Stress-dominated growth of two-dimensional materials on nonplanar substrates

Curved features are ubiquitous on solid surfaces, but the effect of surface curvatures on growth of two-dimensional (2D) materials has not yet been established. Using a newly developed method based on the Metropolis algorithm and taking graphene as a prototype, we find that a curved feature on substrates can result in a variety of topological defects in 2D materials. As the feature's size increases by just nanometers, the defects can vary from adatoms, dislocation pairs, and grain boundary scars to long-range grain boundaries, in contrast to previously reported defect-free modes of rigid colloidal crystals growing on spheres. We identify an important role of curvature-induced lattice stress in lowering the growth rate over the curved features and driving a plastic instability in the materials. When the feature's size increases to several nanometers, the stress effect is compromised by an enhanced effect of geodesic curvature, yielding long-range grain boundaries as a result of increased local growth rate on the feature with respect to that on flat regions. We further provide a 'phase diagram' of defects that helps to guide a rational choice of geometrical parameters of features towards the growth of high-quality 2D materials as well as controllable creation of topological defects.

Automated summary

The study found that curved features on substrates can lead to various topological defects in 2D materials, with a crucial role of curvature-induced lattice stress in lowering the growth rate. As the size increases, the stress effect is compromised by an enhanced effect of geodesic curvature, resulting in an increased local growth rate on the feature.