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Equation 9 · Part 2 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

Symbol λ

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

What this part means

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

Its job in the formula

λ occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Where the article explains it

Projection lithography is an imaging problem, and its resolution obeys the Rayleigh relation R = k1k_1 λNA\frac{\lambda}{\mathrm{NA}}, where λ\lambda is the exposure wavelength, NA\mathrm{NA} is the numerical aperture of the projection optics, and k1k_1 is a dimensionless process factor absorbing illumination scheme, mask engineering and resist behaviour.

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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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.