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Equation 4 · Part 2 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

subscript

k1k_1
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.