Phase Measuring Deflectometry for Wafer Thin-Film Stress Mapping

Wafer-level thin-film stress measurement is essential for reliable semiconductor fabrication. However, existing techniques present limitations in practice. Interferometry achieves high precision but at a cost that becomes prohibitive for large wafers. Meanwhile laser-scanning systems are more affordable but can only provide sparse data points. This work develops a phase-measuring deflectometry (PMD) system to bridge this gap and deliver a full-field solution for wafer stress mapping. The implementation addresses three key challenges in adapting PMD. First, screen positioning and orientation are refined using an inverse bundle-adjustment approach, which performs multi-parameter optimization without re-optimizing the camera model and simultaneously uses residuals to quantify screen deformation. Second, a backward-propagation ray-tracing framework benchmarks two iterative strategies to resolve the slope-height ambiguity which is a fundamental challenge in PMD caused by the absence of a fixed optical center on the source side. The reprojection constraint strategy is selected for its superior convergence precision. Third, this strategy is integrated with regional wavefront reconstruction based on Hermite interpolation to effectively eliminate edge artifacts. Experimental results demonstrate a peak-to-valley error in the reconstructed topography of 0.48 µm for a spherical mirror with a radius of 500 mm. The practical utility of the system is confirmed through curvature mapping of a 12-inch patterned wafer and further validated by stress measurements on an 8-inch bare wafer, which show less than 5% deviation from industry-standard instrumentation. These results validate the proposed PMD method as an accurate and cost-effective approach for production-scale thin-film stress inspection.