E51 · Photoelectron spectroscopy

XPS: Elements, Chemical States & Charging

How can you tell whether a shifted XPS peak comes from a chemical change or from charging? First reference the energy scale independently. Charging moves every peak together; a chemical change moves one state relative to the others. After referencing, a constrained peak fit can back up a chemical interpretation.

Shine X-rays on an oxide layer on silicon, record a survey and two core-level regions, then fit the counts. Separate the chemical states, test how the energy scale is corrected for charging, and compare raw peak ratios with the surface composition after sensitivity correction.

Corrected fitted Si anchor $\text{—}$

Fitted Si oxide signal fraction $\text{—}$

Surface-weighted O equivalent $\text{—}$

Count-scaled fit residual $\text{—}$

More measurements and target

Fitted common raw shift $\text{—}$

Fitted peak areas · counts $\text{—}$

Instrument Gaussian-equivalent FWHM $\text{—}$

Recorded high-resolution counts $\text{—}$

Known residual charge shift $\text{—}$

Known normal depth · 95% escape weight $\text{—}$

Selected Si analyzer kinetic energy $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Fit a curved continuumFits a quadratic background instead of a linear one, using the counts already recorded.Apply assumed sensitivity factorsDivides the O peak area by 2.9 and the Si peak area by 1 before normalizing.Positive charge potential before neutralization

V_c

2\,\mathrm{V}

Neutralized potential fraction

\eta

0

Processing reference correction

\delta_{\mathrm{ref}}

0\,\mathrm{eV}

Advanced settings

Use Mg X-rays instead of AlChanges the photon energy and the photoelectron kinetic energy. The sensitivity factors keep their fixed, assumed teaching values.Known oxide thickness

t

1\,\mathrm{nm}

Emission angle from surface normal

\theta

20\,\mathrm{{}^\circ}

Pass energy

E_p

100\,\mathrm{eV}

Entrance and exit slit width

s

1.2\,\mathrm{mm}

Scan-integrated exposure per scan

\tau

1\,\mathrm{s}

Learning goal and model limits

Interpreting peak ratios needs a measurement model

Fit the chemical states, then correct the energy reference

First predict which changes shift every line together. Fit a curved continuum, apply the sensitivity factors, and use the known Si substrate peak as an anchor to choose the reference correction. Keep the instrument width below 0.35 eV and record at least 5000 fitted Si counts. Recover the anchor within 0.12 eV and the oxide fraction within 3 percentage points. Keep the oxide at least 0.5 nm thick, then check the target. Afterward, compare grazing emission.

Model assumptions

The Si oxide on Si sample is synthetic. Both layers are assumed to have the same Si number density and a common 2 nm escape length, with ideal exponential escape and no elastic scattering. The lines sit at 99.4 and 103.5 eV for Si and 532.9 eV for O. The two Gaussian Si doublets have a 0.63 eV splitting and a 2:1 area ratio. Intrinsic widths, the continuum, the count scale and the relative sensitivities of 1 and 2.9 are teaching assumptions, not an instrument calibration. The Al and Mg source presets change the kinetic energy, while the assumed sensitivities and escape lengths stay fixed. A uniform positive potential on the sample raises every apparent binding energy, and neutralization sets how much of that potential remains. Weighted, constrained fits estimate the peak areas and a common shift from the recorded counts. The background is a smooth linear or quadratic continuum, not Shirley or Tougaard. You supply the reference correction. Here the Si anchor line can serve as a known substrate reference, but it is never a universal charge reference. The reported oxygen percentage is a surface-weighted, two-element equivalent; it is not bulk stoichiometry or an inverted depth profile. The survey and the high-resolution scans are recorded separately and have independent counting noise. Each exposure is taken as the integration time for one scan; animation and processing add no exposure. Noise is Poisson below 40 expected counts and a rounded Gaussian approximation above. The apparatus shows a fixed window of raw energies; fitting windows and reference corrections affect only the analysis. The analyzer width is a Gaussian equivalent for a 150 mm mean radius and a 2-degree entrance half-angle. Differential charging, satellites, Auger peaks, damage, real cross sections, exact electron optics and general chemical identification are left out.

Start with the essentials

Focus question: Does a shifted peak mean a chemical change or charging?
One-sentence intuition: Fit the real counts with stated line and background constraints, reference the energy scale independently, then integrate the peaks and apply consistent sensitivity factors. A layered surface still needs a depth model.

Core mathematical model

Energy relation for a grounded sample, with residual charging

E_{B,\mathrm{raw}}=h\nu-\phi_a-K_a=E_B+eV_c

The analyzer work function sets the instrument's vacuum offset. A positive residual potential on the sample lowers the kinetic energy of arriving electrons, which raises the apparent binding energy; the reference correction subtracts a shift you supply.

How signal weight falls with depth

w(z,\theta)=\exp\!\left[-\frac{z}{\lambda\cos\theta}\right]

The angle is measured from the outward surface normal. The common 2 nm escape length is an assumption with no elastic scattering; it is not a universal effective attenuation length.

Share of the Si signal from the oxide

f_{\mathrm{ox}}=1-\exp\!\left[-\frac{t}{\lambda\cos\theta}\right]

Because both layers have the same Si density and escape length, the total Si signal does not depend on the oxide thickness. Grazing emission gives the oxide more weight but lowers the total escape integral.

Fit model: constrained doublets on a smooth background

D_i\simeq A_0P_{0i}+A_{\mathrm{ox}}P_{\mathrm{ox},i}+b_0+b_1u_i+b_2u_i^2

Each normalized Si template is a doublet with a 2:1 area ratio and a 0.63 eV separation. The areas are nonnegative, and a common energy shift and the background coefficients are fitted. These constraints are assumptions, and the fit is not a unique chemical diagnosis.

Two-element equivalent composition

c_O=\frac{A_O/S_O}{A_O/S_O+A_{\mathrm{Si}}/S_{\mathrm{Si}}}

The assumed sensitivities are 2.9 for O and 1 for Si. They show how the correction works and are not measured instrument factors. For a layered sample the result is a surface-weighted equivalent, not the atomic fraction of a uniform bulk.

Common difficulties

Peak height is not peak area

Typical misconceptionThe tallest peak belongs to the most abundant atoms.

Better mental modelWidths, sensitivities and background all change peak height. Integrate the fitted counts and state the assumptions behind the quantification.

A reference value has limits

Typical misconceptionA standard carbon or Si value corrects any unknown sample.

Better mental modelThis Lab gives you a known substrate. Real charge referencing needs a justified reference, and it can fail when parts of the sample charge differently.

Fitting two components does not mean they were resolved

Typical misconceptionA constrained doublet fit proves both components were resolved.

Better mental modelThe model can return areas even when the instrument width merges the components. Check the width and the counts before you interpret the fit.

Run the experiment

01
Predict a shift of every line
Choose Chemistry or charging? and note the Si and O positions before you change the neutralization.
What to observe: Every line moves together with the residual potential, and the gap between Si and its oxide stays the same.
02
Fit, then correct the energy scale
Lower the pass energy, collect enough counts, turn on Fit a curved continuum and set the Processing reference correction from the known Si substrate line.
What to observe: The fitted common shift comes from the counts. Changing the correction you supply moves only the energy scale on display.
03
Correct the area ratio
Choose Reference and quantify, then switch Apply assumed sensitivity factors on and off.
What to observe: The composition changes, while the recorded spectra and fitted areas stay the same.
04
Test surface sensitivity
Compare normal and grazing emission at the same known oxide thickness, then complete the target.
What to observe: The oxide's share of the signal grows. The reported oxygen fraction changes because of depth weighting; no oxygen has been created.

XPS: Elements, Chemical States & Charging

Chemistry needs a referenced energy scale

Core mathematical model

Energy relation for a grounded sample, with residual charging

How signal weight falls with depth

Share of the Si signal from the oxide

Fit model: constrained doublets on a smooth background

Two-element equivalent composition

Common difficulties

Peak height is not peak area

A reference value has limits

Fitting two components does not mean they were resolved

Run the experiment

Predict a shift of every line

Fit, then correct the energy scale

Correct the area ratio

Test surface sensitivity

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