Direct oriented growth of armchair graphene nanoribbons on germanium

Graphene can be transformed from a semimetal into a semiconductor if it is confined into nanoribbons narrower than 10 nm with controlled crystallographic orientation and well-defined armchair edges. However, the scalable synthesis of nanoribbons with this precision directly on insulating or semiconducting substrates has not been possible. Here we demonstrate the synthesis of graphene nanoribbons on Ge(001) via chemical vapour deposition. The nanoribbons are self-aligning 3° from the Ge〈110〉 directions, are self-defining with predominantly smooth armchair edges, and have tunable width to <10 nm and aspect ratio to >70. In order to realize highly anisotropic ribbons, it is critical to operate in a regime in which the growth rate in the width direction is especially slow, <5 nm h−1. This directional and anisotropic growth enables nanoribbon fabrication directly on conventional semiconductor wafer platforms and, therefore, promises to allow the integration of nanoribbons into future hybrid integrated circuits.

G raphene nanoribbons are excellent charge 1 and thermal 2 conductors that can exhibit high current-carrying capacity 3 and novel magnetic and spin-polarized edge states 4-6 depending on their crystallographic orientation, edge structure and width. Unlike continuous two-dimensional graphene, which is semimetallic, one-dimensional (1D) graphene nanoribbons can be semiconducting, allowing for substantial modulation of their conductance and enabling their application in semiconductor logic, high-frequency communication devices, optoelectronics, photonics and sensors in which a bandgap is needed to achieve high performance. Their bandgap roughly varies inversely with ribbon width and the largest bandgaps are expected for ribbons with armchair edge orientation 7 .
While achieving a ribbon width of o10 nm is necessary to induce a technologically relevant bandgap that is substantially greater than k B T of 25 meV at room temperature 5,7 , sub-10 nm resolution is beyond the limits of conventional optical and electron-beam lithography. Moreover, top-down lithographic techniques in which ribbons are etched from continuous graphene sheets result in nanostructures with relatively rough, defective edges, which lead to Coulomb blockade 8 and localized electronic 9,10 and phonon states 11 and, consequently, degrade the high charge carrier mobility [12][13][14] and thermal conductivity 2 of graphene.
These deficiencies, in part, can be overcome, via bottom-up organic synthesis on metal surfaces [15][16][17] and in solution 18,19 as well as by unzipping graphite 20 and carbon nanotubes 21 in solution, to yield ribbons with sub-10 nm width and smooth edges. However, surface-assisted organic synthesis yields short ribbons (B20 nm) and unzipping graphite and carbon nanotubes does not offer control over the ribbon crystallographic orientation. Moreover, the controlled placement and alignment of ribbons onto substrates from solution has proven to be difficult.
Scalable nanoribbon fabrication has also been reported via epitaxial growth on templated SiC nanofacets 22 and by chemical vapour deposition (CVD) on surface features, such as steps 23 , twins 24 and trenches 25 , as well as on patterned catalysts in which growth is confined to predetermined areas that define the ribbon dimensions [26][27][28][29] . However, with these approaches, ribbons with sub-10 nm width have not been demonstrated and the catalyst template determines the ribbon edge structure rather than a more precise self-defining growth mechanism.
Here we show that the CVD of graphene on Ge(001) can be controlled to yield oriented nanoribbons with sub-10 nm width and smooth armchair edges. Previous work on integrating graphene with Ge has primarily focused on large-area graphene monolayers. For example, continuous graphene films have been transferred onto Ge from other substrates 30,31 . Furthermore, continuous graphene monolayers have been grown via CVD directly on Ge(001) by Wang et al. 32 and Ge(110) and Ge(111) by Lee et al. 33 . However, in these previous studies, nanoribbons were not observed in partial growth experiments. In this work, we report that high aspect ratio nanoribbons can be directly grown on the Ge(001) facet by tailoring the CVD conditions to maximize the anisotropy of crystal growth. It is critical to operate in a regime in which the growth rate is especially slow, o5 nm h À 1 in the width direction. Nanoribbons are grown at atmospheric pressure using various growth temperatures (860oTo935°C), CH 4 mole fractions (3.7 Â 10 À 3 ox CH4 o1.6 Â 10 À 2 ), and H 2 mole fractions (0.17ox H 2 o0.33), as summarized in Supplementary Table 1. By tuning T, x CH4 , x H2 and the growth time (t), the growth anisotropy is tailored to yield ribbons from the bottom-up with controlled width (w), length (l) and aspect ratio. Using conditions in which the anisotropy is maximized, isolated ribbons are prevalent on the Ge(001) surface even after t418 h. In contrast, Wang et al. 32 used a relatively fast growth rate in which continuous graphene films were synthesized on Ge(001) in to100 min.

Results
Growth behaviour. Several general observations are made regarding graphene growth on Ge(001) by analysing representative scanning electron microscopy (SEM), atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) images in Fig. 1a-c. Following nucleation, graphene crystals evolve anisotropically, resulting in nanoribbons with high aspect ratio [110] [110]  Horizontal lines in the boxes define the 25th, 50th and 75th percentiles, whiskers indicate the 5th and 95th percentiles, circles define the range and squares give the mean. Insets of (d,e) are the mean R w and R l , respectively, plotted against t. (g) Histogram of w from the 1 h growth in d-f. The ribbons in a,c are synthesized at 910°C with x CH4 of 0.0092 and x H2 of 0.33 for 2 and 1.5 h, respectively, whereas the ribbons in b are grown at 910°C with x CH4 of 0.0066 and x H2 of 0.28 for 4 h. The ribbons in d-g are synthesized with the same parameters as a,c but t is varied between 1 and 14 h. and smooth, straight edges. Raman spectroscopy indicates that the 2D:G ratio and the 2D peak full-width-at-half-maximum are 6.0 and 28 cm À 1 , respectively, confirming that the nanoribbons are monolayer graphene 34 ( Supplementary Fig. 1). The ribbons preferentially orient closely along the h110i directions of the Ge(001) template, resulting in two ribbon orientations that are approximately perpendicularly aligned. These two orientations exist with equal probability. For ribbons with wo10 nm, the short ribbon edges form 60, 90 or 120°angles with the long ribbon edges. However, for wider ribbons, only angles of 60 and 120°are observed, indicating that all edges are oriented along equivalent crystallographic directions of graphene. While as high as 90% of the graphene crystals that nucleate evolve as ribbons, more compact graphene crystals with lower aspect ratio and edges that are not aligned along Geh110i directions are also observed. Interestingly, the Ge underneath the ribbons is nanofaceted, which is studied further below.
Growth kinetics and evolution. We quantify the growth kinetics to gain insight into the processes that determine the ribbon size and aspect ratio using constant T of 910°C, x CH4 of 0.0092 and x H 2 of 0.33. Both w and l increase with t, along with the ribbonto-ribbon variation in w and l, which is quantified by the range of the box and whiskers in Fig. 1d,e. The mean growth rates in the w and l directions, R w and R l , respectively, are compared in the insets of Fig. 1d,e (where w and l increase on average at twice R w and R l ). Initially, R l is 90 nm h À 1 whereas R w is only 5 nm h À 1 , giving rise to the anisotropic ribbon evolution. While R l is relatively constant with time, R w increases to 410 nm h À 1 after several hours. Accordingly, the mean aspect ratio decreases from 20 to 10 with increasing t (Fig. 1f). Stopping growth after t of 1 h results in ribbons with average w of 9.8 nm (Fig. 1g), which is below the resolution of optical and typical electron-beam lithography, and we anticipate that even narrower w are obtained at earlier t. Figure 1c shows an example of a nanoribbon with w of 7 nm and l of 160 nm. The effects of x CH4 , x H2 and T on the nanoribbon growth rate and the resulting anisotropy are also quantified. The growth rates increase as x CH4 increases (Fig. 2a), x H2 decreases (Fig. 2b), and T increases ( Supplementary Fig. 2). Each of these parameters can be independently tuned to vary R l over an order of magnitude from 30 to 300 nm h À 1 . The anisotropy varies inversely with R l , independent of whether x CH 4 or x H 2 is changed (Fig. 2c). Thus, a critical parameter for realizing high aspect ratio nanoribbons is to operate in a regime in which growth is slow. For example, at low x CH4 of 0.0066 and high x H2 of 0.33, not only is a slow R l of 40 nm h À 1 achieved, but also a much slower R w of 1.4 nm h À 1 , yielding ribbons with an aspect ratio of 30, on average, and as high as 70 ( Supplementary Fig. 3). Minimizing R w also makes it possible to tailor w with high precision. Empirical rate laws are identified (insets of Fig. 2a, . Furthermore, an Arrhenius temperature dependence is observed with an activation energy of 7.2 ± 0.4 eV ( Supplementary Fig. 2). For comparison, the activation energy for graphene growth on Cu is only 1-3 eV (ref. 35). However, graphene growth on Cu at atmospheric pressure yields hexagonal crystals instead of nanoribbons 36 , highlighting that different mechanisms control growth.
We also find that the 1D nature of growth is insensitive to the bulk Ge dopant concentration (N Sb o1.5 Â 10 18  ½ directions. The LEED pattern in Fig. 3b obtained at 67 eV shows that the graphene lattice primarily exists within two families of crystallographic orientations, denoted by the orange and purple hexagons. Dark-field imaging in Fig. 3c indicates that the purple family of diffraction spots originates from ribbons that are oriented with their long axis approximately parallel to Ge[110] whereas the orange family of spots originates from ribbons that are oriented with their long axis approximately parallel to Ge 110 ½ . Both of these families of ribbons have edges that are macroscopically aligned with the armchair direction of graphene. This armchair edge orientation is unique because graphene crystals grown on Cu and Ni typically have edges that are aligned along the zigzag direction of graphene 25,37 . Within each family, there are two unique graphene orientations that are rotated 2.9 ± 0.4°(B3°) relative to the Geh110i directions, as indicated by the diffraction spots belonging to the orange family that are circled in red and blue in Fig. 3b. These nanoribbon orientations are depicted in Fig. 3d. Dark-field imaging in Fig. 3c indicates that some of the ribbons are single crystalline, corresponding to either the þ 3°or À 3°graphene orientation, whereas others are bi-crystalline, in which the crystal lattice of one half of the ribbon is rotated by 2 Â 3°¼ 6°with respect to the other half. This indicates that the nanoribbons nucleate in their centre and then grow in opposite directions along their length. These dynamics potentially explain why the ribbons are elevated in their centre (Fig. 1c); the sublimation of Ge may be locally suppressed under the ribbons as they grow. Interestingly, the lattice of the non-ribbon graphene crystals with lower aspect ratio and edges not aligned on Geh110i, like the one observed in Fig. 1a, is rotated with respect to the lattice of the nanoribbons, typically by 15°as observed in Fig. 3b. This difference indicates that the anisotropic nanoribbon growth is driven only when there is a specific relative orientation between the graphene lattice and the Ge(001) surface.
Scanning tunneling microscopy. Ultra-high vacuum STM is performed to substantiate the LEED data and to determine the atomic nature of the graphene nanoribbon edges on Ge(001). The STM image and its corresponding fast Fourier transform (FFT) in Fig. 4a indicate that the ribbon edges are straight and parallel to the armchair direction of graphene with little edge roughness and that the graphene lattice is rotated 3°from the Geh110i directions, consistent with the LEED data. The Ge underneath the nanoribbons retains the common (2 Â 1) dimer reconstruction ( Fig. 4b-d) even after ambient exposure. Contamination of the bare Ge surface upon exposure to ambient often precludes precise topographical imaging of the nanoribbon edge structure. Using the topographic data alone, we can set an upper limit on the edge roughness. For example, the representative 40 nm ribbon segment in Fig. 4a has roughness of o0.5 nm (two lattice constants of graphene). However, we can learn more about the edge structure from quantum interference patterns caused by intervalley backscattering (Fig. 4e) of charge carriers at the ribbon edges. The ring-like shapes with a ffiffi ffi 3 p Â ffiffi ffi 3 p À Á R30°unit cell highlighted with the rhombuses in Fig. 4g and the armchair-like patterns with periodicity (l f ) of 3.7 Å in Fig. 4g are consistent with electron backscattering at armchair edges 16,38 and are clearly revealed by the prominence of the K/K 0 points in the FFT in Fig. 4f. The presence of these coherent interference patterns combined with the small line edge roughness indicates that the edges consist primarily of smooth armchair segments. The interference patterns decay into the interior of the ribbons with length scales comparable to graphene on SiC 38 and metals 39 . The atomic structure of the hexagonal graphene lattice is observed past these decay lengths in the interior of the nanoribbons (Fig. 4g).
Scanning tunneling spectroscopy (STS) is used to probe the electronic density of states of nine nanoribbons with w ranging from 5 to 19 nm ( Supplementary Figs 8-9 and Supplementary Discussion). While it is difficult to make conclusive deductions about the bandgaps from the tunneling spectra due to thermal broadening and tunneling into Ge surface states, the spectra are consistent with those previously reported for semiconducting graphene nanostructures 16,17,40,41 , with suppressed density of states near the Fermi level compared with continuous monolayer graphene on Ge and with the possible development of band edges.
Charge transport measurements. Charge transport measurements are conducted to investigate the electrical properties of 33 nanoribbons using a field-effect transistor geometry (Fig. 5). The ribbons are relatively wide (w410 nm), because these ribbons are more conducive to transfer onto insulating SiO 2 /Si wafers (Fig. 5e). Transfer is required to measure the electrical properties of the ribbons independent of parallel conduction pathways through the Ge substrates used for growth.
The magnitude of the ribbon conductance modulation caused by varying an applied back-gate voltage (that is, the on/off ratio) generally increases as w is reduced below 15 nm (Fig. 5a,d), consistent with the opening of a bandgap that scales inversely with w. The on/off ratios are comparable to those of high-quality chemically exfoliated nanoribbons of similar w (for example, on/off of B1, B5 and B100 have been demonstrated for w of B50, B20 and B10 nm, respectively) 20 . However, the largest gains in on/off ratio are not expected until w is reduced to 3-5 nm.
The on-state conductance (Fig. 5b) and transconductance (Fig. 5c), normalized by w, are not correlated with w and, thus, do not generally deteriorate as w is decreased. The nanoribbon channel resistance and the Pd-nanoribbon contact resistance are not separately quantified. However, the on-state conductance is high (generally ranging from 500 to 5,000 mS mm À 1 ) and the on-state resistance (average of B700 O mm) is similar to literature values for Pd-graphene contact resistance (150-1,640 O mm) [42][43][44][45][46][47][48][49] . Therefore, the data suggest that at the relatively short channel length used here of o220 nm, charge transport is not limited by edge scattering or by channel resistance, but instead by the Pd-nanoribbon contacts. The variability in the on-state conductance (Fig. 5b) and the transconductance (Fig. 5c) data  Characterization of the graphene/germanium interface. As growth progresses, the ribbons eventually merge to form a continuous graphene film that is self-limiting to a monolayer. We analyse these continuous films to characterize the graphene/Ge interface and the Ge nanofaceting beneath graphene. The films have negligible Raman D-band intensity ( Supplementary Fig. 10), indicating an sp 2 graphene lattice with low defect density and a relatively weak graphene/Ge interaction. Similar to graphene on Ge(110) and Ge(111) 33 , the continuous films can be peeled off of the Ge(001) surface using a thin Au layer, indicating that the interaction strength is o60 meV (ref. 50). This weak interaction is consistent with the STM data, which show that the underlying Ge(2 Â 1) reconstruction is unaffected by the ribbons (Fig. 4b-d) and that the quantum interference patterns near the ribbon edges are not disrupted by the substrate (Fig. 4f,g).
Raman spectroscopy shows that the graphene films on Ge(001) are stable in ambient conditions, even at 200°C for 424 h, and X-ray photoelectron spectroscopy (XPS) indicates that the underlying Ge(001) remains unoxidized in ambient conditions for 44 weeks after growth (Supplementary Fig. 10). Thus, the direct synthesis of nanoribbons on Ge(001) yields a pristine nanoribbon/substrate interface compared to that of ribbons deposited from solution or transferred from another surface, during which disorder and impurities are introduced.
Germanium nanofacet formation. As previously observed in Figs 1b,c and 4a, the Ge surface selectively forms nanofacets underneath the nanoribbons. These hill-and-valley structures are similar to surface faceting that has been observed for other combinations of surfaces and adsorbates 51 . These facets are more easily visualized and characterized below continuous graphene films (Fig. 6a). The facet angle (Fig. 6b inset) is shallow for thin ribbons and becomes steeper as the ribbons grow wider and eventually merge to form a continuous graphene film. Underneath continuous films, the angle measured via AFM (Fig. 6b), LEED (Fig. 6c) and X-ray reflectivity (XRR; Supplementary Methods) is 8.1 ± 1.1°, 8.5 ± 1.0°and 7.8 ± 1.1°, respectively, which is consistent with the Ge(107) facet. Interestingly, the faceting below the nanoribbons is reversible upon annealing at 800°C in high vacuum, resulting in a planar interface ( Supplementary Fig. 11).

Discussion
Our experimental data, which show that growth is anisotropic only when the armchair direction of graphene is rotated 3°from the Geh110i directions, provide insight into the mechanisms governing the 1D nature of growth. It is likely that this crystallographic relationship is set during the early stages of nucleation; as the graphene nucleus becomes larger, the energy barrier associated with its rotation significantly increases, which, consequently, fixes the orientation of the nanoribbon lattice during the subsequent growth 52 . The Ge(001) surface consists of two types of terraces that have the same structure but are rotated 90°with respect to each other. It is plausible that on one set of terraces, the armchair direction of the graphene nuclei is rotated 3°from Ge[110] and on the other set of terraces, the armchair direction is rotated 3°from Ge 110 ½ , giving rise to the two families of orientations observed in the LEED and STM data. Nucleation does not seem to be strongly correlated with the density or directionality of steps that exist before nucleation ( Supplementary Figs 12-14 and Supplementary Discussion).
After nucleation, several factors could drive anisotropic ribbon evolution. While step edges may play a role in setting the crystallographic orientation of the nuclei on each terrace, subsequent preferential growth along step edges cannot solely account for the formation of ribbons with smooth edges over long segments. Furthermore, we do not observe residual nanoparticles at the ribbon ends or tapered ribbon growth that might indicate that the ribbon evolution is driven by a catalyst particle like in conventional nanowire growth 53 . Anisotropic diffusion of intermediate hydrocarbons on the Ge surface cannot alone account for the ribbon evolution because low aspect ratio crystals are also observed.
We hypothesize that the anisotropic growth is due to preferential attachment of intermediate hydrocarbons from the Ge surface to the short (faster growing) ribbon edges over the long (slower growing) ribbon edges, which is consistent with the observation that the low aspect ratio crystals have different lattice orientation than that of the nanoribbons. During attachment, the transition state and the corresponding energy barrier will depend on the relative orientation between the nanoribbon edge and the Ge surface. Similar growth phenomena, such as the formation of polygonal graphene crystals with relatively straight edges and sharp vertices 54 and the synthesis of other 1D structures on the (001) face of zinc-blende semiconductors [55][56][57] , have also been attributed to attachmentlimited kinetics. The increase in R w with time ( Fig. 1d) may indicate that the barrier for hydrocarbon attachment to the long (slower growing) ribbon edges decreases as w increases. R w begins to noticeably increase after w exceeds about 30 nm, potentially corresponding to when ribbons begin to outgrow the Ge terrace on which they nucleate. The Ge hill-and-valley structures increase in height and width as w increases; this evolution may also perturb the interactions of the nanoribbon edges with the underlying Ge and, thus, may also modify the attachment barrier. Several challenges in synthesis and fabrication have inhibited progress in nanoribbon research and development. Specifically, (1) the synthesis of nanoribbons with armchair edges, (2) the definition of nanoribbons with width o10 nm and (3) the direct integration of nanoribbons onto insulating or semiconducting platforms have been difficult. This work overcomes these challenges. We demonstrate that by controlling graphene synthesis on Ge(001) via CVD, it is possible to realize oriented nanoribbons with sub-10 nm width, controlled crystallographic orientation and smooth armchair edges. This direct, self-defining growth offers precise control over the ribbon structure beyond the fidelity of top-down lithography and yields a relatively pristine nanoribbon/substrate interface. The ribbons are self-aligning, and ribbons with wo10 nm can still be hundreds of nanometres in length, opening the door for exploration of dense nanoribbon arrays as logic, photonic and sensing components in integrated circuits. Improved control over the ribbon placement will enhance the viability of these applications. These results are also technologically important because they enable a scalable, high throughput pathway for integrating nanoribbons directly on conventional large-area semiconductor wafer platforms that are compatible with planar processing, like Ge wafers and potentially epitaxial Ge films on Si (ref. 33) or GaAs (ref. 58) wafers.

Methods
Graphene synthesis. Before growth, Ge(001) (Wafer World, resistivity 440 O cm, miscut o1°), Ge(110) (University Wafer, resistivity 0.1-0.5 O cm with Ga or Sb dopants) and Ge(111) (Semiconductor Wafer, resistivity 430 O cm) substrates are cleaned via sonication in acetone and isopropyl alcohol for 15 min followed by etching in deionized H 2 O (18 MO cm) at 90°C for 15 min. The Ge substrates are loaded into a horizontal tube furnace with a quartz tube inner diameter of 34 mm and the system is evacuated to B10 À 6 torr. The system is then filled to atmospheric pressure with a mixture of Ar (99.999%) and H 2 (99.999%) using a constant total flow rate of 300 s.c.c.m. The Ge samples are annealed for 30 min at the selected growth temperature and then CH 4 (99.99%) is introduced to begin the synthesis. In order to terminate growth, samples are rapidly cooled in the same atmosphere used during synthesis by sliding the furnace away from the growth region. Specific growth conditions are provided in Supplementary Table 1.
Graphene transfer. In order to transfer the ribbons from Ge to SiO 2 /Si for Raman spectroscopy and charge transport measurements, poly(methyl methacrylate) (PMMA) is spin coated onto the graphene/Ge substrate. The PMMA/graphene/Ge stack is floated on a solution of 28:1:1 H 2 O:HF:H 2 O 2 to etch the Ge layer. The PMMA/graphene stack is transferred to H 2 O to clean the ribbons and then lifted out of the H 2 O using a SiO 2 /Si substrate. The PMMA is dissolved in acetone and the sample is washed with isopropyl alcohol.
Characterization. After growth, the samples are characterized with SEM (Zeiss LEO 1530) and AFM (Veeco MultiMode SPM) in tapping mode. For each nanoribbon synthesis, the w and l of B250 ribbons are measured from SEM images using ImageJ. Raman spectroscopy (Thermo Scientific DXRxi) in Supplementary  Fig. 1 is performed using excitation wavelength of 532 nm, power of 10 mW and spot size of 0.6 mm. Graphene degradation studies in Supplementary Fig. 10 are conducted with Raman spectroscopy (Horiba Jobin Yvon LabRAM Aramis) with excitation wavelength of 442 nm, power of 0.01 mW and spot size of 1 mm. XPS (Thermo Scientific K-Alpha) is performed with spot size of 30 mm and energy resolution of 0.57 eV. LEEM and LEED (SPECS Fe-LEEM/PEEM P90) are conducted using incident electron energies of B25 eV and between 19-135 eV, respectively. STM and STS (Omicron VT, base pressure of 10 À 12 mbar) are performed simultaneously at 300 K using electrochemically etched W tips. STS data is generated by superimposing a 30 mV modulation at 10 kHz on top of the bias voltage and analysing the tunnelling current with a SR830 Lock-In Amplifier. XRR measurements (Bruker D8 Discover with a VÅNTEC 500 Area Detector) are performed with a Cu Ka X-ray source.
Device fabrication. The nanoribbons are transferred onto SiO 2 /Si wafers as described, above. Electron-beam lithography is used to define source and drain electrodes with channel lengths between 75 and 220 nm. Thermal evaporation is used to deposit Pd electrodes 35 nm in thickness. The back-gate electrode and back-gate dielectric are the Si wafer and 15 nm of thermally grown SiO 2 , respectively. Each field-effect transistor is measured at room temperature in ambient conditions using a source voltage of À 0.1 V.