Charge Correction
For samples
not electrically connected to the instrument the potential at the surface
floats to a stable state possibly different from the potential on the
instrument, the result of which are spectra with peak positions offset in
energy from the expected values. The most common cause for shifts in peak
positions is an analysis using insulting materials, where assuming adequate
charge compensation, XPS spectra are possible without deformation of the
peak-shapes, but for which a calibration of the binding energy scale in the
form of a uniform energy adjustment is required. CasaXPS corrects for energy
shifts using the Calibration property page on the Spectrum Processing dialog
window. There are several methods for energy calibrating a file of spectra and
the following section describes the steps involved.
The
information required to shift the peaks to a new position is simply two values
representing the measure and the true peak positions. Although there are
several strategies for energy calibration, in essence all represent different
means for determining these two values.
Energy Calibration Based on Locating a Synthetic Peak
A data
envelope is the sum of all the individual peaks beneath the measured curve and
while a maximum intensity is identifiable, the position of the maximum does not
necessarily directly relate to a given transition. The relative intensities of
the underlying transitions may cause the position of the maximum to vary whilst
the location of these constituent peaks are fixed and determined by physics.
The desire is therefore to identify the peaks contributing to the data envelope
and then energy-calibrate the spectrum so as to position one of these synthetic
peaks at a known energy. Consider the example shown in Figure 1, where a carbon
1s spectrum taken from a nylon sample illustrates the case in point. Four
synthetic components are used to model the C 1s data and these peaks must be
fitted to the envelope before the position of the lowest binding energy
component is used to charge reference the sample. A sequence of CasaXPS steps
leading to the energy calibration of the C 1s spectrum is as follows:
- Create a quantification region
defining the background to the C 1s peak.
- Create a peak model for the
data.
- Select the synthetic component
on the Component property page and press the Component pushbutton on the Calibration property page (shown
in Figure 1). The values for the Measured
and True text-fields are
updated from the position of the selected component and, if the selected component
name matches as entry in the Element Library, the True text-field is updated from the library.
- Make any adjustments to the True text-field necessary to
define the position of the selected component.
- Tick the boxes labelled Regions and Components in the Adjust section on the Calibration property
page.
- Press the Apply button on the Calibration property page.
For the
example in Figure 1, a detail description of the above steps follows.
Creating the Background
Regions and
Components are created on the Quantification Parameters dialog window
.
The Regions property page is partially displayed over the CasaXPS main window
in Figure 2, where the parameters for a single quantification region are listed
under the heading A. To create a
region, the button on the Regions property page labelled Create is pressed. Initially, the limits for the quantification
region, and therefore the energy interval over which the background is defined,
are determined from the current zoom state for the displayed spectrum. After
creation the limits specified via the Start and End parameters in column A may be entered manually or adjusted
using the mouse. Each field on the Regions property page table can be selected
using the cursor and the left-mouse button. On selection, the parameter field
becomes a text-field and a new value can be entered; the value is only accepted
when the Enter key is pressed on the keyboard. Alternatively, provided the
Region property page is the top-most property page on the Quantification
Parameters dialog window, the cursor when dragged using the left-mouse button
allows the limits for the quantification region to be adjusted by eye. Two grey
vertical lines mark the extremities of the quantification region and the
appearance of these grey limits indicates the Start and End parameters are
susceptible to alteration via the mouse.
The background type is set to Linear, meaning a linear polynomial is
used to interpolate the background defined by two energy/intensity coordinates
at the start and end limits of the quantification region. The start and end
energies for the quantification region are chosen so that the interpolating
polynomial best describes the
background below the peaks. The intensity at which the background is defined at
an interval limit is, in this example, modified by two quantification region
parameters: the Av Width parameter and the Start/End Offset parameter. The Av
Width parameter specifies the number of data channels either side of the start
and end channels over which the intensities should be averaged to arrive at the
intensity used to define the interpolating polynomial. Figure 2 indicates the
Av Width is set to two, which specifies that two intensities either side of the
background limit channel should be included in the average. That is, in total five
data channels are averaged to determine the intensity at a limit (Figure 3).
The intensity, so determined, is further altered by the St. Offset and End
Offset parameters. These offset parameters represent a percentage offset for
the intensity determined by the Av Width parameter. If the offset were
specified to be one hundred percent, then the background would go down to zero-intensity
at the limit, whereas if the offset is zero then the intensity is equal to the
value determined by the Av Width parameter. The values for the
Creating the Peak Model
Creating a
synthetic peak model for an unknown material is challenging, at best. For this
reason a well known material, namely nylon, is chosen as the example data. Given
the C 1s spectrum in Figure 2, the first response is to reach for The XPS of
Polymers Database edited by Beamson and Briggs. The data envelope and
least-squares optimisation using synthetic line shapes offers numerous possible
peak models none of which are likely to represent the true chemistry of the
surface. Faced with an unresolved set of peaks clearly responsible for the
structure to lower binding energy of the two resolved shapes in Figure 2,
simply adding peaks until the best residual is obtained would result in the
inclusion of anywhere between three and six synthetic peaks. Thus, by using the
experience and chemical knowledge of Beamson and Briggs, a four component model
describing the C 1s spectrum of nylon is selected. Once again, knowing the
number of peaks again is not sufficient to create an accurate description of
the data simply based upon line-shapes and unconstrained optimised peak
parameters. The challenge is therefore to select line-shapes and constrain the
optimisation parameters to ensure the peak model conforms to a hypothetical
stoichiometry. The data in Figure 2 was collected on a Kratos Axis 165, while
the Beamson and Briggs data derives from a Scienta ESCA 300. Line-shapes from
two different instruments are subject to variation due to the response of the
analyser and also the efficiency of the charge compensation mechanism. As a
consequence, the line-shapes used in the Beamson and Briggs database are not
necessarily applicable to the Axis 165 data, thus leading to a degree of
self-expression when choosing the Gaussian/Lorentzian and asymmetry mixtures,
but nevertheless, the guidance offered by the Beamson and Briggs model is
invaluable.
The peak
model shown in Figure 2 is constructed using the Components property page (Figure
4) on the Quantification Parameters dialog window. The four components are
created by pressing the Create
button followed by adjusting the newly created peak to a plausible position and
size. The mechanism for modifying the parameters of a synthetic peak involve
mouse actions, where the left mouse button allows the position and height of a
peak to be adjusted; dragging the position of the peak maximum causes these two
parameters to update. The FWHM of a peak is also adjustable under mouse
control; however the action of dragging the peak from about the half height on
the side of a peak updates the FWHM and the height. The height adjusts at the same
time as the FWHM to maintain the area of the peak. To change the FWHM alone,
the Shift keyboard key must be held down during the drag movement. As new peaks
are added to the model, the size and position of each newly created peak is
determined from the greatest variation in the residual between the data and the
current synthetic envelope. All the component parameters are offered on the
Components property page and can be manually entered using the same type of
text-field available on the Regions property page.
Without
constraining the component parameters, when optimised, these parameters take on
values determined by mathematics. In an ideal world, the line-shapes and
background would be exactly those required to describe the physics responsible
for the spectral shapes, also the data would be devoid on noise. Within this
ideal world, the optimisation step would stand a chance of returning meaningful
values for the parameters; however, simply the presence of noise in the spectra
would be enough to cause problems to unconstrained optimisation, let alone the
absence of the true background and line-shapes from the calculation. When
analysing real spectra, the influence of noise and the lack of the exact
functional forms for the line-shapes forces the use of parametric constraints. The
Component property page tabulates the components (Figure 4) where each set of
component parameters are displayed in a column beneath a header labelled with an
alphabetic character. Constraints between peak parameters are defined in terms
of these labels heading the columns. Figure 2 includes an annotation table in
which the constraint relationships are listed. For example, the highly
correlated peaks in columns A and B on the Components property page (Figure 4)
require a position constraint in column B of the form “A + offset” to ensure
the expected chemical shifts are realised in the model. Similarly, the FWHM
between columns B and C are constrained to be identical; the area relationship
between B and C is also defined by the Area Constraint field in column C using
the string “B * 1”. After adding these constraints to the four component peak
model, optimisation using the Marquardt algorithm returns a set of component
parameters which are both optimal when describing the data and also plausible
when describing the chemistry.
Energy Calibration
The peak
model in Figure 2, once optimised, is intended to represent the relative
positions for the chemically shifted C 1s peaks. The remaining step is then to
apply an energy shift to the data to align one of the component peaks with a
known line position, so that the model is positioned in an absolute sense.
Again following Beamson and Briggs, the position for the component labelled C
1s 1 is assumed to be 285 eV binding energy. Using the Calibration property
page, the objective is therefore to enter into the Measured text-field (Figure 1) the value for the un-calibrated C 1s
1 peak position and the value of 285 in the True text-field. Whilst these values could be entered manually, a
link between the selected component on the Component property and the Measured text-field on the Calibration
property page allows the value to be automatically transferred. There is a
further interaction between the True
text-field and the element library also involving the selected component on the
Components property page. Transferring the position of the component labelled C
1s 1 is as simple as pressing the header button labelled A, causing the column
below the header to turn blue, then pressing the Component button on the
Calibration property page. If the name field in the selected component matches
an entry in the current element library, then the energy for the matched entry
is entered into the True text-field.
If no match is found then the True
text-fields is updated from the value for the component position. In either
event, the Measured
text-field is updated from the position field of the selected component on the
Component property page. If the value entered into the True text-field is not the intended position for the selected
component, the correct value should be entered.
Although
the two values for the Measured and True text-fields are sufficient
information for calibrating the spectrum, the specification is not complete
until the decision is made regarding the action to be applied to the currently
existing region and component parameters. Tick boxes within the section headed Adjust optionally allow regions and/or
components to be shifted at the same time as the data. For the current example,
both tick boxes should be ticked, the result of which is the region and
components are also move at the same time as the spectrum is calibrated.
Applying
the shift determined from the two input parameters can be applied to the
spectrum in the active tile via the Apply
button or, if more than one spectrum requires an identical shift, the
calibration can be applied using the Apply
to Selection button (Figure 1). The latter button refers to the selection
of VAMAS blocks in the right-hand-side of the experiment frame.
Undo and
Retrospective Calibration Adjustments Involving Regions and Components
The
scenario described in the previous section, in which the position of a
synthetic peak determines the energy calibration for a set of spectra, is
sometimes performed following an initial investigation of the material using a
survey spectrum. For example, an elemental quantification table may suffice for
some data and so the usual steps of calibrating the spectra based on the
position of the C 1s line taken from the low resolution survey data, followed
by creating quantification regions is enough to characterise the material.
However, following the initial investigation, it may become apparent that
chemical state information is required and therefore one or more high
resolution spectra are modelled using synthetic components. Once a peak model
is involved, the precision of the component assignments becomes of more
importance than the position of the C 1s peak in the survey spectrum, and as
such the initial calibration must be replaced by a new energy shift determined
from one of the components in a similar fashion to the previous section. In
CasaXPS, although it is possible to apply more than one calibration command to
a spectrum, the actual energy shift is determined from the last in a sequence
of such commands. Data already shifted, however will be located with respect to
the current calibration and so it is necessary to undo the current calibration
before computing the new energy shift. There are several issues relating to
this process and these will be discussed in the following example.
Consider
the spectra in Figure 5. The survey spectrum is initially quantified by
assigning quantification regions to each of the peaks representative of the
elemental intensities, and then using the C 1s region on the survey spectrum,
an energy calibration is performed to ensure the peak position for the C 1s maximum
is located at binding energy 285.00 eV. The data from the high resolution
spectrum is calibrated using the same difference between the measured and the
true energies determined from the survey C 1s region. At the time of
calibration, the high resolution C1s data has no regions or synthetic
components defined. If at a later time, regions and components are added to the
high resolution C 1s spectrum, the situation will exist where the spectrum is
shifted in energy, however the region and components are relative to the
calibrated data. If the data is re-calibrated to position one of the model
peaks, simply undoing the calibration step from the Processing History property
page will leave the region and components at the positions determined from the
previously calibrated spectrum, while returning the spectrum itself to the
un-calibrated locations. It is therefore necessary to manipulate the data with
a little more care when make such adjustments; these more subtle adjustments
are performed on the Calibration property page. The problem with simply using
the Processing History property page to remove the calibration is that the
processing history has no record of the regions and components created after
the initial calibration step. To remedy the missing information the Calibration
property page includes a button for undoing the calibration on a selection of
VAMAS blocks where the intention to move or not move the region and/or
components is indicated, prior to pressing the Undo Selection pushbutton, by the tick boxes in the section headed Adjust labelled Regions and Components
(Figure 6).
The steps,
performed on these data during the initial calibration based on the survey
spectrum and then subsequent re-calibration based on a model peak, are as
follows:
- Create quantification regions
on the survey spectrum. Since for
this particular spectrum the photoelectric lines are easily identified
using the Find Peaks button on
either the Element Table or the Periodic Table property pages of the
Element library
,
the Create Regions button on
these same pages can be used to initially create the quantification
regions. The location of these initially created regions must be checked
and re-aligned, if necessary, using the Regions property page on the
Quantification Parameters dialog window
.
Display the Quantification Parameters dialog window and press the Reset 
toolbar
button for initialising the zoom-list. Then press the Zoom-Out 
toolbar
button to cycle through a zoomed display of these newly created regions
making any adjustments as necessary. - Define the Measured and the
True binding energies for the C 1s peak in the survey spectrum. Using both the Regions property page on
the Quantification dialog window and the Calibration property page on the
Spectrum Processing dialog window, select the C 1s region from the Regions
property page as illustrated in Figure 6 and press the Region button
indicated on the Calibration property page (also Figure 6). The value for
the Measured
text-field is determined from the selected Region on the Regions property
page, while the True value is
loaded from the element library entry for which the Name field from the
selected region produces a match. If the element library energy is not the
required value for the data in question, then the True text-field should be adjusted appropriately.
- Apply the energy shift to the
spectra measured under the same sample charge state. Using the right-hand-side of the Experiment frame, select those
VAMAS block for which the calibration is appropriate; in this case both
the survey and the high resolution spectra are acquired under the same
charging conditions and therefore all should be included in the
calibration step. Once the VAMAS blocks are selected, tick the Regions tick-box in the Adjust section and press the
button labelled Apply to Selection
on the Calibration property page. An entry in the processing history is
made for each VAMAS block selected at the time the Apply to Selection pushbutton is pressed. The Regions tick-box must be ticked
because the survey spectrum includes quantification regions and without
instructing the calibration command to do so, the start and end energies
for the quantification regions would not be adjusted at the same time as
the energy scale for the underlying data.
At this
point in the analysis, the spectra appear as seen in Figure 5, however the peak
model displayed in Figure 5 is yet to be created and so only the energy scale
for the C 1s data is affected by the calibration command.
- Create the region and four
synthetic components (as seen in Figure 5) displayed in the C 1s tile. The peak model uses a linear background
and four Gaussian Lorentzian synthetic components. The model is guided
towards the peak positions tabulated in Figure 5 using constraints for the
area of each of the three less intense lines, where the constraint simply
forces all three to have identical area. One further constraint forces the
FWHM of the peaks labelled Peak 1b and Peak 1c to take on a common value.
Without constraints, the four peaks would optimise to a mathematical
minimum almost certainly unrelated to the true line positions; the primary
reasons for the difference between the mathematical optimum and the
chemical optimum are the uncertainty in the true line-shapes coupled with
the presence of noise in the data. The constraints for the components in
Figure 5 are entered into the constraint fields on the Components property
page, where the specific constraint for the FWHM of the two peaks Peak 1b
and Peak 1c is entered in the FWHM constraint field in column headed C and
is defined using the character heading B, namely B*1. The constraint
should read: the FWHM of C is equal to the FWHM of B multiplied by one.
Having
created the peak model for the C 1s spectrum in Figure 5, it is apparent the
components within the model should be the means by which the energy calibration
is determined. A common assignment for the carbon components is to set the
position for the peak labelled Peak 1a to binding energy 285.00 and therefore
the calibration based on the survey must be redone.
- Undo the current calibration
for all spectra from which no regions or components where created after
the initial calibration step. Assuming
none of the spectra involved are processed using other spectrum processing
options, select all those spectra for which no regions and/or components
have been defined since the survey scan was used to calibrate the data set
and overlay the spectra in the active tile. Press the Reset All button on the Processing History property page. Note, the calibration command recorded in the Processing
History provides the information to determine whether the regions and/or
the components were present and moved when the calibration was performed.
If a region or component was defined on the data when the calibration was
performed, the calibration command will include the strings “Regions” or
“Comps”, for example “Calib M = 283.226 A = 285 Regions Comps BE”
appears in the Processing History list for a spectrum for which regions
and components were present when the command was applied and the command
included the instruction to move, in energy, the quantification items at
the same time as the spectral bins. Provided the correspondence between
the regions and components on the data matches the existence of these key
words in the calibration command, the calibration can be undone using the
processing history. If a miss-match exists between these values, then the
Calibration property page must be used to selectively undo the calibration
command.
- Undo the calibration for those
spectra for which regions and components have been added subsequent to the
initial calibration step. For the
current example, the C 1s region and components were created following the
calibration of the spectral data and so removing the calibration for the C
1s data requires the use of the Undo Selection button on the
Calibration property page (Figure 6). The Undo Selection button acts on those VAMAS blocks selected in
the right-hand-side of the Experiment Frame and the positions of quantification
items are adjusted based upon the state of the Regions and Comps
tick-boxes in the Adjust section. Regardless of the order in which the regions
and components were created in relation to the initial calibration, the
Undo Selection button will either move the regions and components at the
same time as the spectral bins or leave these quantification items alone
based on the settings of the tick boxes in the Adjust section (Figure 6).
- Apply the new calibration based
on the lowest binding energy C 1s synthetic component from the high
resolution peak model. The procedure
for defining the new calibration is identical to the example using nylon
in the previous section. Figure 7 displays the C 1s high resolution
spectrum as an inset tile within the tile displaying the survey spectrum,
where both spectra are calibrated using the shift determined from the
synthetic peak labelled Peak 1a.
Computing
the Location of a Peak Maximum without the use of Quantification Regions
So far, the
method for defining the measured peak position has relied on the use of a quantification
region or a synthetic component. There are situations where this method is
limiting, particularly for data where significant charge compensation is
required and where the batch processing option is applicable. The problem with
using quantification regions to identify a peak position is that the range over
which a peak may appear in the un-calibrated data is possibly large compared to
the interval over which the intensity for a peak is computed. It is therefore necessary
to separate the function of identifying a peak maximum for use with the
calibration command from the interval of the spectrum defined by a
quantification region. The primary requirement for calibrating a spectrum
before quantification regions are defined comes from the batch processing
feature. Here, a template VAMAS file containing all the processing and
quantification items is used to define the steps required to process a raw file
of equivalent data. The successful positioning of the quantification items is
dependent on the spectra first being energy corrected, without which the limits
to the quantification regions might miss the intended peak.
An
alternative means of computing the measured peak maximum within a range of data
bins is possible using a range of energies in the form of a pair of comma
separated values entered in the Measured
text-field on the Calibration property page. A True value must be assign
as before, however when a comma separated pair of energy values are entered in
the Measured
text-field, the set of data bins defined by the energy interval are searched
for the bin containing the maximum counts, then this bin plus adjacent bins are
used to compute the energy corresponding to the maximum of a quadratic
polynomial approximating the data near the maximum intensity in a least-squares
sense. When the Apply button is
pressed, the spectrum is shifted to locate the maximum determined from the
quadratic at the value specified in the True text-field. The intensities
used in the calculation are not background subtracted, therefore the
calibration may differ from the peak position subsequently computed from a
quantification region defined using a standard background type. A similar
situation would exist if the spectrum were calibrated computing the measured
value from a quantification region with background type linear and then
subsequently changing the background type to Shirley; the effective peak
maximum would move as a consequence of the different background approximations.
A further feature of this method for determining the energy shift is that if
the Apply to Selection pushbutton is
used instead of the Apply button, then each spectrum within the selection is
calibrated using a command string including a reference to the VAMAS block from
which the energy shift was determined. The significance of the reference to the
originating VAMAS block lies in the use of this form of calibration when
applied via the batch processing mechanism. The reference to the VAMAS block
involves the absolute index of the VAMAS block within the VAMAS file and, while
applicable to batch processing, is not so useful when propagating processing
commands via the Browser Actions dialog window. In fact, for the most part,
calibration is not the type of command for which propagation is appropriate since either the charge
compensation is applicable to all spectra within a file, in which case the Apply to Selection button is used, or
the charge state varies throughout an experiment, for example a depth profile,
and so no one energy shift is easily applied to all spectra. The latter case is
dealt with using the techniques described in the section on energy calibration
and intensity normalisation.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5: High Resolution C 1s region and survey spectra, both spectra energy-calibrated using the C 1s peak from the survey spectrum.
Figure 6
Figure 7