EDS Spectrum Simulator

English · 日本語

An interactive web app for building intuition about EDS/EDX measurements — counting statistics (Poisson noise), detector response, and thin-film / multilayer matrix effects. Built with Streamlit, Plotly and xraylib.

▶ Live demo (no install): https://edssimulator-xjd8gyxkgdwezujsfevvha.streamlit.app/

🌐 The app UI is available in English and Japanese (toggle at the top of the sidebar).

A 1 % trace element (Ti) is invisible in the noise when under-counted (Max ~2,000), but emerges once enough counts are collected (Max ~90,000) — the same sample, only the measurement condition changed.

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Why

Analysts often misread EDS results. Two common failure modes this tool makes tangible:

• "No peak, so the element is absent." A 1 % element can be completely buried in the √N background noise at a few thousand counts. Increase probe current / live time and it appears — with no change in composition.
• "Higher kV is always better." For an ALD-thin film on a substrate, most of the interaction volume is the substrate. Lowering the accelerating voltage shrinks the φ(ρz) generation depth, suppresses the substrate signal, and relatively enhances the film S/N.

Features

• Counting statistics: Kramers bremsstrahlung + Gaussian characteristic peaks, with numpy.random.poisson shot noise. Max counts scales linearly with probe current × live time.
• xraylib database: accurate line energies, absorption edges, fluorescence yields, and Be-window / self-absorption via mass attenuation coefficients. Line intensities use an electron-impact excitation model (Bethe ionization × fluorescence yield × radiative rate), so multi-shell elements (e.g. Au M vs L) get the right overvoltage-dependent ratios.
• Multilayer thin film: stack up to 5 layers (surface → substrate). Each layer/substrate is given as a chemical formula (e.g. TiN, TiO2, Al2O3); absorption by overlying layers is computed with Bragg's additivity rule. Analytical Packwood-Brown φ(ρz) depth distribution anchored to the Kanaya-Okayama electron range, integrated with scipy.integrate.quad.
• Two modes: homogeneous bulk (statistics) and thin film / substrate (multilayer).
• Bilingual UI: switch between English and Japanese at runtime.

Quick start

Docker (recommended)

docker compose up --build
# open http://localhost:8501

pip

pip install -r requirements.txt
streamlit run app.py

xraylib ships PyPI wheels for every OS and Python 3.10–3.13, so pip installs it directly. Without it, the app falls back to a small built-in table (Phase 1 fully works, Phase 2/3 accuracy limited).

conda (optional)

conda create -n eds-sim python=3.12
conda activate eds-sim
pip install -r requirements.txt
streamlit run app.py

Example structures

Structure	Layers (surface → substrate)	What it shows
Electrode with adhesion layer	Au / Ti / Si	The Ti adhesion layer under Au is hard to see
Diffusion barrier + native oxide	SiO2 / TiN / Si	Compound layers and a native oxide
Surface contamination	C / O / Au / Si	Light-element deposits vs Be-window absorption

Project layout

EDS_simulator/
├── app.py                 # Streamlit UI / plotting
├── i18n.py                # UI strings (English / Japanese)
├── eds_sim/               # physics package
│   ├── config.py          # constants / dataclasses
│   ├── continuum.py       # Kramers bremsstrahlung
│   ├── characteristic.py  # characteristic lines -> Gaussians (bulk / layered)
│   ├── composition.py     # formula parsing, compound density / MAC (Bragg)
│   ├── detector.py        # resolution, window absorption, efficiency
│   ├── depth.py           # phi(rho z) and thin-film / substrate depth integrals
│   ├── elements.py        # xraylib helpers (lazy import, fallback)
│   └── spectrum.py        # assembly + Poisson noise
├── tests/                 # smoke tests (pytest)
├── requirements.txt
└── Dockerfile / docker-compose.yml

Model assumptions & limitations

• Bremsstrahlung uses the Kramers approximation; characteristic lines use xraylib line energies.
• Line intensities use a Bethe electron-impact ionization cross-section (∝ ln U / U, U = E0/Ec) × fluorescence yield × radiative rate — appropriate for electron-beam EDS, not the photon-excited (XRF) cross-sections.
• Detector resolution follows the standard Fano-statistics formula (calibrated to 130 eV at Mn Kα); window absorption is the Be-window mass attenuation.
• Peak-to-background ratio and absolute counts are an empirical calibration for visualization, not first-principles quantitative values (peak_to_background, intensity_scale).
• The thin-film φ(ρz) is Packwood-Brown with a Kanaya-Okayama depth scale; the electron-scattering matrix is approximated by the substrate composition (thin films, ρz ≪ range), so a thick heavy top layer underestimates electron slowing-down.
• Compound formulas support simple formulas only (no parentheses). Density comes from a preset table / single-element values, otherwise a nominal default (manual entry recommended).

Roadmap

• Parenthetical / hydrate formulas (e.g. Ca(OH)2).
• Expand the compound-density preset table.
• Absorption-edge visualization on the spectrum.
• Refined electron-impact cross-sections (Casnati / Bote-Salvat) and Coster-Kronig.

Tests

pip install pytest
pytest tests/ -v

License

Apache License 2.0 — see LICENSE and NOTICE.

Citation

If this tool is useful in your work, please cite it (see CITATION.cff).

Author

Yossy (Tohoku Yossy) — materials scientist (thin-film synthesis, surface analysis). GitHub: @yharada520