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Published equation contexts

mλ≈2dcos⁡θm\lambda \approx 2d\cos\theta

Why this formula appears here

A single reflective surface will not do it. The mirrors used in EUV systems are not a polished metal surface but a stack of dozens of alternating molybdenum and silicon layers, each only a few atomic layers thick, engineered so that the many weak partial reflections at each interface add together in phase. A close analogue to the classical Bragg condition for layered reflectors, mλ≈2dcos⁡θm\lambda \approx 2d\cos\theta. describes why the stack works at all: at near-normal incidence, θ\theta is small and cos⁡\cosθ\theta is close to one, so the first-order condition reduces to roughly λ\lambda ≈\approx 2d , meaning a bilayer period d of a little under 7 nanometers should reflect strongly somewhere near 13.5–14 nanometers.…

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mm

Symbol m

m is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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λ\lambda

Symbol λ

λ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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θ\theta

Symbol θ

θ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (1)

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mλ≈2dcos⁡θ,m\lambda \approx 2d\cos\theta,

Equation 1 · Semiconductors

How Advanced Semiconductor Fabrication Actually Works

This equation gives an approximation: it relates the quantities while allowing an approximation.

A single reflective surface will not do it. The mirrors used in EUV systems are not a polished metal surface but a stack of dozens of alternating molybdenum and silicon layers, each only a few atomic layers thick, engineered so that the many weak partial reflections at each interface add together in phase. A close analogue to the classical Bragg condition for layered reflectors, mλ≈2dcos⁡θm\lambda \approx 2d\cos\theta. describes why the stack works at all: at near-normal incidence, θ\theta is small and cos⁡\cosθ\theta is close to one, so the first-order condition reduces to roughly λ\lambda ≈\approx 2d , meaning a bilayer period d of a little under 7 nanometers should reflect strongly somewhere near 13.5–14 nanometers.…

Meanings in this article

  • dd: the meaning a bilayer period.
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