Electrical transport across metal/two-dimensional carbon junctions: Edge versus side contacts

Metal/two-dimensional carbon junctions are characterized by using a nanoprobe in an ultrahigh vacuum environment. Significant differences were found in bias voltage (V) dependence of differential conductance (dI/dV) between edge- and side-contact; the former exhibits a clear linear relationship (i.e., dI/dV \propto V), whereas the latter is characterized by a nonlinear dependence, dI/dV \propto V3/2. Theoretical calculations confirm the experimental results, which are due to the robust two-dimensional nature of the carbon materials under study. Our work demonstrates the importance of contact geometry in graphene-based electronic devices.


I. INTRODUCTION
An ideal graphene is a monatomic layer of carbon atoms arranged on a honeycomb lattice. This unique lattice structure leads to the formation of quasi-relativistic low-energy excitations near the K points at the corners of the first Brillouin zone; the quasi-particles are chiral and massless Dirac fermions with the electrons and holes degenerated at the Dirac points (or K points). [1][2][3][4][5] These unique electronic structures in turn give rise to a number of peculiar physical properties of graphene distinguishing it from conventional two-dimensional electron gas systems, some of which are desirable for high-frequency electronics applications. [6][7][8] Comparing to graphene itself, however, our understanding of metal (M) -graphene (G) contact is still far from complete, which may eventually limit the performance of graphene-based electronic devices. 9 Experimental and theoretical studies have shown that both the nature of atomic bonding at the metal-graphene interface and band structure of graphene near the Fermi level play crucial roles in determining the transport properties of M-G junctions. [9][10][11][12][13] Here, we demonstrate that, in addition to the type of contact materials and corresponding nature of atomic bonding between metal and graphene, the contact geometry, i.e., an edge-or side-contact, 14

II. EXPERIMENTS
also plays an important role in electron transport across the M-G junctions.
Compared to the side-contact, which is routinely employed for electrical transport measurement of graphene or graphene electronic devices, it remains a great challenge to form a pure edge-contact with graphene without touching its surface due to its ultra small thickness. In order to overcome this difficulty, in this work, we use a position-controllable nanoprobe to form edge-contacts with two different types of twodimensional (2D) carbons, both of which have free-standing edges above the substrate surface on which they are either grown or placed. The first type of 2D carbon is so-called carbon nanowalls (CNWs), 15,16 which are curved carbon nano-sheets grown almost vertically on flat substrates. Figure 1(a) shows the schematic of an edge-contact between 2D carbon and a tungsten (W) probe. In order to form a reliable contact, our measurements were performed using an Omicron ultrahigh vacuum (UHV) system with a base pressure in the range of 3-8×10 -11 Torr. Equipped in the UHV system are a scanning electron microscope (SEM) and four independently controllable nanoprobes with autoapproaching capability, which allows for position-specific measurements with good reproducibility. Figure 1(b) shows an example of an edge-contact formed by a tungsten probe and a piece of CNW. The size of the contact is determined mainly by the thickness of the CNW which is about one to several nanometers at the edge, 15,16 and is adjustable through monitoring the zero-bias contact resistance. The second type of 2D carbon is obtained in-situ through mechanical exfoliation of highly ordered pyrolytic graphite (HOPG) by using a large-size probe which itself also forms a low-resistance contact with HOPG during the subsequent electrical measurements (see Figure 1(c)). As can be seen in this figure, an edge-contact can be readily formed between a second W probe and the edge of an exfoliated 2D carbon sheets. The precise positioning of probe allows for formation of contacts between the probe and different points of the edge. Again, the actual contact size can be adjusted manually through monitoring the contact resistance.
Alternatively, an edge-contact can also be formed by probing directly the edge of a small piece of HOPG flake placed with an off-angle from the flat surface of a substrate holder.
All the electrical measurements were performed using a standard lock-in technique at room temperature. During the measurements, one of the probes was used to form a lowresistance contact and the other is adjusted manually to have a different contact resistance. The automatic approaching function helps to make reliable and reproducible contact without damaging the sample and the probe, unless the substrate is an insulator in which case the first probe has to be sacrificed by being pressed manually on the sample. CNWs is about 0.336 nm, which is slightly larger than that of graphite. 17 This is presumably caused by the local curvature in the CNWs.

A. Structural properties of CNWs
The CNWs can be grown on any type of substrates provided that substrates can sustain a temperature of 650-700 o C. [15][16][17] In this work, the CNWs have been grown on both SiO 2 /Si and Cu substrates. The CNWs grown on the Cu substrates can be peeled off easily due to weak bonding between carbon and Cu. After peeling-off, a thin layer of carbon is often found present on the Cu substrate near the unpeeled region (see Figure   3(a)). In order to understand quantitatively the chemical composition and structure of this thin layer of material, Auger element mapping has been carried out for three different regions of a same sample: region with CNWs (i), exposed Cu substrate covered by a thin layer of carbon (ii), and completely exposed Cu substrate (iii). The Auger spectra taken from regions (i) and (ii) resembles closely the Auger spectra of few layer graphene reported by Xu at al., 18  Under the ballistic transport approximation, the conductance of one transverse mode of a graphene point-contact is , corresponding to a resistance of 6.45 kΩ. Therefore, during the measurements, the ZBR has been varied in the range of ~3 -30 kΩ. Although there is no clear definition between the point-contact and tunneling regimes, the pointcontact regime can be considered as being in the range where ZBR is close to the resistance quanta of one conduction channel. When the ZBR reaches a value which is several times that of the resistance quanta, it is more appropriate to treat the contact as being in the tunneling regime. As can be seen from Figure 4(a), the differential conductance is linear to the bias voltage for all the ZBR values that have been measured.
The experiments have been repeated on different CNW samples and also at many different locations for a same sample, which exhibited excellent reproducibility.

C. dI/dV curves for edge-contacts with Fe-coated CNWs
After a series of measurements were completed on bare CNWs, the sample was insitu coated with a thin layer of Fe in the preparation chamber and then transferred back to the measurement chamber for performing the same series of electrical measurements without breaking the vacuum. As it is shown in Figure 2 This kind of parabolic dI/dV curve is normally obtained in metal-insulator-metal tunnel junction. 21

D. Comparison of edge-and side-contacts formed with CNWs
The good agreement between theoretical and experimental curves for the Fecoated sample confirms unambiguously that the linear curves shown in Fig. 4(a) are due to the CNW-W edge-contact.
The same measurements were then performed on CNWs grown on a Cu substrate, which allows for partial peeling-off of CNW from the substrate. Note that the conducting substrate does not affect the measurement results because the resistance measured mainly comes from the contact with a larger resistance. respectively, the results demonstrate that the dI/dV curves are indeed dependent on the relative orientation between the probe (or more accurately, current direction) and base plane of the carbon lattice.

E. Comparison of side-and edge-contact formed with HOPG and exfoliated graphene sheets
In order to further confirm the results shown in Figures 4 and 5, we repeated the same series of experiments on HOPG and exfoliated graphene sheets. In order to reduce the influence of surface contaminants, the top layer of HOPG was in-situ peeled off using a probe. Compared to CNWs, it was found that it is generally more difficult to form reliable side-contact with thick HOPG plates due to its flatness and hardness. However, once a stable contact is formed, the measurement results are reproducible at different locations on the HOPG surface. On the other hand, it is relatively easy to form a stable contact from the edges for both thick flakes and few-layer graphene sheets [see Figure   1

F. Theoretical calculation of dI/dV curves
The experimental results may be understood intuitively by considering the difference in relative orientation of the Fermi surface of graphene (with a disk shape) with respect to the current direction for two different contacts, as illustrated schematically in Figure 9 Figure 10(b), we show the calculated dI/dV as a function of bias voltage. Clearly, in this case, dI/dV is a linear function of , which is actually expected since in this case, the transport is governed by density of states (DOS) of graphene that is linear at the vicinity of Fermi energy. Contact resistance will introduce the scattering of electrons at interfaces, and consequently decrease the current. If the scattering is energy independent, dI/dV will still approximately be linear as a function of V but with a decreased slope.
We next consider the case that the probe axis is perpendicular to the base plane of HOPG, i.e., surface-contact. The electron transport process in this case is illustrated in Figure 11, which is different from that of edge-contact in a sense that in this case, in order to tunnel into graphene, electrons in the probe have to possess a finite momentum in the direction normal to the graphene plane, ⊥ k . The external bias applied is approximately shared equally by the shift of Fermi levels of both the tip and graphene, then one has components of wave vector in the tip, respectively. As shown in the right panel of Figure   10, in this case, we also assume that every state in graphene can accept tunneling of electrons from the tip with a unity transmission. Since the DOS of graphene is given by dI V dV ∝ .

IV. CONCLUSIONS
In summary, we have experimentally shown that the electron transport across metal/two-dimensional carbon interface is anisotropic, depending on whether the contact is made from the edge or surface. Experimental results may be understood by taking into account the electron spectrum of both metal and graphene, and also the momentumresolved DOS of the system. The results are useful for further optimization of metalgraphene contact, a crucial issue pertaining to device applications of graphene.