Random Yield Loss is yield loss caused by randomly distributed defects — particles, contamination, crystal defects, and other stochastic events that land at random locations on the wafer, with their impact on yield determined by defect density $D_0$ and die area $A$.

Random Yield Models

• Poisson: $Y = e^{-D_0 A}$ — simple model assuming uniform defect distribution.
• Negative Binomial: $Y = (1 + D_0 A / alpha)^{-alpha}$ — accounts for defect clustering; $alpha$ typically 1-5.
• Murphy's Model: $Y = left(frac{1 - e^{-D_0 A}}{D_0 A} ight)^2$ — intermediate between Poisson and negative binomial.
• Defect Density: $D_0$ measured from wafer inspection — defects per cm² across killer defect types.

Why It Matters

• Area Dependence: Larger die have lower yield — yield drops exponentially with die area for a given defect density.
• Clean Fab: Reducing $D_0$ requires cleaner tools, chemicals, and environment — every particle source matters.
• Economic: Random defects determine the fundamental yield floor — cannot be eliminated by design changes.

Random Yield Loss is the lottery of defects — stochastic yield loss from randomly distributed particles and contamination that scales with die area.