Yeah. ASML doesn't make the mirrors, but they have exclusive sales rights, exactly as you say. And yes, positioning them, for example, both in the fixed sense (mounting the mirrors in the machine) and in the dynamic sense (rapidly positioning wafers to nanometer-or-better accuracy below the beam, I forgot how quick exactly but it's 10s to 100s of times per second to maintain production rates) is very much not easy either. But it's "been done" (by teams of phds). Producing the mirrors has not been duplicated.

Of course, producing the EUV beam in the first place has also not been duplicated and it's Californian technology.

Intel 18A has a different strategy all together. I mean, it's not like they're saying much about it, but from the little we know, it's very different.

No the beam source we know how to create; it's just that the way to do so requires a factory sized machine that better be feeding 10~30 steppers or a pair for uptime/maintenance windows and then probably more like 50 steppers.

Free electron lasers are not hard at "mere EUV", and the accelerators to feed aren't either, it's just that an efficient setup requires recycling the beam which means bending it back which means a large (factory hall sized) accelerator at the beam energies needed for good EUV light.

Uhh, you do not need an accelerator to generate EUV. It's literally just molten tin hit with a laser.

The tin plasma source is the one we don't know how to reproduce; in contrast we know how to do it with an electron-syncrotron (though IIRC for the energies here it is technically practical to do with just a linac) and there are AFAIK several vendors that can provide you the hardware for such an accelerator; the know-how is distributed among many applied particle physicists all around the world; and the FEL hardware to make the actual EUV beam(s) is not high-tech compared to even the high-vacuum accelerator cavities.

The main difficulty of that approach is that physical constraints of field strengths (exceeding those would cause stray electrons to spontaneously free themselves from any vaguely conducting surfaces they are on, and fly around the accelerator, causing arcing damage, wasting energy, and disturbing the beam/beam-control-sensors), the thing has to be fairly large; also, building it with a bit more incremental power is a cheap upgrade (at least if done at design time of the accelerator) up to around a dozen EUV scanners worth of light output.

Complicated by that you ideally want redundancy to not have EUV scanner downtime just because the accelerator needs maintenance, so in practice you'd want like 3~5 accelerators each sized for 20~30 scanners in one building with EUV-routing-flexibility to have n+1 redundancy for the accelerators.

But those 40~120 EUV scanners, especially if you include the rest of the fab to actually run them in production, is a very large investment. Like, somewhere between 1 and 5 % of TSMC's market cap. Not under 2 aircraft-carriers (the big ones)... it's in no way a "low-risk" investment. But, back before GlobalFoundries gave up on the EUV race, a free electron laser was exactly what they were working on bringing to use for EUV litho (it's mostly a energy efficiency question around recovering energy from the electron beam after it was used to generate the EUV, and the substantial difficulties of efficciently redirecting the EUV from the source to the scanners, that's still open research with FEL illumination for EUV scanners).

Weiss makes the mirrors.