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Y=e−AcD0Y = e^{-A_c D_0}

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A finished, fully-processed 300-millimeter wafer at an advanced node carries somewhere in the neighborhood of several hundred to a few thousand individual dies, and not all of them will work. The simplest model process engineers reach for treats random defects as a Poisson process across the wafer: given an average defect density D0D_0 (critical defects per unit area) and a die’s critical area AcA_c (the area within which a defect is actually fatal to that die’s function), the expected fraction of working die is Y=e−AcD0Y = e^{-A_c D_0}. This Poisson form is known to be pessimistic in practice, because real defects cluster rather than distributing independently across the wafer — a…

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e−AcD0e^{-A_c D_0}

Symbol e^-A_c D_0

e−e^-AcA_c D0D_0 is one of the signed contributions combined to compute the quantity on the left.

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Y=e−AcD0Y = e^{-A_c D_0}

Equation 4 · Semiconductors

Advanced Semiconductor Fabrication in Practice: An Advanced Technical Guide

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A finished, fully-processed 300-millimeter wafer at an advanced node carries somewhere in the neighborhood of several hundred to a few thousand individual dies, and not all of them will work. The simplest model process engineers reach for treats random defects as a Poisson process across the wafer: given an average defect density D0D_0 (critical defects per unit area) and a die’s critical area AcA_c (the area within which a defect is actually fatal to that die’s function), the expected fraction of working die is Y=e−AcD0Y = e^{-A_c D_0}. This Poisson form is known to be pessimistic in practice, because real defects cluster rather than distributing independently across the wafer — a…

Meanings in this article

  • YY: the expected fraction of working die.
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