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

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λ/(2 NA)\lambda / (2\,\mathrm{NA})

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λ\lambda

Symbol λ

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

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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. Two-beam interference sets a hard floor: for a periodic line-and-space pattern the smallest printable half-pitch is λ\lambda / (2\,NA\mathrm{NA}) , which is k1k_1 = 0.25 in the convention where R is a half-pitch. Everything the industry calls resolution enhancement — off-axis illumination, phase shifting, optical proximity correction, inverse lithography — is an attempt to drive k1k_1 down toward that floor without printing garbage.

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