change of matrix material or interfacial anomalies. It should be emphasized, however, that each spectrum used to profile a sample must have quantification items assigned and so regions or synthetic components must be created directly or propagated to each spectrum in the profile.

Survey Spectra: Creating Quantification Regions, Relative Sensitivity Factors and Transmission Correction

As discussed above, the easiest method for defining quantification regions on a survey spectrum is using the automatic peak identification options on the Element Library dialog window followed by pressing the Create Regions button on the same dialog window. For well behaved spectra, such as the data shown in Figure 2, the results are generally achieved with minimal user intervention, however not all samples are as accommodating and some form of adjustments to the automatically created regions becomes necessary. The primary aim of the following is to describe the options available for the manual creation of quantification regions. The example chosen to illustrate the manual creation of quantification regions is also useful in understanding some of the issues associated with the quantification of a sample. The sample is pure gold, so the only significant peaks derive from the same material at different kinetic energies and from a range of symmetries (4s, 4p1/2, 4p 3/2, 4d, 4f and 5p3/2), which makes it possible to investigate the factors influencing quantification in a known regime.

Figure 4 is a gold spectrum taken from a Kratos Axis Ultra at UMIST in Manchester UK. The initial problem is to define the appropriate quantification regions for this unusual situation in which every transition for which relative sensitivity factors are available are used to measure the gold signal. If all is well, the atomic concentration table should report the same value regardless of the transition chosen. Figure 4 does indeed offer a quantification report demonstrating this property; however the route to such a report involves several steps worthy of discussion.

Figure 4: Gold Spectrum taken from a Kratos Axis Ultra

Manual Creation of Quantification Regions

The basic means of creating a quantification region is the Create button on the Quantification Parameters dialog window shown on Figure 1. On pressing the Create button, a new quantification region is created on the first spectra displayed in the Active Tile, where the start and end energy values for the region are determined from the interval displayed in the Active Tile. Additional information from the element library is entered into the region, such as the RSF, provided the name field in the newly created region matches the element/transition fields for an entry in the current element library loaded in CasaXPS. Since on creation via this route, the name field for the regions is constructed from the species/transition VAMAS fields for the data in the Active Tile, the RSF retrieval will only work for spectra in which the species/transition fields have been correctly assigned in the VAMAS data file. In the case of a survey spectrum, where multiple species/transitions are present, the RSF will not be retrieved and therefore must be entered manually. When creating regions on a survey spectrum such as the gold spectrum in Figure 4, the steps to follow are:

Display the spectrum in the Active Tile.
Zoom into the peak for which the region must be defined.
Press the Create button on the Regions property page on the Quantification Parameters dialog window.
Set the name for the region just created by entering the element/transition strings for the name preceded by the # character and press the enter key on the keyboard.

To display a spectrum in the Active Tile: Using the mouse left-hand button, double click the VAMAS block on the right-hand-side of the Experiment Frame. Alternatively, select the VAMAS block using the left-hand mouse button and press the toolbar button.

To zoom into a section of a spectrum: Use the left-hand mouse button to drag out a box over the display area of interest and once a box is displayed, click inside the box. The display will rescale to display the rectangular region previously bounded by the box.

Once the enter key on the keyboard is pressed, the # character is removed from the string entered for the name and the RSF is retrieved from the matching entry in the element library. The region name field can subsequently be altered to any string not starting with the # character without further updates to the RSF.

Figure 5 illustrates the use of the # character to force the region to retrieve the RSF from the element library. The element library name field for the doublet peaks displayed in the Active Tile in Figure 5 is Au 4d, therefore to retrieve the RSF for the region create for the displayed energy interval, the name field for the region is entered using the string #Au 4d. When the Enter Key is pressed, the region name is modified to Au 4d and this new string is used to match an entry in the current element library. If a match is found, both the RSF and the TAG string are updated within the region parameters, shown in Figure 6.

Figure 5: Zoomed energy interval showing a newly created region prior to the use of the region name field to trigger the update of the RSF and TAG fields.

Figure 6: Region parameters following the input of the string #Au 4d.

Relative Sensitivity Factors and Other Corrections

If information is retrieved from the element library, the name entered for the region must be an exact match for an entry in the element library. In the case of doublet states, spectral features derive from two peaks; these two peaks are labelled with the same principal and orbital quantum numbers n and l, but differentiated by the total angular momentum quantum number j. For example, in a gold spectrum, the doublet pair at about binding energy 83 eV are assigned to the two transitions Au 4f_5/2 and Au 4f_7/2 (Figure 7). The RSF for these individual peaks are different and so if only one peak from a doublet pair is used to measure the intensity for an element, the name used for the region should be identical to the name field in the element library for the chosen transition. In the case of the gold spectrum shown in Figure 4, the Au 4f doublet pair overlap to the point where it is necessary to use the total counts associated with the two peaks, in which case the RSF corresponding to the name Au 4f is used to scale the intensity prior to comparison with other transitions. This is in contrast to the 4p_1/2and4p_3/2 transitions, where the peaks are easily resolved and so the individual RSF entries for the two peaks are included in the quantification table in Figure 4. Ideally, the use of the combined intensity of the doublet pair is preferred from a statistical perspective; however in practice the influences of time, background and interfering peaks often force the use on one peak when quantifying a material. The default CasaXPS library therefore includes three entries per doublet pair, one for each individual peak in the doublet and one for the total intensity for the two peaks. The rule for using doublet peaks is to use the entry without a subscript for situations where both peaks are included in the measurement, that is both peaks should have the same RSF, and to only use the subscripted entries for cases when one peak from a doublet pair is included in the quantification table.

Figure 7: Element Library dialog window showing the three possible choices for the Au 4f transition.

The default CasaXPS library contains Scofield cross-sections for the relative sensitivity factors. These Scofield cross-sections were computed using Hartree-Fock theory to determine the relative intensity of the transitions throughout the periodic table for a given photon energy. The cross-sections are relative to the C 1s transition and the default CasaXPS library includes entries for both Mg and Al x-ray anodes. The theory used to calculate the cross-sections does not, however, include corrections for instrumental and sample dependent intensity variations. Without these corrections, XPS yields good relative measurements but poor absolute quantities. That is to say, a run of identical samples, when quantified using Scofield cross-sections, will produce good agreement between the resulting tables, however the numerical values will not compare favourable to the true proportions of the materials comprising the samples. It is therefore important to account for these additional intensity variations as part of the quantification procedure. The principal corrections are: instrumental transmission correction, instrument dependent angular distribution corrections to the measured transition and escape depth variations as a function of kinetic energy. The quantification table shown in Figure 4 has been computed using Scofield cross-sections corrected for all three intensity adjustments. Once these corrections are made to the intensity of the peaks used in quantification, the only remaining issues are that of background definition and matrix dependent effects. The former is at the user’s discretion, while the latter is beyond the scope of a one-size-fits-all library approach; however multiple CasaXPS libraries are easily maintained via the Input property page on the Element Library dialog window and so matrix dependent RSF tables can be accommodated within CasaXPS.

Most modern instruments offer transmission correction to account for the variation in performance of a spectrometer as a function of kinetic energy for the ejected electrons when measured using the different operating modes of the instrument. Various mathematical models are employed to describe these transmission functions; however the one that best fits the Scofield library is the transmission function correction procedure developed by the National Physical Laboratory (NPL) in the UK. For each operating mode of an instrument, a set of survey spectra from clean copper, silver and gold samples are acquired and these are reference back to a spectrum determined on a well characterised spectrometer at NPL. The result of the procedure is a transmission curve for each operating mode of the instrument and these transmission curves are added to the data whenever an acquisition is performed. Regardless of the source for the transmission curve, when added to the VAMAS data file as a corresponding variable, CasaXPS automatically detects the presence of the transmission curve and performs the correction at the time a quantification table is computed.

Once the instrumental transmission is accounted for, there is still an energy depend correction required originating from the sample. The depth below the sample surface from which electrons are collected by the spectrometer varies as a function of kinetic energy of the ejected electrons; sometimes referred to as the escape-depth correction, this adjustment to the peak intensities takes the form of dividing the area of a peak by the kinetic energy of the peak maximum raised to a constant power n, where n is typically a value between 0.5 and 1.0. In CasaXPS, the intensity is adjusted by multiplying by the energy raise to an exponent, and therefore the value used for the exponent should be a negative number.

Both transmission correction and escape-depth correction are applied by default, assuming the information is made available to CasaXPS. The transmission curve must be present in the VAMAS block as a second corresponding variable; however the value for the escape-depth correction is either present in the VAMAS block containing the spectrum or entered on the Regions property page in the text-fields within the Intensity Calibration section (Figure 1). A configuration file entry in the ParameterFile.txt file located in the CasaXPS.DEF directory allows the default value for a new VAMAS block to be specified different from zero. The values used to correct the peak intensities for transmission and escape depth are computed at the energy of the peak maximum. There is, however, a subtle difference between the meanings of “the energy at the peak maximum” for these two quantities. The transmission curve relates to the peak maximum with respect to the instrument and therefore relates to the kinetic energy of the electrons in flight through the analyser. In contrast, the escape-depth is considered by CasaXPS to relate to the kinetic energy of the ejected electron within the sample. For these reasons, the transmission correction is computed using the energy at the peak maximum before any energy calibration is performed, while the escape-depth correction is performed using the kinetic energy for the calibrated peak position.

Transmission and escape-depth corrections are energy dependent adjustments applied to the measured intensities; however there is a further correction related to the instrumental geometry and the symmetry of the electronic states used in quantification. The so called angular distribution correction can be viewed as a correction, which must be applied to the Scofield cross-sections, to account for intensity variation resulting from the angle of the x-ray source to the angle of the ejected electrons (analyser axis). If the angle in question is different from the, so called, magic angle of 54^o 44′ minutes for which correction is unnecessary, the values for the Scofield cross-sections must be adjusted to account for the angular distribution of photoelectrons ionized by unpolarized light impinging on an nl sub-shell.

The instrument used to acquire the gold spectrum in Figure 4 (a Kratos Axis Ultra) had an angle of 60^o between the x-ray source and the analyser axis, therefore a direct application of uncorrected Scofield cross-sections would not yield the quantification shown in Figure 4. In fact, the RSFs used to characterize the set of gold transitions where determined by correcting the Scofield cross-sections for both the angular distribution correction factors and the transmission function determined using the NPL instrument calibration procedure. The relative percentage concentration values were also computed using an escape-depth correction where the value for the exponent was -0.69. The table in Figure 4 illustrates the possibility of measuring the gold signal from any one of the six transitions resolvable in the gold spectrum. Given the range of kinetic energies for the peak positions and the variation in the electronic states, the consistent nature of the relative intensities is very good. The problem with offering this table as a paradigm for all quantification lies in the choice of background type and the quantification region limits. In the case of the gold spectrum in Figure 4, all the quantification regions are defined with linear background types and the energy intervals over which integration is performed are chosen to be reasonable subject to the constraint that a good result is achieved. There is greater uncertainty associated with real samples and the choice of background type and integration limits are without doubt the greatest source of error with respect to the precision of an XPS measurement. Nevertheless, without these corrections to the intensity calculation, it was not possible to reproduce the quantification in Figure 4 with the same consistency.

Angular distribution corrected Scofield cross-sections are calculated in CasaXPS for properly defined VAMAS files. The required information for the use of automatically corrected RSFs is a comment line placed in the VAMAS file comment section of the VAMAS file and an appropriate entry in the ParametersFile.txt configuration file. At present only VAMAS files converted from PHI MULTIPAK data files contain the required information, but as an alternative, CasaXPS libraries of corrected Scofield cross-sections are possible to construct. The library used to quantify the gold spectrum was created for a specific instrument, but the corrected Scofield cross-sections are such that spectrometers characterised relative to the gold spectrum in Figure 4, could write relative transmission functions to the data enabling the same modified Scofield library to be used in general. Since the gold spectrum was acquired on a Kratos Axis Ultra, the use of this gold spectrum and associated library is most appropriate for other Kratos Axis instruments.

Atomic Concentration Report

The quantification report displayed over the gold survey spectrum in Figure 4 is typical of the types of information used to characterise a sample. Various quantities are computed from the data, such as peak positions, FWHM and peak area, however the column reported under the heading At%, is in general, the atomic concentration calculated from the intensities following the application of all the corrections discussed above. Clearly, in the case of a pure gold sample the atomic concentration is 100% gold and the quantification table in Figure 4 is merely establishing the relative accuracy of measuring the gold intensity using any one of the six regions on display. When quantifying a real sample, the quantification table derives from a selection of regions, where one transition is chosen for each element identified as contributing to the peaks in the data. Given that m elements are so defined and therefore m regions defined on the spectrum, the calculation for the relative proportions of the sample surface or percentage atomic concentration is given by the formula:

The percentage atomic concentration for the i^th element X_i is defined by the adjusted intensity A_i as follows:

The terms contributing to the adjusted intensity are: the measured intensity for a peak I_i (either integrated peak area or peak height), the transmission function evaluated at the peak position T(E_i), the relative sensitivity factor R_i_,, kinetic energy E_i and escape-depth exponent n.

Data Orientated Discussion

The general overview presented above is now expanded using specific examples to illustrate the practical aspects of using CasaXPS to quantify spectra.

Quantification using High Resolution Spectra

Although elemental quantification is commonly performed on low resolution survey spectra, circumstances occasionally require the use of high resolution spectra for this purpose. A common reason for using narrow scan spectra is poor signal-to-noise in the data. The greatest source of error when computing the area of a peak results from noise-levels within the data channels used to tie the calculated background to the data. For weak peaks it may be necessary to increase the dwell-time compared to stronger peaks; the aim of most analysts is to acquire the data in the minimum time subject to the constraint of sufficient precision. The experiment shown in Figure 8 is an example of the case in point. A small amount of chromium is barely evident on the survey spectrum in Figure 8; however, using an increased dwell-time for a narrow energy interval containing the Cr 2p doublet allows efficient use of time when measuring the Cr signal to the require precision.

Figure 8:

Data acquired using different dwell-times, number of scans and energy step sizes are accounted for correctly by integrating the peak areas using the units of counts per sec electron Volts (CPSeV), thus eliminating these parameters from the quantification calculation. Switching lens modes or pass energy when acquiring the different narrow scan spectra will require the proper use of transmission functions to allow quantification to proceed.

The analysis of the experimental data shown in Figure 8 is as follows.

Charge correction: The first step is usually to correct the data for energy shifts due to charging of the sample under the influence of the x-rays. The Calibration property page of the Processing dialog window offers a range of procedures for charge correcting spectra (Figure 9). When the experiment consists of a set of narrow scan spectra, most likely the set of spectra all require an identical energy shift, where the value for the energy shift is determined by locating the peak on one spectrum. There are several ways of performing this task, however in the example shown in Figure 8 the calibration of the file was performed using the following approach:

Define a quantification region on the Si 2p spectrum (described below).
Select the VAMAS block containing the Si 2p data.
In the True text-field on the Calibration property page, enter the require energy for the peak position defined by the peak maximum in the quantification region previously defined on the Si 2p spectrum.
Un-tick the box labelled Use Reference Intensity and press the button labelled Apply by Row (1^st Region).

The result of these steps is to calibrate the energy for each spectrum in the same row as the Si 2p by shifting the energy scale by the amount required to place the maximum of the Si 2p peak at the energy entered in the True field on the Calibration property page. The position of the Si 2p peak is determined from the first region defined on the Si 2p spectrum. In this case there is only one quantification region defined on the Si 2p spectrum, but if more than one were defined, then the region in column A of the Regions property page of the Quantification Parameters dialog window is the one used in the shift operation.

Figure 9

It is also worth noting that each row of spectra in the right-hand-side, when calibrated using the Apply by Row (1^st Region), is independently adjusted. That is to say, each row in which the appropriate Si 2p VAMAS block is selected will be treated as a separate calculation to determine the energy shifts. Thus multiple samples loaded into the same VAMAS file, which appear in separate rows, can be treated in this manner. The restriction, however, is that every spectrum in a row is shifted without exception. For situations where for whatever reasons only a subset of a row should be calibrated identically, other means of calibrating selected spectra are available on the Calibration property page of the Processing dialog window.

Quantification issues: Quantification using narrow scan spectra requires the creation of quantification regions for each significant peak in the data. The VAMAS block for each narrow scan spectrum used in the quantification maintains the region information for the data held within the VAMAS block. It is therefore necessary to individually display the narrow scan spectra and create appropriate quantification regions. Once the regions are created, quantification proceeds via the Report Spec property page on the Quantification dialog window, where quantification is performed on only those data within the VAMAS blocks selected in the right-hand-side of the Experiment Frame.

Region creation: For the data in Figure 8, the VAMAS blocks are assigned the correct species/transition fields, so creating quantification regions is as simple as displaying the data in the left-hand-side of the Experiment Frame, invoking the Quantification Parameters dialog window and pressing the Create button on the Regions property page. The RSF for each region is retrieved from the current element library; this is because the name field within the element library matches the strings assigned for the species/transition in the VAMAS block. Once regions are created for each narrow scan spectrum, switching to the Report Spec property page on the Quantification Parameters dialog window and selecting the VAMAS blocks as seen in Figure 10 allows quantification to proceed based on the users choice.

Figure 10: Report Spec Property Page on the Quantification Parameters Dialog Window.

Quantification via the Standard Report: The data shown highlighted in Figure 10 represents four narrow scan spectra in which a single quantification region has been created on each spectrum, namely, the Si 2p, O 1s, C 1s and Cr 2p peaks. When a region is initially created using the Create pushbutton on the Regions property page, the name field for the region is automatically entered using a concatenation of the element/transition strings for which a match occurred with an element library. Although the regions are assigned to individual spectra, there is a feedback mechanism for checking which regions are active with respect to the Report Spec option as a consequence of the current browser selection: all quantification items defined on the selected VAMAS block will have their names entered into the scrolled-list entitled Quantification Items Names in the Custom Report section of the Report Spec property page. It is therefore worth glancing through the list following making the selection of those VAMAS block for inclusion in the quantification table. Note the Quantification Item Names scrolled-list only includes distinct strings in the list. That is to say, if two regions are assigned the same name, then only one entry will appear in the Quantification Item Names scrolled-list, however, a Standard Report will create an entry in the final table, one for each region or component defined on the selected data, subject to which Standard Report button in pressed. This is in contrast to the Custom Report, in which any combination of regions and components defined on the selected data are always included in the calculation of the quantification table. Further, if two or more regions and/or components are assigned the same name fields, then only one entry will appear in the Custom Report table for identically named quantification items and the intensity from all items with the same name are summed to produce the intensity used in the resulting table.

The steps to generate a Standard Report are as follows:

Select the VAMAS blocks containing the required data in the right-hand-side of the Experiment Frame.
Press the Regions pushbutton on the Standard Report Section of the Report Spec property page.
If required, press the copy button to transfer the quantification tables onto the clipboard for use in other applications such as Excel.

The quantification report shown in Figure 11 was generated using the Regions pushbutton, where the Use Config File tick-box was ticked. A much wider range of quantification table fields are possible, however for many only a subset of the full table is desirable and using a configuration file named RegionQuantTable.txt in the CasaXPS.DEF directory allows the specification of which fields are displayed when the table is generated. If the tick box for the use of the configuration file is not ticked, a much more verbose from of the table is created. It is also worth noting, the configuration file definition file also allows the user to display additional fields not visible in the default quantification table.

Figure 11: Standard Report Table

Quantification of a Nylon Sample using Tags

The data file shown in Figure 12 represents an example where a combination of a low resolution survey spectrum and a high resolution C 1s narrow scan spectrum results in a more complete quantification table than if the two spectra are treated separately. Figure 12 shows data taken from a Kratos Axis 165 and, although the Kratos system does include a method for transmission correction, the data shown was exported without the original transmission curves, so a direct comparison of the intensities measured from the survey data and the peak model shown for the C 1s narrow scan region is not possible. Further, the VAMAS file containing these spectra include neither the N 1s nor O 1s data acquired using the same operating modes as the C 1s region, therefore the only way to exploit the information from the C 1s data envelope is to use the Tag mechanism in CasaXPS; that is, to proportion the elemental concentration for C 1s measured using the survey spectrum in accordance with the relative intensities from the high resolution peak model.

Figure 12: Quantification using Tag fields.

The Tag mechanism in CasaXPS relies on the proper assignment of strings for each region or component in the calculation. That is to say, the Tag strings are identical for only those components and quantification region for which the concentration, as measured by the region, is to be broken down in the proportions calculated from the relative intensities of synthetic peaks. In the example of nylon seen in Figure 12, there are three peaks used in the elemental concentration. When the regions defining the O 1s, C 1s and N 1s intensities are created, the Tag field must be entered with a value other than NoTag and must also be distinct from one another. The default Tag field, when a region is created using information from the element library, is the same string found in the Name field for the region. Figure 13 shows the table from the Regions property page where the Tag fields are entered using the element/transitions for the regions in question, although any other strings would have been equally as good provided the three strings are all different. However, whatever the Tag string used for the C 1s region must also be used for the Tag fields entered in the C 1s components seen in the insert tile in Figure 12. Since the peak model for the C 1s region also requires the creation of a region, it is as equally important to ensure the Tag field for the C 1s region defined on the narrow scan spectrum is assigned the string NoTag. The significance of the string NoTag is that only quantification items for which the Tag field is different from NoTag are included in a Tag based quantification report. Since the area of the peak determined from the region on the narrow scan C 1s data is of no use when compared to the O 1s and N 1s areas measured from the survey spectrum (owing to the different instrumental operating modes used to acquire the data), it is important the region from the C 1s narrow scan spectrum is excluded from the quantification calculation by this means. A simple way to set a Tag field to NoTag is to delete all characters from the text-field and press return. The Tag field will automatically load the NoTag string.

Figure 13: Tables from the Regions and Components Property Page on the Quantification Parameters dialog window.

The quantification report displayed over the survey spectrum in Figure 12 is a form of annotation. A table of information added to the display using the Quantification property page on the Annotation dialog window (Figure 14) is both very useful, but also very dangerous if misused. The information in the table does not come directly from the VAMAS block maintaining the data display in the Active Tile, but rather is dependent on the VAMAS blocks selected in the right-hand-side of the Experiment Frame. The danger is clearly that the table shown on the display may derive from a completely different spectrum in the same file; however the advantage of these quantification tables is that related spectra can be combined to produce information as useful as seen in Figure 12. Namely, the survey spectrum provides the elemental quantification, while the C 1s narrow scan VAMAS block provides the relative intensities of the four carbon peaks. The mechanism by which the quantification table is created for the annotation is in fact identical to the procedure used to generate general quantification tables using the Standard Report on the Report Spec property page from the Quantification Parameters dialog window. If the desire is to annotate a spectrum using information only derived from the spectrum displayed in a tile, then either the Regions or Component property pages on the Annotation dialog window are appropriate.

Figure 14: Annotation dialog window displaying the Quantification property page.

One consequence of using the quantification table annotation is also seen in Figure 12, where the peak model for the C 1s envelope must also conform to the chemistry of the sample, namely the intensity of the O 1s peak must relate to the highest binding energy C 1s synthetic peak. It is therefore possible to adjust the C 1s peak model whilst monitoring the affect of the relative intensities on the O 1s and C 1s peaks. Further, Figure 12 illustrates a use for the insert tile, where the parent tile displays the survey spectrum together with the quantification table, whilst the insert tile displays the C 1s narrow scan region, thus the components for the C 1s spectrum can be changed whilst still viewing the quantification table. A display such as the one shown in Figure 12 is created as follows:

Select the survey VAMAS block in the right-hand-side of the Experiment Frame.
Press the Display toolbar button.
Draw a zoom box in a vacant area of the tile sufficiently large to display the C 1s spectrum and press the Insert key-board key.
Select the VAMAS block containing the C 1s spectrum.
Select the newly created insert tile and press the Overlay toolbar button.
Select both the VAMAS blocks containing the survey spectrum and the C 1s narrow scan region in the right-hand-side of the Experiment Frame. Given that a quantification table annotation is defined on the survey spectrum, the act of selecting both these VAMAS blocks will result in the display of the table shown in Figure 12.

Note: Quantification annotation behaves in the same way as the Standard Report tables created from the Report Spec property page. That is, VAMAS blocks can only be quantified against each other provided the VAMAS blocks appear in the same row of VAMAS blocks as seen in the right-hand-side of the Experiment Frame.

A table of quantification results identical to the quantification annotation table in Figure 12 is generated using the Standard Report button (see Figure 10) on the Report Spec property page of the Quantification Parameters dialog window. Again, the C 1s and survey VAMAS blocks must be selected in the right-hand-side of the Experiment Frame prior to pressing the button. Once the quantification table window is displayed in CasaXPS, the values from the table are saved to file via the File menu or alternatively placed on the clipboard via the Copy toolbar button.

A Multi-layer Depth Profile Example

The data set shown in Figure 15 is a profile measured using a PHI Quantum 2000 where the sample was a multi-layer material. Not all depth profiles have so many interfaces, however even the presence of one boundary within the profile may require specific adjustments to both quantification regions and synthetic components to permit an accurate description of the chemistry as the environment alters across an interface. The ability to create quantification items on a spectrum-by-spectrum basis allows variations due to matrix effects to be easily accommodated within CasaXPS and results in profiles representative of the material rather than the limitations imposed by requiring one model to fit all. The key to analysing depth profiles is to realise that:

Each spectrum requires the definition of quantification regions and components.
The browser on the right-hand-side of the Experiment Frame permits the propagation of a specific model to only those VAMAS blocks currently selected.

If a sequence of spectra can all be modelled with the same set of region and components, the task is therefore to define the required region and components on one representative spectrum, then using the browser, select the remaining spectra for which the model is appropriate and propagate the model from the one spectrum to all those so indicated.

Figure 15: Multi-layer Depth Profile Data Set (PHI Quantum 2000)

The importance of maintaining the quantification items as individual parameters for each spectrum is illustrated in Figure 16, where the niobium spectra are displayed together with the quantification regions corresponding to the initial surface before ion-gun action and following the first ion-gun etch cycle. The action of the ion-gun transforms a well defined doublet pair into an envelope derived from a number of such doublet pairs. It is clearly preferable to select spectrum specific start and end energies for the integration regions; the consequence of only using one set of region parameters applied to all the Nb 3d spectra is a more noisy profile trace in the final result.

Figure 16: Niobium spectra illustrating the variation in the data envelope before and after the first ion-gun etch cycle.

By way of example, consider the Si 2p spectra in the data set shown in Figure 15. The silicon signal is effectively reduced to noise when the etch cycle is within the niobium layer, however at the interface between the silicon and niobium oxides a small Si 2p peak appears to the right of the silicon oxide peak. In order to minimise the influence of noise and accommodate the intermittent appearance of the minor peak in the silicon profile, it is necessary to adjust the region limits on a spectrum by spectrum basis. One method of creating the required quantification regions throughout the profile is as follows:

Select all the Si 2p spectra in the right-hand-side of the Experiment Frame. If the heading button for the column of Si 2p VAMAS block in the right-side browser is pressed once, every VAMAS block below the header button will become selected.
Press the Overlay toolbar button. The entire set of Si 2p spectra will appear overlaid in the Active Tile.
Using the Regions property page on the Quantification Parameters dialog window, create a quantification region by pressing the Create button. The element/transition fields for these data are correctly assigned and agree with the desired entries in the current element library; therefore the RSF is retrieved from the library when the region is created. Note that the region is only created on the first spectrum in the Active Tile, namely, the VAMAS block selected first when the browser selection was made prior to pressing the Overlay toolbar button.
Adjust the quantification region parameters, for example the Av Width field might be set to “1” and the start and end parameters adjusted under mouse control such that the region looks plausible for all the spectra display in the Active Tile.
Propagate the region to all the Si 2p spectra: ensure the Si 2p column of VAMAS blocks are all selected in the right-hand-side Browser, right-click the mouse over the tile displaying the Si 2p spectrum for which the region was defined, ensure the Region tick-box in the propagate section of the Browser Actions dialog window is ticked and none others, confirm the list of destination VAMAS blocks agrees with the intended Si 2p list and press the OK button. Since the Si 2p spectra are overlaid in the Active Tile, the newly created quantification regions together with the resulting backgrounds will appear in the display showing all the silicon spectra. Note, however, the fact that the spectra are displayed in the Active Tile is a convenient way of visualising the result of the propagation and it is the Browser selection which dictates the destination for the propagation action, not the set of spectra in the Active Tile.
Use the arrow keyboard keys to step through the set of Si 2p spectra making adjustments to the region parameters as required. If the Quantification Parameters dialog window is open and the Region property page is the front-most page, then the mouse can be used to adjust region limits.

The depth profile in Figure 15 is a relatively small profile and the interfaces are close together, however for larger sequences of etch-cycles where sub-ranges of spectra are accommodated by the same set of region parameters, the propagation mechanism can be used to selectively transfer a region to a subset of spectra. That is, the propagation operation is performed on only those VAMAS blocks selected in the right-hand-side of the Experiment Frame and there is no requirement to select the entire column of Si 2p spectra as suggested above. Similarly, regions and synthetic components can be propagated using the identical mechanism when the use of subsets within a profile sequence becomes more important; optimised peaks require more attention than regions typically do. Small adjustments to peak constraints can often make a big difference to the quality of the final depth profile, particular when these small alterations to the peak model are applied to the appropriate part of the data set.

Now, continuing with the remaining element/transitions in the profile, regions and/or components must be defined for each of the four columns of VAMAS block seen in Figure 15. Only the O 1s spectra are quantified using synthetic components, where two O 1s Gaussian-Lorentzian line-shapes are used to fit the data. These two peaks are labelled O 1s 1 and O 1s 2, principally to emphasize the importance, when using the Custom Report to generate the quantification table, of distinct names for quantification items. If two quantification items (regions or components) are assigned the same name, then the Custom Report (Figure 17) will add the intensities from these identically named quantification items together before calculating the concentration table. If, for example, the region for one of these O 1s spectra had been named O 1s and the same name O 1s given to both the synthetic peaks, the result from the Custom Report would be in error by a factor of two. That is, the intensity from the region and the two synthetic peaks would be summed together and used to compute the oxygen concentration. It is therefore important to assign distinct names to quantification items unless it is desired to sum the intensities involved. There are many situations where two or more regions might be appropriately assigned the same name with the view to improving the statistic in a measurement. For example, Figure 4 shows the Au 4p doublet pair widely separated such that a single region spanning the energy interval containing both peaks would struggle to define a plausible background. On the other hand, two regions as seen in Figure 4, easily define the background for the individual peaks and by assigning the same name to these regions, the intensity from both would be summed by the Custom Report.

Figure 17: Custom Report section prepared for generating a profile from the data selected in the right-hand-side of the Experiment Frame.

A key point to note is that the Custom Report always works with all the quantification items defined on the selected VAMAS blocks, regardless of whether the Region or Component button is pressed to initialise the Name/Formula table seen in Figure 17. It is the Name/Formula table that defines the report and the buttons between the Quantification Items table and the Name/Formula table are only a quick way of initialising the Name/Formula table. Unwanted entries in the Name/Formula table can be removed by right-click over the name field of the Name/Formula list; a dialog window appears offering the option to modify, insert or delete a field in the Name/Formula table.

The Name/Formula table shown in Figure 17 was prepared by first selecting the entire data set, then pressing the button labelled All between the two scrolled lists on the Custom Report section. Since the O 1s spectra have both a region named O 1s and two components named O 1s 1 and O 1s 2, it is necessary to exclude the region from the calculation. A consequence of calling these quantification items by different names is that each has a distinct entry in the Name/Formula table and therefore the O1s entry corresponding to the region can be deleted. The strings used in the Name column of the table is at the user’s discretion, however the Formula entries must be constructed using exactly the strings used to name the quantification items. Thus the formula to add the intensity from the two components should be entered as follows: O 1s 1 + O 1s 2, where both the case and the spaces in the names O 1s 1 and O 1s 2 are important. Since formulae in the Name/Formula table can be any arithmetic expression using constants such as 1 and 2, and the quantification item names also include these digits, allowing such terms as 2 * O 1s 2 + 1 within a formula forces the use of exact strings for quantification item names.

The goal of processing a depth profile is to monitor the trend of each element as a function of depth. The data set seen in Figure 17 lists the VAMAS blocks in rows corresponding to etch-time; however the quantification table displayed in Figure 18 lists the intensity and concentration determined from the VAMAS blocks as a function of depth. The conversion from etch-time to depth, in this example, is achieved by specifying the depth of the crater corresponding to the total etch-time. The toolbar button, when pressed, offers a dialog window in which the interval for the crater depth dimension can be entered corresponding to the sequence of etch-times, and selecting the Depth radio button prior to pressing the OK button results in the new abscissa values and labels. The change of experimental variable from etch-time to depth is made under the assumption of a constant sputter-rate and a uniform etch-time during the course of the experiment. If the etch-time is none uniform, the Depth (Interpolate) radio button should be used rather than the Depth option. If more complex relationships exist between the etch-time and depth, then the quantification table must be exported to a spreadsheet for further processing.

Figure 18: Custom Report Table.

The quantification report shown in Figure 18 is generated by preparing the Name/Formula table as seen in Figure 17 and then pressing the Area Report button within the Custom Report section. The resulting quantification report only includes values determined from the intensity parameters computed using either the integrated quantification region area or the area parameter from synthetic components. The raw intensities are adjusted for relative sensitivity of the transitions using the RSF entered into the quantification items, transmission correction, if available and selected via the Regions property page, and escape-depth correction using the value also entered on the Regions property page. The first column in Figure 18 is the experimental variable and is followed by the adjusted integrated intensities for each entry in the Name/Formula list, which in turn is followed by the percentage atomic concentration computed from the intensity entries.

The Custom Report is designed for depth-profiles or any other trend experiments. The File Menu, also displayed in Figure 18, offers a choice of saving the table to an ASCII file or creating a VAMAS file containing one VAMAS block for each column in the quantification table. Once selected, the Create Profile menu option results in a new Experiment Frame appearing within the CasaXPS main window. The trends within the profile can be overlaid and annotated with a key as seen in Figure 19 using the Tile Display dialog window. Apart from offering many configurable display options, in particular the Display property page on the Tile Display dialog window allows a key to be added to the display. A further option on the File Menu available for spectrum and profile display allows a prepared tile format to be saved to a separate file from the VAMAS file. These ASCII tile format files default to a file extension of .tff and can be retrieved at a later time to return the display of a VAMAS file to an earlier state. Saving and reloading a tile format file is performed using two options on the File Menu.

Figure 19: Depth Profile created from the table shown in Figure 18.