Theory 059/Engineering & Materials /Semiconductor manufacturing
Yield Follows Cluster Size
Yield models count defects per unit area. One big defect can kill where several small ones do not.
Semiconductor yield is set by the ratio of defect cluster size to die size rather than by defect density alone, so a process with more defects in small clusters can out-yield one with fewer but larger clusters.
01The evidence
Yield models based on defect density explain mature processes and fail when defect sizes are clustered, which is common at new nodes.
02The tension
Density-based yield models treat defects as points. That assumption holds only when clusters are small relative to dies.
03The mechanism
A defect kills a die only if it lands within the die and is larger than the critical size for the feature. A cluster of small defects may not kill, while a single large one will.
That makes the cluster-size-to-die-size ratio the controlling variable, and predicts that yield should collapse when clusters approach die size rather than when density rises.
04What this is not
Density models assume point defects. This accounts for cluster size, which explains yield loss at new nodes.
05Predictions
- P1Yield should track the cluster-to-die ratio.
- P2Small-cluster processes should out-yield large-cluster ones at equal density.
- P3Die size scaling should change the exponent.
06Refutation
Yield tracking density at controlled cluster size would restore the Poisson model.
07What it changes
It would change defect inspection targets.