Characterization of a Single Metal Impurity in Graphene

Eric Cockayne Ceramics Division, NIST, Gaithersburg

Gregory M. RutterJoseph A. Stroscio

Center for Nanoscale Science & Technology, NIST

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

Large scale graphene growth:Several techniques; this talk: thermaldesorption of Si from SiC surface

Thermal desorption of Si from SiC:large area graphene, but defects frequently observed

Goal: elucidate nature of defectswith the ultimate aim of reducing oreliminating the defects

In 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 Diameter of strong modulation ~ 2 to 3 nm Center of defect is dark Dark spokes observed.

Appearance of defect very similar in variousexperiments (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))

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

Ab initio electronic structure

VASP used DFT, ultrasoft pseudopotentials212 eV plane wave cutoff324 and 432 C-atom bilayer supercells + 1 defect8748 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 VConvert constant current -> constant integrated DOS; plot height vs. position

Tight binding electronic structure

Mo d levels and C 2pz levels put into modelTight binding parameters determined via least squares fitting to ab initio data~150000 k points in BZ of primitive supercell needed for converged DOS plotsUp to 3888 atoms in bilayer supercell investigated

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 Substitution

Defect atom can be anything: focus on Mo and Si

Best fit: intercalated Mo

Graphene layers remain nearly flat (h < 0.25 A) for intercalated Mo

Magnetism?Mo position Magnetic moment M(B)

isolated atom 6.0adatom 0.0intercalated 0.0substitution 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)

324 C + 1 Mo: DOS shows three defect-associated peaks near EDirac

STM images vs. bias

Tersoff and Hamann approximation: I ~ local DOS integrated from EF to E

Experiment

DFT simulationsqrt(3) modulationmore sensitive to bias voltage than expt.central contrast dark for + bias

Ebias = -0.3 eV Ebias = +0.3 eV

Plots a-g show, inorder of increasingenergy, the zone centerstates near EDirac withsignificant Mo d participation

State E-EDirac 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 eVBright center: singlet; m = 0; dark center; doublet; m nonzero

Can individual state(s) be identified that match experimental STM images?

BilayerTrilayer

Simulated STM images

Images for equivalent defect state nearly identical:Effect of intercalated Mo atom is confined to nearby layersSuggests effect of substrate is small.

Tight binding model

Include only C 2pz & Mo 4d orbitals

Intralayer C-C coupling to 2nd neighbors;

interlayer coupling for “stacked” atoms

Mo-C coupling terms to 10 neighborsshown

Parameters found by least square fittingto ab initio data

C-C results similar to those in literature

Variance of C-C interations essential:For these terms:

A = 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.

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

Low energy peak remains nearly constant as system gets largerHigh energy peaks: large changes; not convergedOscillations: real or artifact of sharp distorted/undistorted boundary in model?

-0.2 0.8

-1.5 1.5 -1.5 1.5

E- EDirac (eV)

+2nm

0

-2nm

Simulation Expt. Simulation; normalized

Energy/distance DOS: Simulation vs. Expt.

Conclusions (as of 3/31/10)

Most positive result: For intercalated Mo, states withenergy around EDirac + 0.9 eV reproducemost results of experiments

Most intriguing result:Simulated energy-distanceplot for interstitial showssqrt(3) modulation betweensharp bounds in energy

Biggest remaining puzzles:Why don’t fine details in STMsimulations (e.g. dark spokes) agree with experiment?

Why isn’t the positive energydefect peak as distinct as itseems experimentally?

Top priorities:Extend expt. measurements tocover entire energy range of interestExtend TB model to predict STM imagesIf necessary, vary paramters in TBmodel to account for possible DFTerrors

Working hypothesis:experimental “pinwheel”defect is due to intercalatedmetal ion

“New” defect: rotated central region(J. Meyer, Ulm, MRS Spring meeting 2010)

6 pentagons + 6 heptagonsE = +7.1 eV

c/w Stone-Wales defect2 pentagons + 2 heptagonsE = + 4.2 eV

Vacancy (unreconstructed) E = +10.0 eV

Other defects? Stone-Wales; vacancy?

Conclusions (as of 4/27/10)

Most positive result: For intercalated Mo, states withenergy around EDirac + 0.9 eV reproducemost results of experiments

Most intriguing result:Simulated energy-distanceplot for interstitial showssqrt(3) modulation betweensharp bounds in energy

Biggest remaining puzzles:Why don’t fine details in STMsimulations (e.g. dark spokes) agree with experiment?

Why isn’t the positive energydefect peak as distinct as itseems experimentally?

Top priorities:Extend expt. measurements tocover entire energy range of interestExtend TB model to predict STM imagesIf necessary, vary paramters in TBmodel to account for possible DFTerrors

Working hypothesis:pinwheel defect is dueto rotational grain boundary type defect