Optical Lithography Resolution

How small a feature a projection scanner can print. A reticle (mask) pattern is imaged through a lens of numerical aperture $\mathrm{NA}$ at wavelength $\lambda$ . The lens pupil passes only spatial frequencies $|f|\le \mathrm{NA}/\lambda$ , so the aerial image is $I(x)=\big|\,\mathcal F^{-1}[\,\mathrm{pupil}(f)\,\mathcal F\{t\}(f)\,]\big|^2$ and the resolvable half-pitch is the Rayleigh limit $R=k_1\lambda/\mathrm{NA}$ . The reticle here is a line/space test pattern whose half-pitch shrinks left to right; in the aerial image the coarse zones print crisply and the zones finer than $R$ blur to flat grey. The bottom bars are the per-zone contrast (red once a zone is below the Rayleigh limit). Switch the wavelength from i-line (365 nm) through DUV/ArF (193 nm) to EUV (13.5 nm) and watch the resolvable pitch collapse: smaller $\lambda$ is sharper. Everything is closed form (gate-tested).

Figure 1. A multi-pitch line/space reticle (top), its pupil-filtered coherent aerial image (middle), and the per-zone Michelson contrast (bottom); zones finer than the Rayleigh limit R = k1 lambda / NA blur out (bars turn red). Method: closed-form Fourier-optics imaging (DFT, pupil low-pass at NA/lambda) plus the Rayleigh formula (gate-tested sim.js), Canvas2D; the live readouts are lambda, the cutoff, R, and the finest resolved pitch.

wavelength

NA1.00

k1 factor0.50

WHAT TO TRY

Switch the wavelength down the lithography roadmap from i-line to KrF to ArF to EUV: the Rayleigh resolution R = k1 lambda / NA shrinks, and more of the fine-pitch zones turn from red (unresolved) to blue (resolved) in the contrast panel.
Raise the numerical aperture NA: the lens pupil passes higher spatial frequencies, so finer pitches keep their contrast in the aerial image. The cutoff in the readout moves to smaller features.
Lower the k1 factor: resolution enhancement (off-axis illumination, phase shifting) pushes k1 below 0.5 toward the 0.25 single-exposure limit, printing features finer than the wavelength itself.