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

Why this formula appears here

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

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 ] .

Meanings in this article

  • λ\lambda: the exposure wavelength, NA\mathrm{NA} is the numerical aperture of the projection optics.
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