I have been trying to get my head around Electron-Beam Lithography and have a small issue with what has been said in the linked YT video.

At 11:35 Chris Mack says that

The more energy the electrons have the further they travel (this I understand) and the less backscattering occurs (this I don't understand).

Why does the energy of the electrons influence how much backscattering occurs? Also he mentioned that

'Higher energy for electrons means less interaction with the material.'

Why is that? I have a hard time understanding why higher energies would influence these two things.

Any answers are helpful, also I would be fine with being pointed into the correct direction and research it myself.

  • $\begingroup$ Could it be relativistic effects? High-energy electrons would have to move with a speed close to the speed of light, and would experience time dilation. Given transition rates in the rest frame of the electron, they will be much lower in the frame where it moves with high speed. $\endgroup$
    – Darkseid
    Jul 20, 2019 at 12:46
  • 2
    $\begingroup$ A handwaving way to look at this is with the Heisenberg uncertainty for momentum and space: $Δ(x)Δ(p)<h/(4π)$ . The higher the momentum, the higher the energy the smaller the volume the electron occupies, and the fewer atoms it finds to interact with. In general it is a complicated effect, see pdg.lbl.gov/2019/reviews/… $\endgroup$
    – anna v
    Jul 20, 2019 at 13:07
  • $\begingroup$ Thanks for the answer it was very helpful, I'll have a look at this. I did not anticipate that it would be this complicated (: $\endgroup$ Jul 20, 2019 at 14:08

1 Answer 1


"Why does the energy of the electrons influence how much backscattering occurs?"

When we look at the angular differential cross-sections, we see the higher energy electrons have tendency to make more forward scattering than a lower energy electron. Therefore, you get less backscattering.

"Higher energy for electrons means less interaction with the material." Yes. There can be three different aspects of this question:

1) Fundamentally, you see the scattering cross-sections of higher energy electron is lower. That means the mean free path is longer. So, the higher energy electron travels longer between each interactions.

2) If you look at bond-breaking cross-sections, it makes a peak around a few electron volt. That means low energy electrons are much more effective to actually deform the resist.

3) High energy electrons travel deep and loses its energy far away from the resist. Therefore, it has a lot of interaction but not around the sensitive material (resist).


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