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Recently, I noticed that most devices that produce X-rays are somewhat 'crude'. It is usual for these devices to either heat something up to the point where the bremsstrahlung is in the X-ray region - for example implosion backlighters in big laser facilities.

Another more commercial method is using cathode ray tubes - accelerating an electron to a high energy and then decelerating it quickly to produce X-rays.

Are there no solid-state devices as 'elegant' as LEDs to produce x-rays? Is there a strict physical limitation why these cannot be produced?

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    $\begingroup$ There are no solids with that large of a band gap. Just not an energy range seen in chemistry and chemical bonding. $\endgroup$
    – Jon Custer
    Commented Jun 2, 2020 at 19:54

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The problem is what mechanism can you use to produce X-Rays with solids... atomic or molecular, band transition, whatever you use in solids do not enter the X-Ray regime when it comes to produce high energy photons. Moreover, as Bragg showed, solids are more like a diffraction grating for X-Rays, since the separation of atoms in crystals are of the order of the wavelength in this case. And other processes, such as in the nucleus, would demand reactions which are either difficult, too energetic or would deplete a solid rapidly or make it more dangerous because of the use of radioactive isotopes.

X-Ray sources need be recharged not used one time and the mechanisms for such recharge process are available through for example the sudden deceleration of electrons. Cold atoms such as those in solid state devices do not work with these energies and sources which are rapidly depleted are neither good nor efficient.

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