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Sandbox Physics

E60 · Electron excitation and surface spectroscopy

Scanning Auger: A Few Nanometres

Scan two Auger windows at every surface pixel. Subtract counted sidebands, differentiate stored spectra and infer the remaining film thickness while balancing counts, escape depth and beam damage.

Interactive modelScanning Auger: A Few Nanometres
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{—}

Physics tutorial

Scanning Auger: A Few Nanometres

BackgroundScan two Auger windows at every surface pixel. Subtract counted sidebands, differentiate stored spectra and infer the remaining film thickness while balancing counts, escape depth and beam damage.

Why it mattersTarget: film-thickness mean error at most 0.25 nm, at least 90 percent resolved pixels, selected-pixel SNR at least 8, analyzer FWHM at most 12 eV and prescribed changed fraction at most 12 percent.

Start with the essentials

Focus question
Can a clean elemental map hide damaged chemistry?
One-sentence intuition
A count-derived map still depends on continuum subtraction, escape geometry and the specimen surviving the measurement.

Core mathematical model

Near-surface weighting

ℓn=λcos⁡θqO=1−e−t/ℓnqCu=e−t/ℓn\begin{aligned}\ell_n&=\lambda\cos\theta\\q_O&=1-e^{-t/\ell_n}\\q_{Cu}&=e^{-t/\ell_n}\end{aligned}

Equal prescribed escape lengths and sensitivity, before the dose-induced response change.

Inference from acquired windows

Si=∑j∈Wi(Nj−B^j)q^O=SOSO+SCut^=−ℓnln⁡(1−q^O)\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 estimate a linear continuum. Weak or saturated pixels stay unresolved; the model assumes equal sensitivities.

Counting and cumulative dose

Ninc=IτeD=nENincp2s=e−aD/Dc\begin{aligned}N_{inc}&=\frac{I\tau}{e}\\D&=\frac{n_E N_{inc}}{p^2}\\s&=e^{-aD/D_c}\end{aligned}

Dwell is per energy position. Dose includes all 140 positions at a pixel; the survival law is prescribed.

Common difficulties

Separate references from data

Typical misconceptionThe ideal input is the inferred result.

Better mental modelGold known-input views are independent audits. The teal result uses stored counts only.

Exposure does not fix every error

Typical misconceptionEnough counts guarantee the right answer.

Better mental modelCounts reduce counting noise, but continuum errors, calibration, finite instrument width and prescribed damage remain.

Run the experiment

  1. 01

    Predict a false map

    Compare no background subtraction with the resolved preset. Inspect both raw windows and the net-yield maps.

    What to observe: A continuum contributes counts even where the corresponding element signal is weak.
  2. 02

    Process one dataset

    Change the selected pixel and derivative smoothing. Toggle sideband subtraction without changing acquisition.

    What to observe: Smoothing changes the derivative, not the stored spectra or thickness estimate.
  3. 03

    Challenge surface sensitivity

    Increase collection angle, then remove one nanometre. Compare inferred thickness with the separate known residual film.

    What to observe: Grazing collection suppresses the buried Cu signal; sputtering changes what surface remains.
  4. 04

    Balance information and change

    Restore normal collection, narrow the analyzer response, subtract background and increase dwell only as far as needed. Check the target.

    What to observe: Longer exposure can produce higher SNR while moving farther from the undamaged reference.