2025 International Conference on Sensing, Measurement & Data Analytics in the era of Artificial Intelligence (ICSMD 2025)

This study provides a rigorous mathematical proof of the equivalence between the convex hull method and the classical Wulff–Jaccodine (WJ) method in crystal etching morphology prediction. By establishing the correspondence between the convex hull of the reciprocal rate function and the intersection of half-spaces, we demonstrate that the morphological boundaries constructed by the two methods are completely identical. This result not only confirms the mathematical rigor of the convex hull method but also highlights its significant engineering value: by automatically selecting key directions and eliminating redundant constraints, the convex hull method substantially reduces computational complexity compared with traditional approaches. In modeling problems involving three-dimensional complex structures or high-dimensional rate functions, the convex hull method can markedly improve computational efficiency while preserving predictive accuracy. This feature renders it directly applicable to MEMS device design, crystal etching process optimization, and large-scale numerical simulations. Looking ahead, the method shows strong potential for extension to multi-faceted three-dimensional modeling and multi-physics coupled etching problems, thereby providing more reliable and efficient modeling tools for micro–nano fabrication.