Coulomb blockade behavior in nanostructured graphene with direct contacts

Transcription

1 Copyright 213 by American Scientific Publishers All rights reserved. Printed in the United States of America /213/3/92/5 doi:1.1166/mex Coulomb blockade behavior in nanostructured graphene with direct contacts Satoshi Moriyama 1,, Yoshifumi Morita 2, Eiichiro Watanabe 3, and Daiju Tsuya 3 1 International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 35-, Japan 2 Faculty of Engineering, Gunma University, Kiryu, Gunma , Japan 3 Nanotechnology Innovation Station, NIMS, Sengen, Tsukuba, Ibaraki 35-7, Japan ABSTRACT This paper proposes a new graphene-based quantum-dot device structure, in which nanostructured graphene islands are perfectly isolated and metallic contacts are directly deposited onto them without constrictions. Such a configuration is expected to be free from disturbances resulting from the structural fluctuation of constrictions, and allows for direct contact with a nanostructured two-dimensional electron gas. Transport spectroscopy analysis of this device structure was performed, and its Coulomb blockade behavior at low temperatures was revealed. Irregular Coulomb diamonds are observed in these devices, which is an indication of the formation of a multiple-quantum-dot system. Keywords: Graphene, Coulomb Blockade Effect, Quantum Dots, Nanostructures, Low-Temperature Electron Transport. 1. INTRODUCTION Graphene displays fascinating electronic properties because of its genuine two-dimensional (2D) character, 1 and may be used in applications of next-generation electronics. 5 8 The scope of its properties ranges from a long spin-relaxation time to the highest known roomtemperature mobility. In this context, for the preparation of nanostructured devices, it is intriguing to tailor the shape of graphene that is in contact with electrodes by means of microfabrication techniques. A step along this line has been achieved with the fabrication of graphene using electron beam lithography. However, confining the carrier in graphene (with a linear energy dispersion dubbed the (massless) Dirac fermion ) is crucial for the realization of Single Electron Transistors (SETs) in fabricated graphene nanostructures. 9 1 In general, confining Author to whom correspondence should be addressed. MORIYAMA.Satoshi@nims.go.jp massless Dirac fermions is difficult because of Klein tunneling and the zero-band-gap electronic structure. 15 Moreover, although attempts have been made to design graphene devices with confinement, they often suffer from severe design limitations. They basically consist of small quantum-dot islands for geometric confinement, to which narrow graphene constrictions are connected. In this case, the performance of such devices has been limited because of the detailed constriction and edge orientation. In this study, we report an alternative device structure for achieving confinement, in which nanostructured graphene islands are perfectly isolated and metallic contacts are directly deposited onto them without constrictions. Such a configuration realizes direct contact with a nanostructured two-dimensional electron gas (2DEG). This device structure may lead to various types of nano2deg junctions, e.g., superconductor (or magnet)-nano2deg junction, by selecting the contact materials. Therefore, we believe that this approach may open the door to the development of new graphene-based quantum devices. 92 Mater. Express, Vol. 3, No. 1, 213

2 Coulomb blockade behavior in nanostructured graphene with direct contacts Materials Express 2. EXPERIMENTAL DETAILS Graphene samples were prepared by micromechanical cleavage of Kish graphite deposited on the surface of an oxidized silicon substrate (9-nm thickness). On the basis of optical microscope contrast and Raman spectroscopy measurements, 16 a number of graphene flakes were selected and confirmed to consist of singlelayer graphene. 17 Figure 1(c) shows the Raman spectra obtained using the 51.5 nm laser line with the laser spot ( 1 m) focused on the inner portion of the measured flake. The sharp 2D peak without an internal structure is characteristic for single-layer graphene. The D peak around 135 cm 1 is not visible, indicating that intervalley scattering is absent in the measured flake and the graphene is defect free. The nanographene structures were then patterned using electron beam (EB) lithography with a poly(methyl methacrylate) (PMMA) resist as the etch mask. Oxygen reactive ion etching was used to etch away the unprotected graphene. Next EB lithography was again used to deposit metal (titanium) electrodes on the nanographene structures to fabricate source drain contacts. The thickness of the titanium electrodes was 2 nm. Finally, the samples were annealed in Ar and H 2 (3%) at 3 C for 5 min. Figure 1(a) shows the optical microscope image of our experimental sample. A Hall-bar-type electrode device configuration is presented in the upper section to indicate the quality of the graphene flakes. The width of the Hall-bar is 1 m. Two-terminal nanostructured graphene device is shown in the lower section. A scanning electron microscope image of the nanostructured graphene device, where the graphene is directly connected to the metal electrodes, is shown Figure 1(b). The diameter of the graphene is 55 nm, and the length between the contacts is 2 nm. A highly-p-doped silicon substrate was used to apply the back-gate voltage. All of the electrical transport measurements were carried out in 3 He cryostat with a superconducting magnet. The source drain current I was measured as a function of both the source-drain voltage (V sd and the back-gate voltage (V g, and the differential conductance di/dv sd was obtained by numerically differentiating the I V sd curve. 3. RESULTS AND DISCUSSION The electron transport of the Hall-bar device in a magnetic field perpendicular to the device is shown in Figures 1(d) and (e), where four-terminal condition is applied. A half-integer quantum Hall effect (QHE) of the sample was observed at low temperatures, which is consistent with previous reports (see 18 for a review). A QHE occurs when the gate voltage is tuned such that the Fermi energy lies between the energies of the extended states in the Landau levels. However, in contrast to a conventional QHE, for single-layer graphene, the so-called N = Landau level is pinned at zero energy and a +1/2 -shift of the quantized Hall conductance takes place for massless Dirac fermions. Moreover, the spin and valley degeneracies cause four-fold degeneracy. Therefore, in total, the quantized value of the Hall conductance becomes (m + 1/2 = m + 2 (or 1/ m + 2 for the resistance). Note that m = / 1 corresponds to the filled/empty N = Landau levels, respectively. From the experimental results, the flake mobility ( was estimated to be 2,5 cm 2 /Vs, and the mean free path (l mfp was estimated to be 3 nm at 1 12 cm 2 for the hole- and electron-carrier densities, according to 1/ xx = en = 2e 2 /h k F l mfp, where xx is the longitudinal resistivity, e is the fundamental unit of charge, n is the carrier density, h is Plank s constant, and the Fermi wave vector k F is given by ( n 1/2.On the basis of these results and Raman spectroscopy analysis, it can be concluded that this device consists of genuine single-layer graphene. Note that this data is for the hall-bar device. Considering the fabrication process, we believe that it should show the similar character as our nanostructured graphene device. Next, measurement of the electrical transport properties of the nanostructured graphene device shown in the bottom of Figure 1(a) was carried out. Figures 2(a) and (b) show the typical I V sd and I V g characteristics of the nanostructured graphene device at room temperature, respectively. The device exhibits linear I V sd data, which gives a twoterminal resistance of k. This value is much larger than the sheet resistance obtained from the result of fourterminal measurement [see the inset of Fig. 1(d)]. Therefore, it can be concluded that this two-terminal resistance is dominated by the contact resistance between the metal (titanium) and nanostructured graphene. In Figure 2(b), the I V g curve shows V-shaped behavior. This behavior has been established in graphene, and the dip corresponds to the charge neutrality point. 18 In this case we found no shift in the charge neutrality point, although we also observed that the shift is not universal and depends on the detail of the fabrication process. A large scale transport gap was confirmed near the charge neutrality point at low temperatures, as has been reported for previous device structures, and Figure 2(c) displays the differential conductance as a function of V sd and V g near the charge neutrality point. The conductance is suppressed in the small source drain voltage range (yellow regions), which is a manifestation of the Coulomb blockade effect. Furthermore, in the Coulomb blockade regime, the height of the diamonds along the V sd -axis indicates the addition energy required to add one charge carrier to the island. The measured addition energy varies from a few mev to the tens of mev range. These irregular Coulomb diamond patterns indicate that a multiple-quantum-dot system is formed in the device. 22 Figure 2(d) shows the magnetic field dependence of the Coulomb oscillations (I V g trace), where the magnetic field is applied perpendicular to the device and the peak positions are robust Mater. Express, Vol. 3,

3 Coulomb blockade behavior in nanostructured graphene with direct contacts (a) (b) (c) 51.5 nm 2D Intensity [arb. unit] G (d) ρ xx [kω] D Raman shift [cm 1 ] (e) ρ xy [h/e 2 ] /2 (h/e 2 ) 1/6 (h/e 2 ) 28 1/6 (h/e 2 ) 1/2 (h/e 2 ) Fig. 1. Device configurations. (a) Optical microscope image of the measured sample. A Hall-bar device is shown in the upper section (separated to white-dashed lines for guide to eyes) to indicate the quality of the graphene flakes. Two-terminal nanostructured graphene device is shown in the lower section. Scale bar is 1 m. (b) Scanning electron microscope image of the nanostructured graphene with direct contacts. Scale bar is 1 m. (c) Raman spectra of the measured flake. (d) Longitudinal resistivity ( xx of the Hall-bar device at T = 1 6 K and B = 8 T. Inset : Longitudinal resistivity at B = T. (e) Hall resistivity ( xy of the Hall-bar device at T = 1 6 K and B = 8 T. A half-integer Hall plateau is observed, which is the hallmark of the quantum Hall effect of single-layer graphene. under the magnetic field. It is believed that the results seen in the figure are because of random charged impurity centers in the graphene in conjugation with a gap stemming from the geometry of the constriction, which should lead to the formation of multiple quantum dots 2 21 due to the presence of puddles of carriers. Support for this scenario has been reported in recent scanning tunneling microscopy (STM) experiments We calculated the quantum-dot diameter (d by the simple isolated 2D island model, d = e 2 / r E c, where r is the dielectric constant and E C is the charging energy. 22 By substituting r = for SiO 2 and charging energies estimated by the Coulomb diamonds size in Figure 2(c) into the formula, the quantum-dot diameter was obtained as 8 2 nm, which is slightly larger than the puddle size reported by the STM results. However, this estimation gives upper limits of the quantum-dot size because the model assumes an isolated disk, and this result could be explained by considering the effects of the interdot coupling between the multiple quantum dots. 9 Mater. Express, Vol. 3, 213

4 Coulomb blockade behavior in nanostructured graphene with direct contacts Materials Express (a) 3 (b) V sd [mv] (c) V sd [mv] (d) T 5. T 2.5 T. T 3 2 di/dv sd [μs] Fig. 2. Transport properties of the nanostructured graphene device. (a) Current I as a function of V sd at V g = V at room temperature. (b) Current I as a function of V g at V sd = 1 mv at room temperature. (c) A color-scale plot of the calculated differential conductance (di/dv sd as a function of V sd and V g at T = 23 K and B = T. (d) Magnetic field dependence of the current I as a function of V g at V sd = 2 mv and T = 23 K. Each trace is artificially shifted for clarity (offset: 1 na). In Ref. [25], quantum-dots were formed as puddles because of the substrate-induced disorder potential, and the Coulomb-blockade peak positions were basically independent of the magnetic field, which is consistent with our experimental results.. CONCLUSIONS We proposed a new graphene quantum device structure, in which nanostructured graphene islands are perfectly isolated, and metallic contacts are directly deposited Mater. Express, Vol. 3,

5 Coulomb blockade behavior in nanostructured graphene with direct contacts onto them without constrictions. Transport spectroscopy measurements of this device structure revealed Coulomb blockade behavior at low temperatures, indicating that a multiple-quantum-dot system is formed in the device. These results are an important step toward increasing our understanding of quantum transport in nanostructured graphene and the realization of single-dirac fermion devices. We believe that the high-quality graphene sheet used in this study enabled the systematic, tailor-made design of our device structure. Acknowledgments: This study was supported by a Grant-in-Aid for Scientific Research (B), a Grantin-Aid for Young Scientists (B), a Grant-in-Aid for Exploratory Research, NIMS Nanofabrication Platform in Nanotechnology Platform Project, and the World Premier International Research Center Initiative on Materials Nanoarchitectonics from the Japan Ministry of Education, Culture, Sports, Science and Technology. References and Notes 1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov; Electric field effect in atomically thin carbon films; Science 36, 666 (2). 2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov; Twodimensional gas of massless dirac fermions in graphene; Nature 38, 197 (25). 3. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim; Experimental observation of the quantum Hall effect and Berry s phase in graphene; Nature 38, 21 (25).. K. S. 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