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NA
Why this formula appears here
where λ is the exposure wavelength, NA is the numerical aperture of the projection optics, and k1 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 / (2\,NA) , which is k1 = 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 k1 down toward that floor without printing garbage.
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Published contexts (3)
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Equation 3 · AI Hardware & Semiconductors
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
where λ is the exposure wavelength, NA is the numerical aperture of the projection optics, and k1 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 / (2\,NA) , which is k1 = 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 k1 down toward that floor without printing garbage.
Equation guide → ·
Article →Equation 10 · AI Hardware & Semiconductors
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Depth of focus falls with the square of numerical aperture. Resolution is bought linearly in 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 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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Article →Equation 11 · AI Hardware & Semiconductors
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Depth of focus falls with the square of numerical aperture. Resolution is bought linearly in 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 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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