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

 

FWHM

  • 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-Shapes

  • 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 

  • 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 

  • 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.

Residual

  • 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.

BE Differences

  • 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

  • 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

 

 

GUIDELINE

 

Flow Chart for Peak-fitting – Horizontal Layout

 

GUIDELINE

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.

 

 

GUIDELINE

 

Typical Data Collection Settings for a Chemical State Spectrum

X-ray Beam
Size		 Pass
Energy		  Spectral
Window		  # of Scans Dwell Time
/data point		  # 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.

 

GUIDELINE

 

Ultimate Resolution of Chemical State Differences

 

 

 

GUIDELINE

 

Typical Resolution Possible by Peak-fitting: for ΔBE ~ 1eV

 

 

GUIDELINE

 

Effect of Pass Energy on FWHM & Peakshapes

 

 

 

 

GUIDELINE

Peak-fitting Lesson #1:  Basics – Simple Spectrum

  1. 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.
  2. 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.
  3. If sample is conductor, do NOT shift any spectra even if the C (1s) is >286 eV
  4. 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.)
  5. Do you see shoulders on right side of all chemical state spectra? Charging!
  6. Never smooth any data.  (If you smooth, then that means you need to collect data for 2-3 times longer.)
  7. For spectra that are 20-30 eV wide, use the Shirley (s-shaped) background
  8. Look at raw spectra. How many peaks can you imagine?
  9. Vertically expand Y axis to inspect baseline and decide the best location for both endpoints.
  10. Use endpoint averaging, 3-5 points, or 0.5 to 1 eV wide for the Shirley background.
  11. Place the endpoints in a “flat” region of the background 2-3 eV away from any part of the real data.
  12. Now you are ready to add your first synthetic peak.
  13. Select a peak-shape using 80% Gaussian and 20% Lorentzian for chemical compounds.
  14. Select and use a 80:20 G:L peak-shape for all synthetic peaks in a simple spectrum.
  15. 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.
  16. 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.
  17. 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.
  18. Add minimum number of peaks.
  19. 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.
  20. The C (1s) spectrum peak-fit envelop should have 3-4 synthetic peaks.
  21. Start peak-fit iteration process.
  22. 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.
  23. Is reduced Chi-Squared <20? If not, add another peak. Run fit again.
  24. Is reduced Chi-Squared <4? Excellent. If not < 4, then add constraints.
  25. Save all peak-fits and labels to permanent memory.

 

 

WARNINGS

 

  1. If you try to use a FWHM > 1.8 eV for any peak for any element, then you are probably wasting your time.
  2. The hydrocarbon peak is always the most intense C (1s) signal, unless you happen to work on Teflon-like materials.
  3. The peak area ratio of the 3 or 4 synthetic peaks for adventitious carbon changes when the chemistry of the sample changes.
  4. 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.
  5. 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).
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Many metals have “shake-up” signals that often overlap the main XPS signals.
  12. Ti, V, Cr, Mn, Fe, Co, Ni, and Cu have Multiplet Splitting signals due to valence-core electron pairing.  These have many peaks.
  13. Polymers can have low levels of hydrocarbon and alcohol type contaminations that exactly overlap the C and O signals of the pure polymer.

 

 

 

RULES

 

  • 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.

 

 

GUIDELINE

 

Use Overlays of Chemical State Spectra to Guide Peak-fitting

 

 

 

 

 

GUIDELINE

Use Overlays of FULL SET of Chemical State Spectra

to Cross-Correlate Chemical States in a Peak-fit

 

 

 

 

GUIDELINE

 

DATA Collection Settings – Directly Affect Peak-fit Results & Information