1. Characterization of a Single Metal Impurity in Graphene Eric Cockayne Ceramics Division, NIST, Gaithersburg Gregory M. Rutter Joseph A. Stroscio Center for Nanoscale Science & Technology, NIST

2. Castro-Neto et al., Physics World (2006) Castro-Neto, Nature Mater. 6, 176 (2007). Graphene: Unusual electronic structure; promising candidate for applications Microelectronics: high carrier mobility → high speed devices Resistance standard → unusual quantum Hall effect

3. Large scale graphene growth: Several techniques; this talk: thermal desorption of Si from SiC surface Thermal desorption of Si from SiC: large area graphene, but defects frequently observed Goal: elucidate nature of defects with the ultimate aim of reducing or eliminating the defects In particular, will focus in pseudo-six fold defect very commonly observed Properties of defect found in STM images: Near sixfold symmetry; actually threefold Sqrt(3) modulation of graphene lattice Diameter of strong modulation ~ 2 to 3 nm Center of defect is dark Dark spokes observed. Appearance of defect very similar in various experiments (Rutter et al., Science 317, 219 (2007); Guisinger et al., J. Vac. Sci. Techn A 26, 932 (2008); Simone et al., Eur. Phys. J. B 69, 351 (2009))

4. dI/dV plot ~ local density of states sharply peaked in energy, about 0.5 eV above the Dirac point Energy/distance breakdown of “pinwheel” defect

5. Ab initio electronic structure VASP used DFT, ultrasoft pseudopotentials 212 eV plane wave cutoff 324 and 432 C-atom bilayer supercells + 1 defect 8748 k points per BZ of primitive cell STM topograph simulations Tersoff & Hamann approximation (Phys. Rev. B 31, 805 (1985)): tunneling current proportional to local density of states between Fermi level and bias V Convert constant current -> constant integrated DOS; plot height vs. position Tight binding electronic structure Mo d levels and C 2p z levels put into model Tight binding parameters determined via least squares fitting to ab initio data ~150000 k points in BZ of primitive supercell needed for converged DOS plots Up to 3888 atoms in bilayer supercell investigated Methods: ab initio & tight binding

6. Based on pseudosixfold nature of defect and fact that it is only observed in graphene bilayers/multilayers, hypothesize that defect is on axis of the center of a hexagon in the topmost layer of Bernal stacked graphene Adatom IntercalationSubstitution Defect atom can be anything: focus on Mo and Si Best fit: intercalated Mo

7. Graphene layers remain nearly flat (  h < 0.25 A) for intercalated Mo Magnetism? Mo position Magnetic moment M(  B) isolated atom 6.0 adatom 0.0 intercalated 0.0 substitution 2.0 c/w M = 2.0 for Cr substitution in monolayer (Krasheninnikov et al., PRL 102, 126807 (2009); Santos et al,arXiv:0910.0400)

8. 324 C + 1 Mo: DOS shows three defect-associated peaks near E Dirac

9. STM images vs. bias Tersoff and Hamann approximation: I ~ local DOS integrated from E F to E Experiment DFT simulation sqrt(3) modulation more sensitive to bias voltage than expt. central contrast dark for + bias E bias = -0.3 eV E bias = +0.3 eV

10. Plots a-g show, in order of increasing energy, the zone center states near E Dirac with significant Mo d participation State E-E Dirac mult. a -0.57 2 b -0.49 1 c -0.17 2 d +0.02 2 e +0.20 1 f +0.33 2 g +0.88 2 Range of E ~ 1.5 eV Bright center: singlet; m = 0; dark center; doublet; m nonzero Can individual state(s) be identified that match experimental STM images?

11. Bilayer Trilayer Simulated STM images Images for equivalent defect state nearly identical: Effect of intercalated Mo atom is confined to nearby layers Suggests effect of substrate is small.

12. Tight binding model Include only C 2p z & Mo 4d orbitals Intralayer C-C coupling to 2nd neighbors; interlayer coupling for “stacked” atoms Mo-C coupling terms to 10 neighbors shown Parameters found by least square fitting to ab initio data C-C results similar to those in literature Variance of C-C interations essential: For these terms: A = A ideal + B(d – d ideal ); where A, B fit to each C-C interaction parameter; guarantees correct results reproduced for ideal graphene For larger supercells, graphene distorted around Mo as in ab initio results; rest of structure “padded” with ideal graphene.

13. Effect of stacked (gap) vs. unstacked (gapless) C sublattices seen in ideal bilayer DOS Three strong defect peaks of ab initio calculations reproduced

15. Low energy peak remains nearly constant as system gets larger High energy peaks: large changes; not converged Oscillations: real or artifact of sharp distorted/undistorted boundary in model?

16. -0.2 0.8 -1.5 1.5 E- E Dirac (eV) +2nm 0 -2nm Simulation Expt. Simulation; normalized Energy/distance DOS: Simulation vs. Expt.

17. Conclusions (as of 3/31/10) Most positive result: For intercalated Mo, states with energy around E Dirac + 0.9 eV reproduce most results of experiments Most intriguing result: Simulated energy-distance plot for interstitial shows sqrt(3) modulation between sharp bounds in energy Biggest remaining puzzles: Why don’t fine details in STM simulations (e.g. dark spokes) agree with experiment? Why isn’t the positive energy defect peak as distinct as it seems experimentally? Top priorities: Extend expt. measurements to cover entire energy range of interest Extend TB model to predict STM images If necessary, vary paramters in TB model to account for possible DFT errors Working hypothesis: experimental “pinwheel” defect is due to intercalated metal ion

18. “New” defect: rotated central region (J. Meyer, Ulm, MRS Spring meeting 2010) 6 pentagons + 6 heptagons E = +7.1 eV c/w Stone-Wales defect 2 pentagons + 2 heptagons E = + 4.2 eV Vacancy (unreconstructed) E = +10.0 eV

20. Other defects? Stone-Wales; vacancy?

21. Conclusions (as of 4/27/10) Most positive result: For intercalated Mo, states with energy around E Dirac + 0.9 eV reproduce most results of experiments Most intriguing result: Simulated energy-distance plot for interstitial shows sqrt(3) modulation between sharp bounds in energy Biggest remaining puzzles: Why don’t fine details in STM simulations (e.g. dark spokes) agree with experiment? Why isn’t the positive energy defect peak as distinct as it seems experimentally? Top priorities: Extend expt. measurements to cover entire energy range of interest Extend TB model to predict STM images If necessary, vary paramters in TB model to account for possible DFT errors Working hypothesis: pinwheel defect is due to rotational grain boundary type defect