Magnetotransport of High-Performance Graphene

Jan 6, 2012 - (5) Bolotin, K. I.; Sikes, K. J.; Hone, J.; Stormer, H. L.; Kim, P. Phys. Rev. Lett. 2008, 101 (9), 096802. (6) Du, X.; Skachko, I.; Due...
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Letter pubs.acs.org/NanoLett

Transport/Magnetotransport of High-Performance Graphene Transistors on Organic Molecule-Functionalized Substrates Shao-Yu Chen,† Po-Hsun Ho,‡ Ren-Jye Shiue,†,§ Chun-Wei Chen,*,‡ and Wei-Hua Wang*,† †

Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan Department of Materials Science and Engineering, National Taiwan University, Taipei 106, Taiwan

‡

S Supporting Information *

ABSTRACT: In this article, we present the transport and magnetotransport of high-quality graphene transistors on conventional SiO2/Si substrates by modification with organic molecule octadecyltrichlorosilane (OTS) self-assembled monolayers (SAMs). Graphene devices on OTS SAM-functionalized substrates with high carrier mobility, low intrinsic doping, suppressed carrier scattering, and reduced thermal activation of resistivity at room temperature were observed. Most interestingly, the remarkable magnetotransport of graphene devices with pronounced quantum Hall effect, strong Shubnikov-de Haas oscillations, a nonzero Berry’s phase, and a short carrier scattering time also confirms the high quality of graphene on this ultrasmooth organic SAMmodified platform. The high-performance graphene transistors on the solution-processable OTS SAM-functionalized SiO2/Si substrates are promising for the future development of large-area and low-cost fabrications of graphene-based nanoelectronics. KEYWORDS: Graphene, high carrier mobility, magnetotransport, organic molecules, surface-functionalized substrates, self-assembled monolayer

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substrate20 is very attractive because this method is fully compatible with commercially available substrates and requires no transfer processes. It has been reported that the surface functionalization of the SiO2/Si substrates can drastically reduce charged impurities and surface traps on the substrates and improve the transport properties of graphene.21−24 In this work, we present high-mobility graphene devices on octadecyltrichlorosilane (OTS) SAM-functionalized SiO2/Si substrates with very low extrinsic doping levels, a small charge inhomogeneity, and reduced thermal activation of resistivity at room temperature. Most interestingly, the remarkable magnetotransport of graphene devices with pronounced quantum Hall effect (QHE) and strong Shubnikov-de Haas (ShdH) oscillations also confirms the high quality of graphene on this ultrasmooth organic SAM-modified platform. The prominent transport and magnetotransport behaviors of graphene on the solution-processable OTS-functionalized SiO2/Si substrates are very promising for the future development of large-area and low-cost fabrications of graphene-based nanoelectronics.

raphene, which consists of a single atom-thick plane of carbon atoms arranged in a honeycomb lattice, has attracted a significant amount of research interest because of its novel electronic, mechanical, and thermal properties arising from its unique 2D energy dispersion.1−3 Extraordinary carrier transport properties of graphene have been observed in suspended graphene devices.4−7 Nevertheless, suspended graphene generally suffers from both electrical and mechanical vulnerability, which may largely limit the practical applications of graphene-based electronic devices. As a result, locating optimal substrates is a significant issue in the development of high-performance graphene electronics. It is well-known that the carrier mobility of graphene on the conventional SiO2/Si substrates is usually limited by scattering from substrate surface roughness,8,9 charged surface state or impurities,10−12 or surface phonons of SiO2.13,14 Recently, graphene devices on atomically flat hexagonal boron nitride (h-BN) substrates have exhibited excellent transport characteristics.15−18 However, the device fabrications involve both the manufacturing of high-quality h-BN substrates19 and multitransfer processes that might be very challenging in the future integration of large-area graphene device fabrications. In contrast, the organic self-assembled monolayer (SAM) functionalization of a conventional SiO2/Si © 2012 American Chemical Society

Received: November 16, 2011 Revised: January 3, 2012 Published: January 6, 2012 964

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Figure 1 shows the schematic representation of graphene on top of the OTS-functionalized SiO2/Si substrate. The detailed

Figure 1. A schematic representation of graphene on an OTSmodified SiO2/Si substrate. OTS molecules are densely packed on the SiO2/Si substrate and form an ultrasmooth SAM via intermolecular van der Waals force. Inset: the Si atom (yellow) at the headgroup of the OTS molecule covalently bonds to an oxygen atom (green) of the silanol group on the SiO2/Si substrate.

fabrication procedures of organic SAM-functionalized substrates and graphene devices are described in the Supporting Information Sections S1 and S2. In brief, the densely packed OTS SAM can be formed as a result of covalent bonding to the SiO2 substrate along with intermolecular van der Waals force between the long hydrocarbon chains of OTS molecules.25 Figure 2a,b shows the surface topography images of a typical SiO2/Si substrate and an OTS-modified substrate, respectively, revealed by atomic force microscopy (AFM). For all of the characterized substrates (more than 10 test samples for each type), the surface roughness is estimated to be approximately 0.3−0.4 nm for SiO2/Si substrates and 0.15−0.2 nm for OTS-modified substrates. Figure 2e shows the histogram of surface roughness, which indicates the improved smoothness of the OTS SAM-modified substrate (FWHM ∼ 0.3 nm) compared to that of the bare SiO2/Si substrate (FWHM ∼ 0.5 nm). Accordingly, the graphene on the ultrasmooth OTS-SAMmodified substrate also exhibits very low roughness (FWHM ∼ 0.3 nm). The surface properties due to the formation of highly ordered OTS molecules26 on SiO2/Si substrates may be further evident from the contact angle measurements on bare SiO2/Si and OTS-modified substrates as shown in Figure 2c,d, respectively. It is known that the SiO2 substrate is hydrophilic due to the reaction sites, such as silanol groups, on its surface27 (more detail provided in the Supporting Information Section S3). The modification of SiO2/Si substrate surfaces with an OTS SAM layer effectively reduces the number of dangling bonds and drastically excludes surface-adsorbed polar molecules (e.g., water), which may cause doping or charged impurity scattering on graphene. The contact angle of the OTS-modified substrates (109°) is significantly larger than that of the bare SiO2/Si substrates (45°), indicating the hydrophobic nature of OTS SAM-modified substrates. Next, monolayer graphene flakes are mechanically exfoliated onto the pretreated substrates. We employ a resist-free fabrication of electrical contacts to avoid the resist residue and other contaminations from lithographic processes (Supporting Information Section S2). Moreover, as the resist exhibits poor

Figure 2. Surface characterizations by AFM and contact angle measurements. The difference in surface topography is shown by the AFM images of (a) typical SiO2/Si and (b) typical OTS-modified substrates. The scale bar is 1 μm. The measured contact angles of (c) typical SiO2 and (d) typical OTS-modified substrates are 45 and 109°, respectively. The contact angle measurement reveals the highly hydrophobic surface property of the OTS-modified substrate. (e) Histogram of the height distribution for the SiO2/Si substrate (black), the OTS-modified substrate (red), and graphene on an OTS SAM (blue). The histogram is calculated from the AFM images, and the solid lines are fitted by a Gaussian distribution. The FWHM of the height distribution are 0.5 and 0.3 nm for the SiO2/Si and OTSmodified substrates, respectively. It is noted that the FWHM of graphene on an OTS SAM is very close to that of the OTS-modified substrate.

adhesion to the hydrophobic surface of OTS SAM, the resist-free approach becomes necessary. We perform a four-terminal device geometry by combining two TEM grids within the shadow mask framework. Followed by a mild annealing at 110 °C for 2 h, the hysteretic behavior of devices due to charge traps (from adsorbates) during the fabrication processes can be eliminated. Electrical measurements of the devices reveal the high-performance transport behaviors of graphene on OTS-SAM-modified substrates. Figure 3a shows the resistivity (ρ) versus gate voltage (VG) curves of a typical graphene/OTS SAM device (sample A) and a reference device with graphene on a bare SiO2/Si substrate (sample B) at T = 2 K. Typically, the field effect of ρ in graphene is largely affected by the existence of dipolar adsorbates on SiO2/ Si substrates, which commonly leads to a broadening peak and electron−hole asymmetry in the ρ−VG curve. For the reference sample B, the VG at the charge neutrality point (VCNP) is 22 V, indicating a strong p-type doping that is possibly due to water 965

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Figure 4. QHE of graphene on OTS-modified substrates at B = 9 T and T = 2 K. (a) Longitudinal resistance Rxx as a function of gate voltage for sample A. A series of QH plateaus where Rxx vanishes is clearly shown for ν = ±2, ±6, and ±10 in the electron and hole branches. (b) Gate voltage dependence of the two-terminal conductance for sample A. The observed plateaus at 2, 6, and 10 e2/h are in accordance with the half-integer QHE in monolayer graphene.

Figure 3. (a) Resistivity versus gate voltage curves of graphene on OTS SAM (blue) and SiO2/Si (orange) substrates at T = 2 K. (b) The electron and hole mobility vs carrier density for graphene on an OTS SAM (sample A) at T = 2 K. The mobility of the electron and hole is as high as 60 000 cm2/V·s for n ≈ 5 × 1010 cm−2. Inset: the saturation carrier density is estimated by the intersection of two segment lines. (c) The distribution of Drude mobility versus charge neutrality point for 7 graphene/OTS SAM samples (blue upward triangles) and 4 graphene/SiO2/Si samples (orange upside-down triangles) at T = 2 K. (d) Resistivity of sample A as a function of temperature for VG = ±10, ±15, and ±40 V.

α = 6.4 × 1010 cm−2 V−1, which can be derived from the ShdH oscillations as described below [Figure 5e]. The saturation densities for samples A and B are 5 × 1010 and 1.6 × 1011 cm−2, respectively, indicating a smaller charge inhomogeneity in graphene on OTS SAMs (more detail provided in the Supporting Information Section S4). Once the saturation density nsat is determined, we can estimate the Drude mobility (μD) based on the model μD = σ/ne. Figure 3b shows the extraction of electron and hole mobilities (μD) of sample A as a function of carrier densities, and mobilities μD as high as approximately 60 000 cm2/ V·s for both electrons and holes at T = 2 K were obtained. Figure 3c shows the distribution of μD and VCNP for all of the samples we fabricated, including 7 graphene/OTS SAM samples and 4 graphene/SiO2/Si samples. The μD values of graphene/ OTS SAM devices range from 40 000 to 60 000 cm2/V·s, which are remarkably higher than those of the graphene/SiO2/Si devices with values of 14 000 to 27 000 cm2/V·s. In addition, all of the graphene/OTS SAM devices consistently exhibit VCNP near zero gate voltage, whereas the VCNP points of the graphene/SiO2/Si devices exhibit a large scattering between −13 and 22 V as a result of the higher levels of residual doping on the surface. For further

molecules adsorbed onto the SiO2/Si substrate. In contrast, the plotted curve of the graphene/OTS SAM device (sample A) is symmetric for electrons and holes with VCNP near zero gate voltage, indicating that the hydrophobic OTS layer on a SiO2/Si substrate may effectively prevent the adsorption of dipolar molecules and therefore minimize undesirable doping. To extract the mobility of graphene, there have been different procedures reported in the literature. Here, we employ two different methods to estimate the Drude mobility (μD)6 and density-independent mobility (μC)9,15 for comparison with the reported values in literature. For the estimation of μD, we first calculate the saturation density, nsat, defined as the value below which carrier transport is mainly dominated by electron−hole puddles,6 as illustrated in the inset of Figure 3b. The carrier density is converted from VG by the relationship n = α(VG − VCNP), where 966

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Figure 5. The magnetotransport characteristics of graphene on an OTS-modified substrate. ShdH oscillations in the (a) hole and (b) electron branches for different carrier concentrations corresponding to VG = ±15, ±25, ±35, and ±45 V. (c) The ShdH oscillations in a low magnetic field for the hole branch at n = 3.2 × 1011 cm−2 (V = −5 V). The minima of the oscillations are indicated by the arrows. (d) A fan diagram composed of the Landau index vs 1/Bn at different gate voltages. (e) The carrier concentration n = 4e/hBF(VG) is linearly dependent on the gate voltage, and the carrier density capacitance α can be extracted.

Therefore, the high-mobility graphene/OTS SAM devices accompanied by small residual doping, suppressed carrier scattering, and reduced activation of resistivity suggest the smooth and chemically inert OTS-SAM-modified surface thus acts as an excellent platform to fabricate highly performed graphene devices by a facile technique. The high-quality graphene/OTS SAM devices can be further manifested by the following comprehensive magnetotransport measurements. Figure 4a shows longitudinal resistance (Rxx) as a function of VG for sample A at a fixed magnetic field B = 9 T and T = 2 K. The characteristics of the QHE, that is, a series of plateaus where Rxx vanishes, can be clearly observed for filling factors ν = ±2, ±6, and ±10 in the high-quality monolayer graphene/OTS SAM device. Rxx remains zero within QH plateaus when the Fermi energy (EF) lies between Landau levels (LLs) and exhibits peaks when EF intersects with a LL. The gate voltages corresponding to the QH plateaus exhibit a relatively symmetric distribution centered at zero VG. Moreover, the characteristics of Rxx values, which exhibit the pure longitudinal components of the QHE, do not indicate coupling of transverse components Rxy in our device based on the four-terminal geometry. We also perform a two-terminal measurement of the same device to reveal the characteristics of the half-integer QHE of the monolayer graphene device on OTS SAM substrates. Figure 4b shows the two-terminal conductance (G) as a function of VG for sample A. The conductance in the QH regime exhibits very pronounced zeroth order QH plateaus for both the electron and the hole. The conductance at zeroth order QH plateaus accurately lies on G = gs(n + 1/2)e2/h = 2e2/h, where n = 0 and gs = 4 arise from the spin and valley

comparison, we also estimate the density-independent mobility (μC) by applying the self-consistent Boltzmann equation, ρ = σ−1 = (neμC + σo)−1 + ρS, to extrapolate the carrier mobilities considering both short- and long-range scattering, where ρS is the resistivity contributed by short-range scattering and σo is the residual conductivity at the Dirac point. Sample A consistently exhibits higher μC values for the hole and electron mobilities of 28 000 and 21 000 cm2/V·s, respectively, whereas the μC values for the hole and electron mobilities for sample B were lower at 10 000 and 9000 cm2/V·s, respectively (Supporting Information Section S5). The scattering mechanisms in the graphene/OTS SAM samples can be further revealed by the temperature-dependent resistivity ρ as a function of temperature for VG = ±10, ±15, and ±40 V, as shown in Figure 3d. In the temperature range of 50 K < T < 150 K, ρ increases linearly with temperature, which is mainly attributed to scattering by longitudinal acoustic phonons in graphene.28 The slope Δρ/ΔT ranges from 0.5 × 10−4 to 1.2 × 10−4 Ω/K, and the deformation potential can be determined as DA ≈ 15−20 eV (Supporting Information Section S6), which is in reasonable agreement with earlier studies.12,29 Notably, we observe the reduced activation of resistivity close to room temperature for n ≥ 1012 cm−2 (|VG| ≥ 15 V). The sharply activated resistivity near room temperature in graphene on SiO2/Si substrates has been reported,9 and it is attributed to the remote phonon scattering on the SiO2 surface13,14 or out-of-plane acoustic phonon due to rippling in graphene.30,31 Our data indicate that the OTS SAM can largely suppress the thermal activation of resistivity32 and thus minimize the reduction of carrier mobility at room temperature. 967

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under contract numbers NSC 98-2112-M-001-005-MY3 and NSC 99-2119-M-002-012.

degeneracy of each LL, respectively. The higher order (1st and 2nd) QH plateaus are not fully developed but are still recognizable, which might arise from the finite longitudinal conductance in the two-terminal geometry.33,34 The VG values corresponding to the QH plateaus observed in the two-terminal geometry also exhibit a good coincidence with those in the Rxx versus VG curve of Figure 4a. Figure 5a,b plots the curves of resistance versus out-of-plane magnetic field for the hole and electron branches, respectively, where the ShdH oscillations were observed. Figure 5c shows the ShdH oscillations of sample A at a carrier density n = 3.2 × 1011 cm−2. The onset magnetic field of the ShdH oscillations is found to be as low as 580 mT and the estimated scattering time is about 0.11 ps, based on the equation τ = ℏ(πn)1/2/evFBSdH.35 The fan diagram of the ShdH oscillations at different gate voltages is shown in Figure 5d, where the values of 1/Bn at the nth minimum in Rxx are plotted against the Landau index n. Their linear relationship is outlined with dotted lines and extrapolated to the y-axis at 0.5 (−0.5) for the electron (hole), indicating the nonzero Berry’s phase of the monolayer graphene.36 From Figure 5d, we can obtain the ShdH oscillation period 1/BF from the slope for each gate voltage. The gate voltage dependence of carrier density can then be calculated by n = 4e/hBF(VG), which is shown in Figure 5e. The linear gate voltage dependence of carrier density is clearly observed for both the electron and the hole. The carrier density capacitance of the graphene on OTS-modified substrates is found to be symmetric for the electron and hole branches with α = n/VG = 6.4 × 1010 cm−2 V−1. In summary, we have demonstrated the prominent transport and magnetotransport characteristics of graphene devices on solution-processable OTS-functionalized SiO2/Si substrates. The graphene transistors have exhibited high carrier mobilities, small residual doping, and low-charge inhomogeneity accompanied with pronounced QHE and strong ShdH oscillations. The facile technique to fabricate high-performance graphene transistors using organic molecule-modified substrates can be a potential candidate for the future development of large-area and low-cost graphene-based electronic devices.

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ASSOCIATED CONTENT

S Supporting Information *

Surface modification of SiO2/Si substrates by OTS SAM, fabrication and electrical measurements of monolayer graphene devices, surface characterization, charge inhomogeneity, density-independent carrier mobility (μC), and temperature dependence of resistivity. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*(W.-H.W.) Tel: +886-2-2366-8208. Fax: +886-2-2362-0200. E-mail: [email protected]. (C.-W.C.) Tel: +886-23366-5205. Fax: +886-2-2363-4562. E-mail: chunwei@ntu. edu.tw. Present Address §

Department of Electrical Engineering, Columbia University, New York, New York 10027, United States.

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ACKNOWLEDGMENTS W.-H.W. thanks Mei-Yin Chou for insightful discussions. This work was supported by the National Science Council of Taiwan 968

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