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Structured epitaxial graphene: growth and properties

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2012 J. Phys. D: Appl. Phys. 45 154010

(http://iopscience.iop.org/0022-3727/45/15/154010)

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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 45 (2012) 154010 (12pp) doi:10.1088/0022-3727/45/15/154010

Structured epitaxial graphene: growthand propertiesYike Hu1, Ming Ruan1, Zelei Guo1, Rui Dong1, James Palmer1,John Hankinson1, Claire Berger1,2 and Walt A de Heer1

1 School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA2 CNRS-Institut Neel, Grenoble 38042, France

Received 3 January 2012, in final form 23 February 2012Published 29 March 2012Online at stacks.iop.org/JPhysD/45/154010

AbstractGraphene is generally considered to be a strong candidate to succeed silicon as an electronicmaterial. However, to date, it actually has not yet demonstrated capabilities that exceedstandard semiconducting materials. Currently demonstrated viable graphene devices areessentially limited to micrometre-sized ultrahigh-frequency analogue field effect transistorsand quantum Hall effect devices for metrology. Nanoscopically patterned graphene tends tohave disordered edges that severely reduce mobilities thereby obviating its advantage overother materials. Here we show that graphene grown on structured silicon carbide surfacesovercomes the edge roughness and promises to provide an inroad into nanoscale patterning ofgraphene. We show that high-quality ribbons and rings can be made using this technique. Wealso report on the progress towards high-mobility graphene monolayers on silicon carbide fordevice applications.

(Some figures may appear in colour only in the online journal)

1. Introduction

Whether graphene will or will not become an importantelectronic material critically hinges on our ability to producehigh-quality graphene and to pattern it at the nanoscale.Currently, the predominant paradigm for producing graphenedevices of any kind is to start with an extended graphenesheet, which may be produced by a variety of methods[1–3], and subsequently to pattern the sheet using standardmicroelectronics lithography methods [4–8]. Typicallylithography is performed by coating the graphene sheet with aresist material which is subsequently exposed to light or/andelectron beam, producing an image on the resist, that issubsequently developed to expose the graphene surface. Theexposed graphene is then cut, typically using an oxygenplasma, which removes the exposed graphene resulting in apatterned graphene layer. However, if patterned graphene isseen as a macro-molecule, then this ‘top-down’ method ofproducing it is very different from the method that is usuallyused to produce large molecules, either in the laboratory or innature. In fact, the chemical approach would be to producelarge molecules by assembling them from smaller ones, i.e. a‘bottom-up’ approach [9].

While lithographically patterned structures are adequatefor large devices, which rely primarily on the two-dimensional

(2D) electronic properties of graphene, in fact, graphene’spromise for electronics, as well as for new fundamentalphysics, relies primarily on its lower dimensional properties(i.e. nanoribbons and quantum dots). That is, grapheneis most interesting when feature sizes are of the order ofits Fermi wavelength so that quantum confinement effectsmanifest themselves. The carbon nanotube, with its well-known size and helicity-dependent electronic properties, isthe archetype for quantum confined graphitic structures. Infact, considerations of nanotube properties were the primarymotivation for graphitic electronics research [1].

Graphene is a zero bandgap semiconductor (i.e. asemimetal). Modern digital microelectronics relies on thebandgap of the semiconductor so that field effect transistorscan be produced with large on-to-off switching ratios in orderto minimize leakage currents when the transistor is in the ‘off’state. However, this off condition cannot be reached with 2Dgraphene, not even at extremely low temperatures.

While devices based on 2D graphene (i.e. devices withfeature sizes greater than 100 nm) are not considered tobe useful for digital electronics, this material is useful forultrahigh-frequency analogue electronics [10]. Fast graphenetransistors have been produced using 2D graphene. Eventhough these devices have very small on-to-off ratios (ofthe order of 10) they nevertheless have gain above unity at

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J. Phys. D: Appl. Phys. 45 (2012) 154010 Y Hu et al

frequencies exceeding 200 GHz [11, 12], which brings themin the range of state-of-the-art semiconducting devices [13].In order to push these limits even closer to the THz rangeswill require further significant improvements of grapheneperformance (as well as reductions in contact resistancesand higher quality dielectrics). It should be mentioned that2D graphene Hall bars patterned on epitaxial graphene areconsidered to be important in metrology as quantum Hall basedresistance standards [14].

It was theoretically known that quantum confinedstructures, such as graphene ribbons, could have bandgapsunder certain conditions [15, 16]. The size of the bandgapEg is predicted to be of the order of Eg = 1 eV/W whereW is the width of the ribbon. Consequently, theoretically,very narrow ribbons can have significant bandgaps. Thereare however caveats. The size of the bandgap depends onthe condition of the edge. In fact, theoretically, only grapheneribbons with armchair edges are semiconductors, and for them,only those where the width is an integer multiple of threehexagons [15, 16]. All other graphene ribbons, including thosewith zigzag edges and chiral ribbons that are intermediatebetween zigzag and armchair, are all expected to be metallic(in general) [17]. Note, however, that theory does predict thatbandgaps may open under certain circumstances [18].

It is therefore considered to be surprising that severalrecent papers report that lithographically patterned graphenenanoribbons from exfoliated graphene deposited on SiO2 areall semiconducting with bandgaps that are of the order of1 eV/Eg [5–8, 19]. The bandgap was established by adjustingthe charge density of the patterned graphene ribbon by applyinga potential to a Si backgate in the usual way. It was noted thatwith decreasing charge density the conductance dramaticallydecreases (by several orders of magnitude) similar to thedecrease in conductance that is observed in a semiconductor,from which the bandgap was determined.

However, it was later determined [6–8, 19] that (in mostcases) the bandgap was actually a mobility gap. That is,the edges of these patterned ribbons are disordered causingscattering. The rough edges caused the graphene ribbon toresemble a series of ‘quantum dots’ causing strong localizationof the charge carriers and a large reduction in the mobilityat low charge densities. While an interesting phenomenonin itself, materials that rely on such mobility gaps are notconsidered to be suitable for high-speed digital electronics.

In order to reduce edge scattering in narrow ribbons theedge roughness should be reduced. This suggests significantmodifications in the patterning method itself. Here weshow examples of quality nanostructures produced directlyon tailored silicon carbide surfaces without post-growthlithography processing. Progress towards high-mobilityepitaxial graphene monolayers for device applications is alsoreported.

2. Structured monolayer graphene growth on siliconcarbide

Epitaxial graphene on silicon carbide ranks among the mostpromising candidates for large-scale graphene electronics.

Epitaxial graphene grown on silicon carbide has severaladvantages over epitaxial graphene grown on metal substrates.One advantage is that the material need not be transferredfrom the metal to another dielectric substrate. The SiCsubstrate is a large bandgap semiconductor widely used inthe industry and schemes are developed for integration withsilicon [20]. The interface between epitaxial graphene andthe silicon carbide substrate is reasonably well understood onthe atomic scale [21]. One of the most important advantagesof epitaxially grown graphene sheets is that there are notrapped impurities under the graphene (although interface canbe modified by passivation and intercalation), and it can bereadily patterned. Large-area graphene (on both polar faces ofSiC) has been grown by several groups [1, 12, 14, 20, 22–28].Further investigations are required, however, before large-areagraphene layers with uniform properties are produced.

Another advantage is that graphene growth can bedirected. That is, by proper tailoring of the substrate, graphenecan be grown only where it is desired as shown in detail below.This method of graphene growth circumvents the damaginglithographic patterning step that causes the large mobility dropsin the patterned graphene ribbons mentioned above. Moreover,surprisingly, all graphene ribbons produced by this methodare found to be metallic. There is no evidence of a bandgap,in contrast to lithographically patterned graphenes that showevidence of bandgaps or mobility gaps. These observationsindicate that scattering at the edges is suppressed comparedwith ribbons produced using standard lithography methods.

Structured graphene growth is pursued along two distincttracts: large-area graphene growth on the carbon-terminatedsurface, and sidewall graphene structured growth [29] on thesilicon-terminated surfaces. Both of these approaches aretreated in detail below.

It is worth mentioning that the often-stated disadvantageof epitaxial graphene on silicon carbide substrates is the priceof the substrate itself. This would indeed be an important factorif the aim were to compete with silicon-based electronics.However, the ultimate goal is to succeed silicon, that is tobuild devices that exceed silicon in at least one key parameter,be it feature size, speed or power consumption. In those casesthe substrate cost (which even now is minor compared with theprocessing cost) is not important. There are many examplesof disruptive technologies that were initially costly butsignificantly outperformed prior technologies: semiconductorelectronics and air travel are prime examples.

3. Structured C-face graphene growth

It is well known that the mobilities of graphene monolayersgrown on the (0 0 0 −1) face (the C-face) are significantlygreater (typically by a factor of 3–10) than those graphene onthe (0 0 0 1) face (the Si-face). For this reason considerableeffort has been expended to control the graphene growthon the C-face, in particular for the 2D mono-graphenedevices mentioned above. High-quality graphene mono- andmultilayers are grown on the C-face of hexagonal siliconcarbide (either 6H or 4H) using the confinement controlledsublimation method (CCS) [22]. Briefly, in this method, a

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Figure 1. AFM images of graphene on the (0 0 0 −1) face of 4H-SiC. (a) AFM image of a graphene monolayer on a stepped (0 0 0 −1)surface; the graphene layer exhibits pleats (bright lines) and is confined to the central patch. Note the molten appearance of the areas notcovered by graphene. Bright spots are due to post-production contamination. (b) AFM image of a multilayer graphene patch draped over thedistinct central stepped region of the image that extends to the top. (c) Optical image of monolayer graphene growth at a screw dislocation.

silicon carbide chip is heated in vacuum, inside a graphitecapsule, which is supplied with a small leak. One or moregraphene layers form at temperatures between 1500 and1600 C. Uniform monolayer graphene growth is difficult toachieve over the entire 4×5 mm SiC chip surface. In particular,while large-area growth has been accomplished consistingof a continuous graphene layer covering the entire surface,below this layer (which over most of the area is a monolayer)there are occasionally patches with additional graphene layers.Even though the top-most layer is continuous, these patchesaffect the transport properties, and ideally they should beeliminated. This sub-layer partial growth is more critical onthe Si-face because the A–B stacked bilayers do not have thesame electronic structure as the monolayers. On the C-face themonolayer electronic structure is preserved for multilayers dueto the orientational stacking (see below) [30, 31] For quantumHall effect (QHE) based metrology applications it is importantthat the graphene is uniform and continuous on predeterminedlocations, which can then be patterned. While high-qualitycontinuous and uniform multilayer epitaxial graphene filmsare relatively easy to produce [22], uniform monolayers arestill challenging. Progress made in this direction is describedbelow.

Graphene growth on the C-face nucleates primarily atnatural substrate steps [24] (caused by step bunching), etchedsteps and defects such as screw dislocations (figure 1). Themonolayer growth patches at steps (figure 1(a)) are uniformlydistributed over the silicon carbide chip surface. However,growth at screw dislocations (figure 1(b)) is not controlled andtypically results in rather deep cervices covered with multilayergraphene. It is clear that screw dislocations are an impedimentto uniform growth.

Raman spectroscopy is a powerful characterization toolfor graphene deposited on silicon oxide and it has beenextensively treated in the literature [32]. Raman spectrafor epitaxial graphene are basically similar, however, withsome significant and important differences [25, 31]. Mostimportantly, the Raman spectrum of the silicon carbidesubstrate itself is superimposed on the graphene spectrum withintense features in the range 1500–2000 cm−1 (figure 2(a),

red curve). The other characteristic bands (D, G and 2D) areused for diagnostic purposes. For Bernal stacked multilayergraphene, the 2D band evolves as a superposition of peaksdue to the evolution of the electronic structure with increasingnumber of layers that converges to the graphite band structure[32]. However, the evolution in C-face graphene is subtlersince each layer has the same electronic structure as that ofa single layer. Consequently, the Raman spectra of thickC-face graphene multilayers are essentially identical to thatof a monolayer [31]. However, the 2D band does broadenfor the first few layers. This broadening is (most likely)primarily caused by the charge density variations from onelayer to the next: the bottom-most layer is negatively charged(n ∼ 5×10−12 cm−2) due to the SiC substrate, while the othersare essentially neutral. Shifts in the 2D band due to changein the Fermi level have been discussed in [33]. Moreover,the top-most layer is (often) p-doped due to environmentaleffects. In any case, as for exfoliated graphene on siliconcarbide, monolayer graphene on SiC can be identified by itssignature 2D band.

The positions of the G band and the 2D band as afunction of charge density for monolayer graphene (on theC-face) are shown in figure 2. The charge densities weredetermined from the Hall resistance. Note that the charge ona graphene monolayer is the sum of the interface charge andthe environmentally induced charge. An epitaxial graphenemonolayer is intrinsically negatively charged but it graduallybecomes positively charged after exposure to the ambient.Heating in vacuum restores its virgin condition. An increasein the energies of these two Raman bands with increasingcharge density (either positive or negative) is also observed inexfoliated graphene. While the increase in the G band agreesquantitatively with that observed for electrostatically gatedexfoliated graphene, the shift in the 2D band is significantlylarger than that observed in exfoliated graphene. We furthernote that in contrast to exfoliated graphene, the ratio of the2D peak intensity and the G band intensity is not a reliableindicator for monolayer graphene as it is found to vary from2 to 9. However, we have found that the ratio of the intensityof the G band and the SiC bands is a reliable indicator of

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Figure 2. (a) Typical examples of micro-Raman spectra used to identify monolayer graphene, top trace: graphene, bottom trace, bare SiCsubstrate (Raman laser wavelength λ = 532 nm, spectral resolution � = 0.3 cm−1). Note the G band at 1585 cm−1 and the prominent 2Dband at 2685 cm−1 that can be fitted with a single Lorentzian (with a typical width of 30 cm−1). (b) Peak position of the G band; (c) peakposition of the 2D band as a function of charge density.

the graphene layer thickness, which is particularly accurate inidentifying graphene monolayers on the C-face. The D band istypically very small in C-face graphene indicating low defectdensities in the material.

In figure 3 we present a more detailed analysis of a C-facemonolayer including both topographic AFM data and scanningRaman spectroscopy data. Usually, epitaxial graphene onthe C-face can be recognized by the pleats, as shown infigure 3(a); however, occasionally an anomalous pleat-freeregion is observed within a monolayer patch. A micro-Ramanmap of this patch (figures 3(b) and (c)) shows that the areas withpleats have a normal Raman spectrum with a peak 2D intensityat 2680 cm−1, while the Raman spectrum in the anomalousregion has its 2D peak intensity at 2760 cm−1. This shift in theRaman band indicates that this region is probably stressed andmore strongly coupled to the substrate than normal.

Attempts to structure silicon carbide, by etching mesasor pits, in order to direct graphene growth on the C-facehave had good success (figure 4). It appears that graphene

growth initiates at specific corners of the hexagonal pit etchedin C-face SiC. Further work will reveal whether this canlead to a process. In the mean time, very high qualitymonolayer graphene patches that spontaneously form on theSiC surface are optically identified with AFM, ellipsometry,optical transmission or Raman spectroscopy and then patternedusing conventional methods.

3.1. Electronic transport and devices on the C-face

The enhanced mobility of C-face graphene is an importantconsideration for micrometre scale graphene devices includingHall bars for metrology as well as high-frequency transistors.These larger patterned structures do not rely on quantumconfinement but rather exploit the intrinsic 2D grapheneproperties. Hall bar resistance standards are based onthe QHE, which requires high-mobility graphene that willexhibit well-developed quantum Hall plateaus at relativelyhigh temperatures (i.e. above cryogenic temperatures [30])and relatively low magnetic fields (a few tesla). Terahertz

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Figure 3. Detailed analysis of a monolayer graphene patch on the C-face. (a) AFM topology map (scale bar = 10 µm), showing themonolayer patch draped over several substrate steps. The graphene layer can be recognized by the pleats (white lines) that crisscross thepatch. (b) Raman intensity map of the 2D Raman band recorded at 2678 cm−1 clearly revealing the graphene-covered region (same scale as(a)). (c) Raman intensity map recorded at 2764 cm−1 showing that this anomalous pleat-free region is covered with a monolayer of strainedgraphene. (d) Micro-Raman spectra of areas in (b) (black—bottom trace) and (c) (red—top trace) showing a considerable shift in the latter,which may be caused by an anomalously strong coupling to the substrate.

Figure 4. Monolayer graphene growth on 4H-SiC (0 0 0 −1) on a pre-patterned structure indicates preferred sites for graphene growth.(a) AFM image for hexagon-trench structure after graphitization. The structure is etched to a depth of ∼50 nm using the inductively coupledplasma (ICP) method. SiC steps flow inside the trench. Faint graphene pleats are visible. (b) EFM amplitude scan shows contrast betweendarker graphene regions and lighter SiC regions as verified in the Raman 2D band intensity map (c); scale bar: 2 µm.

transistors require graphene that has a high mobility at highcharge densities (see below). These transistors (envisionedfor telecommunications) will be used for amplifiers andoscillators. They need to have significant gain at highfrequencies, but large on-to-off ratios (that are essential fordigital applications) are not required.

Figure 5 presents the progress on monolayer epitaxialgraphene Hall bars on the C-face that show the characteristichalf-integer QHE as in [34]: (a) low charge density allows

for QHE plateaus at moderate magnetic field, (b) step-freenon-patterned monolayer flake, (d)–(f ) top-gated single layer.High-mobility graphene (µ ∼ 18 000 cm2 V−1 s−1 at a chargedensity n ∼ 1012 cm−2) is typical for the C-face.

More precisely, the negative charge nS ∼ 5 × 1012 cm−2

at the interface with SiC, can be partially compensated byexposition to the environment, and tuned from n to p. Infigure 5(a), the C-face single layer was coated with PMMA,rinsed in hot acetone and hot water to remove resist residues.

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Figure 5. QHE in epitaxial graphene C-face for micrometre wide samples resistivity: black trace, left-hand side label; Hall: red trace,right-hand side label. (a) Hall bar (µ = 39 800 cm2 V−1 s−1, n = 0.19 × 1012 cm−2); (b) monolayer step-free non-patterned flake(ρxx = 320 �, µ = 21 100 cm2 V−1 s−1 at charge density nS = 0.92 × 1012 cm−2); (c) plot of resistivity versus charge density formicrometre-sized single layer C-face Hall bars. The dotted line corresponds to ρ = (80e2/h)−1 from [41]; (d)–(f ) top-gated Hall bar(1 µm × 4.3 µm). (d) Resistivity ρxx (black) and Hall conductance σxy (red) versus gate voltage at 4 K and 9 T, showing plateaus in then- and p-doped regimes; (e) (red curves) Hall resistance ρxy versus magnetic field measured at two gate voltages and comparable n andp charge density (i) Vg = 0.4 V, n-doping nS = 5 × 1011 cm−2, µ = 6200 cm2 V−1 s−1, (ii) Vg = 0 V, p-doping, nS = 5.6 × 1011 cm−2,µ = 8500 cm2 V−1 s−1; (black) resistivity ρxx at Vg = 0.4 V. A significant reduction in the mobility (compared with bare samples above) iscaused by the application of the top gate.

The process was repeated several times until the charge densitywas adjusted to a value well below nS < 1 × 1012 cm−2. It isinteresting that even at this low density (n-doping nS ∼ 0.19×1012 cm−2) the resistivity ρxx = 800 � remains low, yieldinga Hall mobility µ = 1/(nSeρxx) = 39 800 cm2 V−1 s−1. TheHall resistance ρxy is linear at low fields (away from the QHEplateaus) and does not present the kink or rounding previously

associated with the contribution of multilayers [30]. At ahigher field, the Hall resistance ρxy shows two very well-defined quantum Hall plateaus and the onset of the third oneat ρxy = (h/νe2), with filling factors ν = 2, 6 and 10(ν = 4n+ 2; n = 0, 1, 2) expected from single layer graphene.As already observed on both C- and Si-faces [14, 30] the ν = 2plateau extends into a large field region, over 4.5 T and up to

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Figure 6. C-face graphene FET transistor for high-frequency applications. (a) Source drain current versus source drain voltage. Maximumcurrent density >1.5 mA µm−1; gm > 0.4 mS µm−1; n = 1.6 × 1012 cm−2; µFET = 8700 cm2 V−1 s−1. The various curves (from bottom totop) were obtained for Vg from 1.5 to −1.5 V in 0.5 V increments. (b) Gain (H21) versus frequency measured up to 50 GHz. Theextrapolated unit gain cutoff frequency fT = 90 GHz (after de-embedding). (Inset) Optical microscopy image of the transistor (gate lengthis 150 nm). It is expected that fT will increase significantly by reducing the gate length to 15 nm, showing the source S, drain D and gate G.

the highest field, 7 T in this experiment. The resistivity ρxx

remains vanishingly small in the plateau region. All theseobservations corroborate that this is a high-mobility low n-doped single layer. Low doping density and high mobility canbe finely tuned by environment exposure for both p- and n-doping. This demonstrates that epitaxial graphene can be usedas QHE resistance standards even in moderate magnetic fields.Similar results are consistently found on all the monolayerepitaxial graphene devices measured. Another example isgiven in figure 5(b) for a non-patterned monolayer. Here alsothe ν = 2, 6, 10 plateaus are clearly observed concomitantwith zero resistivity at high fields. Note also the absence of asizable localization peak at low fields in all devices.

Applying top gate electrodes for individual deviceswitching significantly decreases the mobilities, as alreadyreported [27]. Nevertheless, useful devices can still be madewith significantly large mobilities to demonstrate the QHE,as shown in figures 5(d)–(f ). Note that alternative back-gating strategies, which work in a certain temperature range,are only useful for global gating [28]. A top gate was depositedon another single layer by evaporating aluminium metal ata slow rate (0.2 A s−1) in low vacuum, allowing aluminiumto oxidize during deposition. A subsequent deposition athigher rate (1 A s−1) covers the alumina with an aluminiummetallic gate. The results for a Hall bar (width 1 µm, length4.3 µm) are presented in figures 5(d)–(f ). The resistivityas a function of gate voltage at 4 K undergoes a maximumfor Vg ∼ 0.3 V, clearly showing the conductance modulationby the electrostatic field on both sides of the Dirac point(figure 5(f )) with a high to low resistivity ratio R(Vg =3 V)/Rmax = Ioff/Ion = 13. This value is common for2D single layer graphene. The gate efficiency to change thecharge density nS can be directly measured by the linear Hallresistance ρxy for different gate voltages at low fields. The gatevoltage Vg = 0.3 V at the Dirac point gives a charge densitynS = 6.2 × 1011 cm−2 induced by the gate to compensate forthe natural sample doping. This is very close to the dopingnS = 5.6×1011 cm−2 measured from ρxy at zero gate voltage.

A gate voltage sweep at 9 T shown in figure 5(d) revealsfully developed quantum Hall plateaus at σxy = νe2/h

for ν = 2, 6, 10, 14 (σxy is the transverse conductivity).The plateau corresponding to resistivity ρxx minima and avanishing resistivity for the ν = 2 plateau clearly demonstratesthat this is a single layer. Field sweep at two gate voltages, inthe p- and n-doped region, shows a well-resolved ν = 2 plateauthat extends into a large field region. In particular, this showsthe QHE can be switched from p to n using the top gate. Notethat the mobility for n-doping is significantly lower than thatfor p-doping.

Finally, the reciprocal relation between resistivity andcharge density nS = 1/(eρxy) is depicted in figure 5(c) formicrometre-sized C-face single layer graphene Hall bars. Asexpected for single layer graphene ρxx increases at low chargedensities, but it is interesting to note that ρxx is quite lowcompared with the results reported for exfoliated graphene,where ρxx ≈ (4 − 6e2/h)−1 = 4–6 k� [35]. The resistivitysaturates at a high charge density to a value remarkablyclose to 1/(80e2/h) = 320 �, which was estimated byOrlita et al [36] from their observation of a scattering timeinversely proportional to the energy (h/τ = 0.026E) in IRspectroscopy measurements for the screened inner layers ofmultilayered epitaxial graphene. The charge inhomogeneityδnS can be estimated [37] from the width of ρxx(Vg), for top-

gated samples. From ρxx = ρs + (eµ

√n2

S + δn2S)

−1 we find

δnS = 2 ×1011 cm−2, ρs = 130 � and µ = 8500 cm2 V−1 s−1

(p-doped side) (µ = 6200 cm2 V−1 s−1, n-doped side) for thesample in figure 5(f ), in very good agreement with the Hallmobility values. The δnS values found for the top-gated singlelayers are of the same order as single layer on SiO2. It appearstherefore that charge inhomogeneity alone cannot account forthe low ρxx values.

The basic structure and characteristics of a high-frequencygraphene field effect transistor is shown in figure 6. The devicehas elongated source, drain and gate structures (typically of theorder of several micrometres) in order to ensure high-current

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Figure 7. Examples of sidewall graphene structures, showing AFM images (top rows) and EFM images (bottom rows). Top and bottomrows are of the same scale. The EFM images provide a bright contrast for graphene and a dark contrast for SiC, thereby providing a simplemethod to locate graphene-covered surfaces. (a) Sidewall graphene ribbons grown along bunched SiC step edges of steps due to the slightmiscut of the crystal. (b) Sidewall graphene growth along patterned SiC surface that was etched to a depth of 15 nm. Note the serpentinesidewall that was etched to provide for a wide lead (after annealing) for the narrow, straight ribbon segments, demonstrating the flexibility ofthe method. (c) Graphene ring supplied with leads. The original patterned SiC structure consisted of a circular SiC mesa connected to radialSiC walls. Graphene grown on the sidewall of the mesa produced the graphene ring and graphene grown on the walls produced the leads.HSQ was used as an etching mask. (d) Array of graphene nanoribbons. Narrow parallel grooves were patterned covering the entire SiCchip. More than 30% of the surface is covered with graphene ribbons. The SiC etching depth was 150 nm and photolithography was used toproduce the Ni etching mask.

operation. The other dimensions are optimized for high-frequency performance. In particular, the channel is ideallyshort and the contact resistances are ideally low [10, 13].Parasitic capacitances between the various components aredesigned to be as small as possible. While the highestfrequency operation of graphene-based transistors has beenslowly inching up, the current goal of THz operation hasnot yet been achieved. However, the problems appear to beprimarily technical and surmountable [38]. While epitaxialgraphene as a viable channel material for THz applicationshas been established, there are still considerable problems inproviding low-resistance leads, which determine the accessresistance. This may be surprising since, from figure 5(c), theconductivity of (doped) graphene (≈10 µ� cm) is comparableto that of copper at room temperature. Nevertheless, theminimum resistance of a graphene lead (the so-called access

resistance) is of the order of a few hundred ohms per squareso that, for example, the source lead with a length-to-widthaspect ratio of 10 to 1 has a resistance of several k�. This canbe reduced by cladding the graphene with a metal; however,the metal to graphene resistance is also large. Currently,the minimum access resistance reported is about 350 � permicrometre of channel width [12]. This is still very large forTHz applications.

4. Structured growth on the Si face

Graphene is known to nucleate at step edges, and growthrates are known to depend on the crystal face. Growth isconsiderably slower on the Si-face than on the C-face. Thesefacts are advantageously used in the structured growth method(also called the templated growth method [29]) where the

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silicon carbide surface is first etched to produce steps. Duringthe high-temperature annealing using the CCS method, theetched steps crystallize and a graphene film forms on them.The growth times and temperatures are adjusted so that amonolayer graphene film forms only on the step edges andnot (or minimally) on the (0 0 0 1) surfaces.

High-temperature annealing causes vertically etched steps(on the order of 10 nm deep) to produce (1–10n) facets witha normal that has an angle of 23◦ with respect to the {0 0 0 1}direction.

Cross-sectional, high-resolution transmission electronmicroscopy of graphene on steps on SiC by Norimatsu et al [39]has shown that the graphene terminates perpendicular to thesilicon carbide surface both on the bottom of the step or on thesteps themselves. This effect has also been observed usingscanning tunnelling microscopy on small graphene islandson (0 0 0 1) SiC [26]. Moreover, these atomic resolutionstudies further show that the graphene edges are along thezigzag direction, indicating that the graphene sidewall ribbonsare zigzag ribbons. This is very important since the edgestructure determines the electronic properties of the ribbons.In particular, zigzag ribbons are always metallic [17].

As noted by Kusunoki et al [40], the zigzag nature of thegraphene edges is further confirmed by the electron diffractionimages of carbon nanotubes grown on SiC, which are alwaysof the zigzag variety, which indicates that they terminate with azigzag edge on the silicon carbide surface. This very importantobservation that sidewall graphene ribbons have zigzag edgesthat terminate in silicon carbide has profound implications forgraphene nanoelectronics. For one thing, this implies thatthe edges are passivated and well defined, that is, they donot possess the chemical reactivity and structural disorder oflithographically patterned graphene structures.

The procedure to produce sidewall graphene structures isoutlined next (see also figure 7). The Si-face of 4H (or 6H)SiC is lithographically patterned using standard lithographymethods to produce an etch mask (using, for example, alithographic resist such as PMMA) on the surface. The maskedsurface is then subjected to a plasma etch (typically with SF6)to etch the desired pattern to a predetermined depth into thesurface. This procedure can be repeated several times toproduce structures with varying depths. Alternatively, wideribbons can be produced by fusing narrower ribbons, as shownin figure 7(b). The resulting structure is then annealed usingthe CCS method [22] at a temperature of about 1550 ◦C forabout 10 min, which anneals the steps (typically produced onfacets where n ranges from 1 for shallow trenches to about10 for deep ones) with typically a monolayer of graphene onthe steps. Next, if desired, gate structures can be patterned ontop of the sidewall ribbons in the usual way. It is occasionallydesirable to etch away spurious graphene ribbons that haveformed on the sidewalls of the steps on the substrate that areinevitably present due to the slight miscut of the original crystal(figure 7(a)). However, judicious choice of the orientation ofthe patterned structure with respect to the miscut minimizesthis problem.

Figure 7 shows several examples of several sidewallgraphene structures produced by this method to demonstrate

Figure 8. Examples of structured graphene nanoribbon andconnection for four-probe measurement. (a) AFM image ofU-shaped deep trenches connecting a shallow trench overlappedwith EFM of a Hall bar structure. (b)–(d) Zoom on the shallowtrench. (b) AFM image after SiC patterning, (c) AFM image aftersubsequent graphitization, showing the rounding of the trench due toSiC step flow at high temperatures, (d) EFM image of (c) showingtwo nanoribbons grown on the side wall of the trench; from [29].

its effectiveness. Atomic force microscopy (AFM)images present the topography, while electrostatic forcemicroscopy (EFM) images provide a characteristic contrastthat distinguishes graphene from silicon carbide (figure 7).

Narrow graphene ribbons are particularly importantfor graphene-based nanoelectronics. As mentioned above,sidewall ribbons are expected to have zigzag edges, whichwe find are (always) metallic. It should be noted that, incontrast, all graphene ribbons produced to date using standardlithography methods are found to be semiconducting, i.e. havea transport gap at a low temperature or close to the chargeneutrality point. This is actually not expected since grapheneribbons are generally expected to be metallic [17] (the onlyexception being specific graphene ribbons with armchair edgesmentioned above). It is now generally accepted that thebandgaps observed in narrow graphene ribbons produced bystandard lithography methods are in fact mobility gaps causedby the rough edges [6–8, 19]. In contrast, all of the gatedsidewall graphene ribbons produced by the methods outlinedhere are metallic, consistent with expectations. Moreover,we have observed that a majority of these sidewall ribbonsshow evidence of (quasi) ballistic transport involving a singleconducting channel with mean free paths on the order of 1 µm,which is significantly greater than the typical mean free pathin 2D graphene. The narrow graphene ribbons produced forthese studies are produced as follows (see figure 8).

Two opposing deep (>100 nm) U-shaped trenches are firstetched. Subsequently a narrow (∼10 nm) trench is etched,connecting the U trenches (figure 8(a)). After CCS thermalannealing, the sidewalls of the U trenches form broad grapheneleads for the two narrow graphene sidewall ribbons between

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J. Phys. D: Appl. Phys. 45 (2012) 154010 Y Hu et al

Figure 9. Examples of structured graphene and their electronic properties. (a) 3D AFM topology image overlapped with EFM of a Hall barstructure. Bright area on the sidewalls shows where graphene has formed. (b) SEM image of the Hall bar in (a) after contact pads (light greysquares) were patterned. (c) VCD versus IAB measurements at various temperatures of the structure in (b) showing ohmic behaviour at roomtemperature and non-linear behaviour at low temperatures. (d) Shubnikov–de Haas oscillations observed of the sidewall Hall bar shownin the lower inset. The magnetic field is at 23◦ from the normal of the SiC (0001) surface and approximately perpendicular to thesidewall ribbon. (Upper inset) Landau plot of the peak positions from which the carrier density is determined to be 5.1 × 1012 cm−2.(e) Magnetoresistance oscillations of the 7.1 µm diameter sidewall ring structure shown in (f ) (inset). (f ) Fourier transform of (e) showingdistinct maxima. The arrows indicate the positions where Aharonov–Bohm quantum interference maxima (fundamental and overtones) areexpected.

the U’s. Metal contacts provided to the graphene leadsallow for four-point transport measurements of the grapheneribbon. Figure 8 provides some details of the production andcharacterization methods used. Specifically, as shown, theEFM resolution is of 30 nm, which is considerably greaterthan that of Raman (with about 1 µm resolution) for detectinggraphene nanostructures. Moreover, the EFM method canbe improved by modelling the tip to graphene interaction, toprovide a resolution of 10 nm.

While structured graphene is most suited for graphenenanostructures, it can also be used for Hall bars and othermicrometre-sized devices. An example is shown in figure 9where a graphene ribbon that is about 1 µm wide and severalmicrometres long is connected to six leads in the Hall barconfiguration for transport measurements. For this sample,a distinct anomalous diode-like effect is observed in thisribbon when the resistance is measured between two opposing

electrodes, as shown in figure 9(c). Ideally, the resistance (inthe absence of a magnetic field) is expected to be zero; however,a significant resistance is obtained. This normally indicates amisalignment of the voltage contacts. However, the diode-likebehaviour signifies that non-linear effects play a role. Notethat at 4 K, the resistance even changes sign. Similar non-linear properties are seen in nanoscopic phase coherent ballisticjunctions and it is expected that coherent transport plays arole in this case as well. This interpretation is fortified by theobservation that the anomalous behaviour vanishes at roomtemperature, which is consistent with expected reduction inthe phase coherence length (to <20 nm) at room temperature.As expected, this wide sidewall Hall bar presents regularShubnikov–de Haas oscillations, like other micrometre-sizedpatterned ribbons [4] (figure 9(d)). The position of theresistance maxima in field (Landau plot), see figure 9(d), isa straight line from which the carrier density is determined to

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be nS = 5.1 × 1012 cm−2. The magnetic field was tilted at 23◦

from the normal of the SiC (0 0 0 1) surface to be approximatelyperpendicular to the sidewall ribbon.

Patterned sidewall rings connected to wide ribbons thatserve as contact probes show distinct magnetoresistanceoscillations, as shown in figure 9(e). The Fourier transform(figure 9(f )) reveals the regularity of the oscillations.The arrows indicate the positions where Aharonov–Bohmquantum interference maxima (fundamental and overtones) areexpected. This clearly indicates that phase coherence lengthis of the order of the size of the ring.

5. Conclusion

We have presented recent results on a variety of patternedgraphene structures, on both carbon- and silicon-terminatedfaces of hexagonal silicon carbide. We have demonstratedthat structured graphene growth is a powerful and flexiblemethod to control the shapes of graphene structures andthat a wide variety of structures can be produced both forfundamental studies as well as for applications. It presentsan important step towards the realization of high-mobilityquasi-one-dimensional graphene structures that do not sufferfrom the strong localization effects observed in conventionallypatterned graphene structures, which all but obviate graphene’sadvantages at the nanoscale.

Acknowledgments

This research was supported by the W M Keck Foundation,the Partner University Fund from the Embassy of France,the AFSOR grant No FA 9550-10-1-0367 and the NSFMRSEC Program under Grant No DMR-0820382. Theauthors thank E Conrad, M Kindermann and Z G Jiangfor insightful discussions and John Cressler, Partha SarathiChakraborty and Nelson Lourenco for the high-frequencytransport measurements.

References

[1] Berger C et al 2004 Ultrathin epitaxial graphite: 2D electrongas properties and a route toward graphene-basednanoelectronics J. Phys. Chem. B 108 19912

[2] Park S and Ruoff R S 2009 Chemical methods for theproduction of graphenes Nature Nanotechnol. 4 217

[3] Li X et al 2009 Large-area synthesis of high-quality anduniform graphene films on copper foils Science 324 1312

[4] Berger C et al 2006 Electronic confinement and coherence inpatterned epitaxial graphene Science 312 1191

[5] Han M Y, Ozyilmaz B, Zhang Y and Kim P 2007 Energyband-gap engineering of graphene nanoribbons Phys. Rev.Lett. 98 206805

[6] Oostinga J B, Sacepe B, Craciun M F and Morpurgo A F 2010Magnetotransport through graphene nanoribbons Phys. Rev.B 81 193408

[7] Stampfer C, Gutttinger J, Hellmueller S, Molitor F, Ensslin Kand Ihn T 2009 Energy gaps in etched graphenenanoribbons Phys. Rev. Lett. 102 056403

[8] Gallagher P, Todd K and Goldhaber-Gordon D 2010Disorder-induced gap behavior in graphene nanoribbonsPhys. Rev. B 81 115409

[9] Palma C-A and Samorı P 2011 Blueprinting macromolecularelectronics Nature Chem. 3 431

[10] Schwierz F 2010 Graphene transistors Nature Nanotechnol.5 487

[11] Liao L, Lin Y-C, Bao M, Cheng R, Bai J, Liu Y, Qu Y,Wang K L, Huang Y and Duan X 2010 High-speedgraphene transistors with a self-aligned nanowire gateNature 467 305

[12] Lin Y-M F, Farmer D B, Jenkins K A, Wu Y, Tedesco J L,Myers-Ward R L E, Eddy C R Jr, Gaskill D K,Dimitrakopoulos C and Avouris P 2011 Enhancedperformance in epitaxial graphene FETs with optimizedchannel morphology IEEE Electron Device Lett. 32 1343

[13] Krithivasan R, Lu Y, Cressler J D, Rieh J S, Khater M H,Ahlgren D and Freeman G 2006 Half-terahertz operation ofSiGeHBTs IEEE Electron Device Lett. 27 567

[14] Janssen T J B M, Tzalenchuk A, Yakimova R, Kubatkin S,Lara-Avila S, Kopylov S and Fal’ko V I 2011 Anomalouslystrong pinning of the filling factor ν = 2 in epitaxialgraphene Phys. Rev. B 83 233402

[15] Nakada K, Fujita M, Dresselhaus G and Dresselhaus M S 1996Edge state in graphene ribbons: nanometer size effect andedge shape dependence Phys. Rev. B 54 17954

[16] Wakabayashi K, Fujita M, Ajiki H and Sigrist M 1999Electronic and magnetic properties of nanographite ribbonsPhys. Rev. B 59 8271

[17] Wakabayashi K, Takane Y, Yamamoto M and Sigrist M 2009Edge effect on electronic transport properties of graphenenanoribbons and presence of perfectly conducting channelCarbon 47 124

[18] Son Y W, Cohen M L and Louie S G 2006 Energy gaps ingraphene nanoribbons Phys. Rev. Lett. 97 089901

[19] Han M Y, Brant J C and Kim P 2010 Electron transport indisordered graphene nanoribbons Phys. Rev. Lett.104 056801

[20] Fukidome H, Miyamoto Y, Handa H, Saito E and Suemitsu M2010 Epitaxial growth processes of graphene on siliconsubstrates Japan. J. Appl. Phys. 49 01AH03

[21] Hass J, Millan-Otoya J E, First P N and Conrad E H 2008Interface structure of epitaxial graphene grown on4H-SiC(0001) Phys. Rev. B 78 205424

[22] de Heer W A, Berger C, Ruan M, Sprinkle M, Li X, Hu Y,Zhang B, Hankinson J and Conrad E H 2011 Large area andstructured epitaxial graphene produced by confinementcontrolled sublimation of silicon carbide Proc. Natl Acad.Sci. USA 108 16900

[23] Emtsev K V et al 2009 Towards wafer-size graphene layers byatmospheric pressure graphitization of silicon carbideNature Mater. 8 203

[24] Ohta T, Bartelt N C, Nie S, Thurmer K and Kellogg G L 2010Role of carbon surface diffusion on the growth of epitaxialgraphene on SiC Phys. Rev. B 81 121411R

[25] Rohrl J, Hundhausen M, Emtsev K V, Seyller T, Graupner Rand Ley L 2008 Raman spectra of epitaxial graphene onSiC(0001) Appl. Phys. Lett. 92 201918

[26] Tiberj A et al 2011 Multiscale investigation of graphene layerson 6H-SiC(000-1) Nano Scale Res. Lett. 6 171

[27] Robinson J A, LaBella M, Trumbull K A, Weng X J,Cavelero R, Daniels T, Hughes Z, Hollander M, Fanton Mand Snyder D 2010 Epitaxial graphene materialsintegration: effects of dielectric overlayers on structural andelectronic properties ACS Nano 4 2667

[28] Waldmann D, Jobst J, Speck F, Seyller T, Krieger M andWeber H B 2011 Bottom-gated epitaxial graphene NatureMater. 10 357

[29] Sprinkle M, Ruan M, Hu Y, Hankinson J, Rubio-Roy M,Zhang B, Wu X, Berger C and de Heer W A 2010 Scalabletemplated growth of graphene nanoribbons on SiC NatureNanotechnol. 5 727

11

J. Phys. D: Appl. Phys. 45 (2012) 154010 Y Hu et al

[30] de Heer W A et al 2010 Epitaxial graphene electronicstructure and transport J. Phys. D: Appl. Phys.43 374007

[31] Faugeras C, Nerriere A, Potemski M, Mahmood A,Dujardin E, Berger C and de Heer W A 2008 Few-layergraphene on SiC, pyrolitic graphite, and graphene: a Ramanscattering study Appl. Phys. Lett. 92 011914

[32] Ferrari A C et al 2006 Raman spectrum of graphene andgraphene layers Phys. Rev. Lett. 97 187401

[33] Das A et al 2008 Monitoring dopants by Raman scattering inan electrochemically top-gated graphene transistor NatureNanotechnol. 3 211

[34] Wu X S, Hu Y K, Ruan M, Madiomanana N K, Hankinson J,Sprinkle M, Berger C and de Heer W A 2009 Half integerquantum Hall effect in high mobility single layer epitaxialgraphene Appl. Phys. Lett. 95 223108

[35] Chen J H, Jang C, Adam S, Fuhrer M S, Williams E D andIshigami M 2008 Charged-impurity scattering in grapheneNature Phys. 4 377

[36] Orlita M, Faugeras C, Plochocka P, Neugebauer P, Martinez G,Maude D K, Barra A L, Sprinkle M, Berger C, de Heer W A

and Potemski M 2008 Approaching the Dirac point inhigh-mobility multilayer epitaxial graphene Phys. Rev. Lett.101 267601

[37] Farmer D B, Chiu H Y, Lin Y M, Jenkins K A, Xia F N andAvouris P 2009 Utilization of a buffered dielectric toachieve high field-effect carrier mobility in graphenetransistors Nano Lett. 9 4474

[38] Liao L, Bai J W, Cheng R, Lin Y C, Jiang S, Qu Y Q, Huang Yand Duan X F 2010 Sub-100 nm channel length graphenetransistors Nano Lett. 10 3952

[39] Norimatsu W and Kusunoki M 2010 Formation process ofgraphene on SiC (0 0 0 1) Physica E 42 691

[40] Kusunoki M, Suzuki T, Honjo C, Hirayama T and Shibata N2002 Selective synthesis of zigzag-type aligned carbonnanotubes on SiC (0 0 0 −1) wafers Chem. Phys. Lett.366 458

[41] Orlita M, Faugeras C, Grill R, Wysmolek A, Strupinski W,Berger C, de Heer W A, Martinez G and Potemski M 2011Carrier scattering from dynamical magneto-conductivity inquasi-neutral epitaxial graphene Phys. Rev. Lett. at press(arXiv:1101.0848)

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