Visualizing lattice-mismatch-dependent strain relaxation in epitaxially grown MoS₂/WS₂and MoS₂/WSe₂hetero-bilayers

Strain relaxation at lattice-mismatched interfaces is critical for epitaxial growth and high-quality single-crystal films. While van der Waals (vdW) epitaxy is considered as a promising platform due to its high tolerance to lattice mismatch, its actual response to lattice mismatch remains largely unexplored. Here, we investigate the effect of lattice mismatch on vdW interfaces by epitaxially growing MoS₂on WS₂or WSe₂substrate. annular dark-field scanning transmission electron microscopy reveals that MoS₂/WS₂with a negligible lattice mismatch of ∼0.22% forms a fully commensurate structure, whereas MoS₂/WSe₂with a large lattice mismatch of ∼3.96% exhibits non-uniform moiré patterns, characteristic of an incommensurate interface. Detailed analysis shows that the MoS₂/WS₂hetero-bilayers exhibit perfectly aligned structure through compression of MoS₂, whereas the MoS₂/WSe₂hetero-bilayers show elongation and rotation of moiré orientation driven by tensile strain. Notably, even small twist angles induce significant changes in moiré orientation, resulting in bent fringes that are indicative of local rotational distortions. Large lattice mismatch drives localized lattice distortion, where rotation of the MoS₂lattice emerges as an energetically favorable mechanism for strain release, in contrast to commensurate alignment in small-mismatch systems. Our results establish moiré pattern analysis as a powerful framework for directly visualizing spatially varying strain and its relaxation pathways in vdW hetero-bilayers. Our work reveals previously inaccessible interfacial deformation modes in vdW hetero-bilayers and establishes moiré analysis as a powerful platform for strain engineering in 2D electronic and optoelectronic materials.