ASML is the only provider of EUV lithographic machines. TSMC is just slightly ahead of Samsung and Intel at utilizing that technology. I honestly can't see how anymore puts TSMC above ASML.

Yeah this story doesn't make much sense. Intel and Samsung are only a few years behind TSMC, recreating ASML and their sole suppliers even within 10 years would be quite a stretch.

ASML is concentrated in a country that has been politically stable and uncontested for 80 years and doesn't seek the media spotlight. It is easy to overlook. Nobody really pays much attention to the Netherlands or it's non existing foreign ambitions and there is no state involvement in ASML. Basically no drama means no journalism.

Carl Zeiss makes some amazing optics to allow it all to happen https://www.asianometry.com/p/how-carl-zeiss-crafted-a-house...

To quote:

To make these EUV mirrors, each 2 to 4 nanometer layer of molybdenum and silicon has to be deposited one by one. Fifty times, without fatal defects.

After that, each mirror has to be painstakingly polished. The acceptable surface deviation metric is 50 picometers, or 50 trillionths of a meter. That is a staggering number.

To put that into perspective. 50 picometers on a mirror that is 450 millimeters wide. If that 450 millimeter mirror was blown up to the size of the United States, 4,500 kilometers or 2,800 miles wide, then 50 picometers would be just 0.5 mm tall.

Altho there's a couple ways to define an atomic radius, molybdenum's and silicon's empirically measured covalent atomic radii are 145 and 110 picometers respectively [1]. So 50pm is a very small bump indeed.

[1] https://en.wikipedia.org/wiki/Atomic_radius