THIN-FILM STRESS FROM NONSPHERICAL SUBSTRATE BENDING MEASUREMENTS

The usual formula for finding thin film deposition stress from the curvature of substrate wafers assumes small out-of-plane deflections and spherical bending. These are significant limitations because deposition stress often produces large deflections and ellipsoidal surfaces ranging from almost spherical to almost cylindrical depending on the film and substrate materials and on the deposition conditions. The present paper examines a nonlinear bending model proposed by Harper and Wu as well as by Masters, Salamon, and Fahnline and its usefulness for calculating deposition stress for both spherical and nonspherical bending. Algebraic solutions of the model predict spherical bending for small deflections and ellipsoidal bending for large deflections even for isotropic films and substrates. An initial experimental test of the nonlinear theory confirms its usefulness with data obtained by measuring the ellipsoidal and spherical curvatures of thin Ta films direct current magnetron deposited on different thickness and size polycarbonate wafers.