# The resolution limit for lithography in practice?

For a given wavelength of light $\lambda$, and a given numerical aperture (NA), I always see the statement in papers/etc. that we can perform lithographic patterning at the Rayleigh limit given by $\approx \frac{0.61 \lambda}{NA}$. This seems really odd to me because, in practice, I've always assumed that the upper-bound for how well one can do is a function of a particular polymer/etc. resist's threshold irradiance before exhibiting a chemical change?

In practice how far apart do we need to space e.g. two Airy disks in order to have two well-defined lithographic features? Don't we also need to care about partial spatial coherence of the light (after passing through e.g. pinholes in a mask) leading to some kind of constructive interference?

• You're quite right that the Airy disk formula only gives a rough idea. The exact description of what sized objects can be resolvable depdends on the imaging system's signal to noise ratio and also how the image interacts with the "object regognition algorithm": the human observer or software: very clean systems can "resolve" at under the "rayleigh limit", most "diffraction limited" ones though are constrained to greater than the diffraction limit by noise. In your case, you also have a threshold for a nonlinear process to think about, so you are right to be skeptical of the "rayleigh formula". – WetSavannaAnimal Dec 30 '13 at 1:06

• @Alfred Woods Well, I'm looking for some specific examples with respect to common polymer systems (or exotic polymer systems!) used for lithography. I suppose we can say though that $k \geq 0.61$? – RGrey Mar 2 '14 at 0:01