low energy electron repulsion, numerical simulation results

[guiding_light]

An important issue in electron-based lithography and scanning tunneling microscopy involving low-energy electrons is the repulsion between two adjacent electrons. The electrons can be secondaries or part of the STM current. The repulsion between a pair of electrons initially traveling in parallel at a given initial velocity and the effect on the separation between them can be calculated simply since this is a non-relativistic problem.

The repulsion follows Coulomb's law and gives the instantaneous acceleration. The instantaneous velocity is previous velocity plus instantaneous acceleration * dt. The separation is dt*instantaneous velocity plus previous separation.

This is a fairly simple exercise that can be carried out in an Excel spreadsheet.

If the initial kinetic energy of the electrons is 5 eV, and the initial separation is 2 nm, the final separation between the two electrons after traversing forward 30 nm is 10 nm.

[plasma_guy]

No mention of scattering or energy loss, so these must be ignored?

[guiding_light]

Yes, these were ignored to see for how long the pair of electrons could stay separated within a given distance. It should hold for vacuum.

In a medium, you also have elastic scattering. This will automatically cause the two initially close, near-parallel trajectories to diverge. This would be a bigger effect than the Coulomb repulsion anyway.

You also have inelastic scattering in the medium. This takes place less often than elastic scattering at low energies. Reducing the energy would mean less distance traversed before the Coulomb repulsion has the same effect.