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.