E61 · Photoelectron spectroscopy

AP-XPS: Through a Liquid Film

Can you recover the solid signal beneath a liquid film? Yes, when enough electrons escape and the solid, liquid and gas peaks can be separated. Comparing the covered solid with a bare sample under the same gas isolates the extra attenuation from the liquid. Converting that ratio to thickness needs a known escape length and an unchanged solid state; differential pumping keeps the analyzer under vacuum.

Measure solid, liquid and gas peaks in one energy scan. Compare the covered solid with a separate bare sample under the same gas, recover the film thickness and follow the pressure drop through three pumped stages. The gas-reaction mode separately explores changing chemistry and exposure averaging.

Liquid thickness from counts $\text{—}$

Buried solid B fraction from counts $\text{—}$

Calculated final-stage pressure $\text{—}$

Recorded covered-sample counts $\text{—}$

More measurements and target

Calculated first-stage pressure $\text{—}$

Calculated second-stage pressure $\text{—}$

Thickness error against separate input $\text{—}$

Solid fraction error against separate input $\text{—}$

Covered solid fitted peak counts $\text{—}$

Matched bare-solid fitted peak counts $\text{—}$

Liquid fitted peak counts $\text{—}$

Gas fitted peak counts $\text{—}$

Supplied liquid escape length $\text{—}$

Count-scaled spectrum residual $\text{—}$

Calculated total gas survival $\text{—}$

Fitted exposure-averaged oxidized fraction $\text{—}$

Measured solid area / matched vacuum area $\text{—}$

Fitted solid and gas peak areas · counts $\text{—}$

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

Recorded operando counts $\text{—}$

Known exposure-averaged fraction $\text{—}$

Known reaction start / end fractions $\text{—}$

Known gas transport survival $\text{—}$

Assumed gas mean free path $\text{—}$

Oxidized-line analyzer kinetic energy $\text{—}$

Count-scaled fit residual $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Record: 0 gas reaction · 1 liquid film

m_i

1

Chamber gas pressure

p

10\,\mathrm{mbar}

Scan-integrated exposure per acquisition

\tau

1\,\mathrm{s}

Supplied liquid film thickness

t_l

12\,\mathrm{nm}

Multiplier on the three pump speeds

\gamma_S

1

Assigned effective admission conductance

C_1

0.02\,\mathrm{\frac{L}{s}}

Advanced settings

Fit a curved continuumRefits the stored counts with a quadratic background instead of a linear one.Include the gas-phase lineFits a known gas-phase template separately from the two solid chemical states.Include the liquid componentRefit the same recorded counts with the distinct supplied liquid line.Sample–aperture distance

d

1.5\,\mathrm{mm}

Sample and gas temperature

T

400\,\mathrm{K}

Reaction age at scan start

t_0

4\,\mathrm{s}

Photon energy

h\nu

1500\,\mathrm{eV}

Pass energy

E_p

100\,\mathrm{eV}

Entrance and exit slit width

s

1.2\,\mathrm{mm}

Tender X-ray photon energy

h\nu_l

4000\,\mathrm{eV}

Scan view: 0 solid A · 1 B · 2 liquid · 3 gas

j

0

Assigned stationary solid B fraction

f_s

0.65

Learning goal and model limits

Pressure changes chemistry and transmission

Can you recover the solid signal beneath a liquid film?

Liquid task: recover thickness within 0.3 nm and the buried solid B fraction within three percentage points, with more than 4000 fitted solid counts and width below 0.6 eV. Include liquid, gas and curved background. Final-stage pressure must stay below one millionth of a mbar; the assigned admission model is scoped to at most 5 mbar. These are conditional teaching targets. The gas-reaction mode keeps its earlier state, survival and time-average target.

Model assumptions

The liquid branch uses a supplied stationary two-state solid beneath a uniform synthetic liquid film. A 4 keV default photon source produces a scanned spectrum with solid A and B, gas and liquid markers at 100, 103.2, 105.5 and 108.5 eV. These are assigned lines, not chemical-state standards. The sample pressure is maintained externally. Three constant-speed pumps and supplied effective conductances solve a steady gas-throughput balance in mbar and litres per second. The admission conductance is an assigned effective transport coefficient, not a molecular-orifice calculation for a high-pressure gas. The task range is zero to 5 mbar; no pump base pressure, outgassing, flow-regime transition or gas heating is calculated. Electron attenuation integrates the sample gap and three separately specified stage lengths. The liquid uses an assumed common escape length, anchored at the 10 nm water value at 3.92 keV quoted by Axnanda et al.; its energy extrapolation is assigned and is not a material calibration. The film is maintained externally; evaporation, electrochemistry, charging, lateral variations and elastic scattering are omitted. A separate synthetic bare-solid acquisition retains the same supplied stationary solid state and gas conditions with independent noise. The inverse fits only recorded spectra and supplied line/escape calibrations. It estimates the liquid thickness from the covered-to-bare solid-area ratio and estimates the buried solid B fraction from its two peaks. It does not receive the actual thickness or solid composition. Ratios above one retain negative apparent thickness. Missing components, weak solid signal or excessive final-stage pressure reject the task. The apparatus shows one representative scan setting at a time: selecting a line retunes the schematic analyzer reference without reacquiring the spectrum. Film depth, piping and particle densities are schematic; gas dots use a bounded logarithmic density. The retained gas-reaction branch has its own assumptions: The material is synthetic, with reduced, oxidized and gas-phase lines at 100, 103.2 and 105.5 eV. Line widths, equal sensitivities for the two solid states, reaction rates, the gas cross section, the continuum and the photon flux are teaching assumptions. Electron survival in the gas follows the exponential law for a uniform ideal gas, with the ideal-gas number density and an assumed cross section that depends on energy. Local pressure drops and gas flow are not solved. The aperture is fixed at 0.2 mm, the gap is at least twice its diameter, and the collected signal is assumed to fall as the inverse square of the gap. The differential pumping stages are only drawn; their pressures are not calculated. Two competing first-order reactions start from 5% oxidized, and each spectrum uses the exact average state over the chosen exposure interval. The matched vacuum spectrum is a separate synthetic control with its own noise: it freezes that average state, keeps the same geometry and removes the gas. It does not show what a real sample would do if the chamber were pumped down. Nonnegative peak areas and a linear or quadratic continuum are fitted to the stored counts; if the residual is too large or the signal too weak, no state is reported. Photon flux and cross-section changes are assumed. Real gas chemistry, catalysis, liquid interfaces, charging and elastic scattering are left out. The animation clock does not advance reaction time or exposure. Counts carry Poisson noise below 40 expected counts and rounded Gaussian noise above. The analyzer width is a Gaussian equivalent for a 150 mm radius and a 2-degree entrance half-angle. Apparatus lengths are magnified, and detector colors use a logarithmic display gain.

Physics tutorial

A solid beneath liquid and gas

BackgroundPhotoelectrons from a buried solid must cross a liquid film and a gas path before reaching the analyzer. The liquid also emits its own spectrum. Start with a supplied stationary two-state solid, fit the distinct signals and compare with a separate bare sample under the same gas. Three pumped stages keep the analyzer pressure low.

Why it mattersThe covered-to-bare solid-area ratio removes the shared gas attenuation, provided the solid state and measurement geometry match. Its logarithm gives a liquid thickness only after supplying the escape length. Follow the calculated stage pressures as you weaken the pumps; a good spectrum also requires an appropriate analyzer vacuum.

Start with the essentials

Focus question: Can you recover the solid signal beneath a liquid film?
One-sentence intuition: Liquid attenuation, gas attenuation and solid composition enter different parts of the measurement. Separate their spectral components and use a matched control before interpreting a peak height.

Core mathematical model

Gas throughput and pumped-stage balance

\begin{aligned}Q_i&=C_i(p_{i-1}-p_i)\\Q_i-Q_{i+1}&=S_i p_i\\Q_4&=0\end{aligned}

Pressures are in mbar, conductances and pump speeds in litres per second, and throughputs in mbar litres per second. The supplied admission coefficient is an effective value, not an unqualified molecular-orifice law.

Liquid thickness from a matched solid signal

\begin{aligned}R_l&=\frac{A_{s,\mathrm{covered}}}{A_{s,\mathrm{bare}}}\\\widehat t_l&=-\lambda_l\ln R_l\end{aligned}

The independent bare control uses the same gas and stationary solid mixture. The estimate conditions on uniform thickness and a known liquid escape length; a noisy ratio above one gives a negative apparent thickness.

Separate solid, liquid and gas signals

\begin{aligned}D_i&\simeq A_A P_{Ai}+A_B P_{Bi}\\&\quad+A_l P_{li}+A_g P_{gi}+B_i\end{aligned}

Only recorded spectra and supplied line shapes enter this fit. Recovering these components does not identify arbitrary chemical states or reconstruct a depth profile.

Gas-reaction mode: Gas number density

n_g=\frac{p}{k_B T}

Pressure is converted from mbar to pascals and distance from millimetres to metres. In this uniform-gas teaching model, the sample and the gas are at the same chosen temperature.

Gas-reaction mode: Fraction of electrons that cross the gas unscattered

\mathcal{T}_g=\exp(-n_g\sigma_g d)

The assumed cross section depends on the electron's kinetic energy, and a shorter gap means less loss. Scattering moves electrons into loss channels the model leaves out, so this survival fraction counts only unscattered electrons, not every electron.

Gas-reaction mode: Competing oxidation and reduction

\frac{df}{dt}=k_{\mathrm{ox}}(1-f)-k_{\mathrm{red}}f

The oxidation and reduction rates are invented and thermally activated, and they keep the oxidized fraction between zero and one. They show how a surface can change while it works; they do not describe any real catalyst.

Gas-reaction mode: Average state over the exposure

\overline{f}=\frac{1}{\tau}\int_{t_0}^{t_0+\tau} f(t)\,dt

The spectrum adds up the signal from the whole exposure. A longer exposure gives more counts but says less precisely when the state was measured. The animation does not advance this physical interval.

Gas-reaction mode: Fit model: two solid peaks, a gas peak and a background

D_i\simeq A_rP_{ri}+A_oP_{oi}+A_gP_{gi}+B_i

The fit gives nonnegative areas to two solid states of equal sensitivity and to the gas line, on top of a smooth linear or quadratic continuum. Leaving out a line can leave a large residual.

Gas-reaction mode: Oxidized fraction and transmission from peak areas

\widehat f=\frac{A_o}{A_r+A_o},\qquad\widehat{\mathcal{T}}_g=\frac{A_r+A_o}{A_{r,\mathrm{vac}}+A_{o,\mathrm{vac}}}

The synthetic vacuum control keeps the exposure-averaged state fixed, uses the same optics and draws its own random counts. Pumping a real chamber down could change the chemistry, so a comparison with a real vacuum spectrum needs extra justification.

Common difficulties

A bare control must match the buried solid

Typical misconceptionAny bare sample gives the reference needed for a film thickness.

Better mental modelThe ratio isolates the liquid only if the solid composition, geometry, source and gas conditions match. This task supplies that synthetic control; an actual experiment must establish the matching.

The pressure here is far below one atmosphere

Typical misconceptionAmbient-pressure spectroscopy means every pressure setting is atmospheric.

Better mental modelThis Lab goes up to 20 mbar, which counts as near-ambient. The name covers a family of instruments and does not promise operation at a full atmosphere.

The vacuum control is synthetic

Typical misconceptionThe matched vacuum spectrum shows what the real sample would look like after the gas is pumped out.

Better mental modelThe control holds the chemistry fixed on purpose, so that it shows only the loss in the gas. A real sample changes in its own way as the chamber is pumped down.

An exposure covers a stretch of time

Typical misconceptionA long spectrum tells me the state at the moment it finishes.

Better mental modelThe counts add up the populations as they change during the scan. The known kinetics curve is a separate reference; it is not reconstructed from one spectrum.

Run the experiment

01
Separate what lies above the solid
Start with the liquid-film preset. Compare the covered spectrum with its independently recorded bare-solid control.
What to observe: The liquid line is added while the solid peaks lose intensity; the gas condition is the same in both acquisitions.
02
Test the spectral interpretation
Switch the liquid or gas template off in advanced settings, then restore it.
What to observe: The raw count spectrum stays fixed, while an incomplete model leaves a larger residual.
03
Keep the analyzer under vacuum
Reduce the pump-speed multiplier or increase admission conductance. Inspect all three stage pressures.
What to observe: With the pumps stopped, the stages equilibrate with the supplied sample pressure; the vacuum target fails.
04
Find the buried-signal limit
Compare the bare, thick-film and low-count presets, and switch the representative scan line.
What to observe: A thick film can leave too few solid electrons for the precision target. Changing the scan view changes the displayed optical setting, not the stored counts.
05
Predict what raising the pressure does
In Gas reaction and time averaging mode: Start with Vacuum control, then choose Recover the working state. Compare the solid peak areas, the gas peak area and the fitted state.
What to observe: Higher pressure speeds up the assumed oxidation and also removes electrons leaving the solid.
06
Shorten the path through the gas
In Gas reaction and time averaging mode: Choose Gas blocks the solid, then shorten the gap and lower the pressure until the fit gives a usable solid state.
What to observe: If the counts are too low or the residual is too large, no result is reported. A fit that only looks smooth is not enough.
07
Separate the background and the gas peak
In Gas reaction and time averaging mode: Keep every acquisition setting fixed and switch Fit a curved continuum and Include the gas-phase line on and off.
What to observe: The stored counts do not change. Only the fitted areas and residuals change with the processing choices.
08
Trade counts for timing
In Gas reaction and time averaging mode: Complete the target, then choose Long exposure averages change. Compare the state at the start, at the end and on average.
What to observe: The fit tracks the average over the exposure, which can be far from the final state.

Core mathematical model

Gas throughput and pumped-stage balance

Liquid thickness from a matched solid signal

Separate solid, liquid and gas signals

Gas-reaction mode: Gas number density

Gas-reaction mode: Fraction of electrons that cross the gas unscattered

Gas-reaction mode: Competing oxidation and reduction

Gas-reaction mode: Average state over the exposure

Gas-reaction mode: Fit model: two solid peaks, a gas peak and a background

Gas-reaction mode: Oxidized fraction and transmission from peak areas

Common difficulties

A bare control must match the buried solid

The pressure here is far below one atmosphere

The vacuum control is synthetic

An exposure covers a stretch of time

Run the experiment

Separate what lies above the solid

Test the spectral interpretation

Keep the analyzer under vacuum

Find the buried-signal limit

Predict what raising the pressure does

Shorten the path through the gas

Separate the background and the gas peak

Trade counts for timing