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Equation 9 · Part 5 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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