  Trapped substances between a 2D crystal, such as graphene, and an atomically
flat substrate, for example, hexagonal boron nitride, give rise to the
formation of bubbles. We show that the size, shape and internal pressure inside
these bubbles are determined by the competition between van der Waals
attraction of a 2D crystal to the substrate and the elastic energy needed to
deform the atomically thin layer. This presents opportunities to use bubbles to
study the elasticity of 2D materials as well as the conditions of confinement,
yet none of these have been explored so far, either theoretically or
experimentally. We have created a variety of bubbles formed by monolayers of
graphene, hBN and MoS2 mechanically exfoliated onto hBN, graphite and MoS2
substrates. Their shapes, analyzed using atomic force microscopy, are found to
exhibit universal scaling with well-defined aspect ratios, in agreement with
theoretical analysis based on general properties of membranes. We also measured
the pressure induced by the confinement, which increased with decreasing
bubble's size and reached tens on MPa inside submicron bubbles. This agrees
with our theory estimates and suggests that for bubbles with radii < 10 nm
hydrostatic pressures can reach close to 1 GPa, which may modify the properties
of a trapped material.
