High Numerical Aperture Photolithography for Semiconductor Fabrication

With device geometries on semiconductor chips continuing to shrink in order to pack ever more transistors onto a chip, semiconductor manufacturers reached a point where the device features they needed to make were smaller than the wavelength of visible light, previously used to print structures on chips through the process of photolithography. High-end chip manufacturers such as Taiwan Semiconductor (TSMC), Samsung, and Intel have migrated their cutting edge fabrication to extreme ultraviolet photolithography (EUV), using a wavelength of 13.5 nanometres, a part of the electromagnetic spectrum previously called “soft X-rays” before being renamed to something less scary. (By comparison, visible light is in the range from 380 [violet] to 750 [red] nanometres.)

EUV is a technology which not only allows building things never imagined during the golden age of science fiction, it is made up of parts that, had Doc Smith dropped them into one of his Skylark novels, would have been considered techno-confabulation (“400,000° Celsius laser-driven tin plasma light source”).

But, as those who wish to survive in the semiconductor business must constantly ask, “What’s next?” As node sizes scale below the next major milestone of 3 nanometres, the sole survivor in the high-end photolithography market, Netherlands’ ASML (formerly Advanced Semiconductor Materials Lithography before, like all big companies, it decided a meaningless name was more appropriate) has decided the next milestone will be achieved by increasing what is called the “numerical aperture” of its photolithography machines. Numerical aperture (NA) is a dimensionless quantity that measures the amount of light an optical system can deliver to its target (similar to an f-stop in visible light photography). Present-day EUV machines from ASML have a NA of 0.33, which allows a resolution of 13 nanometres (note that the optical resolution of the photolithography machine, the feature size on the chip, and the “node size” of the process are all different things, with the latter having more to do with the marketing department than engineering or manufacturing). The next generation high numerical aperture (high-NA) EUV machines under development by ASML aim to increase NA to 0.55, initially allowing 8 nanometre resolution, with scaling to as small as 3 nanometres in the future. This requires hardware even more science-fictioney than existing EUV, but also revision of the entire fabrication process. Masks (the master pattern printed on the chips), photoresists (exposed by the lithography process), and even the silicon wafers and positioning equipment (that must have extraordinary flatness and precision to cope with the minuscule depth of field at such resolutions) must adapt. Here is an overview from Semiconductor Engineering, “Gearing Up For High-NA EUV”.

None of this comes cheaply. High-NA EUV lithography machines are estimated to cost around US$ 320 million each, around twice the cost of existing EUV machines, with higher costs all along the processing chain.

And beyond? ASML expect to deliver the first high-NA (0.55 NA) machine for prototyping before the end of 2023, with production shipments starting in 2025. Looking further out, forecasters envision “hyper-NA” technology, increasing numerical aperture as high as 0.75, to be introduced around 2035. ASML Chief Technical Officer Martin van den Brink isn’t so sure that’s going to happen—in a September 2022 interview, he said:

We’re researching it, but that doesn’t mean it will make it into production. For years, I’ve been suspecting that high-NA will be the last NA, and this belief hasn’t changed.

For ‘standard’ EUV, the NA is 0.33, for high-NA, it’s 0.55 and for hyper-NA, it would be “above 0.7, maybe 0.75. Theoretically, it can be done. Technologically, it can be done. But how much room is left in the market for even larger lenses? Could we even sell those systems? I was paranoid about high-NA and I’m even more paranoid about hyper-NA. If the cost of hyper-NA grows as fast as we’ve seen with high-NA, it will pretty much be economically unfeasible. Although, in itself, that’s also a technological issue. And that’s what we’re looking into.

We were going to make sure that high-NA would happen. For hyper-NA, we’re accepting that there may be an insurmountable cost constraint, not in the least because transistor shrink is slowing down. Thanks to system integration, it will still be worthwhile to keep developing new chip generations – that’s the good news. But at this point, the question has become very real: which chip structures are too small to manufacture economically?

We shall see. Perhaps by then our artificial intelligence overlords will figure out how to do it and command us to make it so.


This leaves me thinking the expression “rocket science” may need to be replaced with “chip science” or “photolithography science”. Could it be that all future progress may be limited by the number of people extant with the intellect and knowledge necessary to advance chip improvement? (or even replace chips with the “next thing”?).


Indeed…. Rockets are complex, intolerant of inattention to detail, and make loud and expensive kabooms when something goes wrong, but they are almost trivial alongside semiconductor fabrication. Imagine: we have now come to think it is almost a mundane matter that we can build objects with components numbering in the billions, all of which must work perfectly every time or else the product is junk, manufactured in quantities measured in billions (worldwide microcontroller shipments in 2021 were estimated at 31 billion units, and that doesn’t count memory chips, flash memory, microprocessors, mobile device components, etc.), which operate a million times faster than their ancestors of just 70 years before, run reliably for a decade or more, and are sold at prices so low many are now employed in devices considered disposable which can be purchased for less than an hour’s work at minimum wage in most developed countries.

Nothing like this has ever happened before in all of human history. Indeed, only biological evolution has ever produced comparable increases in component count and complexity, and it took billions of years, not less time than a single human lifespan.

In particular, one might speculate that such a development could only happen during a period of exponential growth of the human population such that there are sufficient “smart fraction” people able to find one another and collaborate on this enormous, global-scale endeavour. I will have a post to-morrow on the consequences of a shrinking population on this kind of innovation.


Hah! Who’s going to catch that reference without following the link?

{ Other than old geeks like me who inherited the 1970 paperback set from their equally geeky father? }


True, the specious argument advanced by some technoeschatologists that this exponential has been going on for all of history notwithstanding.

People just don’t get exponentials, not even ones to which they have become accustomed. Perhaps especially not those.

It may have been easier pre Popper/Kuhn to convince people that lossless compression was a revolution in the scientific method itself rather than a mere scientific revolution. By now everyone is sort of like: “Are you f****** nuts? Every grade school kid understands executable file archives.”


Fascinating thought that economics rather than physics or technology might be the factor which limits the size to which chip structures can practically be shrunk. Also fascinating that the economics are already such that a single Dutch company has a global monopoly on high-end chip manufacturing equipment – and it seems that no-one can see any economic potential from risking capital to compete with that company.

One other factor out there is what is the need for ever-smaller faster chips? Surely not to allow faster-downloading higher-definition cat videos? Most major engineering simulations are probably already past the point of maximum useful complexity, due to limitations on the data available to describe the initial conditions.


While ASML is in a near-monopoly position (and, at present, has an absolute monopoly on EUV equipment), they are, like IBM in its heyday, a system integrator that buys much of its content from an external supply chain rather than a vertically integrated manufacturer. In their most recent (2022) annual report, they listed €21.2 billion net sales (on 345 lithography systems sold), and a total of €12.4 billion spent on sourcing from around 5000 external suppliers. For example, all of the optics in their machines are supplied by Zeiss, a partnership that goes back more than three decades. From “Risk factors”:

The number of lithography systems we are able to produce may be limited by the production capacity of one of our key suppliers, Carl Zeiss SMT GmbH, which is our sole supplier of lenses, mirrors, illuminators, collectors and other critical optical components (which we refer to as optics). We have an exclusive arrangement with Carl Zeiss SMT GmbH, and if they are unable to maintain and increase production levels, we could be unable to fulfill orders, which could have a material impact on our business and damage relationships with our customers. If Carl Zeiss SMT GmbH were to terminate its supply relationship with us or be unable to maintain production of optics over a prolonged period, we would effectively cease to be able to conduct our business.

ASML also partners with universities and industrial research labs on R&D projects and outsources part of their technology development to these contracts.

Thus, their dominance in the market is not so much based upon control of in-house intellectual property but excellence in integrating components into a solution that gets the job done in a timely fashion for customers and providing after-sale service and product upgrades to their installed base.

1 Like

No, they’re not. Many computational fluid dynamics problems, even run on the fastest supercomputers, cannot run with a sufficiently fine cell size to simulate the behaviour of vehicles in environments such as supersonic and hypersonic flight or the internal fluid flow of jet and rocket engines. Engineers find themselves designing sub-optimal structures purely because only the simplest cases are tractable computationally, or have to resort to iterative, trial-and-error flight and test stand experiments with sub- or full-scale hardware to see what will happen. While time on supercomputers is expensive, bending metal and blowing it up costs a lot more and takes far longer than crunching numbers.

Lack of computing resources to model at fine granularity is the main obstacle to reliable weather prediction today (and has been for many years). There are plenty of raw data available, but when it takes three weeks to compute the forecast for tomorrow, it isn’t of any use.

The entire evolution of the high end of computing from 1950 to the present has been driven by the market for each successive generation of faster machines with larger storage capacity. This has been accompanied by confident predictions that the latest and greatest machine was the end of the line and no application would justify the cost of developing the next and, so far, all of these predictions have been wrong. Maybe now, for the first time, it’s the case, but that’s not the way to bet (especially since the training of large artificial intelligence models, a market which didn’t exist 18 months ago, now appears able to saturate all of the supercomputing resources available to it and is still hungry for more).


In a sense, that makes it even more interesting that no-one apparently wants to risk the capital in developing a competitor, since they would not necessarily have to invest in a broad range of manufacturing capacities. Cutting deals with alternate suppliers, organizing an even more responsive support organization, offering better financing terms, accepting lower margins – all of that sounds like standard competitive business practices. Presumably some Chinese/Russian/Indian organization will eventually be stood up to compete with ASML – it just seems surprising that no Western capitalist wants to take on the challenge of busting a monopoly.


Agreed that for some physical processes, such as single phase fluid dynamics, computational resources may be the current limitation. Initialization for such models is not a problem, because fluid properties and system dimensions are very precisely knowable.

But for many major engineering uses, the limitation is a version of the challenge for weather forecasting – the models simply do not have sufficiently granular measured data to characterize the initial conditions reliably. Certainly, that is the challenge for models used in fields such as geology, foundation engineering, oil & gas. The data on the sub-surface is inevitably sparse. A lot of the numbers required to initialize such models are simply guesses – educated guesses, but still guesses. Further discretization of such models simply requires even more guesses. It is highly debatable whether reducing cell size in such models increases the accuracy of predictions.


DOTA2 is an e-sport (computer gaming sport). DOTA is classified as a MOBA (Multi-player Online Battle Arena) with teams of five facing off. The players control a character (Hero in DOTA slang) and there are approximately 175 hero characters in the selection pool from which to select at the beginning of the game. The International tournament as is the considered the world championship tournament with a prize fund of $40 million. Unlike many e-sports, player actions per minute isn’t as critical for success.

OpenAI developed OpenAI Five as a research project to play DOTA2. In 2019 it beat the professional team (OG) that won The International that year. There were limitations put on the game in order for OpenAI to compete. The hero pool was reduced. I think it was reduced to 18. The number was selected because OpenAI only had 18 characters trained up to pro level. Each character has it’s own neural net.

From OpenAI on the AI that won in 2019:

In total, the current version of OpenAI Five has consumed 800 petaflop/s-days and experienced about 45,000 years of Dota self-play over 10 realtime months (up from about 10,000 years over 1.5 realtime months as of The International), for an average of 250 years of simulated experience per day. The Finals version of OpenAI Five has a 99.9% winrate versus the TI version.B

In 2018 their previous model lost at The International and the 10 real-time months needed for the OpenAI Five model was due to limitations of compute.

They tried to train up more characters in for the 2019 championship.

We spent several weeks training with hero pools up to 25 heroes, bringing those heroes to approximately 5k MMR (about 95th percentile of Dota players). Although they were still improving, they weren’t learning fast enough to reach pro level before Finals

When I learned about OpenAI Five a couple years ago, I was surprised that OpenAI or some other AI group did not try to make the AI commercially available. The professional DOTA2 teams train very hard. They will train 12 hours a day. Unless you play on a LAN, all games are played through Steam and all games are recorded. To me there are several disadvantages to this way of preparing. The professional team does not play together very often and all the games are available for their competition to watch. The opposing team is often just another selection of random players that are ranked as professionals. They do not have a coordinated character selection and strategy.

Having a tool to train in secret against the best in the world seems like it would be very valuable. It would allow the team to test various character combinations and strategies. Most players, including pro players, have a limited set of characters they will play in competition. The AI would allow the team to model other teams typical character selections in order to prepare for a given opponent. Maybe it would be possible to tune the AI to play a character like an opponent. The average game takes around 1/2 hour, but is typically broken up into 3 phases. The AI would allow a team to train specific parts of the game without having to play the entire game.

Given the advantages, I assume the reason AI isn’t available for this application is the cost and time to train up a model. I don’t know how much it cost OpenAI for 800 petaflops/s for 10 months, but I assume it was using resources that cost in the 100s of millions.

Makes me think that if there was access that amount of compute for 1 million there could be many opportunities beyond what is needed for large corporations and government entities.