E56 · Photoelectron microscopy

Micro / Nano ARPES: Spots & Domains

Translate a two-domain specimen through a focused photon beam. Inspect a recorded spectrum at each raster point and use two energy gates to map the narrow domain. Balance optical throughput, counting noise, energy resolution and accumulated exposure.

Recorded low-energy gate fraction $\text{—}$

Conditional counting interval half-width $\text{—}$

Recorded counts in both gates $\text{—}$

Known survival during selected dwell $\text{—}$

Analyzer energy FWHM $\text{—}$

Transmitted photon rate $\text{—}$

Total raster duration $\text{—}$

Maximum final dose / critical dose $\text{—}$

Experiment target $\text{—}$

Predict · tune · inspect

Can a smaller spot reveal a domain without erasing it?

Photon spot FWHM

w

1\,\mathrm{\mu m}

Incident flux scale

f_\gamma

1

Dwell per raster point

t_d

0.05\,\mathrm{s}

Sample temperature

T

40\,\mathrm{K}

Analyzer pass energy

E_p

10\,\mathrm{eV}

Analyzer slit width

w_s

0.15\,\mathrm{mm}

Select stored raster column

x_s

0\,\mathrm{\mu m}

Select stored raster row

y_s

0\,\mathrm{\mu m}

Target: low-energy gate fraction above 0.85; more than 500 gate counts; counting half-width below 0.03; known survival above 85 percent; analyzer width below 0.04 eV. Selection adds no dose.

Synthetic 4 micrometre square specimen: a 0.625 micrometre wide, 1.5 micrometre tall rectangular domain has a band bottom at −0.42 eV; its surroundings have a bottom at −0.22 eV. Both have assumed parabolic dispersion and equal emission yield. Fixed 40 eV photons, grounded 4.5 eV work functions and a ±2 degree slit. A 17 by 17 raster runs left to right, then bottom to top; its fixed 0.25 micrometre step limits spatial-map sampling even when the optical footprint is smaller. Gaussian intensity spot widths are FWHM; finite specimen cells integrate its illumination. An assumed focusing-throughput law changes transmitted flux as the spot shrinks. Photon exposure accumulates locally over overlapping raster points. Assumed exponential band survival is integrated during each dwell; lost band weight adds a uniform damage continuum. Critical dose and yield are teaching parameters, not a real material calibration. Temperature sets Fermi occupation. A Gaussian-equivalent analyzer width convolves the intrinsic Gaussian line. Two fixed energy gates give a recorded count fraction, not chemical concentration or a unique volume fraction. The reported score-interval half-width is conditional counting uncertainty and omits background and systematic errors. Selection displays an already recorded raster frame and adds no exposure. The domain reference and final dose model are separate from acquired spectra. The physical collector shows a local energy window of those counts. Angular relay and optical focus are schematic; there is no wave-optical zone-plate calculation, angular resolution convolution, space charge, kz selection, heating or transport. Counts below mean 40 are Poisson; larger means use rounded Gaussian draws. Each changed acquisition setting starts a fresh specimen raster.

Start with the essentials

Focus question: Can a smaller spot reveal a domain without erasing it?
One-sentence intuition: Use recorded energy gates to locate a domain, then inspect the spectrum and the separate dose model. A bright map alone does not establish composition.

Core mathematical model

Gaussian optical intensity

\sigma_r=\frac{w}{\sqrt{8\ln 2}}

Intensity FWHM sets the Gaussian width used in cell-integrated illumination.

Finite-dose average survival

\overline s=e^{-D_0}\frac{1-e^{-\delta D}}{\delta D}

Dose is normalized to the assumed critical dose; use the continuous limit for vanishing additional dose.

Recorded gate fraction

r_B=\frac{C_B}{C_A+C_B}

Only stored detector counts enter this ratio. Equal line yields and separated gates are assumptions.

Common difficulties

A recorded fraction needs a model

Typical misconceptionA map directly reveals the true specimen.

Better mental modelUse recorded energy gates to locate a domain, then inspect the spectrum and the separate dose model. A bright map alone does not establish composition.

Run the experiment

01
Predict domain mixing
Compare the wide-spot and resolved-domain presets.
What to observe: The two bands mix with a wide spot and separate near the small domain.
02
Inspect stored positions
Move the selected column and row, then check the target on the narrow domain.
What to observe: Selection changes the displayed spectrum while the recorded map and accumulated dose remain fixed.
03
Challenge resolution and preservation
Compare the count-starved, damaged and open-slit presets.
What to observe: More counts can hide damage; a small spot cannot repair a broad energy response.