PEAK-FITTING – FACTS, GUIDELINES, & RULES
for Monochromatic XPS Spectra
(Peak-fitting – Self Training Movies)*** (LINKED)
FACTS, Guidelines, Advice, & Warnings
for FWHM, Peak-shapes, Backgrounds, Chemical Shifts, Peak Area Ratios,
Chi-Squared, BE Differences, Residual, Charge Correction, Smoothing
FACTS & Limits
- These FACTS were experimentally derived from peak-fitting the principle XPS signals of pure metals, and pure chemical compounds, many in single crystal form.
- FWHM (peak-width) is very important when peak-fitting any chemical state spectrum.
- The FWHM for principle peaks for most chemical compounds is <1.9 eV and >0.9 eV (see Crist FWHM and BE Table for Compounds
- The FWHM for the symmetrical metal peak of most pure metals or elements is <1.0 eV and >0.3 eV (see Crist FWHM and BE Table for Pure Element)
- The smallest FWHM for a pure metal, by a stand-alone monochromatic XPS system, is 0.32 eV for the Re (4f7) peak
- The smallest FWHM for pure Silicon (Siº) is 0.34 eV for the Si (2p3) peak when the Pass Energy is <10-15 eV. Depending on HSA ability.
- The smallest FWHM for the O (1s) peak in any chemical compound is 1.0 eV for Cu2O when using PE=50 eV. A smaller PE does NOT decrease FWHM.
- The smallest FWHM for the Mo (3d5) peak is 0.71 eV for MoS2 (natural crystal), and 0.71 eV for Ag2S (natural crystal)
- The ultimate FWHM of many XPS hemispherical analyzers is ~0.001 eV. Older ones are ~0.1 eV.
- The FWHM (energy spread) in the Al monochromatic X-ray energy (~1486.7 eV) is between 0.16 eV and 0.25 eV. The ultimate limit for FWHM using Al X-rays.
- The FWHM for Ag (3d5) is ~0.6 eV when the Pass Energy of many XPS systems is 10 eV.
- The FWHM for Ag (3d5) is ~0.9 eV when the Pass Energy of many XPS systems is 50 eV.
- The FWHM for Ag (3d5) is ~1.8 eV when the Pass Energy of many XPS systems is 200 eV.
- PEAK-SHAPE is another key variable when peak-fitting any chemical state spectrum. Most software use the sum or product of Gaussian and Lorentzian peak-shapes.
- The peak-shape of a few pure metals, elements, and conductive compounds require an asymmetric tail that uses the Doniach-Sunjic asymmetric tail.
- The peak-shape for principle peaks for most chemical compounds use a range of Gaussian:Lorentzian (G:L) ratios. From 90:10 to 70:30. Most common is: 80:20 G:L.
- The peak-shape of pure metals and elements use a 80:20 Gaussian:Lorentzian peak-shape ratio for peaks in the 0 – 500 eV range.
- The peak-shape of pure metals and elements use a 50:50 Gaussian:Lorentzian peak-shape ratio for peaks in the >700 eV range.
- The Voigt peak-shape is an alternative peak-shape that may provide a smaller Chi-square and slightly smaller FWHM that the Gaussian-Lorentzian Sum peak-shape.
- A few pure metals, such as Fe, Co, Ni, and W have a “multiplet-splitting” and/or “2-electron transition” satellite peak
- Peak-shapes can be defined using advanced peak-shapes such as Voigt, Gelius, Doniach-Sunjic, …
Background Shapes & Endpoints
- Background shapes have a direct effect on the relative peak areas produced by the peak-fit
- There are 5 basic background shapes: Iterated Shirley, Sherwood, Tougaard, Smart, Linear
- Iterated Shirley is the most popular to use.
- The endpoint used at the high BE end has a HUGE effect on peak-fitting results
- Endpoint can be defined as a single data-point (channel) for both the starting and ending endpoints. (Acceptable only if the noise is very small.)
- Endpoints normally involve the averaging of 3-10 data-points at both the starting and ending endpoints. (As a result, background is inside the BG noise)
- Advanced software offer variations of Tougaard BG w 2 or 3 parameters, Shirley-Vegh-Salvi-Castle (Peak-Shirley)
- For normal peak-fits, we do not subtract (remove) the background. For theoretical level studies it may be useful to truly remove the background shape.
- Using a larger than necessary Lorentzian peak shape can hide small components.
Chemical Shifts – XPS
- Chemical shift is defined as the difference in BE between the pure element (e.g. Si) and a chemical state (species) of that element (e.g. SiO2)
- For chemical compounds the chemical shift difference is typically 1.0 and 1.2 eV for compounds having a difference of 1 in oxidation state
- Chemical shift differences between two chemical states can be as large as 4.0 eV (e.g. S versus SO4)
- Chemical shift differences between two chemical states can be as small as 0.05 eV (see AuCu allow series – 75:25, 50:50, 25:75)
- For metal alloys it is possible to measure chemical shift differences as small as 0.05 eV ( AuCu series)
- For intermetallic solid state solutions of 2-3 metals (not an alloy) there is NO chemical shift difference as the ratio is changed (NiCo)
- Argon ion etching, which often implants Ar+ ion, can produce very small chemical shifts ~0.05
- Peak area ratios are defined by theory. Ratios can be defined by theory based on number of electrons or based on theoretical calculation.
- Spin-orbit coupling pairs can be “constrained” to theoretical or calculated ratios
- Chemical state peaks from the same XPS signal can be constrained based on the empirical ratios of the chemical states known to be present
- Spin-Orbit pairs examples are: A ratio of 2.0 for the Si (2p3) : Si (2p1) spin-orbit pair. To peak-fit this pair, the peak areas from these two peaks should be constrained to 2.0
- If you use Scofield’s cross-sections for Si (2p3) and Si (2p1), then the ratio is 1.96. In this case, constrain the peak area ratio to be 1.96.
- In the case of peak-fitting the C (1s) from PET (Mylar), the peak area ratio is 3:1:1 if you fit for 3 peaks – hydrocarbon, ether, and ester peaks.
- For the C (1s) of PET you need to constrain 3 peak area ratios based on empirical values. If contamination is present, then the ratio will not be established. Add a contamination peak.
- For the O (1s) of PET you need to constrain 2 peak area ratios to be 1:1. Do not include the pi-pi* signal at ~536 eV.
- Chi-squared is a measure of the “goodness of fit” for an iterated peak-fit. It reflects the difference between the synthetic peaks and the raw spectrum.
- Chi-squared values are affected by the: number of data-points, noise, signal intensity, and the peak area difference between sum of synthetic peaks and raw peak area.
- A reduced “chi-squared” value is the true chi-squared value divided by 100 to allow the user to have a better “feel” for the quality of the fit result.
- Based on practical experience a “chi-squared” value between 1 and 2 implies a very good peak-fit.
- A reduced “chi-squared” value between 2 and 4 implies that the fit has not yet been fully optimized but is acceptable.
- A reduced “chi-squared” value larger than 5 implies that one or more signals may be missing from the peak-fit effort.
- The residual plot is a graphical representation of the “goodness of fit” based on the raw peak area and the total of the synthetic peak areas.
- A relatively flat uniform line is best and show only statistical noise. If multiple points deflect then an improvement is needed.
- The regions where the line deflects greatly from the centerline represent regions with poor fit, that may require a new peak, a change in FWHM, or other change.
- In some cases we know the difference in BE between two peaks. For example: BE Si (2p3) – BE (2p1) = 0.602 eV
- When we know BE differences we should use them as constraints in a high quality peak-fit
- The BE difference between spin-orbit pairs are usually a fixed value, but there are a few exceptions: TiO2 vs Ti
Charge Correction (Referencing)
- Charge correction (referencing) for insulators is useful to help decide what chemical states are present or absent
- If you need charge correction, then do that at the very beginning before adding a background shape
- Smoothing can be useful if truly needed. It is much better to collect chemical state spectra with a high S/N value to avoid smoothing.
- Smoothing can hide small components in a peak-fit
Flow Chart for Peak-fitting – Horizontal Layout
Flow Chart for Peak-fitting – Vertical Layout
- The chart below is an XPS Peak-fitting FLOW-CHART (guide) that I developed when I was working as an XPS demo-sales engineer in Tokyo selling XPS instruments, and training new owners.
- Peak-fitting software has not really advanced that much since 1988. It is faster and has new peak-shapes and background shapes.
- Modern software will automatically insert multiple peaks, but the analyst still needs to manually constrain FWHM, BE differences, Peak-Area ratios and Peak-shapes.
- Manual control of peak-fitting is still the best way.
- Users need a database of FWHM for pure elements and a wide variety of chemical compounds
- Two collections of FWHM are provided in this website.
Typical Data Collection Settings for a Chemical State Spectrum
|# of Scans||Dwell Time
|# of data points||Step Size S/N||Total Time|
If you use a much smaller eV/step size, such as 0.01 eV/step for a 25-30 eV window or >500 pt/25-30 eV window, then your spectra will most likely have a significant amount of unnecessary noise. Modern multi-channel detectors, that use 64-128 channels, will by design, smooth most spectra, minimizing the time needed to collect good quality spectra.
Ultimate Resolution of Chemical State Differences
Typical Resolution Possible by Peak-fitting: for ΔBE ~ 1eV
Effect of Pass Energy on FWHM & Peakshapes
Peak-fitting Lesson #1: Basics – Simple Spectrum
- If the sample is an insulator, then immediately correct for the charging affect on BEs. Charge correct (reference) all spectra to remove the charge shifting effect.
- If you accept to use adventitious hydrocarbon C (1s) peak as your reference point, then correct all spectra so that largest C (1s) peak appears at ~285.0 or 284.8 eV.
- If sample is conductor, do NOT shift any spectra even if the C (1s) is >286 eV
- It is best to peak-fit the C (1s) chemical state spectrum, and then the O (1s) chemical state spectrum. (We learn if DIFFERENTIAL charging is present or absent.)
- Do you see shoulders on right side of all chemical state spectra? Charging!
- Never smooth any data. (If you smooth, then that means you need to collect data for 2-3 times longer.)
- For spectra that are 20-30 eV wide, use the Shirley (s-shaped) background
- Look at raw spectra. How many peaks can you imagine?
- Vertically expand Y axis to inspect baseline and decide the best location for both endpoints.
- Use endpoint averaging, 3-5 points, or 0.5 to 1 eV wide for the Shirley background.
- Place the endpoints in a “flat” region of the background 2-3 eV away from any part of the real data.
- Now you are ready to add your first synthetic peak.
- Select a peak-shape using 80% Gaussian and 20% Lorentzian for chemical compounds.
- Select and use a 80:20 G:L peak-shape for all synthetic peaks in a simple spectrum.
- At the far right of the C (1s) spectrum, add the first synthetic peak or draw a peak FWHM that is ~1.2 eV wide . This peak should be the tallest peak inside the C (1s) spectrum. This is your “hydrocarbon” peak.
- If you have software that automatically adds peaks and immediately peak-fits, then turn that off until you learn more.
Auto-peak-fit can be useful, but usually causes confusion and makes bad choices.
- Now add another new synthetic peak that is 1.0 to 1.5 eV higher in BE. Again, use a FWHM of ~1.2 eV.
- Add minimum number of peaks.
- Finish adding new synthetic peaks to the C (1s). Each new synthetic peak is roughly 1.2-1.5 eV higher than the peak at the right.
- The C (1s) spectrum peak-fit envelop should have 3-4 synthetic peaks.
- Start peak-fit iteration process.
- After you start peak-fit iterations, the software will automatically adjust the FWHM of all the peaks until you have a reasonable result or small chi-squared value.
- Is reduced Chi-Squared <20? If not, add another peak. Run fit again.
- Is reduced Chi-Squared <4? Excellent. If not < 4, then add constraints.
- Save all peak-fits and labels to permanent memory.
- If you try to use a FWHM > 1.8 eV for any peak for any element, then you are probably wasting your time.
- The hydrocarbon peak is always the most intense C (1s) signal, unless you happen to work on Teflon-like materials.
- The peak area ratio of the 3 or 4 synthetic peaks for adventitious carbon changes when the chemistry of the sample changes.
- In some cases, researchers use many more data points to make smoothing easier to use. Detectors having 16-128 channels have already been smoothed your data.
- Smoothing is not useful if you are trying to do serious work. You really need data that have a high S/N ratio. Depending on your instrument, you should collect chemical state spectra for 5-15 minutes time for each element. Be sure to include C (1s) and valence band region (-10 to +30 eV).
- It is best to use a Pass Energy that produces a FWHM = 1.0 eV for ion etched Silver, Ag (3d5). Using a smaller Pass Energy, you will get a slight improvement in FWHM but you lose a lot of signal intensity. In rare cases, you will resolve a shoulder for insulating materials. For conductors, we might resolve a new peak.
- If you have an insulating (non-conductive) sample, then you need to be sure your Flood Gun (charge neutralizer) is properly aligned. Charging broadens peak widths, lose information.
- If your Flood Gun is not properly aligned, you might also have differential charging that produces peaks that are wider than necessary, which hides data.
- Before you start serious peak-fitting, do a quick peak-fit of the C (1s) and the O (1s) signals. The hydrocarbon signal should have a FWHM <1.5 eV. If not, then you have a charging problem. If you have a FWHM <1.2 eV, then you have excellent data and you can start peak-fitting.
- Peak-fitting the O (1s) signal can be easy or can be very very difficult. If your quick peak-fit shows a FWHM <1.6 eV then you have good data. If your O (1s) has a FWHM > 2 eV, then you have at least 2 different types of Oxygen. Oxygen spectra often look symmetrical and can include 2-3 different types of Oxygen.
- Many metals have “shake-up” signals that often overlap the main XPS signals.
- Ti, V, Cr, Mn, Fe, Co, Ni, and Cu have Multiplet Splitting signals due to valence-core electron pairing. These have many peaks.
- Polymers can have low levels of hydrocarbon and alcohol type contaminations that exactly overlap the C and O signals of the pure polymer.
- Before adding any synthetic peaks, count the number of peaks and obvious shoulders.
- After adding a new synthetic peak, define the chemical state of that new synthetic peak
- Never use peak FWHM <0.9 eV (unless you have reference data. Nearly all peak FWHM are between 1.0 – 1.8 eV. Shake-up peaks are exception.)
- Use the minimum number of synthetic peaks (total of 6-8 is normal upper limit)
- Number of peaks and obvious shoulders equals starting number of synthetic peaks
- Constrain (Fix) all synthetic peaks to have the same FWHM for the first peak-fit iteration. (Then release those constraints.)
- If Chi-Square after first iteration is >20, then add a new synthetic peak
- Never smooth data unless signal is very, very weak
- Never ion etch sample to remove low level Carbon or Oxygen contamination. (FWHM will falsely increase by >20% and lose information)
- If XPS signal has a spin-orbit pair that overlap, then use peak-area ratios and use BE differences
- Ti, V, Cr, Mn, Fe, Co, Ni, and Cu can be complicated due to overlaps of main peaks, multiplet splitting peaks and shake-up peaks. Study other peak-fits.
- If sloping tails are present on low BE side of all XPS signals (e.g. C (1s), O (1s), metal 1, metal 2), do not try to peak-fit. Improve charge control and collect new data.
Use Overlays of Chemical State Spectra to Guide Peak-fitting
Use Overlays of FULL SET of Chemical State Spectra
to Cross-Correlate Chemical States in a Peak-fit
DATA Collection Settings – Directly Affect Peak-fit Results & Information