$$k_1 = 0.25$$

Equation 6 · AI Hardware & Semiconductors

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

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

where $\lambda$ is the exposure wavelength, $\mathrm{NA}$ is the numerical aperture of the projection optics, and $k_1$ 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 $\lambda$ / (2\,$\mathrm{NA}$) , which is $k_1$ = 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 $k_1$ down toward that floor without printing garbage.

Meanings in this article

• $k_1$: a dimensionless process factor absorbing illumination scheme, mask engineering and resist behaviour.

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