Statistical characterization of light point defects on silicon wafers

Particles on wafers constitute a significant challenge to electronic device makers today. Instruments for detecting particles on silicon wafers all depend upon the measurement of scattered light giving rise to the practice of referring to such measurements as light point defects or LPD counts. The lognormal probability distribution provides a good model for LPD's except that, in recent years, the number of LPD's on wafers has dropped to the point where a significant fraction of wafers tested show no LPD's detected. This paper describes how the lognormal model provides a good representation for LPD counts when the zero counts are treated appropriately. Using example data of LPD measurements, alternative probability models will be shown to be inferior. Precedent for this approach will be provided as coming from analogous problems in the biological sciences.