Below the critical voltage, knock-on stops. Radiolysis does not care about the voltage.
The beam can move atoms (knock-on), break bonds (radiolysis) and heat the specimen. Before you call a change real, check each one. This lab gives you the numbers: the voltage below which knock-on stops, the test that tells radiolysis from knock-on, how many electrons per Å2 your settings deliver, and how hot a probe can make the spot under it.
Ed: one representative value per element. Real values depend on direction and on whether the atom sits at a surface or edge, where it is easier to remove.
Moving A or Ed switches the material to "your own". Knock-on happens only above the critical voltage. Below it, damage you see is something else.
A picture, not a model of one material: damage grows with each electron and heals at rate k2. Units are arbitrary. k2 = 0 is the knock-on-like case.
Critical dose: the dose at which the feature you care about is gone (for example, diffraction spots fade to 1/e). Use a value measured on your own material if you can.
Energy left per nm = average loss per inelastic event ÷ inelastic mean free path. About 0.26 eV/nm fits carbon at TEM voltages; it falls as the voltage rises. Heat sink: roughly the radius of the grid hole or the edge of the foil. Metals: 20 to 400 W/m·K, oxides 1 to 40, carbon films about 1.6, polymers 0.1 to 0.5.
| Check | What you do | Tab | What it tells you |
|---|---|---|---|
| 1 Knock-on | Compare your voltage with the critical voltage for the lightest atom that matters. | Knock-on | Below it, knock-on is impossible. Above it, lowering the voltage is the fix. |
| 2 Dose rate | Give the same total dose at two very different dose rates, on fresh areas. | Radiolysis | A different outcome means something heals or diffuses between hits: not knock-on alone. |
| 3 Dose series | Image one area again and again and track a feature (diffraction spots, a spectrum edge) against accumulated dose. | Dose budget | The dose at which it fades is your critical dose. Stay well below it. |
| 4 Your dose | Work out e/Å2 per second (TEM) or per frame (STEM) from current, beam size, pixel size and dwell. | Dose budget | How long, or how many frames, you have before the feature is gone. |
| 5 Heating | Estimate the temperature rise for your current and material. | Beam heating | Usually a few K or less in a thin foil. Large only for poor conductors, large currents or foils with poor contact. |
| 6 Control | Watch a region the beam has not seen. For in-situ tests, repeat with the beam blanked except for short snapshots. | If the change happens only where the beam was, the beam is part of it. |
The knock-on formula is exact for a free, resting nucleus. It leaves out atoms at surfaces and edges (easier to remove), thermal vibration (which lowers the threshold a little) and channelling. The displacement energies are single representative values. The radiolysis tab is a picture with arbitrary units, made to show the dose-rate test, not a rate model for any material; real radiolysis can also show a true dose-rate threshold. The dose tab assumes a uniform beam and, in STEM, a probe smaller than a pixel. The heating tab uses the thin-foil result of Egerton, Li and Malac with radiation neglected; it assumes a uniform foil connected to a heat sink at a fixed distance, and the value for energy left per nm is an estimate. Contamination and charging, two other common beam effects, are not covered.
On this site: Scattering in the TEM · FIB specimen prep: what the ion beam does · EELS thickness calculator · Quantitative HAADF · GPA strain mapping
Two tests. Lower the voltage below the critical voltage: knock-on stops, radiolysis often gets worse. Change the dose rate at the same total dose: radiolysis changes, knock-on does not.
Only for knock-on. At lower voltage each electron loses more energy in the sample, so radiolysis per electron goes up. For beam-sensitive organics and many oxides, a higher voltage can be better.
Cooling slows the movement of broken bonds and radicals, so less damage becomes permanent. It does little for knock-on, which is a direct collision.
Rarely, in a thin foil. The electrons pass through and leave only tens of eV each. A few K is typical. Poor conductors, large currents and foils that are cut off from their support are the exceptions. Estimates that use the full beam power are far too high for thin foils.
Checked (October 2026). The critical voltage is solved exactly from Emax = 2E(E + 2mc²)/(Mc²) = Ed (Egerton, Li and Malac 2004) and agrees with an independent calculation to the last digit: 86 kV for carbon with Ed = 17 eV, 178 kV for aluminium (17 eV), 165 kV for silicon (15 eV), 396 kV for copper (19 eV) and 1328 kV for gold (34 eV). At 200 kV a copper nucleus can receive at most 8.26 eV. The dose arithmetic (100 pA over a 1 µm disc gives 7.95 electrons per Ų per second) matches by hand.
@misc{tripathy2026beamdamage,
author = {Tripathy, Manisha},
title = {Beam Damage in the TEM},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/beam-damage}},
note = {Interactive web tool}
}