Two-dimensional (2D) crystal growth over substrate features is fundamentally guided by the Gauss-Bonnet theorem, which mandates that rigid, planar crystals cannot conform to surfaces with nonzero Gaussian curvature. Here, we reveal how topographic curvature of lithographically designed substrate features govern the strain and growth dynamics of triangular WS2 monolayer single crystals. Single crystals grow conformally without strain over deep trenches and other features with zero Gaussian curvature; however, features with nonzero Gaussian curvature can easily impart sufficient strain to initiate grain boundaries and fractured growth in different directions. Within a strain-tolerant regime, however, triangular single crystals can accommodate considerable (<1.1%) localized strain exerted by surface features that shift the bandgap up to 150 meV. Within this regime, the crystal growth accelerates in specific directions, which we describe using a growth model. These results present a previously unexplored strategy to strain-engineer the growth directions and optoelectronic properties of 2D crystals.
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