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Equation 5 · Advanced Semiconductor Fabrication in Practice: An Advanced Technical Guide

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D0D_0

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D0D_0

Symbol D_0

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subscript

subscript

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This Poisson form is known to be pessimistic in practice, because real defects cluster rather than distributing independently across the wafer — a particle-contamination event or a localized etch non-uniformity produces several nearby failures at once, not one failure drawn independently from a uniform background. Models that account for clustering (the negative binomial family, of which Murphy’s model is a well-known special case) generally predict a higher yield than the naive Poisson formula for the same nominal defect density, because clustering means large stretches of the wafer are defect-free even at a defect density that would look damaging if it were spread evenly. Which model…
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This Poisson form is known to be pessimistic in practice, because real defects cluster rather than distributing independently across the wafer — a particle-contamination event or a localized etch non-uniformity produces several nearby failures at once, not one failure drawn independently from a uniform background. Models that account for clustering (the negative binomial family, of which Murphy’s model is a well-known special case) generally predict a higher yield than the naive Poisson formula for the same nominal defect density, because clustering means large stretches of the wafer are defect-free even at a defect density that would look damaging if it were spread evenly. Which model actually fits a given fab’s data is an empirical question the fab’s yield-management team answers continuously, not a constant chosen once — D0D_0 itself falls over the life of a node as the “yield learning curve” progresses, and a large part of a fab’s early operating cost on any new node is spent buying that learning curve down before volume production.

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