Engineered Strain in 2D Materials by Direct Growth on Deterministically Patterned Grayscale Topographies

Strain is a proven technique for modifying the bandgap and enhancing carrier mobility in 2D materials. Most current strain engineering techniques rely on the post-growth transfer of these atomically thin materials from growth substrates to target surfaces, limiting their integration into nanoelectronics. Here, we present a new approach where strain in 2D materials is already introduced directly during their growth on grayscale-patterned topographies instead of flat surfaces. Both strain levels and orientations are deterministically engineered by controlling grayscale surface contour lengths through thermal expansion mismatches in nanostructured stacks, where the conformally grown and firmly attached 2D material is forced to match the underlying morphology change during cooling. With this method, we experimentally demonstrate precise control of localized tensile strain from 0 to 0.5% in grown MoS₂ monolayer along both uni- and multiaxial directions, while higher strain levels are shown to be theoretically possible. This strain-engineered growth of 2D material films directly on the target substrates is a generic and adaptable approach to various combinations of grayscale-thin-film/substrates and eliminates all the transfer-related limitations of previous approaches, thus paving the way for integrating strained 2D materials into next-generation nanoelectronics.