---
title: "Micro / Nano ARPES: Spots & Domains Interactive Lab | Sandbox Physics"
description: "Can a smaller light spot resolve a narrow domain without damaging it? Only if spot size, counts and exposure are balanced."
canonical_url: "https://sandboxphysics.com/labs/micro-arpes/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/micro-arpes/"
last_modified: "2026-10-27"
---

E56 · Photoelectron microscopy

# Micro / Nano ARPES: Spots & Domains

**Can a smaller light spot resolve a narrow domain without damaging it?** Only if spot size, counts and exposure are balanced. A tighter focus resolves a narrow domain but collects fewer counts, so the spectrum gets noisier. Exposing longer to make up the counts piles dose onto the domain and can damage it. You need a small enough spot, enough counts and a domain that survives, all at once.

Move a sample with two domains through a focused photon beam. Look at the spectrum recorded at each raster point, and use two energy gates to map the narrow domain. Balance the photon throughput of the optics, counting noise, energy resolution and the dose that builds up on the sample.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The sample is a synthetic 4 micrometre square. A rectangular domain 0.625 micrometre wide and 1.5 micrometre tall has its band bottom at −0.42 eV, and the surrounding region has its band bottom at −0.22 eV. Both regions have an assumed parabolic dispersion and the same emission yield. The photons are fixed at 40 eV, the grounded work functions are 4.5 eV and the slit accepts ±2 degrees. A 17 by 17 raster runs left to right, then bottom to top. Its fixed 0.25 micrometre step limits how finely the map is sampled, even when the optical spot is smaller. Spot widths are the FWHM of a Gaussian intensity profile, and each finite sample cell integrates the light that falls on it. An assumed focusing-throughput law reduces the transmitted flux as the spot shrinks. Where raster points overlap, the photon dose adds up locally. The band survives with an assumed exponential law integrated over each dwell, and the lost band weight becomes a uniform damage continuum. The critical dose and yield are teaching parameters, not a calibration for a real material. Temperature sets the Fermi occupation. A Gaussian-equivalent analyzer width is convolved with the intrinsic Gaussian line. Two fixed energy gates give a fraction of recorded counts; this is not a chemical concentration and does not fix a unique volume fraction. The reported score-interval half-width is a conditional counting uncertainty and leaves out background and systematic errors. Selecting a point shows a raster frame that was already recorded and adds no exposure. The domain reference and the final dose model are kept separate from the acquired spectra. The drawn collector shows a local energy window of those counts. The angular relay and the optical focus are schematic. There is no wave-optics zone-plate calculation, angular-resolution convolution, space charge, selection of perpendicular momentum, heating or transport. Counts below a mean of 40 are Poisson, and larger means use rounded Gaussian draws. Changing any acquisition setting starts a new raster on a fresh sample.

Physics tutorial

## A spatial map is a series of spectra

**Background** Focusing optics illuminate only a small region of the sample. As the sample moves, different domains contribute to the spectrum.

**Why it matters** A smaller spot shows finer detail, but it delivers less flux and concentrates the dose. Because neighboring raster points overlap, a pixel can be exposed before its own spectrum is recorded.

Start with the essentials

- **Focus question**: Can a smaller light spot resolve a narrow domain without damaging it?
- **One-sentence intuition**: Locate a domain with the recorded energy gates, then check its spectrum and the separate dose model. A bright map alone does not tell you the composition.

### Core mathematical model

#### Spot width and Gaussian width

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

The intensity FWHM sets the Gaussian width used to integrate the illumination over each sample cell.

#### Average band survival during one dwell

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

Dose is measured in units of the assumed critical dose. When the added dose goes to zero, use the continuous limit.

#### Fraction of counts in one energy gate

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

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

### Common difficulties

#### A map is not the sample itself

**Typical misconception** The map shows the true sample directly.

**Better mental model** The map shows the fraction of recorded counts in two energy gates. Find the domain on the map, then check its spectrum and the separate dose model; brightness alone does not give the composition.

### Run the experiment

1. 01

   #### Predict how the domains mix

   Compare Wide spot mixes domains with Resolve the narrow domain.

   **What to observe:** With a wide spot the two bands mix. With a small spot near the narrow domain they separate.

2. 02

   #### Inspect recorded positions

   Move Select stored raster column and Select stored raster row, then press Check target on the narrow domain.

   **What to observe:** Selecting a point changes the spectrum on display, while the recorded map and the accumulated dose stay fixed.

3. 03

   #### Test resolution against damage

   Compare Nano spot without enough counts, Long exposure damages the scan and Open slit merges the gates.

   **What to observe:** More counts can hide damage, and a small spot cannot fix a broad energy response.

Physical conclusion

Fine spatial resolution, precise counts and an undamaged sample have to be achieved together.

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)