E60 · Electron excitation and surface spectroscopy

Auger Spectra: What Sputtering Leaves Behind

Does removing one nanometre leave a one-nanometre-thinner film? Sputtering can mix a surface and change its chemistry while removing material. Auger counts weight what remains by escape depth, so a sharp-film thickness estimate can differ from the actual retained amount. Compare the recorded history with its separately labelled material inventory.

Follow a film through successive sputter steps. Compare the material actually retained with the thickness inferred from recorded Auger spectra, and see how mixing and changed chemistry break the sharp-film picture.

Count-derived sharp-layer equivalent $\text{—}$

Separate actual retained inventory $\text{—}$

Completed removal depth $\text{—}$

Changed oxygen signal from counts $\text{—}$

More measurements and target

Oxygen signal error against separate input $\text{—}$

Reduced Poisson deviance $\text{—}$

Selected recorded count sum $\text{—}$

Selected completed step $\text{—}$

Selected O net counts $\text{—}$

Selected Cu net counts $\text{—}$

Film thickness from counts $\text{—}$

Separate undamaged residual thickness $\text{—}$

Mean error on resolved pixels $\text{—}$

Weaker selected peak SNR $\text{—}$

Resolved pixel fraction $\text{—}$

95 percent normal escape depth $\text{—}$

Summed incident dose $\text{—}$

Prescribed changed-response fraction $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Record: 0 static map · 1 sputter history

m_s

1

Dwell per energy position per pixel

\tau

0.1\,\mathrm{ms}

Removal rate in one-second ion steps

v_s

0.15\,\mathrm{\frac{nm}{s}}

Assigned mixing RMS after one nm erosion

w_m

0.25\,\mathrm{nm}

Assigned chemical conversion per nm

k_s

0.5\,\mathrm{nm^{-1}}

Inspect stored sputter step

k

4

Advanced settings

Primary electron energy

E_0

5\,\mathrm{keV}

Analyzer response FWHM

w_a

18\,\mathrm{eV}

Collection angle from surface normal

\theta

0\,\mathrm{^\circ}

Completed ideal sputter removal

z_s

0\,\mathrm{nm}

Prescribed damage susceptibility

a

0.1

Counted sideband subtraction: 1 on

b

0

Selected stored pixel index

k

300

Derivative smoothing radius in bins

r

0

Initial uniform film thickness

t_0

1.8\,\mathrm{nm}

Counting noise: 0 expected · 1 sampled

n_P

1

Learning goal and model limits

Predict · acquire · process · explain

Does removing one nanometre leave a one-nanometre-thinner film?

History target: at least ten of thirteen count spectra must identify the calibrated components. The selected oxygen fraction must differ from its separate forward check by at most three percentage points, with reduced Poisson deviance below 2.5 and more than 100 fitted peak counts. This does not reconstruct a depth profile. The static map retains its separate target: 90 percent resolved pixels, mean thickness error at most 0.25 nm, selected SNR at least 8, width at most 12 eV and changed response at most 12 percent.

Model assumptions

The history branch alternates twelve one-second sputter steps with separate electron-spectrum acquisitions at a uniform test spot. It stores the pristine spectrum and every subsequent step. Depth points inward from the current surface. A conservative finite-volume diffusion surrogate mixes native and changed oxygen-bearing material; its depth-dependent coefficient is assigned from the supplied mixing length. A first-order chemical rule transfers native material to a changed state without deleting oxygen. Calibrated removal translates the profile and tracks the material actually lost. All populations and removed inventory are retained at every step. The signal integrates these populations against an exponential escape kernel; equal sensitivities and a 0.8 nm escape length are assumed. Native O, changed O and Cu use illustrative line markers at 510, 536 and 918 eV, not chemical-state standards. The inverse fits only recorded counts to those response shapes and a linear continuum; it receives no depth profile, sputter parameters or retained mass. Its sharp-layer equivalent thickness is an attenuation quantity, not the geometric thickness of a mixed film. The actual retained inventory and ideal unmixed film are separately labelled forward checks. Ion exposure time excludes electron acquisition and switching time. Mixing and conversion coefficients and the removal rate are teaching inputs, not fitted ion-energy yields or a full MRI model. Roughness, preferential sputtering, redeposition and crater geometry are omitted. Electron acquisition is assumed nonperturbative in this branch; electron-induced response change is explored in the separate static-map mode. Noise-free records show expected counts. The physical surface color shows the known current top-layer mixture. Ion and electron acquisitions alternate; the ion source is parked while an electron spectrum is recorded. The retained static-map branch has its own assumptions: The specimen is a synthetic oxygen-containing film on copper (Cu). The approximate O KLL and Cu LMM centers at 510 and 918 eV are teaching markers, not chemical-state standards. Each of the two windows is 140 eV wide with 2 eV steps. The map has 24 by 24 pixels at 50 nm pitch, and the current is fixed at 100 pA. The Gaussian lines have an intrinsic FWHM of 6 eV. Equal assumed sensitivity factors and equal 0.8 nm escape lengths make the film-thickness inversion possible; the model gives no calibrated atomic concentration and no real-material electron transport. The collection angle is measured from the upward surface normal. The background is a set linear continuum, and the sidebands are recorded counts. Counts come from a fixed random seed: Poisson below 40 expected counts, a normal approximation above. The dose at each pixel adds up all its energy positions. A set exponential dose rule moves oxygen response over to copper response to show beam-induced chemical change; it is not measured kinetics. Removed depth is an ideal, completed sputter step, with no sputter rate, preferential sputtering, roughness or mixing. The source, collection lens and half-turn electron analyzer are schematic, and no fields are integrated. Smoothing the derivative never reacquires counts. The thickness inversion uses only counts and calibration; the known undamaged film is a separate check. Dark cells are unresolved, not zero thickness.

Physics tutorial

Auger Spectra: What Sputtering Leaves Behind

BackgroundRemoving a layer also bombards the material left behind. Follow twelve one-second ion steps at a uniform test spot, each followed by a separately recorded Auger spectrum. Mixing can drive oxygen-bearing material below the original interface, and chemical conversion can change its spectral response without removing it. The retained static-map mode separately explores lateral composition and electron-beam response changes.

Why it mattersCompare three quantities through the stored history: completed removal depth, the actual retained material inventory and a sharp-layer equivalent thickness fitted from counts. The spectral target checks identifiability and agreement with a separate forward signal, not recovery of an unknown depth profile. The static map keeps its earlier pixel-coverage, thickness-error and beam-damage target.

Start with the essentials

Focus question: Does removing one nanometre leave a one-nanometre-thinner film?
One-sentence intuition: An escape-weighted spectrum does not count all remaining atoms equally. Once a sharp film becomes a mixed depth distribution, its attenuation-equivalent thickness need not equal its retained material inventory.

Core mathematical model

Retained material balance

\begin{aligned}M_k&=\int_0^\infty(c_n+c_c)\,dz\\M_k+M_{\rm removed,k}&=M_0\end{aligned}

Native-to-changed conversion conserves oxygen-bearing material; only removal changes the total inventory.

What a depth-weighted spectrum measures

\begin{aligned}\ell_n&=\lambda\cos\theta\\q_j&=\int_0^\infty c_j(z)\frac{e^{-z/\ell_n}}{\ell_n}\,dz\\q_{Cu}&=1-q_n-q_c\end{aligned}

The two oxygen populations and complementary copper use assigned equal sensitivities and escape lengths.

An apparent sharp-film thickness

\begin{aligned}\widehat q_O&=\frac{\widehat A_n+\widehat A_c}{\widehat A_n+\widehat A_c+\widehat A_{Cu}}\\\widehat t_{\rm sharp}&=-\ell_n\ln(1-\widehat q_O)\end{aligned}

Peak amplitudes come from the count spectrum and calibrated shapes. This is a sharp-layer equivalent; the inverse never receives the actual depth distribution.

Static map: How film thickness weights the two signals

\begin{aligned}\ell_n&=\lambda\cos\theta\\q_O&=1-e^{-t/\ell_n}\\q_{Cu}&=e^{-t/\ell_n}\end{aligned}

This holds for equal assumed escape lengths and sensitivities, before the dose changes the response.

Static map: Film thickness from the recorded windows

\begin{aligned}S_i&=\sum_{j\in W_i}(N_j-\widehat B_j)\\\widehat q_O&=\frac{S_O}{S_O+S_{Cu}}\\\widehat t&=-\ell_n\ln(1-\widehat q_O)\end{aligned}

Sideband counts give an estimate of the linear background. Pixels that are too weak or saturated stay unresolved, and the model assumes equal sensitivities.

Static map: Electron count and accumulated dose

\begin{aligned}N_{inc}&=\frac{I\tau}{e}\\D&=\frac{n_E N_{inc}}{p^2}\\s&=e^{-aD/D_c}\end{aligned}

Dwell time is set per energy position. The dose at a pixel includes all 140 positions, and the survival law is a set rule.

Common difficulties

Equal removed depth need not leave equal material

Typical misconceptionSubtract the removed depth from the initial thickness and the specimen is known.

Better mental modelThat subtraction describes an unmixed sharp film. The history stores actual depth populations, chemical conversion and material removed; the spectrum then weights the retained distribution by escape depth.

Reference curves are not data

Typical misconceptionThe ideal input is the result inferred from the counts.

Better mental modelThe gold views show the known input and serve only as an independent check. The teal result comes from the stored counts alone.

Longer exposure does not fix every error

Typical misconceptionIf I collect enough counts, the answer will be right.

Better mental modelMore counts reduce counting noise. Errors from the continuum background, the calibration, the finite instrument width and the set damage remain.

Run the experiment

01
Compare removal with what remains
Compare the mixed-surface and undisturbed-layer presets. Move the stored-step control through the same acquired history.
What to observe: The gray sharp-film estimate tracks simple removal; the gold retained inventory follows actual material loss.
02
Separate chemistry from disappearance
Choose the changed-chemistry preset and inspect the two oxygen markers and the copper window.
What to observe: A changed oxygen component can grow without an equal loss of oxygen-bearing material.
03
Test the sharp-film assumption
Compare the teal count-derived equivalent with the gold retained inventory, then inspect the separate known depth profile.
What to observe: A good line-shape fit does not make a mixed depth profile a sharp film.
04
Remove the ion perturbation
Choose Before sputtering, then raise the removal rate with zero mixing and zero conversion. Compare with the low-count preset.
What to observe: Zero removal changes no material. Too few counts must stay unresolved rather than produce a convincing thickness.
05
Predict a false map
In Static map and electron damage mode: Compare no background subtraction with the resolved preset. Look at both raw windows and the net-yield maps.
What to observe: The continuum background adds counts even where the element's own signal is weak.
06
Process one dataset
In Static map and electron damage mode: Change the selected pixel and the derivative smoothing. Switch sideband subtraction on and off without changing the acquisition.
What to observe: Smoothing changes the derivative, but not the stored spectra or the thickness estimate.
07
Test the surface sensitivity
In Static map and electron damage mode: Increase the collection angle, then remove one nanometre. Compare the inferred thickness with the separate known remaining film.
What to observe: Grazing collection suppresses the signal from the buried copper; sputtering changes which surface is left.
08
Get enough signal without changing the specimen
In Static map and electron damage mode: Return to normal collection, narrow the analyzer response, subtract the background and raise the dwell only as far as needed. Check the target.
What to observe: A longer exposure can raise the signal-to-noise ratio and at the same time move the result farther from the undamaged reference.

Core mathematical model

Retained material balance

What a depth-weighted spectrum measures

An apparent sharp-film thickness

Static map: How film thickness weights the two signals

Static map: Film thickness from the recorded windows

Static map: Electron count and accumulated dose

Common difficulties

Equal removed depth need not leave equal material

Reference curves are not data

Longer exposure does not fix every error

Run the experiment

Compare removal with what remains

Separate chemistry from disappearance

Test the sharp-film assumption

Remove the ion perturbation

Predict a false map

Process one dataset

Test the surface sensitivity

Get enough signal without changing the specimen