When a high energy electron beam lands on an insulating substrate, some electrons must be embedded. How are they dissipated?

they would spread out very slowly but if there is a conductor nearby connected to ground, it could be faster. But even metal has resistance. Electron beam samples with insulators charge differently all the time. Not very reliable.

- Even insulators have some volume conductivity. Very dependent on water contents and temperature. And generally very low, so low that it's quite difficult to measure. And nonlinear anyway.

- Generally masked by surface conductivity, but not in your case.

- As electrons get trapped in, they repel incoming electrons which then land somewhere else. So to get proper images from an electron microscope, surfaces are coated with gold.

- If the charge gets big enough, dielectric breakdown and damage. Unless distances are tiny enough that tunnelling works.

- Apply your semiconductor knowledge here as well. Conduction band, valence band, bending... Keeping in mind that insulators are generally amorphous so their bands aren't well defined and are full of traps and deep levels, which keep charge carries.

The most common substrates are silicon and glass. If the electron beam goes all the way to grounded silicon, it is a closed path. If the electrons get mired in the oxide or glass, the situation is tricky. As the primary electron slows down, it generates more and more ions and electrons, so actually it is no sweat for it to eventually recombine when it stops. But the charge balance has to be done all along the electron path so to speak. So the excess charge should eventually be pushed up to the surface. The surface is usually already positive from ejected electrons, so the surfacing electron can help neutralize. In the end, though, you still have to close the circuit, so you need something grounded to collect excess or ejected electrons. It does not have to be on the sample. I have seen parts of the stage charge up because of too many electrons flying around. The beam current is no longer steady once you impact the substrate, there has to be charging and discharging. And this depends on how long you dwell on a particular sample area, etc.

The trapping of electrons or positive charge in the resist could deflect the electron beam as well as damage the device.