yield semiconductor

**Yield** — the percentage of functional dies on a processed wafer, the most critical economic metric in semiconductor manufacturing. **Formula (Murphy/Poisson Model)** $$Y = e^{-D_0 \cdot A}$$ where $D_0$ is defect density (defects/cm$^2$) and $A$ is die area (cm$^2$). **Typical Values** - Mature process: 95%+ yield - New process (early production): 30-60% - Very large dies (GPU/CPU): 50-80% even at maturity - Small dies: 90%+ more easily **Yield Loss Sources** - **Random defects**: Particles, scratches, pattern defects - **Systematic defects**: Process-related (lithography focus errors, CMP non-uniformity) - **Parametric failures**: Transistors work but don't meet speed/power specs **Yield Improvement** - Defect reduction (cleanroom control, filter improvements) - Design for manufacturability (DFM rules) - Redundancy (spare rows/columns in memory) - Binning: Sort dies by speed grade — faster dies sold at premium **Economics**: On a 300mm wafer, a 1% yield improvement on a large die can mean millions of dollars annually.