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Equation 9 · Part 1 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

Symbol k_2

DOF=k2λNA2.\mathrm{DOF} = k_2 \frac{\lambda}{\mathrm{NA}^2}.
k2k_2

What this part means

k2k_2 is an input to the expression that computes the quantity on the left.

Its job in the formula

k2k_2 is an input to the expression that computes the quantity on the left.

The passage around this formula

The relation that is usually left out of popular accounts is the one that costs money: DOF=k2λNA2\mathrm{DOF} = k_2 \frac{\lambda}{\mathrm{NA}^2}. Depth of focus falls with the square of numerical aperture. Resolution is bought linearly in NA\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 NA\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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