This paper proposes and systematizes a unified Eikonal–Wulff framework for predicting the anisotropic wet -etching morphology of two-dimensional crystals . Starting from the "shortest arrival time" principle, the static Hamilton–Jacobi/Eikonal equations are derived, and the existence and uniqueness of the solution are guaranteed by the viscosity theory. Furthermore, the duality of the Hamiltonian and the Wulff-shaped support function is shown to be equivalent to the Huygens–Minkowski construction. A reproducible engineering pipeline is provided: H is constructed from the directional velocity R(θ), and after convexification, the arrival time field is solved using a FSM and aligned with the literature baseline. This method combines geometric intuition with PDE scalability, making it suitable for early-stage quartz MEMS design and extensible to multi-physics coupling and three-dimensional applications.

anisotropic wet etching，Eikonal，Wulff shape，fast sweep method，quartz MEMS