Elastic properties of suspended graphene

Licentiate thesis, 2012

This thesis concerns describing the mechanical properties of the two dimensional material graphene by continuum elasticity theory. In particular, Nano ElectroMechanical Systems (NEMS) where part of the graphene sheet is made suspended, are considered. In the first paper, the motion of a suspended graphene sheet is used to enhance the operation of a carbon nanotube field effect transistor. Here, the suspended graphene is used as a top-gate, controlling the charge density on the carbon nanotube channel. It is shown that the motion of the graphene sheet increases the sensitivity of the charge density on the carbon nanotube to the applied gate voltage. A factor limiting the applicability of mechanical resonators in electronics is damping of the mechanical motion. In an ongoing project, a specific mode of dissipation, namely the coupling between the flexural motion of the graphene sheet to phonons in the graphene and the underlying substrate, is investigated on a theoretical basis. It is found that this mechanism gives rise to both linear and amplitude dependent (nonlinear) damping. In paper II, the rigidity of graphene toward bending is investigated in collaboration with an experimental group at Gothenburg University. Here, compressive strain was built up in the graphene membrane through thermal cycling. Upon making the membrane suspended, the strain was released, causing the graphene to buckle. This type of buckled structures display an instability at a certain critical pressure. This critical pressure was then related to the bending rigidity of graphene. The bending rigidity was measured both for bilayered and monolayered graphene, with the result $\kappa_{Bi}\approx 30^{+20}_{-15}$eV and $\kappa_{Mono}\approx 7^{+4}_{-3}$ eV.