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Equation 21 · Part 3 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

=

Y(2S)=Y(S)2Y(2S) = Y(S)^2
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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