Voltage-induced graphene blister — a theoretical analysis

Suspended graphene nanopores are widely used in nanofluidic devices, as the machined graphene defects can be downscaled to the angstrom scale. Our recent experimental results showed that the suspended graphene can become delaminated from the edges of SiN nanopore under an applied electrical field, theoretical understanding of this process is still lacking. In this work, we analytically studied the voltage-induced blistering of suspended graphene using an energy approach. The external electric field induces accumulation of ions at the graphene-electrolyte interface, causing Maxwell stress resulting in bending and stretching of the graphene and blister formation. We theoretically derived the angle of the graphene blister to the SiN nanopore by energy approach. We found that once the vertical component of the Maxwell stress on the graphene at the perimeter of SiN nanopore exceeds the van der Waals force between the graphene and substrate, the graphene starts to detach from the edges of SiN nanopore. We derived that the threshold voltage of single-layer graphene detachment is in order of 100 mV, which needs to be cautioned for electrical measurements of suspended graphene nanofluidic devices since the voltage amplitude is just in the range of voltage operation for typical electrochemical measurements. The threshold voltage increases as SiN nanopore becomes smaller and increases with the number of graphene layers. Our work theoretically describes the blister formation and delamination of graphene from its substrate nanopores. We expect this theory to be useful for optimizing and understanding the unexpected conduction phenomena observed in suspended graphene nanofluidic devices.