random yield loss

**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.