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Van der Waals heterostructures are constructed by stacking different atomiclayers and can inherit many novel electronic and optical properties from theconstituting atomic layers. Mechanical stability is of key importance for thehigh performance of nano devices based on the van der Waals heterostructure. Inparticular, buckling instability is a critical mechanical issue for theheterostructure due to its two-dimensional nature. Using graphene/MoS$_2$heterostructure as an example, the present work demonstrates the relationshipbetween the buckling instability and the inevitable misfit strain in theheterostructure by molecular dynamics simulations. The misfit strain has ratherdifferent effects on the buckling phenomenon depending on the magnitude of themisfit strain.  (1) For negative misfit strain, the buckling stability of the heterostructureis reduced by the misfit strain. It is because the graphene layer, whichinitiates the buckling process in the heterostructure of negative misfitstrain, is pre-compressed by the misfit strain that accelerates the buckling ofthe graphene layer.  (2) For small positive misfit strain, the buckling stability for thegraphene/MoS$_2$ heterostructure is elevated. The underlying mechanism is thatthe graphene layer initiates the buckling process of the heterostructure and ispre-stretched by the small positive misfit strain, which decelerates thebuckling of the graphene layer.  (3) For large positive misfit strain, the graphene layer is pre-stretchedwhile the MoS$_2$ layer is considerably pre-compressed, so the buckling of theheterostructure is initiated by the MoS$_2$ layer. As a consequence, thebuckling stability of the graphene/MoS$_2$ heterostructure is reduced by theincrease of large positive misfit strain. These findings shall be valuable forunderstanding mechanical properties of van der Waals heterostructures.

Buckling of graphene/MoS$_2$ van der Waals heterostructures: the misfit strain effect