Epitaxial graphene on ruthenium

ARTICLES

PETER W. SUTTER*, JAN-INGO FLEGE AND ELI A. SUTTER

Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA

Published online: 6 April 2008; doi:10.1038/nmat2166

Graphene has been used to explore the fascinating electronic properties of ideal two-dimensional carbon, and shows great promise

for quantum device architectures. The primary method for isolating graphene, micromechanical cleavage of graphite, is diﬃcult to

scale up for applications. Epitaxial growth is an attractive alternative, but achieving large graphene domains with uniform thickness

remains a challenge, and substrate bonding may strongly aﬀect the electronic properties of epitaxial graphene layers. Here, we

show that epitaxy on Ru(0001) produces arrays of macroscopic single-crystalline graphene domains in a controlled, layer-by-layer

fashion. Whereas the ﬁrst graphene layer indeed interacts strongly with the metal substrate, the second layer is almost completely

detached, shows weak electronic coupling to the me tal, and hence retains the inherent elect ronic structure of graphene. Our ﬁndings

demonstrate a route towards rational graphene synthesis on transition-metal templates for applications in electronics, sensing

or catalysis.

Graphene, a two-dimensional honeycomb lattice of sp

-bonded

carbon atoms

, has shown a wealth of exceptional properties

such as anomalous behaviour in the integer quantum Hall eﬀec t

and in quasiparticle coupling

, which are signatures of charge

carriers behaving as massless Dirac fermions. A very high carrier

mobility

and long-range ballistic transport at room temperature

quantum conﬁnement in nanoscale r ibbons

and single-molecule

gas detection sensitivity

qualify graphene as a promising material

for large-scale applications in microelectronics and sensing. To

realize this potential, reliable methods for fabricating large-area

single-crystalline graphene domains are required. Epitaxial growth

on 6H- and 4H-SiC is pursued a ctively, but achieving large

graphene domains with uniform thickness remains a challenge

Graphene synthesis by epitaxy on transition metals has been

considered recently

9–14

. Observations of the structural coherence of

graphene across steps suggest that the sizes of graphene domains

will not be limited by the substr ate step spacing in this case

. Yet,

it remains uncertain if the surface diﬀusion of carbon adatoms can

be of suﬃciently long range to achieve sparse graphene nucleation

and hence epitaxial graphene domains of macroscopic size. In

addition, strong bonding to the support

could substantially alter

the electronic structure of metal-supported graphene, as well as

complicate the separation of graphene sheets from a transition-

metal template for transfer to other substrates.

Here, we combine real-time observ ations of graphene growth

by in situ surface microscopy with characterization by electron

scattering and microscopy, micro-Raman spectroscopy and

transport measurements to explore the properties of epitaxial

graphene on the (0001) surface of ruthenium (Ru). At high

temperatures, a very sparse graphene nucleation enables the

growth of truly macroscopic single-crystalline domains with linear

dimensions exceeding 200 µm. The abilit y to nucleate and grow

further graphene layers in a controlled way enables determination

of the eﬀects of a progressive weakening of substrate interactions on

the electronic properties of the epitaxial graphene. Whereas the ﬁrst

graphene layer couples strongly to the Ru substrate, the second layer

is essentially decoupled and largely recovers the electronic structure

of free-standing graphene. Our ﬁnding s suggest that single- and

(00)

(10)

(01)

100 µm

20 µm

KLL

intensity

Figure 1 Morphology of epitaxial graphene on Ru(0001). a, UHV-SEM image of a

large area of the Ru(0001) surface after ﬁrst-layer graphene growth. Inset: Carbon

KLL (260.6 eV) UHV scanning Auger microscopy image, obtained on this sample.

b, UHV-SEM image of a group of second-layer graphene islands. c, Selected-area

low-energy electron diffraction (electron energy: 45.4 eV) pattern of the Ru(0001)

substrate. d, Diffraction pattern of one-layer epitaxial graphene on Ru(0001)

(52.2 eV). e, Diffraction pattern of two-layer epitaxial graphene (39.1 eV).

few-layer graphene epitaxy on Ru(0001)—and possibly on other

transition-metal substrates—integrated by se lective growth on

transition-metal template pads or combined with methods for

transfer to other substrates can provide high-quality material for

applications in electronics and sensing.

406 nature materials VOL 7 MAY 2008 www.nature.com/naturematerials

ARTICLES

90 s60 s30 s12 s

10 µm

Figure 2 In situ microscopy of graphene epitaxy on Ru(0001). a, Time-lapse sequence of LEEM images showing the initial growth of a ﬁrst-layer graphene island on

Ru(0001) at 850

◦

C. Numbers indica te elapsed time in seconds after the nucleation of the graphene island. Substrate steps, visible as faint dark lines, are aligned from lower

left to upper right. Black dots mark the position of the initial graphene nucleus, demonstrating negligible growth across steps in the ‘uphill’ direction. b, Schematic

cross-sectional view of the preferential, carpet-like expansion of the graphene sheet (g) across ‘downhill’ steps, and suppression of the growth in the ‘uphill’ direction.

Intensity (a.u.)

10 20 30

Energy (eV)

040

Intensity (a.u.)

10 20 30

Energy (eV)

040

Intensity (a.u.)

10 20 30

Energy (eV)

040

Figure 3 Identiﬁcation of the layer spacing of one- and two-layer

graphene/Ru(0001). a, Measured (top) and simulated (bottom) low-energy electron

reﬂectivity, I (V ), of the Ru(0001) substrate. b,c, Best ﬁt of measured and simulated

I(V ) spectra for one- and two-layer epitaxial graphene on Ru(0001). Plan-view

models of the simulated structures are shown next to the spectra.

We made use of the temperature-dependent solubility of

interstitial carbon in transition metals to achieve the controlled

layer-by-layer growth of large graphene domains on Ru(0001). At

high temperature, C is absorbed into the Ru bulk. Slow cooling

from 1,150

◦

C to 825

◦

C lowers the interstitial C solubility by a

factor of 6 (ref. 15), driving signiﬁcant amounts of C to the

surface. The result is an array of lens-shaped islands of macroscopic

size (>100 µm) covering the entire Ru(0001) substrate (Fig. 1a).

Ultrahigh-vacuum (UHV) C

KLL

scanning Auger microscopy shows

that these islands are indeed C-rich, and surrounded by Ru metal

with negligible C

KLL

signal. Combining in situ electron microscopy

and selected-area electron diﬀraction (Fig. 1c–e), we identify these

islands as single-layer epitaxial graphene. On Ru(0001), single-layer

graphene adopts an incommensurate moir

e structure

, similar to

that observed on other transition metals, such as Ir(111) (ref. 9).

Diﬀraction shows that the h10

10i directions of layer and substrate

align, with moir

e repeat vectors a

=(2.93 ±0.08) nm, equivalent

to 10.8±0.3 times the nearest-neighbour distance on Ru(0001). A

marked lowering of the work function compared with that of both

clean Ru and bulk graphite indicates strong substrate bonding and

signiﬁcant charge transfer from the metal to the graphene overlayer.

The interaction of the growing islands with atomic substrate

steps is an important factor in enabling monocrystalline graphene

domains with size exceeding the average step spacing by several

orders of magnitude. In contrast to previous work that showed

dense nucleation at Ru step edges

, epitaxial graphene sheets

on Ru(0001) nucleate very sparsely and rapidly expand by

C incorporation into graphene edge sites under our growth

conditions. In situ low-energy electron microscopy (LEEM) during

growth (Fig. 2) shows a fast expansion of growing graphene

domains parallel to substrate steps and across steps in the ‘downhill’

direction. The crossing of ‘uphill’ steps by the graphene edge is

almost entirely suppressed, lea ding to a straight boundary that

shows virtually no growth. Single-layer graphene should interact

with a ﬂat metal substrate primarily through hybridization of

the out-of-plane π orbitals with metal d bands, whereas in-plane

σ states participate in sp

bonding. This picture breaks down

when the graphene edge meets a substrate step. The epitaxial

orientation on Ru(0001) implies that a graphene sheet projects

a zigzag edge with localized dangling σ bonds

onto atomic

substrate steps. A graphene boundary encountering an ‘uphill’ step

maximizes the orbital overlap and becomes immobilized at the

step edge. Conversely, a gr aphene sheet growing in the ‘downhill’

direction shows minimal overlap of the edge states with the Ru

step, and can ﬂow uninhibited in a car pet-like fashion across

the step

. T his growth mode results in macroscopic graphene

domains reaching well over 100 µm in length (Fig. 1a), far larger

than the substrate step spacing (0.15 µm), exceeding the extension

of the largest monocrystalline epitaxial graphene domains reported

so far—below 1 µm on 4H-SiC(000

1) (ref. 17); about 1 µm on

Ru(0001) (ref. 12) and Ir(111) (ref. 10)—by at least two orders

of magnitude.

If suﬃcient C segregates from the Ru bulk (or is deposited

from a suitable hydrocarbon precursor, such as ethylene

), the

graphene islands grow to a size corresponding to the spacing of the

initial nuclei (>200 µm) and coalesce to a complete ﬁrst layer

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ARTICLES

1,586 cm

–1

2,674 cm

–1

1,599 cm

–1

2,678 cm

–1

2,620

2,720

Intensity (a.u.)

1,520

1,640

1,500 2,000 2,500 3,000

Raman shift (cm

–1

)

Raman shift (cm

–1

)

Raman shift (cm

–1

)

1,000 3,500

5 µm

Figure 4 Micro-Raman characterization of two-layer graphene on Ru(0001). a, Comparison of Raman spectra at 532 nm for mechanically cleaved monolayer graphene

on SiO

(top) and epitaxial two-layer graphene on Ru(0001) (bottom). b, Raman map showing the peak energy of the G band for two adjacent two-layer epitaxial graphene

islands. c, Raman map of the peak energy of the 2D band for the same islands.

At about 80% surface coverage, the nucleation and growth of

islands of a second graphene layer are observed (Fig. 1b) on the

macroscopic ﬁrst-layer domains. A smaller separation of second-

layer nuclei suggests a C adatom mobility that is lower than on

Ru(0001). A well-ordered moir

e structure is observed by selected-

area diﬀraction on the second layer (Fig. 1e). Island edges aligne d

with the direction of substrate steps indicate a residual interaction

between Ru(0001) surface steps and graphene edges, similar to that

observed for the ﬁrst layer.

At this point, the surface consists of two diﬀerent phases. Areas

with two-layer graphene coexist with regions covered by a single

graphene layer. We expect the ﬁrst layer to be covalently bonded to

the Ru substrate by hybridization of C 2p

orbitals with Ru d-states

near the Fermi energy. Charge transfer from the substrate to

subsequent graphene layers should diminish progressively, with the

interlayer coupling asymptotically approaching the van der Waals

interaction of bulk graphite. Assessing this transition is of central

importance for evaluating epitaxy on transition metals as a

scalable synthesis route of one- or few-layer material with the

unique electronic properties of graphene. Going beyond the

existing surface-science studies on epitaxial graphene on Ru(0001)

(refs 10–14), we have used a combination of structural, vibrational

and electronic probes on individual single- and two-layer domains

to address this key issue.

The layer spacing has been determined by intensity–voltage

LEEM

, a technique capable of structural ﬁngerprinting in

submicrometre surface areas. Spec troscopic stacks of images of

a surface were acquired from the (00) diﬀraction beam as a

function of electron energy, V, so that the local image intensity,

I(V ), represents the specular low-energy electron reﬂectivity of a

given surface domain. When combined with dynamical multiple

scattering calculations of the low-energy electron reﬂectivity

this information can be used to determine the spacings of our

graphene layer stacks (Fig. 3). We have applied this method to bare

Ru(0001), as well as single- and two-layer epitaxial graphene on

Ru(0001). Measured and simulated I (V ) curves are in excellent

agreement for the metal surface (Fig. 3a). On graphene, a best

ﬁt between experimental and theoretical I(V ) curves is obtained

for a unique set of layer spacings. We determine a separat ion of

(1.45 ±0.1)

A between the Ru substrate and the ﬁrst graphene

layer (Fig. 3b), and a larger spacing of (3.0 ±0.1)

A be tween the

ﬁrst and second graphene layer in Bernal (A–B) stacking (Fig. 3c).

The addition of the second layer has negligible inﬂuence on the

separation between the ﬁrst graphene layer and the metal, which

remains ﬁxed at 1.45

A. This close spacing clearly reﬂects the

strong bonding interaction between Ru and the ﬁrst graphene

layer. Already with the second layer, however, the interlayer spacing

comes close to that of bulk graphite (3.34

A), suggesting that the

electronic structure of this and further graphene layers may be

aﬀected little by the adja cent metal substrate.

We have used Raman spectroscopy to probe the consequences

of this gr adual decoupling on the vibrational and electronic

properties of transition-metal-supported graphene stacks. R aman

spectra on cleaved monolayer and few-layer graphene on SiO

which served as reference samples, show two primary features: a

G band at ∼1,580 cm

−1

due to the two-fold degenerate E

mode at

the zone centre, and a second-order D

∗

(2D) band at ∼2,700 cm

−1

due to phonons in the highest optical branch near the K point at

the Brillouin zone boundar y

(Fig. 4a). The 2D band results from

a double-resonance process, w hich links the phonon wave vectors

to the electronic band structure, that is, its line shape can serve as a

ﬁngerprint of the electronic structure of massless Dirac fermions of

monolayer or few-layer graphene

Figure 4 summarizes micro-Raman experiments at 532 nm

excitation on single- and two-layer epitaxial graphene on Ru(0001).

The dominant band of the Ru substrate is the transverse-optical

zone-centre phonon mode at ∼190 cm

−1

(ref. 22). Samples with a

single epitaxial graphene layer show no detectable Raman intensity

between 1,000 and 3,000 cm

−1

. With the addition of the second

graphene layer, peaks appear at frequencies close to those of the

G and 2D bands (Fig. 4a). Both bands give rise to narrow single

peaks, which are shifted to hig her energy by 13 cm

−1

and 4 cm

−1

respectively, compared with the same bands in mechanically cleaved

monolayer graphene. In Raman maps, the centre position and

width of these bands remain constant over large areas within

two-layer epitaxial graphene domains several square micrometres

in size (Fig. 4b,c). A local blueshift by ∼10 cm

−1

is detected in a

continuous area within one of the sampled islands.

The double-resonance process that gives rise to the 2D band

has been used to distinguish monolayer and two-layer graphene

For cleaved g raphene, the 2D band is deﬁned largely by the

dispersion and splitting of electronic bands at the Brillouin zone

boundary: a single peak is observed for monolayer graphene,

whereas interlayer coupling splits the band into four distinct

components for bilayer graphene. The 2D band of two-layer

epitaxial graphene on Ru(0001) shows a single peak that is

broadened (full-width at half-maximum 42 cm

−1

) with respect to

that of monolayer graphene on SiO

(full-width at half-maximum

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Resistance (kΩ)

10 μm

Compression

–1 0 1

Voltage V

2,3

(mV)

–2 2

–20

1,4

(μA)

–40

Probe height (a.u.)

Separation (Å)

1203

Resistance (Ω)

Figure 5 Measurement of interlayer electrical transport. a, UHV-SEM image of the arrangement of four contact probes for interlayer resistance measurement.

b, Schematic diagram of the four-probe transport measurement between ﬁrst- and second-layer epitaxial graphene (G

→G

), using probes 1 and 2 for local mechanical

deformation of G

. c, Four-probe current–voltage characteristics for G

→G

transport, and for G

→G

transport at different compression of the interlayer spacing.

d, Comparison of the strain dependence of the electrical resistance in G

→G

(black squares) and G

→G

(blue circles) transport. Dark and light blue curves correspond to

mechanical loading and unloading, respectively. Inset: Exponential scaling of interlayer resistance with calculated layer spacing.

38 cm

−1

). The observ ation of a single narrow peak suggests that our

two-layer samples closely match the electronic str ucture of cleaved

monolayer graphene, with very little observable band splitting due

to interaction of the second layer with the underlying graphene

layer and Ru metal. Hence, the controlled a ddition of further

epitaxial graphene layers could be used to realize the properties of

bilayer and few-layer graphene.

The frequencies and intensity ratios of the G and 2D

peaks observed for two-layer graphene on Ru(0001) (Fig. 4a) are

consistent with results obtained on cleaved graphene, the carrier

density of which is increased by a gate-induced electric ﬁeld

23–25

suggesting that the Fermi level in the epitaxial two-layer graphene

is shifted away from the Dirac point. Chemical doping—reﬂecting

a residual interac tion with the underlying metal, indicated by the

spacing of the ﬁrst and second graphene layers and varying slightly

across the graphene sheets (Fig. 4b,c)—is the most likely cause.

Both the structural data from intensity–voltage LEEM and

the coupled vibrational and electronic signatures in Raman

spectroscopy indicate that the se cond-layer epitaxial graphene

on Ru(0001) is strongly decoupled from the metal substrate.

This decoupling should also be reﬂected in the interlayer

electronic transport. To evaluate carrier transport through epitaxial

graphene stacks, we have carried out room-temperature four-

probe transport measurements in UHV, using an instrument

that enables the controlled positioning of probes on the sample

surface under a ﬁeld-emission scanning electron microscope

(Fig. 5a). Measurements were carried out for two diﬀerent probe

conﬁgurations: G

→G

, two probes each on the ﬁrst and second

graphene layer for measuring transport between graphene sheets;

and G

→G

, all four probes on the ﬁrst graphene layer.

At identical probe spacing, the measured intralayer and

interlayer resistances diﬀer signiﬁcantly. For voltage probes (2,3)

separated by about 10 µm (Fig. 5a), transport in the ﬁrst graphene

layer (G

→ G

) shows a resistance of (10 ±1) . The interlayer

resistance (G

→ G

) is higher by about a factor of 10

, that is,

the electronic coupling between the graphene layers—and hence

between the second graphene sheet and the Ru substrate—is weak.

The electronic interaction between sheets with exposed π

orbitals is important in a variety of contexts. It determines

the anisotropy between the in-plane and c-axis conductance of

bulk graphite

, aﬀects electronic transport in multiwall carbon

nanotubes

27,28

and nanotube bundles

and governs charge transfer

in junctions containing π-conjugated molecules

. Depending on

the alignment of adjacent layers, the interlayer transport involves

either hopping or tunnelling between adjacent π orbitals. T he

coupling mechanism can, in principle, be identiﬁed by measuring

the interlayer resistance as a function of layer spacing. Early

experiments on graphite subje cted to high hydrostatic pressures

indeed showed a lowering of the c-axis resistance at high pressure

A similar type of measurement can be realized on individual

micrometre-sized graphene domains using our nanomanipulated

electrical probes (Fig. 5b–d). With probes 3 and 4 placed on G

probes 1 and 2—in contact with G

—are moved along the sample

normal to deform G

. The relative stiﬀness of the tungsten probe tip

and the graphene layer generates a large mechanical advantage, n,

in the range 10

–10

, that is, a sub-angstrom deformation of G

can

be induced controllably by an n-fold larger displacement of the tip

actuator. Measurements during loading and subsequent unloading

coincide exactly, demonstrating that the graphene sheet is strained

elastically in this process. Reference measurements with all four

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VOL 7 MAY 2008 www.nature.com/naturematerials 409

ARTICLES

probes placed on G

showed no change in electrical characteristics

over a much larger range of loading.

Figure 5c,d shows the four-probe resistance as a funct ion of the

spacing between G

and G

. For low bias voltages (few millivolts),

all measured current–voltage characteristics, I

1,4

2,3

), are linear.

The interlayer resistance varies exponentially with the deformation

of G

, from which we identify direct tunnelling between π-orbitals

on the adjacent graphene sheets as the conduction mechanism.

We ﬁt the measured resistance to a one-dimensional tunnelling

model

, I ∝ V exp(−2d

√

φ/

h), where d and φ are the

width and constant height (at low V) of the tunnelling barrier,

respectively, and m

denotes the electron (eﬀective) mass. Assuming

= m

, we ﬁnd a barrier height of 5.0 eV, consistent with very

weak electronic interlayer coupling of the undeformed graphene

stack at room temperature.

Our experiments on a speciﬁc model system—single- and two-

layer graphene grown epitaxially on a Ru(0001) template—provide

evidence for the feasibility of synthesizing large monocr ystalline

epitaxial graphene domains. A comparison with graphene on

SiC, the epitaxial system that has received most attention so far,

shows surprisingly similar substrate interactions in both cases: a

ﬁrst graphene layer is spaced closely (1.45

A for Ru; 1.65

A for

4H-SiC(000

1) (ref. 32)) and interacts strongly with the substrate,

as reﬂected by a drastic suppression of the work function

. This

layer, which will have distinct electronic and chemical properties

that are yet to be explored, may be seen as a buﬀer layer supporting

the second graphene sheet that is largely decoupled structurally and

electronically, but is doped owing to residual charge t ransfer from

the substrate

. Signiﬁcant diﬀerences between graphene epitaxy

on Ru(0001) and SiC clearly lie in the process conditions and

in the level of structural control achievable. Si sublimation on

SiC at high temperatures (between 1,250 and 1,450

◦

C) apparently

leads to small (<1 µm) multilayer graphene nuclei. Epitaxy on

Ru(0001) at lower temperatures (∼850

◦

C) produces sparse arrays

of graphene nuclei that grow in a controlled layer-by-layer mode to

macroscopic dimensions.

Our ﬁndings open up a number of avenues for exploiting

graphene epitaxy on transition-metal templates. The large ﬁrst-

layer graphene domains could be isolated if etch processes are found

that selectively remove the Ru substrate but do not damage the

graphene layer

. It can be predicted that the weakly bound second

graphene layer be transferred to another substrate, for example,

using intercalation to further weaken the interlayer bonding

analogous to the layer transfer methods used successfully for

other e lectronic materials, such as Ge and strained Si (ref. 35). A

perhaps more intriguing possibility is the integration with other

materials by using lithographically patterned transition-metal pads

as a catalyst and template for directed local graphene growth.

A similar seeding approach using catalytic Au nanoparticles has

been established recently to assemble highly ordered few-layer

graphene sheets conformally on semiconductor (Ge (ref. 36), GaN

(ref. 37)) nanowires. Finally, our demonstration of an atomic-layer

switch, the out-of-plane conductance of which is reversibly altered

over three orders of magnitude by tuning the graphene-substrate

coupling, suggests the possibility of controlling the in-plane carrier

transport in epitaxial or cleaved bilayer or few-layer graphene by

‘mechanical gating’, that is, local mechanical deformations of the

layer stack.

METHODS

GRAPHENE GROWTH AND STRUCTURAL ANALYSIS

Graphene growth was carried out by thermal cycling of a Ru(0001) single crystal

in UHV, as described in the text, while observing the process by in situ LEEM.

Time-lapse LEEM movies were obtained during growth of the ﬁrst and second

epitaxial graphene layer. Selected-area low-energy electron diﬀraction was

carried out on micrometre-sized areas of the bare Ru substrate, as well as the

ﬁrst and second graphene layer. Local intensity–voltage (I(V )) characteristics

were obtained from real-space images of uniform Ru metal, one-layer and

two-layer g raphene, acquired as a function of incident electron energy. Layer

spacings were determined by comparing measured I (V ) characteristics for

the specular diﬀrac ted beam at very low electron energies (1–40 eV) with

simulations by dynamical multiple-scattering low-energy electron diﬀraction

theory

. As an approximation to the incommensurate moir

e structure

observed experimentally, the simulations assumed graphene fully strained

to the Ru substrate, with C atoms occupying hexagonal close-packed and

face-centred-cubic hollow sites. We thus achieved a faithful representation of

the out-of-plane layer separations at reasonable computational eﬃciency.

MICRO-RAMAN SPECTROSCOPY AND MICROSCOPY

Micro-Raman spectra and Raman maps were obtained on both epitaxial

graphene on Ru(0001) and on a reference sample of mechanically cleaved

monolayer graphene in a commercial confocal R aman microscope (WiTec).

We used an excitation wavelength of 532 nm at incident power below 1 mW,

and a ×100 objective providing a diﬀraction-limited spot size of about 400 nm.

Raman maps were acquired by measuring complete spectra on a 0.5 µm grid

over a 25 µm×25 µm sample area. Figure 4b,c was obtained by lorentzian ﬁts to

the G and 2D Raman bands, and plotting the spatial distribution of the Raman

shifts of these bands.

TRANSPORT MEASUREMENTS

Electrical transport measurements were carried out in UHV in a commercial

system (Omicron Nanotechnology) that enables positioning of four

independent probe tips with nanometre accuracy on the sample while

observing the process by ﬁeld-emission scanning electron microscopy (SEM).

The probes consisted of electrochemically sharpened tungsten wires mounted

on and manipulated by piezoelectric actuator elements, and projecting under

◦

onto the sample surface. Their tips were placed above selected epitaxial

graphene structures, biased relative to the sample, and then approached

individually until a tunnelling current was detected. From this tunnelling

contact, the tips were carefully brought into mechanical contact, as judged

from the onset of linear low-bias four-probe current–voltage char acteristics.

A controlled compression of the graphene layer G

and measurement of the

resulting change in interlayer electrical resistance was achieved by driving

one of the probes on G

closer to the sample using a piezoelectric actuator

while measuring both the displacement of the actuator and the four-probe

resistance between G

and G

. The diﬀerent stiﬀnesses of the probe wire

(10 mm long, 0.25 mm diameter) and of the graphene sheet G

converted large

(several hundred

angstr

oms) movements of the actuator into much smaller

deformations of G

. The resulting reduction of the separation between G

and

(Fig. 5d, inset) was inferred from three measured quantities: (1) the relaxed

interlayer spacing, d

) =3.0

A, determined by e lectron diﬀraction;

(2) the interlayer resistance between the undeformed graphene layer G

and the

underlying layer G

(10 k at d

) =3.0

A); and (3) the resistance for

→G

transport, assumed equal to the resistance between G

and G

at zero

spacing (10  at d(G

) =0). Using the interlayer resistances at 3.0

A and

zero spacing as known end points, an exponential ﬁt to the measured resistance

as a function of actuator position provided the conversion between actuator

elongation and deformation of G

, assuming that the two are proportional to

each other (that is, diﬀer by a constant factor). All four-probe current–voltage

curves were measured with the sample held at room temperature, using a

programmable semiconductor test system (Keithley, model 4200SCS).

Received 16 November 2007; accepted 12 March 2008; published 6 April 2008.

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Acknowledgements

The authors thank T. Valla and J. Camacho for access to a cleaved monolayer graphene

sample. Work carried out under the auspices of the US Department of Energy under contract

No. DE-AC02-98CH1-886.

Author contributions

P.W.S. and E.A.S. planned the study, carried out all experiments, and analysed the data. J.-I.F. carried

out the LEED I(V ) simulations. P.W.S. wrote the paper, and all authors commented on the manuscript.

Author information

Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions.

Correspondence and requests for materials should be addressed to P.W.S.

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