E51 · Photoelectron spectroscopy

XPS: Elements, Chemical States & Charging

Illuminate an oxide layer on silicon, record a survey and two core-level regions, then fit the acquired counts. Separate chemical states, test charge referencing and compare raw peak ratios with sensitivity-corrected surface composition.

Corrected fitted Si anchor $\text{—}$

Fitted common raw shift $\text{—}$

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

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

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 $\text{—}$

Count-scaled fit residual $\text{—}$

Experiment target $\text{—}$

Peak ratios need a measurement model

Fit chemistry, then reference the energy

Fit a curved continuumQuadratic instead of linear background; reuse recorded counts.Apply assumed sensitivity factorsDivide O area by 2.9 and Si area by 1 before normalization.Use Mg X-rays instead of AlChanges photon and kinetic energy; fixed teaching sensitivities remain assumed.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}

Positive charge potential before neutralization

V_c

2\,\mathrm{V}

Neutralized potential fraction

\eta

0

Processing reference correction

\delta_{\mathrm{ref}}

0\,\mathrm{eV}

Predict which changes shift every line. Fit a curved continuum, apply sensitivities and use the known Si substrate anchor to choose a reference correction. Resolve the instrument below 0.35 eV, record at least 5000 fitted Si counts, and recover the anchor within 0.12 eV and oxide fraction within 3 percentage points. Keep at least 0.5 nm oxide, then check. Compare grazing emission afterward.

A synthetic Si oxide / Si specimen uses assumed equal Si number density, a common 2 nm escape length and ideal exponential escape without elastic scattering. Line anchors are 99.4 and 103.5 eV for Si and 532.9 eV for O; two Gaussian Si doublets use 0.63 eV splitting and 2:1 areas. Intrinsic widths, continuum, count scale and relative sensitivities of 1 and 2.9 are teaching assumptions, not an instrument calibration. Al and Mg source presets change kinetic energy; assumed sensitivities and escape lengths stay fixed. A uniform positive specimen potential raises all apparent binding energies; neutralization controls the residual potential. Weighted constrained fits estimate peak areas and a common shift from recorded counts. The selected background is a linear or quadratic smooth continuum, not Shirley or Tougaard. Reference correction is supplied by the user; the Si anchor can serve as a known substrate reference here, never as universal charge referencing. Reported oxygen percentage is a surface-weighted two-element equivalent, not bulk stoichiometry or an inverse depth profile. Independent survey and high-resolution scans have separate counting noise. Exposure is assumed scan-integrated time per scan; animation and processing do not add exposure. Noise is Poisson below 40 expected counts and a rounded Gaussian approximation above. Analyzer width is Gaussian-equivalent at a 150 mm mean radius and 2-degree entrance half-angle. No differential charging, satellites, Auger peaks, damage, real cross sections, exact electron optics or general chemical identification is included.

Start with the essentials

Focus question: Is a shifted peak chemistry—or charging?
One-sentence intuition: Fit actual counts with stated line and background constraints. Reference the energy independently, integrate the peaks and apply compatible sensitivities. A layered surface still needs a depth model.

Core mathematical model

Grounded energy relation and residual charging

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

The analyzer work function fixes the instrument vacuum offset. Positive residual sample potential reduces arriving kinetic energy and raises apparent binding energy; a reference correction subtracts a supplied shift.

Signal depth weighting

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

The angle is measured from the outward surface normal. Here the common 2 nm escape length is assumed, without elastic scattering; it is not a universal effective attenuation length.

Assumed oxide signal fraction

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

Equal Si density and escape length in both layers make the total Si equivalent signal independent of thickness. Grazing emission gives greater oxide weight while reducing the total escape integral.

Constrained doublet and 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 contains a 2:1 doublet separated by 0.63 eV. Areas are nonnegative; a common energy shift and background coefficients are fitted. These constraints are assumptions, 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 illustrate the correction and are not measured instrument factors. A layered specimen produces a surface-weighted equivalent, not a homogeneous bulk atomic fraction.

Common difficulties

Height is not area

Typical misconceptionThe tallest peak gives the largest atom fraction.

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

Referencing has a physical scope

Typical misconceptionA standard carbon or Si number corrects every unknown specimen.

Better mental modelThis Lab supplies a known substrate. Real charge referencing needs a justified reference and may fail with differential charging.

A broad fit is not resolved spectroscopy

Typical misconceptionA constrained doublet fit proves both components were resolved.

Better mental modelThe model can return areas even when instrument width merges the components. Inspect width and counts before interpreting the fit.

Run the experiment

01
Predict a common shift
Use Chemistry or charging? and compare Si and O positions before changing neutralization.
What to observe: Every line moves together with residual potential; the Si oxide separation stays fixed.
02
Fit and reference
Lower pass energy, collect enough counts, fit the curved background and set the reference correction using the known Si substrate anchor.
What to observe: The fitted common shift comes from counts; changing the supplied correction moves only the displayed energy scale.
03
Correct the area ratio
Toggle the assumed sensitivities using Reference and quantify.
What to observe: Composition changes while recorded spectra and fitted areas stay fixed.
04
Test surface sensitivity
Compare normal and grazing emission at the same known oxide thickness, then complete the target.
What to observe: The oxide signal fraction increases. The change in reported oxygen fraction is a depth-weighting effect, not creation of oxygen.