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Comment by tlb | Hacker News Reader

Can you explain the exponential rise in mask costs with shrinking? My naive understanding is that you simply can't resolve features below some fraction of the wavelength. How do more expensive masks get beyond that?

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I can split any small pitch exposure into separate, larger pitch exposures. For instance, if I need 40nm pitch, and my system is limited to 80nm, I can do 4 exposures. The next shrink requires 8.

To figure this out, draw a square, and each node is an exposure.

This process works forever in theory, but is limited in practice by the mutual registration of the exposures.

What you can do is basically use partially overlapping beams to energize an area smaller than any of the individual beams (think venn diagram). Its a similar technique (except in 2 dimensions) to radiation therapy where multiple beams of radiation are passed through healthy tissue such that their intersection point is on cancerous tissue. That way only the cancerous tissue receives a highly damaging dose of radiation while the healthy tissue receives significantly lesser dosages.

That doesn't usually work because the the diffraction limit PSF is usually Gaussian and therefore the overlapping region can have lower fluence than the peak regions.

We are not concentrating light below the diffraction limit, instead we are printing features below the diffraction limit with multiple exposures.

See here: https://en.m.wikipedia.org/wiki/Multiple_patterning

Edit: the exponential rise happens because to go 2x smaller I now need to double my # of masks. Of course, in practice overlay accuracy could kill you first.

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