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From the tight-binding picture of insulators, the band-gaps arise from the intrinsic energy differences between atomic orbitals energy levels. The largest I have found so far is roughly 10eV (amorphous SiO2). Of course this picture doesn't always apply, you can have insulating behavior from electron-electron correlations (e.g. a Mott insulator). However, for the most part, Mott gaps tend to be less than a few electron volts, so I am ignoring them.

My questions are the following:

  1. Is there a physical upper limit to the band-gap of insulators in general? What about the case where the constituents are specified?
  2. If there is such a limit, what is the smallest it could possibly be?
  3. What is the largest band-gap of a known material/system?

Naively, one could place an upper bound on the band-gap for a given system by looking at the largest energy difference between the underlaying atomic orbitals. However the number you get with this method tends to be quite large, so I feel that one could do much, much better than this.

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Lithium fluoride is the solid with the largest bandgap, about 14 eV. But absorption already starts with an exciton at 12.9 eV.

Anyway, this is of the order of 1 Rydberg, 13.6 eV, the ionization energy of hydrogen atoms. And of other gases. This is why UV at higher photon energies is called Vacuum UV: nothing is transparent to it, no window materials, no gases.

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  • $\begingroup$ Yes I am aware of the general regime of EUV being easily absorbed by material basically, but i am more concerned about why this cutoff happens, and if you can connect the stupid l atomic ionization energy to limits on band gaps. $\endgroup$ – KF Gauss Oct 14 '17 at 1:52

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