Wafer Bow Stress Calculation Guide
Wafer bow is a practical sign of film stress. A deposited film can pull or push the substrate. The wafer bends because the film and substrate do not share the same strain. This calculator converts measured bow into estimated film stress using a Stoney based method. It is useful for process checks, thin film reviews, and quick engineering notes.
Why Bow Matters
Small bow changes can affect lithography, bonding, dicing, and handling. A wafer that bends too much may lose focus during exposure. It may also create chucking issues. Stress trends are often more useful than one single reading. Compare results from the same tool, span, and measurement method whenever possible.
Inputs You Should Check
Use the measured center bow after subtracting any initial bow. Enter substrate thickness and film thickness with care. Thickness errors can change stress strongly. The substrate thickness is squared in the formula. The film thickness is in the denominator. Use the correct substrate modulus and Poisson ratio. Silicon values differ by crystal direction, so choose the closest known value.
How Results Are Interpreted
The tool reports radius, curvature, stress, corrected stress, strain, and force per width. Positive or negative signs depend on the direction option you choose. Many shops use sign rules differently. Keep your internal convention consistent. The thermal correction is only an estimate. It uses film biaxial modulus, thermal expansion mismatch, and temperature change.
Practical Review Steps
Check the bow value against the measurement span. A very large bow breaks the small deflection assumption. Review the warning message when the bow ratio is high. Run a second case with a different thickness tolerance. This gives a quick sensitivity check. Export the data after each run. The exported file helps audits and process travelers. Save the result with the lot number when possible.
Best Practice
Keep the same units across repeated studies. Record tool settings and wafer orientation. Use the same measurement span for comparison. Do not treat this calculator as a replacement for metrology qualification. It is a planning and review aid. For release decisions, verify results with approved measurement procedures and material data. Review uncertainty whenever material stacks include many layers or patterned zones during final review.