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Equation 1 · Part 2 · Advanced Semiconductor Fabrication in Practice: Design Rules, Foundry PDKs, and the Yield Ramp

Symbol e^-AF

YP=e−AFY_P = e^{-AF}
e−AFe^{-AF}

What this part means

e−e^-AF is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

e−e^-AF is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

The study’s production model uses a standard form for die-sort yield as a function of electrical fault density, treating faults as randomly and independently distributed across a wafer: YP=e−AFY_P = e^{-AF}. where A is the critical area of the circuit — the area of the design actually susceptible to a given class of fault — and F is the fault density measured per unit area [ 7 ] . The relationship is exponential in both variables, which is precisely why yield learning is disproportionately valuable: a fixed absolute reduction in fault density buys a much larger yield improvement once fault density is already low than the same absolute reduction bought when fault density was high.

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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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