Realistically, you can't really compete in a market where ASML is the monopolist. Not because ASML is an ass, but simply because building just a single factory costs billions. Intel regularly invests 10 billion or more in just a single factory that doesn't even have all the necessary tools in-house to produce a chip end to end.

Smaller manufacturers usually serve the long tail, that is rather old process nodes for use cases where bleeding edge performance isn't needed. Bosch for example had its own manufacturing branch.

You might be interested in the YouTube channel ProjectsInFlight, which is currently trying to build a DIY solution for fabbing simple ICs in their garage & documenting the process on YouTube.

CMOS silicon logic can be chemically "printed" using photolithography and commercially available mercury lamps. From the wikipedia article, if I read between the lines those are good down to feature sizes of about 1 micron (1.0µM or 1000nm), limited of course by the accuracy of your wafer setups between processes and the printing of your lithography plates. this is the process used to produce the Intel 80486 which fit 1 million transistors on a chip. seems that laser lithography using KrF lasers can be good down to much smaller but your litho plates become the limiting factor.

so, conservatively- 1µm features would be attainable for a sort of "home brew" startup with little to no venture funding but the correct industrial knowledge. with more funding though i'd guess older laser lithography machines would be attainable on the used market and potentially usable down to 0.4µm or smaller.

There is an answer but you'll probably only manage to get it by going through semiconductor devices history and determining the hardware required at each improvement step, and the cost and acquirability of that hardware. This would take hours - potentially days - of research.

A quick search yielded this blog post though of someone attempting - and managing - production of a basic 1200-transistors semiconductor device in their garage, which I found rather neat. That's with no cleanroom, and with chemicals the purity of which are far removed from the ones the industry uses.

Sam Zeloof (http://sam.zeloof.xyz/) has been working in the area of DIY semiconductor fabrication, and has successfully fabricated working ICs (from 6 - 100 transistors). He's done an incredible job at reaching ~1970's technology levels in a home lab.

Another example of DIY fabrication: https://hackaday.com/2010/03/10/jeri-makes-integrated-circuits/ Jeri Ellsworth made her own silicon inverter.

These examples are still very small-scale compared to even simple microprocessors, etc - but it's fascinating to see this level of technology becoming more accessible.

Theres plenty of smaller, lower volume silicon fabs doing larger scale work, like Cmos 1micron and some doing sub micron down to what was cutting edge ~15 years ago.

Honetly kinda crazy that only one manufacturer can do the current modern stuff, but barely anything other than high end CPU need to be that small.