fraction

The passage around this formula

The relation that is usually left out of popular accounts is the one that costs money: $\mathrm{DOF} = k_2 \frac{\lambda}{\mathrm{NA}^2}$. Depth of focus falls with the square of numerical aperture. Resolution is bought linearly in $\mathrm{NA}$ and paid for quadratically in focus budget. This is why the planarisation step exists at all, why resist films keep getting thinner, and why every increase in $\mathrm{NA}$ makes the mechanical and material problems worse rather than better. The roadmap is explicit that meeting small depths of focus at 0.55 numerical aperture is a key challenge in its own right, and that a longer-term move to still higher aperture would drive resist thicknesses below 20 nm [ 1 ] .

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