correctables and residuals

**Correctables and Residuals** in overlay metrology are the **two components of the total overlay error** — correctables are systematic, repeatable errors that can be modeled and fed back to the scanner for correction, while residuals are the remaining random errors that cannot be corrected. **Decomposition** - **Correctables**: Linear terms (translation, rotation, magnification) and higher-order terms (third/fifth-order polynomials) that the scanner can compensate. - **Residuals**: $OV_{residual} = OV_{measured} - OV_{model}$ — the overlay error remaining after subtracting the best-fit model. - **Model Order**: Higher-order models fit more of the systematic error — but too complex models can fit noise. - **3σ Metrics**: Report both correctable 3σ and residual 3σ — total 3σ = $sqrt{corr^2 + res^2}$. **Why It Matters** - **APC Loop**: Correctables are fed back to the scanner to adjust alignment parameters for the next lot — the feedback loop. - **Improvement Target**: Reducing residuals requires process improvement (wafer flatness, thermal control) — scanner corrections can't help. - **Specification**: Overlay specifications often define maximum correctable AND maximum residual — both must be met. **Correctables and Residuals** are **what can be fixed and what can't** — decomposing overlay errors into correctable systematic and irreducible random components.