Radius-Voltage Relation of Graphene Bubbles Controlled by Gate Voltage

Graphene on the substrate can form bubbles rising above the sheet. In some cases, the bubble is a perfect spherical surface crown, and its radius can be adjusted by external electric field. In this manuscript, we theoretically investigate the voltage dependence of the spherical bubble's radius. The calculated results are in good agreement with recent experiments on the graphene bubble controlled by applied gate voltage [Appl. Phys. Lett. 99, 093103 (2011)].