CTE mismatch warpage

Predict thermal-expansion-mismatch stress, substrate curvature, and edge sag when a coating and its substrate are cured and cooled together. Flags lithography / pick-and-place / handling thresholds.

Timoshenko-Hoffman thermal mismatch stress σ_f = (E_f/(1−ν_f))·(α_s−α_f)·ΔT, then Stoney curvature and parabolic edge sag. 13 substrate materials with datasheet CTE values; 7 film classes (sol-gel inorganic, sol-gel hybrid, sputtered Al₂O₃/TiO₂/SiO₂, evaporated MgF₂, custom).