---
title: "EELS: Energy Loss & Thin-Specimen Signals Interactive Lab | Sandbox Physics"
description: "What do electrons lose when they pass through a thin specimen? Energy. They give it to plasmons, the collective oscillations of the valence electrons, and to tightly bound inner-shell electrons. The spectrum shows a zero-loss peak, a series of plasmon peaks and a core edge. Electrons in the zero-loss peak may still have scattered elastically. Repeated plasmon losses shift and smear the core edge, which is why the specimen has to be thin."
canonical_url: "https://sandboxphysics.com/labs/eels/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/eels/"
last_modified: "2026-10-25"
---

E34 · Electron spectroscopy

# EELS: Energy Loss & Thin-Specimen Signals

**What do electrons lose when they pass through a thin specimen?** Energy. They give it to plasmons, the collective oscillations of the valence electrons, and to tightly bound inner-shell electrons. The spectrum shows a zero-loss peak, a series of plasmon peaks and a core edge. Electrons in the zero-loss peak may still have scattered elastically. Repeated plasmon losses shift and smear the core edge, which is why the specimen has to be thin.

Move the probe across a carbon-rich inclusion and read two windows of the energy-loss spectrum from the transmitted electrons. Pick out the zero-loss peak, the repeated plasmon losses and the carbon core edge, then weigh collection angle, energy sampling, resolution and exposure before you trust the thin-specimen result.

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

Model assumptions

The beam is fixed at 200 kV and the probe current at 0.004 pA. The low-loss mean free path is an adjustable assumption, not a material calibration. Each loss is independent and centered at 16 eV with a 3 eV standard deviation, and the number of losses follows Poisson statistics. Low-loss collection is assumed not to depend on energy. The log ratio shown uses the actual counts from −10 to 130 eV and a finite zero-loss window, so broadening, noise and missing tails bias it. The core signal uses a separate approximation for rare core events: a synthetic carbon K edge near 284 eV is convolved with the low-loss distribution. Its yields, near-edge feature and shift do not identify a real chemical state. Core collection uses an assumed dipole angular distribution with negligible beam convergence. Net core counts subtract the known model background; they are not a fitted elemental analysis. The Gaussian instrument width is given as FWHM. Noise comes from a fixed seed: Poisson below 40 counts, a Gaussian approximation above. The magnetic sector disperses energy schematically at 0.1 scene unit per eV, and no magnetic field or aberrations are solved.

Physics tutorial

## Read a spectrum before naming a material

**Background** A transmitted electron can reach the detector with no measurable loss, give energy to a collective excitation, or excite an inner-shell electron. A spectrometer sorts these outcomes by energy.

**Why it matters** An edge tells you something only when the collection angle, energy response, sampling and specimen thickness are good enough to interpret it.

Start with the essentials

- **Focus question**: What do electrons lose when they pass through a thin specimen?
- **One-sentence intuition**: A zero-loss electron may still have scattered elastically. Repeated low losses shift and broaden the core edge, and the detector dispersion and the energy resolution set two different limits.

### Core mathematical model

#### How many times an electron loses energy

$$
P_n=\frac{\mu^n e^{-\mu}}{n!},\qquad \mu=\frac{t}{\lambda}
$$

Independent inelastic events give a fraction of electrons with no loss and a population that lost energy more than once. The mean free path here is an assumed teaching input.

#### Relative thickness from counts

$$
\left(\frac{t}{\lambda}\right)_{\!\mathrm{app}}=\ln\frac{I_{\mathrm{window}}}{I_{\mathrm{ZLP}}}
$$

Both integrals use the recorded low-loss bins. Because the spectral window and the zero-loss integration are finite, the result can be biased, especially with a broad response or a thick specimen. An absolute thickness also needs a calibrated mean free path.

#### Instrument broadening and pixel integration

$$
\sigma_E=\frac{\Delta E_{\mathrm{FWHM}}}{\sqrt{8\ln2}},\qquad C_j=N_{\mathrm{inc}}\int_{E_j^-}^{E_j^+}p(E)\,\mathrm dE
$$

Resolution and dispersion are different things: narrower detector bins cannot undo an energy response that is already broad. Each bin integrates the probability first, and then counting noise is drawn.

#### A core event can be followed by low losses

$$
S_{\mathrm{core}}(E)\propto\sum_{n=0}^{\infty}P_n\,[S_1*G_n](E-16n\,\mathrm{eV})
$$

In this teaching approximation for rare core events, extra low losses move part of the edge toward higher loss. You can shift the synthetic onset and feature, but no real oxidation state is inferred. Subtracting the known model background gives an optimistic signal-to-noise reference.

### Common difficulties

#### A shifted edge does not name a chemical state

**Typical misconception** Any shifted edge names a unique oxidation state.

**Better mental model** These near-edge shapes are invented. Identifying a chemical state needs reference spectra, calibration and a suitable scattering model.

### Run the experiment

1. 01

   #### Start thin, then make it thicker

   Compare Thin · resolved with Plural scattering. Watch the repeated low-loss peaks and compare the assumed thickness with the estimate from the recorded window.

   **What to observe:** Multiple losses grow and spread the core signal to higher loss. A finite low-loss window can miss part of the tail.

2. 02

   #### Sampling is not resolution

   Keep the specimen thin; compare 0.25 and 2 eV per pixel, then change the energy response from 1 to 6 eV.

   **What to observe:** Fine bins preserve a narrow feature only if the instrument response is already narrow.

3. 03

   #### Locate the signal

   Move the probe out of the carbon-rich region and back again. Then try the synthetic shift preset.

   **What to observe:** The core edge weakens outside the inclusion. The low-loss average stays the same because the whole toy specimen has one mean free path.

4. 04

   #### Meet the target

   Meet the stated limits on thickness, sampling, energy response and expected SNR, then check.

   **What to observe:** The SNR with a known background is an optimistic reference. Real fitting, the detector response and material cross sections need further evidence.

Physical conclusion

Before you interpret an edge, make sure the specimen is thin enough and the energy response is good enough. The synthetic edge shift shows how the measurement works; it does not identify a chemical state.

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)