GRAPHENE SHEET AND NANOMECHANICAL RESONATOR
A graphene sheet is provided. The graphene sheet includes a carbon lattice and a spatial distribution of defects in the carbon lattice. The spatial distribution of defects is configured to tailor the buckling properties of the graphene sheet.
1 - 199 . (canceled)
200 . A graphene sheet comprising:
a carbon lattice; and
a spatial distribution of defects in the carbon lattice;
wherein the spatial distribution of defects controls the buckling properties of the graphene sheet such that the graphene sheet buckles in a pattern.
201 . The graphene sheet of claim 200 , wherein the defects comprise a region of non-hexagonal carbon linkages.
202 . The graphene sheet of claim 201 , wherein the defects are separated by a region of hexagonal carbon linkages.
203 . The graphene sheet of claim 200 , wherein the defects comprise a region of chemical groups coupled to the graphene sheet.
204 . The graphene sheet of claim 200 , wherein the carbon lattice substantially defines a plane, and wherein the defects form an out-of plane formation.
205 . The graphene sheet of claim 204 , wherein the out-of-plane formation is configured to control the global buckling of the graphene sheet.
206 . The graphene sheet of claim 205 , wherein the out-of-plane formation is configured to induce buckling at the out-of-plane formation.
207 . The graphene sheet of claim 205 , wherein the out-of-plane formation is configured to confine buckling.
208 . The graphene sheet of claim 200 , wherein the spatial distribution is configured to define a buckling origination site.
209 . The graphene sheet of claim 200 , wherein the spatial distribution is configured to define a mode shape of the buckling.
210 . The graphene sheet of claim 200 , wherein the spatial distribution is configured to define an axis along which the graphene sheet buckles.
211 . The graphene sheet of claim 200 , wherein the spatial distribution is configured to limit the extent to which the graphene sheet buckles.
212 . The graphene sheet of claim 200 , wherein the spatial distribution comprises a point pattern.
213 . The graphene sheet of claim 200 , wherein the spatial distribution comprises a line pattern.
214 . The graphene sheet of claim 200 , wherein the spatial distribution comprises a plurality of intersecting ridges.
215 . The graphene sheet of claim 200 , wherein the spatial distribution of defects comprises a regular lattice distribution of defects.
216 . The graphene sheet of claim 200 , wherein the spatial distribution of defects comprises a quasi-periodic lattice distribution of defects.
217 . A method of tailoring the buckling properties of a graphene sheet, comprising:
selecting a configuration of a spatial distribution of defects;
growing a graphene sheet; and
forming a spatial distribution of defects in the graphene sheet, the spatial distribution of defects having the selected configuration, the selected configuration controlling the buckling properties of the graphene sheet.
218 . The method of claim 217 , wherein the defects comprise a region of non-hexagonal carbon linkages.
219 . The method of claim 218 , wherein the defects are separated by a region of hexagonal carbon linkages.
220 . The method of claim 217 , wherein the defects comprise a region of chemical groups coupled to the graphene sheet.
221 . The method of claim 220 , wherein graphene sheet comprises a first side and a second side, the second side disposed opposite the first side, and wherein the forming comprises coupling a chemical group to at least one of the first side and the second side of the graphene sheet.
222 . The method of claim 221 , wherein the forming comprises coupling a chemical group to the first side and the second side of the graphene sheet.
223 . The method of claim 217 , wherein the graphene sheet substantially defines a plane, and wherein the forming comprises forming an out-of plane formation of defects.
224 . The method of claim 223 , wherein the out-of-plane formation comprises at least one peak and at least two valleys.
225 . The method of claim 223 , wherein the out-of-plane formation comprises at least one valley and at least two peaks.
226 . The method of claim 223 , wherein the out-of-plane formation comprises a blister and a dimple, and further comprising configuring the out-of-plane formation to buckle such that the blister becomes a dimple and the dimple becomes a blister.
227 . The method of claim 217 , further comprising configuring the spatial distribution to limit the extent to which the graphene sheet buckles.
228 . The method of claim 217 , wherein the forming comprises growing a graphene sheet on a topological template.
229 . The method of claim 217 , wherein the forming comprises using an ion beam.
230 . A nanomechanical resonator, comprising:
a support structure;
a graphene sheet at least partially suspended from the support structure, the graphene sheet having a carbon lattice that substantially defines a plane; and
an actuator configured to actively control the resonant frequency of a portion of the graphene sheet by varying an out-of-plane force applied to the graphene sheet.
231 . The resonator of claim 230 , wherein varying the out-of-plane force varies the out-of-plane coupling of the graphene to the support structure.
232 . The resonator of claim 230 , wherein the graphene sheet includes a length dimension and a width dimension, and wherein the length dimension is at least three times greater than the width dimension
233 . The resonator of claim 232 , wherein the graphene sheet includes a first end and a second end disposed lengthwise opposite the first end, and wherein the graphene sheet is supported at the first end by the support structure.
234 . The resonator of claim 230 , wherein the graphene sheet includes a length dimension and a width dimension, and wherein the length dimension is comparable with the width dimension.
235 . The resonator of claim 234 , wherein the graphene sheet forms a drum head.
236 . The resonator of claim 230 , wherein the graphene sheet is supported by a plurality of supports and is subject to an in-plane stress field.
237 . (canceled)
238 . (canceled)
239 . The resonator of claim 230 , wherein varying the out-of-plane force varies a support boundary condition.
240 . (canceled)
241 . (canceled)
242 . (canceled)
243 . (canceled)
244 . The resonator of claim 230 , wherein the actuator is configured to electrostatically vary the out-of-plane force.
245 . The resonator of claim 230 , wherein the actuator is configured to change the resonant frequency of the graphene sheet to a target value.
246 . (canceled)
247 . The graphene sheet of claim 200 , wherein the spatial distribution comprises a first set of blisters elongated in a first planar direction and a second set of blisters elongated in a second planar direction.
248 . The graphene sheet of claim 247 , wherein the second planar direction is substantially orthogonal to the first planar direction.
249 . The graphene sheet of claim 215 , wherein the spatial distribution comprises a rectangular lattice distribution.
250 . The graphene sheet of claim 215 , wherein the spatial distribution comprises a triangular lattice distribution.
251 . The graphene sheet of claim 215 , wherein the spatial distribution comprises a lattice distribution of intersecting ridges.
252 . The method of claim 217 , wherein the configuration of a spatial distribution of defects is selected to control the global buckling of the graphene sheet.
253 . The method of claim 217 , further comprising selecting a configuration of the spatial distribution of defects to define a mode shape of the buckling.