Why don't we have x-ray emitting LEDs? I've just learnt about how X-rays are produced in existing systems. We barrage a hunk of metal with a beam of electrons, in order to get an effective yield of 20% of the energy converted into useful X-rays (rays with the desired energy level).
While it seams on the surface to be massively inefficient, it wouldn't be a staple if there wasn't a good reason...right?
So why can't we just make an X-ray emitting Diode? Is it the case that the right material that would emit photons at the requisite energy simply doesn't exist?
 A: To emit radiation (in a more quantum way), you need charged particles to do transitions of some kind, that is, to move from one energy level, to the other.
In the case of an LED, light is produced when an electron falls into a hole (effectively a type of transition, where the electron falls from a free band into a lower energy band). The difference in energy between the bands determines the frequency of radiation emitted (by, $E = hf$).
X-Ray radiation is about 1 to 100 KeV. So, one could re-state the question: Where KeV transitions can be found? The answe is, KeV is so energetic, it can only be found (as far as I know), in electronic transitions within the atom, for electrons who are deep and way too close to the atomic nucleus.
Molecular bond energies can vary between a few mili eV, to 10 eV or something, faar away from the 1000 eV required to arrive in X-Ray range. And, in semiconductors, the band energies (which are basically an approximation for a really large molecule), will also be in the order of 1eV.
So, I find it unlikely to exist an X-Ray emitting LED.
I guess an X-ray laser would be more likely to exist, considering lasers can stimulate their transitions not only restricted to bands, but molecular and also atomic, and perhaps literally anything where it is possible to have transitions.
