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The dielectric must be an insulator to maintain bias voltage between foils, otherwise the whole thing will just short out. By an insulator I mean a material with a band gap energy of above a few eV. A semi-conductor for comparison has a band gap of the order of 1eV between the valence & conduction band, and a conductor has negligible or no gap at all. So at normal room temperatures eg 300K which corresponds to 0.025eV of energy for the average electron almost none are excited into the conduction band in an ‘insulator’. However if they are given a kick by the photo-electron from the x-ray absorption, an electron in the ‘insulator’ can gain the few eV needed to be excited into the ‘conduction’ band and so becomes mobile. The high energy photo-electron loosing a corresponding few eV in each interaction.
After a few thousand interactions the high energy photo-electron will have excited lots of secondary electrons and have slowly lost all its energy. This takes time (a few pico seconds) so the dielectric needs to be thick enough for all the energy to be deposited in the dielectric – I’m guessing a few to tens of microns.
If the photo-electron were to get to the next foil (or scatter back to the one it came from) then the atoms excited in the foil will not result in a movement of charge across the electic field created by the bias voltage (the foil being a conductor will all be at the same potential and hence no E-field within it and no motion of electron/hole pairs created, so they will just recombine locally with no nett current). So the proportion of all the original photo-electron’s energy deposited in the dielectric limits the the x-ray energy capture efficiency.
NB. all of this is just based on my understanding of X-ray absorption, and so how to get a measurable current from such an interaction, not on the specifics of the patent