Interface-Governed Deformation of Nanobubbles and Nanotents Formed by Two-Dimensional Materials

Nanoblisters such as nanobubbles and nanotents formed by two-dimensional (2D) materials have been extensively exploited for strain engineering purposes as they can produce self-sustained, nonuniform in-plane strains through out-of-plane deformation. However, deterministic measure and control of strain fields in these systems are challenging because of the atomic thinness and unconventional interface behaviors of 2D materials. Here, we experimentally characterize a simple and unified power law for the profiles of a variety of nanobubbles and nanotents formed by 2D materials such as graphene and MoS_{2} layers. Using membrane theory, we analytically unveil what sets the in-plane strains of these blisters regarding their shape and interface characteristics. Our analytical solutions are validated by Raman spectroscopy measured strain distributions in bulged graphene bubbles supported by strong and weak shear interfaces. We advocate that both the strain magnitudes and distributions can be tuned by 2D material-substrate interface adhesion and friction properties.