Graphene sheet and nanomechanical resonator

Abstract

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.