Screening Crystallographic Planes on Sapphire for Single-Crystal MoS₂ Epitaxy

The epitaxial growth of wafer-scale single-crystal two-dimensional transition metal dichalcogenides (TMDs) is essential for advancing beyond-silicon electronics. While the c-plane of sapphire has been the standard substrate for epitaxy, exploiting the richness of crystallographic planes may help understand universal mechanisms governing van der Waals epitaxy. The vast spectrum of crystallographic planes, which offer diverse surface symmetries and atomic configurations, remains underexplored due to the complex potential energy landscape at each epitaxial interface. Here, we develop a theoretical framework to explore the vast sapphire crystallographic planes for deterministic MoS₂ epitaxy. By evaluating interfacial strain and surface energy as key descriptors across 33 crystallographic planes, we identify five optimal candidates, namely, A(112̅0) C(0001), P(112̅3), R(11̅02), and S(11̅01) We establish that unidirectional alignment is governed by reducing the surface symmetry of the substrate, achieved either through the plane's intrinsic low symmetry (P, R, S) or via engineered step-edges on high-symmetry surfaces (C, A). This universal principle enables the successful growth of wafer-scale single-crystal MoS₂ on all five predicted planes.