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Equation 15 · Part 8 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

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Y=(1+DSc)−c,Y = \left(1 + \frac{D S}{c}\right)^{-c},
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Yield modelling then converts defect density into economics. The widely used negative binomial form is Y=(1+DSc)−cY = \left(1 + \frac{D S}{c}\right)^{-c}. with D the defect density, S the die area, and c a cluster parameter [ 16 ] . As c →\to ∞\infty the expression tends to the Poisson model Y = e−DSe^{-D S} , which assumes defects fall independently and uniformly.

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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