I'd like to hear more about these challenges
As I understand it, primarly because due to the high energy level of x-rays, light x-ray interacts very differently with materials[1]. Primarily they get absorbed, so very difficult to make mirrors or lenses, which are crucial for litography to redirect and focus the light on a specific miniscule point on the wafer.
The primary method is to rely grazing angle reflection, but that per definition only allows you a tiny deflection at a time, nothing like a parabolic mirror or whatnot.
Stochastic effects become a bigger and bigger problem. At some point (EUV) a single photon has enough energy to ionize atoms, causing a cascade that causes effects to bloom outside of the illumination spot.
There are no normal x-ray mirrors. The only way to focus them is to use special grazing mirrors where the x-rays hit them almost parallel to the surface.
https://science.gsfc.nasa.gov/662/instruments/mirrorlab/xopt...