Characterization of a Single Metal Impurity in Graphene

Eric Cockayne Ceramics Division, NIST, Gaithersburg

Gregory M. RutterJoseph A. Stroscio

Center Nanoscale Science & Technology, NIST

Castro-Neto et al., Physics World (2006)

Castro-Neto, Nature Mater. 6, 176 (2007).

Graphene: Unusual electronic structure makes it a promising candidateFor applications

Microelectronics: high carrier mobility → high speed devicesResistance standard → unusual quantum Hall effect

Growth of graphene from by thermaldesorption of Si from SiC leads to largearea of graphene, but defects frequentlyobserved

Goal of this talk: elucidate nature of defectswith the ultimate aim of reducing oreliminating the defectsIn particular, will focus in pseudo-six folddefect very commonly observed

Properties of defect found in STM images: Near sixfold symmetry; actually threefold Sqrt(3) modulation of graphene lattice Center of defect is dark Dark spokes observed. Depending on imaging conditions,diameter around 20-30 Ang.

dI/dV plot ~ local density of states sharply peaked in energy,about 0.5 eV above the Dirac point

Ab initio electronic structureVASP used DFT, ultrasoft pseudopotentials212 eV plane wave cutoff; 324 and 432 supercells for bilayer8748 k points per BZ of primitive cellSTM topographs simulationsTersoff approximation: fixed V current proportional to local density of states between Fermi level and bias VTight binding electronic structureMo d levels and C 2p z levels put into modelTight binding parameters determined via least squares Fitting to ab initio dataUp to 3888 atoms for bilayer supercell~175000 k points in primitive BZ cell

Methods: ab initio & tight binding

Based on pseudosixfold nature of defect and fact that it is onlyobserved in graphene bilayers/multilayers, hypothesize thatdefect is on axis of the center of a hexagon in the topmost layerof Bernal stacked graphene

Adatom Intercalation SubstitutionDefect atom can be anything: focus on Mo and Si

Graphene layers remain nearly flat (Dh < 0.25 Ang) for intercalated Mo

Magnetism?Mo position Magnetic momentisolated atom 6.0adatom 0.0intercalated 0.0substitution 2.0

Bilayer Trilayer

Tight binding modelInclude only C 2pz & Mo 4d orbitalsIntralayer C-C coupling to 2 neighbor;interlayer coupling for A sublatticeMo-C coupling terms to 10 neighborsshownParameters found by least square fittingto ab initio dataVariance of C-C interations essential:For these terms: modelA = Aideal + B(d – dideal); where A, Bfit to each C-C interaction parameter;guarantees correct results reproduced forideal graphene

For larger supercells, graphene distortedaround Mo as in ab initio results; rest ofstructure “padded” with ideal graphene.

Conclusions

Single intercalated metal impurity explains most of features of experimental pseudo-six-fold defect

Coupling of Mo d states with graphene 2pz states responsible Localization plots created Tight binding model created; surprisingly large supercells

necessary for convergence