Characterization of nanomechanical graphene drum structures

Abstract

Characterization of nanomechanical graphene drum structures is presented in this paper. The structures were fabricated by mechanical exfoliation of graphite onto pre-etched circular trenches in silicon dioxide on a silicon substrate. Drum structures with diameters ranging from 3.8 to 5.7 μm and thicknesses down to 8 nm were achieved. Mechanical characterization of the devices was then carried out by using atomic force microscopy (AFM) to measure their electrostatic deflection. The structures were found to have linear spring constants ranging from 3.24 to 37.4 N m −1 and could be actuated to about 18-34% of their thickness before exhibiting nonlinear deflection. An analytical framework was formulated to model the deflection behaviour which was verified through finite element simulations (FEM). The experimental measurements agree well with analytical and finite element results using Young's modulus of 1 TPa. The resonance characteristics of the structures were derived by both plate theory and FEM simulations. It was found that our drum structures could potentially vibrate at frequencies in excess of 25 MHz. The small size and high operating frequencies of our nanomechanical graphene devices make them very promising for resonant mass sensing applications with 10 −20 g Hz −1 sensitivity, a two order of magnitude improvement over other reported silicon structures.

Apparent stiffening of a graphene nanomembrane with initial curvature

“…(7) and (8) imply that for a positive κ 0 , the initial shape of the membrane is concave, in accord with AFM images reported in Refs. 4,12,14,20,21,24. It follows from the first equation in Eq.…”

“…26 To assess how the maximum deflection evolves with elastic modulus when D and E are connected by the conventional relation D = 1 12 Eh 2 (we disregard Poisson's ratio and recall that E stands for the 2D elastic modulus), Eqs. (19), (20) are solved for a monolayer membrane made of reduced graphene oxide with the Young's modulus 0.82 TPa 16 and thickness h = 1.2 nm 27 suspended over a trench with width l = 1 µm (this value equals the diameter of a circular membrane used in experiments 16 ). We set q * = 0.02 MPa and determine the initial curvature from the formula for a circular segment K = 8W 0 /(l 2 + 4W 2 0 ), where the maximum deflection before application of pressure reads W 0 = 20 nm in accord with Ref.…”

“…(19) and (20) are solved numerically with the above parameters for a weakly damaged membrane ( β = 0.9) with various initial deflections W 0 ranging from 1 to 30 nm. Results of simulation are depicted in Figure 4 which demonstrates that an increase in the initial curvature K leads to a reduction in the maximum deflectionδ for all dimensionless pressuresq.…”

“…19 The presence of wrinkles and ripples in 2D nanomembranes is confirmed by observations reported in Refs. 4,20,21, to mention a few. According to, Ref.…”

Graphene resonators : analysis and film transfer.

“…Bunch 8 and Wong 9 both observe that the as-exfoliated graphene sheets tend to wrap down the sidewalls of the via over which it is suspended (Figure 4). Wong dismisses the possibility that this is caused by compressive strain in the graphene, as the graphene is observed to be in mechanical tension by static measurement.…”