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Equation 1 · Part 5 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

fraction

R=k1λNA,R = k_1 \frac{\lambda}{\mathrm{NA}},
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

The passage around this formula

Only one step in the loop carries information, so it deserves the arithmetic. Projection lithography is an imaging problem, and its resolution obeys the Rayleigh relation R=k1λNAR = k_1 \frac{\lambda}{\mathrm{NA}}. 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,…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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