Equation 22 · Part 1 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured
Symbol c
What this part means
the cluster parameter [ 16 ].
Its job in the formula
c is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol c→Article meaning
Where the article explains it
The widely used negative binomial form is Y = ^{-c}, with D the defect density, S the die area, and c a cluster parameter [ 16 ] .
The passage around this formula
The Poisson limit exposes the die-area relationship in one line. Because the exponent is linear in area, doubling die area squares the yield: Y(2S) = Y(S)^2 . A part yielding 80 per cent at one size yields 64 per cent at twice the size and about 41 per cent at four times. Yield does not decline with area; it decays geometrically. Finite c softens this — real defects cluster, clustered defects waste fewer dies than scattered ones, and this is precisely why the industry prefers the negative binomial form over Poisson, which systematically understates large-die yield.
Learn the underlying idea
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
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Sources cited in the article section
- [2] International Roadmap for Devices and Systems 2023 Update: Yield Enhancement ↗
- [16] Chiplet Actuary: A Quantitative Cost Model and Multi-Chiplet Architecture Exploration ↗
- [1] International Roadmap for Devices and Systems 2023 Update: Lithography and Patterning ↗
These citations provide research context; check each source for the exact claim it supports.