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Crystals 2013, 3(1), 257-274; doi:10.3390/cryst3010257
Abstract: The contact resistance between graphene and metal electrodes is crucial for the achievement of high-performance graphene devices. In this study, we review our recent study on the graphene–metal contact characteristics from the following viewpoints: (1) metal preparation method; (2) asymmetric conductance; (3) annealing effect; (4) interfaces impact.
Graphene is a single atomic sheet of carbon atoms in a honeycomb lattice, where the carbon-carbon bonds in the plane are sp2 hybridized. Ever since it was firstly isolated from micromechanical cleavage of bulky graphite flakes in 2004 , graphene has been widely investigated owing to its unique and attractive electrical, physical and chemical properties [1,2,3,4,5,6,7,8,9,10,11]. Graphene is an energy gapless material, in which the conduction and valence bands meet at the Dirac point. Its linear electronic dispersion relation results in a zero effective mass of the carrier with a high Fermi velocity. This material thus exhibits an extraordinarily high carrier mobility of more than 200,000 cm2 V−1s−1 . It is considered to be a potential channel material for field-effect transistors (FETs) application. In addition, graphene has been applied to various practical device applications, such as high frequency devices , gas sensors [5,13], flexible electronics [14,15], and photonics [16,17]. In spite of the very high mobility in the graphene channel, however, the contact resistance between graphene and metal electrodes is crucial to achieving a high performance from the graphene [18,19,20], especially the high on-state current. It has been reported that the control of contact properties is more important than the intrinsic channel mobility, as otherwise the merit of high mobility from the graphene will be diminished significantly . In this paper, we provide a study on the characteristics of graphene–metal contact from the perspectives of: (1) metal preparation method; (2) asymmetric conductance; (3) annealing effect; and (4) interface impact. These findings offer insightful information to achieve high performance graphene devices via process optimization.
2. Impact of Metal Preparation
When measuring contact resistance, the contribution from the graphene sheet resistance should be minimized or eliminated. There are several methodologies to extract the graphene–metal contact resistance, including the transfer length [21,22], four-probe/two-probe [18,19,23], and residual resistance methods [20,24]. We use the last two methods to extract the contact resistance. Ti has been used as metal electrodes in carbon-based devices because of its excellent adhesive capability in SiO2 substrate or other insulators . In this section, we take Ti/graphene as an example to study the impact of different metal deposition methods on Rc.
The total resistance between two contacts is the sum of the semiconductor resistance, the contact resistance, and the metal resistance, where the metal resistance can be neglected owing to good control of metal electrode growth. By subtracting the graphene resistance from the total resistance, one obtains the total contact resistance. The contact resistance for each contact is thus obtained as half of the total resistance [18,26,27]:
Figure 1a shows the I – V characteristics of SLG (single-layer graphene)/Ti devices, where Ti is grown by electron-beam evaporation (EBM) and sputter processes, respectively. In our experiments, graphene is produced by mechanical exfoliation from bulk graphite. Subsequently, graphene is transferred onto degenerated silicon substrate with a thermally grown 90 nm SiO2, serving as a conventional back-gate dielectric. Rtotal can be extracted from the linear I – V curves. The optical image of measured device is shown in inset in Figure 1(a). The linear I – V characteristic indicates that the Ti/SLG contact is ohmic. Note that there are also ohmic contacts between graphene and other metals in our samples, e.g., Al, Ag, Pd, Ni, Au. However, there is a Schottky junction between graphene nano-ribbon (GNR) and metals . The nonlinear I – V characteristic has been reported in GNR–Au, GNR–Al contacts theoretically and experimentally . This Schottky effect in GNR–metal contacts stems from the creation of energy band gap in GNR, where the energy band gap increases with reduction of the GRN width . The graphene resistance Rg is measured at the force current from 1 µA to 1 mA, shown in Figure 1b. It was found that Rg is almost the same at different force currents. By combining the results from two-probe (Figure 1a) and four-probe measurement (Figure 1b), Rc is quantitatively addressed. The Rc of EBM sample is observed to have a lower Rc of 0.83 kΩ as compared to sputter one of 4.2 kΩ. Note that the poor on/off ratio is observed in our graphene FETs, owing to its gapless characteristic.
Note that in the four-probe measurement, the back-gate electrode of graphene FETs is floating, and Rg is almost a constant. While in residual resistance measurement, the Rg is changeable according to the modulation of carrier density in graphene channel. The Rc then can be determined as follows :
The measured contact resistivity ρc of SLG, DLG (double-layer graphene), MLG (multi-layer graphene)/Ti devices, prepared by EBM and sputter processes, is summarized in Figure 3. The standard error is calculated from eight samples for each group. For all the devices fabricated by the EBM process, the ρc does not exhibit strong dependence on the number of graphene layers. It is consistent with the early work, where Rc of SLG, DLG, and TLG FETs (also EBM samples) is insensitive to layer thickness , while for the devices prepared by sputter process, the ρc exhibits layer dependence and increases with decreasing the number of layers. It is worth noting that the ρc of Ti/SLG and Ti/DLG from the former is significantly smaller than that from latter. Note that there is a negligible difference in ρc between the EBM and sputter samples. Thus it is proposed that the sputter Ti atoms would only effectively affect the top layers (up to two layers) of graphene in our case. It is believed that, for MLG, after the top layers create the vacancies, the metal can “penetrate” through the vacancies to contact with the bottom layer directly. Figure 4 shows the ρc distribution of Ti/SLG devices prepared by sputter processes at various powers. It is also observed that the ρc increases more than two orders of magnitude as sputter power enhances. It was reported that the ρc can reach 109 Ω μm in case of sputtered Ti on SLG or MLG . It infers more carbon atoms are milled away when the sputter power increases.
Figure 5 shows the Raman spectra of SLG, DLG, TLG (triple-layer graphene) with and without metal deposition, where they are prepared by (a) EBM; and (b) sputter processes, respectively. Raman spectroscopy has been used to physically probe the electronic structure of graphite and graphene without damaging the sample [31,32,33,34]. Since our graphene sheet is prepared by mechanical exfoliation from bulky graphite, there is no D band in Raman spectra of graphene before metal deposition. There are only two main characteristic peaks of G and 2D bands before metal growth, where the peak position for G and 2D bands are around 1580 and 2670 cm−1, respectively. For EBM samples, there is negligible D band, around at 1350 cm−1, after Ti deposition by EBM process. It is worth noting that D bands are formed after receiving sputtered Ti for all SLG/DLG/TLG samples, significantly different from the ones after EBM process. The D band is caused by disordered or defected structure of graphene sheet [31,35,36]. The intensity ratio of D band to G band (ID/IG) is usually used to estimate the amount of defects in carbon materials. Accordingly, compared to sputtered Ti/graphene contact, a Ti/graphene contact prepared by EBM corresponds to very low defects or carbon vacancies in graphene. It has been reported that the formation energy of carbon vacancies in graphite is around 7.4 eV [37,38]. Thus, the ion energy in the sputter process should be larger than that to create the carbon vacancies in graphene. Generally, it is believed that sputtered Ti atoms possess larger kinetic energy compared to the EBM case, and the energy could be transferred to the graphene layer, resulting in the removal of carbon atoms from the graphene lattice and creating of the carbon vacancies.
In addition to the presence of the D band, the G and 2D band shifts are also observed in sputtered SLG, DLG, and MLG/Ti contacts. In the meantime, it is found that there is no noticeable band shift after Ti deposition onto graphene, where Ti is grown by EBM process, indicating no change in lattice constant in graphene and graphite, shown in Figure 5a. On the contrary, the 2D band and G band have an obvious red shift of ~30 cm−1 and ~20 cm−1 after Ti deposition by sputter process. G band shift caused by charge doping through phonon-electron coupling has been reported by Yan et al. . The 2D band is a second-order two-phonon process and exhibits a strong frequency dependence on the excitation laser energy . However, the additional band shift will be narrow at ~10 cm−1 in case of charge doping [39,40]. Therefore, this band shift cannot be attributed only to the charge doping effect. Tensile stress is also reported to cause the red shift in graphene; the red shift expands with increasing tensile stress [41,42]. As the 2D band originates from the two-phonon double-resonance process, it is closely related to the band structure of graphene layers. It is thus believed that the sputter process can lead to tensile strain in graphene underneath Ti owing to defects formation, thereby enlarging the lattice constant of graphene. The red shift of the 2D and G bands can thus be understood as the tensile strain weakening the bond and thus lowering the vibration frequency due to the elongation of C-C bonds .
A schematic model has been proposed to explain the difference in graphene–metal contacts between large and small grains in contact metal . In their model, the large grains and rough surface of contact metal play an important role in the contact area and small contact area results in large contact resistance. Then, contact resistance can be affected by the grain size and the uniformity of the contact metal films. For sputtered SLG and DLG/Ti devices, there is also the possibility of a smaller contact area, as parts of carbon atoms are milled away from the pristine graphene structure, accordingly increasing the contact resistance. It must be pointed out that the defected carbon or carbon vacancies not only occur in the graphene underneath the metal, but also at the adjunct region of graphene channel and graphene–metal contact. It was reported that the defected graphene will break the symmetry of regular hexagonal C-C bond structures, thus resulting in the intervalley electron scattering [43,44]; accordingly, the mobility will degrade compared to the pristine one. Note that there is possible carbide formation after Ti deposition onto the graphene, similar to surface-carbide formation in additional Ni deposition on graphene . However, the number of Ti-C bonds is very low and their influence on electron transport is negligible . It was also observed that the significant increase in D band sputtered Al/SLG, Al/DLG contacts, asshown in Figure 6. The ID/IG is larger than 2. The 2D band even disappears as the sample is subjected to high sputter power, indicating that the pristine structure of graphene has been significantly destroyed. Note that the reduced Rc is observed in high vacuum deposition condition, suggesting deposition pressure also has a significant influence on the quality of Rc .
3. Asymmetry Conductance
Because graphene is an energy gapless material, it is very similar to the metal–metal contact when graphene is brought into contact with metal. With metal–metal contact, a small redistribution of electrons can screen the potential difference due to the large carrier density, where the potential difference originates from the work function difference in two metals. The screening length λ is expressed by , where N(EF) is the DOS at the EF in graphene. The λ is less than 1 nm for metal–metal contact. However, for graphene–metal contact, DOS is very small compared to metal, especially at the Dirac point, and λ is much larger than that of metal. In addition, graphene itself is sensitive to external perturbations owing to its all-surface and zero volume nature . Charge transfer between graphene and metal may dope the underlying graphene into n-type or p-type, depending on work function differences. Therefore, the metal doping effect must be considered in transfer characteristics of graphene FETs. In Figure 2, it is shown that p-type and n-type branches show a moderate asymmetry and the conductance in the n-type branch is always smaller than that in the p branch. It is consistent with the previous report . This asymmetric conductance behavior was first investigated by comparing devices with invasive electrodes crossing the whole graphene channel width and external electrodes connected to the side of the graphene channel . The graphene FETs with invasive electrode show the asymmetry of conductance in n-type and p-type branches; however, the asymmetry almost never occurs in devices with external electrodes [18,23]. Giovannetti and Khomyakov et al. [49,50] applied density functional theory (DFT) to study how graphene is doped by various metals, including Al, Ag, Cu, Au, Pt. The calculated Fermi energy shift (∆EF) with respect to the conical point can increase by decreasing the distance between graphene and metal. Xia et al., by using scanning photocurrent microscopy (SPCM), illustrated that the charge doping occurs not only underneath the metal, but also extends hundreds of nanometers into adjacent regions in the graphene channel [51,52]. They separated a graphene FET into three segments: (1) the metal-controlled graphene; (2) the transition region affected by both the metal and the back-gate; and (3) the bulk graphene region controlled only by the back-gate. With the modulation of back-gate voltage, the width of transition region (segment 2) is accordingly modified. In their experiments, the detected photocurrent comes from the p–n junction in the graphene sheet, since the photocurrent is proportional to the potential gradient at the excitation position. It exhibits the different polarities along the graphene channel. Lee et al.  observed the photocurrent in graphene FETs with the help of SPCM, resulting from p–n junction formation in the graphene sheet. It was also reported that chemical doping can introduce conductance asymmetry. It is caused by a combination of the neutrality point misalignment at the electrode–channel interface and the non-constant DOS of the graphene electrodes .
Previously, we implemented scanning Kelvin probe microscopy (SKPM) to experimentally address the work function difference between graphene channel and metal electrodes . The graphene underneath the metal is assumed to be pinned, and the constant potential ∆ϕ can be described as follows :
4. Annealing Effect on Contact Junction
In order to improve the performance of graphene–metal contact, the forming gas annealing (FGA) were performed to examine the Rc of the sputtered Ti/SLG junction. Figure 8a shows the transfer characteristics of a SLG field-effect transistor before and after forming gas annealing (FGA), whereby the process is undergoing with N2:H2 mixing at 425 °C for half hours. After FGA treatment, the Rc could not be reduced as expected. The Raman spectra of the Ti/SLG contact are shown in Figure 8b. From Figure 8b, it is observed that the presence of the D band during the sputter process does not disappear, but rather expands. Concurrently, the FWHM of the G band also expands with the D band. The broadening of the D peak is correlated to the distribution of cluster with different orders and dimensions , thus suggesting that there are C–H sp3 bonds  or carbon defects in the graphene layer underneath the metal after FGA treatment, which is very similar to amorphous carbon . From Figure 8a again, it is interesting to observe that the Dirac point is shifted to the right direction, or positive polarity. The right shift of VDirac, and the ∆VDirac is more than 50 V, indicating a strong hole doping effect after FGA. The doped charge density, which is induced by FGA treatment, can be estimated by the following equation [60,61],
5. Interface Impact
There are two interfaces in a graphene–metal contact system: graphen/subtrate and graphene/metal interfaces. Graphene always physically lies on the surface of SiO2/Si substrate, or another oxide/Si substrate, thus the first interface must necessarily be taken into account. Previously, the properties of graphene between SiO2, Al2O3, and HfO2 are studied by using Raman and atomic force microscopy (AFM) . In addition to strong adhesion between graphene and dielectric, a higher hole concentration also occurs as graphene lies in a higher dielectric constant oxide. Figure 9a,b present the schematics illustration of SiO2 surface treated by HF dipping and the re-oxidation process, respectively . The difference between HF dipping and the re-oxidation process is that the SiO2 surface is terminated by OH bonds for the former, and the latter is an O-terminated SiO2 surface. The former is hydrophilic and dopes graphene into the p-type, while the latter is hydrophobic and dopes graphene into the n-type, which is verified in the Raman G band position [66,67]. It is also reported by Casiraghi et al.  that the G band position on substrates are within the range of fluctuation (1580–1588 cm−1) by unintentional electron or hole doping effect for more than 40 graphene samples on SiO2/Si substrate. Watanabe’s observation shows that Rc is independent of work function of contact metal such as Ti, Ag, Co, Cr, Fe, Ni, and Pd . Robinson et al.  also examined the effect of work function difference on ρc with Al, Ti, Cu, Pd, Ni, Pt, where the work function difference with graphene varies from −0.2 eV to 1.2 eV. There is little difference in ρc as the difference in metal/graphene work function varies, indicating that the device fabrication process heavily influences one’s ability to “dope” graphene . This is the possible reason for contact resistance results widely varying among reported experiments, even for the same metal.
The second interface is also important for understanding graphene–metal contacts. Antonio et al.  ascribed double dip in Ids − Vbg to charge transfer between the graphene and the metal electrodes. Nouchi et al.  have also reported that anomalously distorted transportation originated from the partially formed oxide layer in Ni/graphene contact. The previous work assumed that carrier density of graphene underneath metal, described as segment 1 , is pinned [51,52,55]. It is independent from back-gate voltage, which was believed to modulate the graphene channel, rather than the graphene underneath metal. However, Raman and transfer measurements show that carrier density of graphene underneath metal can be modulated, indicating graphene contacting metal is still graphene because of a weak interaction . In their experiments, there exists residual photo-resistor between (PR) graphene and metal. Chen , Xia  and Song’s  observations also demonstrated that contact resistance is Vbg dependent, and also quantum capacitance is observed . To eliminate the side effect of residual PR, Hsu et al.  intentionally inserted an Al sacrificial layer during lithography. Graphene surface roughness underneath the ohmic contacts is reduced; they were able to achieve the improved contact resistance to 200–500 Ω μm. Very recently, Nagashio et al.  developed a photo-resistor-free method to fabricate graphene FETs with Ni electrode. The modulation of the G band of Ni/graphene contact with and without residual PR is compared. The position of G band, corresponding to the doping effect, can be modulated up to 5 cm−1 for Ni/graphene with residual PR, while the shift of the G band is limited to 1–2 cm−1 in PR-free samples. It indicates that the graphene underneath metal even without residual PR is still graphene, but the modulation is restricted, due to strong interaction from π − d coupling between graphene and Ni [50,77]. In the case of Ni/graphene with PR-free process, Rc is not improved compared to the case of PR. Theoretical calculation by Matsuda et al.  shows Rc will reduce in an “end-contacted” graphene–metal interface, where carbon pπ orbitals, as well as pσ orbitals, play important roles in cohesion. Therefore, a sandwich contact structure (metal–graphene–metal) [79,80] and graphitic contact  has been suggested to reduce Rc.
We discuss the characteristics of graphene-metal contact from the viewpoints of metal preparation, asymmetric transportation, annealing effect, and interface impact. These findings provide insightful information into process optimization not only for graphene devices, but also for other layer-material devices such as MoS2, WS2.
This work is supported by the Singapore Agency for Science, Technology and Research (A*STAR) (Project No. 092 151 0088) and NTU-SIMTech Collaborative Project (Project No. U10-J-023SU) and 1000-plan funding in China. This work is also partly supported by a research fellowship of Japan Society for the Promotion of Science (JSPS). W.J. Liu would like to thank K. Nagashio of The University of Tokyo for many fruitful discussions.
Conflict of Interest
The authors declare no conflict of interest.
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