A Study of Vertical Transport through Graphene toward Control of

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A Study of Vertical Transport through Graphene towards Control of Quantum Tunneling Xiaodan Zhu, Sidong Lei, Shin-Hung Tsai, Xiang Zhang, Jun Liu, Gen Yin, Min Tang, Carlos Manuel Torres Jr., Aryan Navabi, Zehua Jin, Shiao-Po Tsai, Hussam Qasem, Yong Wang, Robert Vajtai, Roger K. Lake, Pulickel M. Ajayan, and Kang L. Wang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03221 • Publication Date (Web): 04 Jan 2018 Downloaded from http://pubs.acs.org on January 4, 2018

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A Study of Vertical Transport through Graphene towards Control of Quantum Tunneling Xiaodan Zhu1,2+, Sidong Lei1+*, Shin-Hung Tsai1,2, Xiang Zhang3, Jun Liu4, Gen Yin1, Min Tang4, Carlos M. Torres Jr.5, Aryan Navabi1, Zehua Jin3, Shiao-Po Tsai1, Hussam Qasem1, Yong Wang4, Robert Vajtai3, Roger K. Lake6, Pulickel M. Ajayan3, and Kang L. Wang1,2* 1

Device Research Laboratory, Department of Electrical Engineering, University of California,

Los Angeles, 420 Westwood Plaza, Los Angeles, California 90095, U. S. 2

Department of Materials Science and Engineering, University of California, Los Angeles, 410

Westwood Plaza, Los Angeles, California 90095, U. S. 3

Department of Materials Science and NanoEngineering, Rice University, 6100 Main Street,

Houston, Texas 77005, U. S. 4

Center of Electron Microscopy, State Key Laboratory of Silicon Materials, School of Materials

Science and Engineering, Zhejiang University, 38 Zhe Da Road, Hangzhou, Zhejiang 310027, China 5

Space and Naval Warfare Systems Center Pacific, 53560 Hull Street, San Diego, California

92152, U.S. 6

Department of Electrical and Computer Engineering, University of California, Riverside, 900

University Avenue, Riverside, California 92521, U.S. * Correspondence to: [email protected], [email protected]

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Abstract Vertical integration of van der Waals (vdW) materials with atomic precision is an intriguing possibility brought forward by these 2-dimensional materials. Essential to the design and analysis of these structures is a fundamental understanding of the vertical transport of charge carriers into and across vdW materials, yet little has been done in this area. In this report, we explore the important roles of single layer graphene in the vertical tunneling process as a tunneling barrier. Although a semi-metal in the lateral lattice plane, graphene together with the vdW gap act as a tunneling barrier that is nearly transparent to the vertically tunneling electrons due to its atomic thickness and the transverse momenta mismatch between the injected electrons and the graphene band structure. This is accentuated using electron tunneling spectroscopy (ETS) showing a lack of features corresponding to the Dirac cone band structure. Meanwhile, the graphene acts as a lateral conductor through which the potential and charge distribution across the tunneling barrier can be tuned. These unique properties make graphene an excellent 2dimensional atomic grid, transparent to charge carriers, and yet can control the carrier flux via the electrical potential. A new model on the quantum capacitance's effect on vertical tunneling is developed to further elucidate the role of graphene in modulating the tunneling process. This work may serve as a general guideline for the design and analysis of vdW vertical tunneling devices and heterostructures, as well as the study of electron/spin injection through and into vdW materials.

Keywords: electron tunneling spectroscopy; van der Waals materials; out of plane transport; quantum capacitance;


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Quantum tunneling heterostructures, such as magnetic tunneling junction and Josephson junctions are the fundamental building blocks of modern quantum computing and data storage systems. The emergence of van der Waals (vdW) materials has brought the construction of quantum heterostructures to new frontiers with precise manipulation and control down to the atomic level. vdW materials featuring dangling-bond free surfaces are ideal to be stacked together with well controlled interfaces separated by vdW gaps in between1. Electron tunneling through the vdW gap is a process inherent to all vdW devices, and thus, it has rapidly emerged as one of the most interesting topics in the vdW material research field. This process has led to the realization of novel electronic devices, including resonant tunneling diodes2, 3, tunnel field effect transistors4, 5, hot electron transistors6-9, optoelectronic devices10-12, as well as spintronic applications13-15. So far, the majority of research on the role of vdW materials in tunneling processes still focuses on vdW materials that are insulating in the lateral direction (such as hexagonal boron nitride). Meanwhile, conductive vdW materials are commonly used as the electrodes16-20, where the carriers are collected by the vdW materials and transported laterally along the 2-dimensional (2D) plane. Therefore the band structure of these vdW materials as well as the carrier interaction with elementary excitations can be applied to describe the physical process, and the vertical transport process is ignored. However, the lack of a periodic crystal structure in the normal direction leads to a dramatically different transport mechanism in the vertical direction from that in the lateral. One striking example is that although graphene is typically treated as a semi-metal or zero-gap semiconductor, it behaves as an insulating tunneling barrier for vertical spin injection14. A clear description of this vertical transport is essential, since in many emerging device applications, charge or spin carriers travel perpendicularly through the vdW materials, 3 ACS Paragon Plus Environment

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with limited lateral transport2,

7, 8, 21, 22

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, such as graphene’s role as the base material in hot

electron transistors7, 9, 21, and as the tunneling barrier for spin injection13, 14, 23-26. Here, by the fabrication of graphene vertical tunneling devices, we study the vertical transport process through the graphene layer together with the vdW gaps. By purposely excluding the effect of lateral transport from the structure, we provide insight into the vertical transport in single layer graphene and identify the effects from both quantum and classical transport. Due to the transverse momentum mismatch and the atomic thinness of graphene, the vertical tunneling electrons are unable to interact significantly with the lateral graphene 2D band structure. Meanwhile, the graphene, being a semi-metal in the lateral direction, can store charges and effectively tune the profile of the tunneling barrier via its quantum capacitance, thus imposing an electrical field to control the electrons in a more classical manner. A theoretical model to quantitatively explain the experimental observations and elucidate the role of graphene in vertical tunneling is established. Moreover, our model not only applies to graphene, but is universally applicable for other 2D systems. This result provides a new insight on the out-ofplane transport behavior and can act as an important guideline for both experimental and theoretical efforts to the design and analysis of vdW vertical heterostructure devices. The vertical tunneling device is designed to be composed of vertically stacked Si (n++), graphene and a top Cr/Au electrode, with the optical image and schematic diagram given in Fig. 1a and 1b, respectively. Si (n++) is chosen as the substrate and bottom electrode due to its low surface roughness immediately after treatment of HF, to avoid puncture of the atomically thin graphene. In this configuration, the top Cr/Au contact is aligned to the Si (n++) injection area, so that the electrons are directly collected by the top Cr/Au electrode without lateral transport, and the graphene serves only as a tunneling medium. During the experiment, the Si (n++) was 4 ACS Paragon Plus Environment

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grounded and the voltage was applied via the top contact. As a control experiment, we also fabricated a ‘side contact’ device (refer to Supporting Information, Fig. S1-S3), in which lateral propagation is included, and the graphene serves as the counter electrode with the vdW gap acting as the tunneling barrier. In this structure, the electrons are injected into the graphene from the Si (n++) bottom electrode and captured by graphene. Subsequently the electrons propagate laterally within the graphene sheet before they are collected by the side Cr/Au electrode. Tunneling behavior is observed as a result of the vdW gap formed at the graphene/Si (n++) interface, and a tunneling current on the order of 0.1 A/cm2 is observed. In this scenario, the electrons relax to the eigenstates of graphene instead of vertically passing through graphene, shown explicitly by the Dirac cone feature in the 1st order electron tunneling spectroscopy (ETS). This is similar to results from previous works using scanning tunneling spectroscopy to inject charge carriers from a metal tip through a vacuum gap into graphene, and the charge carriers are collected by a side contact after propagating laterally through the graphene18, 19. This indicates that the vdW gap at the graphene/Si (n++) interface acts effectively as a nanometer vacuum gap. To identify the presence of the graphene induced vdW gap, as well as to characterize the various interfaces of the vertical tunneling structure, a cross-section transmission electron microscopy (TEM) analysis was performed. In this case, a Pt film was deposited on top of the vertical structure to act as a protection layer for the focused ion beam milling process in the sample preparation. The high-angle annular dark field (HAADF) scanning TEM (STEM) image of the sample is shown in Fig. 1c. A spatially resolved energy-dispersive X-ray spectroscopy (EDS) mapping of Si, C, Cr and Au (Fig. 1d) confirmed the layer components of the vertical structure. The graphene is visible in Fig. 1d as a thin line adjacent to the Si substrate. The result of the high resolution STEM (HRSTEM) is shown in Fig. 1e for the interfaces between 5 ACS Paragon Plus Environment

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Si/graphene and graphene/Cr. The intensity profile for the cross section of Fig. 1e is shown in Fig. 1f, in which the three distinct material regions can be identified. The monolayer graphene (plus the vdW gap) appears as a nanometer scale gap on top of the atomically flat Si substrate, and is responsible for the observed direct tunneling behavior to be discussed in detail in the following paragraphs. However, no van der Waals gap can be distinguished from the TEM study. Unlike the H-passivated silicon, the fresh metal surface may have strong interaction with the πorbital of graphene and form bond, thus no fully preserved vdW gap is anticipated to form.


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Figure 1. Device structure and cross-section TEM of the graphene tunneling structure. a, Optical image of the fabricated device with the graphene region outlined by the white dash line. The top Cr/Au electrode is aligned to the exposed Si (n++) region, sandwiching the graphene. b, Schematic diagram showing the device structure of the vertical tunneling device. The cross section is cut along the red dash line in a. The Si (n++) is grounded during measurements and the voltage is applied through the Cr/Au top electrode. c, Low magnification HAADF STEM image showing the cross section of the vertical tunneling structure. The monolayer graphene and the van der Waals gap are visible as a dark line located between Si and Cr, which is outlined by the black dotted line. d, Spatially resolved EDS analysis indicating the distribution of Si, C, Cr and Au. e, HRSTEM image of the Si/graphene/Cr interface revealing the existence of a gap-like feature as outlined by the white dashed lines. f, Height profile from a section of the HRSTEM image in e.

The current density-voltage (J-V) characteristics across the graphene vertical structure are shown in Fig. 2a for various temperatures. The curves show some nonlinearity, but do not show significant rectification. Thus, the vertical transport across graphene and the accompanying vdW gaps is neither ohmic nor Schottky, but of a tunneling nature. There is a slight asymmetry, a direct consequence of a non-uniform voltage drop across the barrier originating from the electron trapping and quantum capacitance of the graphene layer, as to be discussed in detail later. Note the tunneling current density is one order of magnitude larger than that of the ‘side contact’ device. This fact indicates that graphene is almost transparent to electrons, and only a small portion of the electrons are reflected or absorbed by the single layer graphene. This is consistent with quantum simulation results of semiconductor-graphene-semiconductor heterostructures 7 ACS Paragon Plus Environment

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showing that graphene can be treated as a transport barrier with a transmission coefficient dependent on the selected semiconductor material27,

28

. The temperature dependence of the

current density is slightly stronger in the vertical tunneling device, but the trend is still significantly different from that of thermally activated processes such as transport through Schottky junctions as shown in Fig. 2b. It is found that the current density ∝ , characteristic of direct tunneling processes for typical metal-insulator-metal structures29,

30

. Note the sub-

nanometer roughness of the Si substrate may slightly increase the barrier thickness; however, it will not affect this discussion significantly. A control sample with Cr/Au directly in contact with the Si (n++) was fabricated simultaneously, which yields an ohmic behavior, further confirming graphene as the origin of the observed tunneling characteristic as shown in Fig. 2c.

Figure 2. Tunneling characteristic through graphene acts as the tunnel medium. a, J-V characteristics at various temperatures showing slightly larger temperature dependence compared to the ‘side contact’ device. b, J as a function of temperature at 0.5 . The data points can 8 ACS Paragon Plus Environment

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be fitted to a parabolic function (red line), consistent with typical direct tunneling processes through metal-insulator-metal junctions. c, Comparison between the J-V characteristics of vertical structure with (red) and without (blue) graphene in the middle. Insets show schematic diagrams of the corresponding structures. d, 1st order ETS spectrum at various temperatures. A minimum in the dI/dV signal is reached at zero bias regardless of temperature. The lack of a Dirac cone related feature indicates that the injected electrons do not significantly interact with the band structure of graphene. e, Schematic diagram showing the Fermi surface of Si (blue ellipses), graphene (black rings in the middle) and the Au electrode of the vertical graphene tunneling structure. For electrons tunneling from the Si through the graphene to the Au electrode, the majority pass through graphene without interaction with the graphene band structure due to its atomic thickness and the traverse momentum mismatch (red arrow).

Consistent with a direct tunneling process, the 1st ETS of the vertical structure (Fig. 2d) does not show a Dirac cone fingerprint, which is dramatically different from that of the ‘side contact’ device (Supporting Information, Fig. S1d), as well as previous studies with vdW materials acting as the counter electrodes16-19. Instead, the 1st ETS shows a consistent minimum / at zero bias, but no other significant feature. There are some weak kinks and bumps, which are barely visible from the 2nd ETS shown in the Supporting Information, Fig. S4. This observation underscores the fact that the electrons do not interact with the band structure of the graphene significantly during the tunneling process across the graphene, which only acts as a thin tunneling barrier. This is a result of the atomic thickness of graphene, as well as the large momentum mismatch between injected electrons and the graphene band structure, as shown in Fig. 2e, in which the Fermi surface of Si, graphene, and the Au electrode is schematically shown. 9 ACS Paragon Plus Environment

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The momentum of the electrons injected from the valleys near the X point is around 0.98×108 cm-1, while graphene exhibits a Fermi momentum of 1.7×108 cm-1, and thus a large momentum mismatch (red arrow) is present. The same argument applies to electrons injected from the Cr/Au electrode, which has a transverse momentum ranging from zero to the Fermi momentum of the metal (1.2×108 cm-1 for Au). As a result, little interaction occurs as the emitted electrons pass through the graphene and are collected by the Cr/Au electrodes; and the collected electrons relax to the available states of the electrodes. Although the momentum and energy mismatch prevent quantum interaction between the tunneling electrons and the graphene band structure, the graphene layer can still trap fractions of the tunneling electrons. Due to the low density of states in graphene, the electrical potential of graphene will dramatically change (i.e., the quantum capacitance effect31, 32) and modify the electrical field configuration across the van der Waals gap. Therefore, the vdW gap serves as the tunneling barrier between silicon and graphene, so a capacitance measurement as a function of voltage will shed light on the modification of graphene on the tunneling process. The impedance spectroscopy was performed to study this effect, in which the frequency response of the resistance and reactance across the gap was measured as shown in Fig. 3a. At low frequencies, the resistance, ’ saturates while the reactance −’’ tends to zero. As the

oscillation frequency is increased, ’ is reduced towards zero, and a single peak of −’’ emerges.

The Nyquist plot exhibits a single semicircle that passes through the origin of the plot at the high frequency limit (Fig. 3b). This behavior can be readily described by an equivalent circuit consisting of a resistor and a capacitor in parallel (solid curves), and the equivalent circuit is plotted in the inset of Fig. 3b, where CGr and RGr represent the capacitance and resistance of the tunneling junction respectively, and CPad accounts for the capacitance from the surrounding 10 ACS Paragon Plus Environment

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metal contact pads for external circuit connection. The value of RGr and Ctotal = CGr + CPad can be obtained by fitting the frequency response of the reactance for different biases, and the results are given in Supporting Information, Table S1. The decrease of the RGr with increasing bias is expected for the tunneling dominated (as opposed to leakage dominated) transport behavior. The capacitance of the contact pads, Cpad, can be experimentally extracted by measuring devices having different areas of the tunnel junction, as shown in Supporting Information, Fig. S5 and is determined to be 86 pF. It is also found that Cpad is independent of the applied bias in the voltage range investigated (inset of Supporting Information, Fig. S5). Deducting this contribution from Ctotal, CGr can be determined. Finally the experimental determined CGr as a function of the sample bias (VS) is shown in Fig. 3c.


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Figure 3. Capacitance measurement of the graphene vertical structure. a, Resistance (′) and reactance (−’’) as a function of frequency for various applied sample biases. b, Nyquist plot showing −’’ versus ′ for various applied sample biases. A single semi-circle is observed for each curve, and the diameter of the semi-circle is found to decrease with increasing the sample bias, consistent with the tunneling nature of the junction. The purple arrow shows the direction of decreasing frequency. Inset shows the proposed equivalent circuit of the graphene vertical structure, in which a resistor, and a capacitor, connected in parallel are used to describe

the tunnel junction, while accounts for the capacitance of the contact pads. c, Experimental

data of as a function of the applied sample bias (blue triangles) plotted alongside with the theoretically calculated curve (red solid line). d, Schematic diagram depicting the band diagram of the graphene vertical structure. As a result of the limited density of states of graphene, the induced charge is only partially supplied by the graphene, while the rest is shared by the Cr/Au electrode. This leads to voltage drops on both the vdW gaps between Si (n++) and the graphene, , and between the graphene and Cr interface, , the sum of which equals the applied bias. e, Schematic diagram of the graphene vertical tunneling junction showing the charge stored on the Si electrode (), the graphene single layer ( ) as well as on the Cr electrode ( ). The graphene cannot completely shield the electric field lines (green) from Si due to its limited density of states.

Distinct from a typical parallel plate capacitor, the capacitance of the graphene vertical tunneling structure is a sensitive function of the bias due to the quantum capacitance. As a result of the atomic thickness of graphene, the quantum capacitance cannot be treated simply as a capacitance in series or parallel connection to the tunneling barrier capacitance. Previous 12 ACS Paragon Plus Environment

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simulation works on graphene base hot electron transistors have takin into account the quantum capacitance of graphene in these vertical devices through the Dirac density of states33, 34; an analytical expression of the influence of the graphene quantum capacitance on the vertical tunneling process is still not readily available. Herein, we construct a new model to describe the capacitance-voltage characteristic of the graphene and the vdW gap in the vertical direction, which takes into account the atomic thickness and linear density of states of graphene, as well as the asymmetrical interfaces on the two sides of graphene. The schematic energy diagram is shown in Fig. 3d for a positive bias. The slight shift of the Fermi level relative to the Dirac point is ignored for simplicity. With VS, a potential drop, , results across the fully preserved vdW gap between the Si (n++) interface and the graphene, and charge is induced in the graphene sheet. The limited density of states in the graphene will result in a downward shift of the graphene Fermi level relative to the Dirac point ( ); this shift is also equal to the voltage drop across the graphene/Cr interface. This is due to the fact that the Fermi levels of the graphene and Cr are aligned as a result of the orbital hybridization between the two materials35, because of the strong interaction between graphene and chromium, a fully preserved van der Waals gap is not expected to form in between, thus the two materials are expected to share the same Fermi Level due to the strong physical contact and electronic correlation. Another way of looking at the distribution of the voltage drop across the two interfaces is to consider the charge and electric field distributions, as depicted in Fig. 3e. The induced charge is only partially located at the graphene ( ), due to its

linear density of states, with the rest at the Cr/Au electrode ( ), and the sum of which equals the induced charge on the Si electrode ( + ). Thus, the effective electric field at the two

interfaces can be defined using the Gauss’s Law as:


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!

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(1) !

and the applied sample bias is given by: +

+

(2)

Taking into account that the charge stored at the graphene sheet is related to through31: & '

*+,-

.

((!)) (!) ! (3)

in which ((!) is the Fermi-Dirac distribution and ) (!) is the density of states of the graphene (per area), CGr as a function of the sample bias can be obtained by taking the bias dependent potential of graphene into consideration (with the detailed derivation provided in the Supporting Information):

20

1 1 0 + 1 + 1

1 1 1 1 4|| 24|| + 1 − 2 0 + 1 × −

where 4 &

− (4)

2 & (5) ; (ℏ=> )

in which ! ⁄ and ! ⁄ are the effective geometric capacitances of the Si/graphene and the graphene/Cr interfaces, respectively. The experimental data in Fig. 3c can be readily fitted to this expression, shown as the red curve, except for discrepancies near the zero bias, which has been observed and attributed to charge impurities in the graphene sheet by previous works32, 36, 37. The fitted is found to be significantly smaller than , characteristic of a full vdW gap at the Si/graphene interface and an almost disappearing vdW gap at the Cr/graphene 14 ACS Paragon Plus Environment

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interface, respectively. This asymmetry in the two interfaces, together with the quantum capacitance of the graphene, is the physical origin of the asymmetric nature of the tunneling J-V characteristic discussed earlier. This is the first model, to the best of our knowledge, which provide the influences of quantum capacitance on the vertical transport across graphene in an analytical expression, which simultaneously takes into account the atomic thickness of graphene and the graphene-metal/semiconductor interface. In summary, we systematically studied the vertical transport into and across vdW materials using graphene as a model system. It is found that when lateral transport was eliminated in a purely vertical transport, the tunneling electrons interacted weakly with the semimetallic graphene plane due to the atomic thickness, as well as the mismatch of the transverse momentum. Instead, the graphene acts as a very thin grid and is transparent to vertically tunneling charge carriers, meanwhile, it can still modulate the potential and charge distribution across the tunneling barrier via the quantum capacitance effect and thus control the tunneling current. Our study highlights the potential of graphene for use as an electron/spin tunneling barrier for high frequency electronics and spintronics. It can also open new avenues for the design and analysis of 2D material heterostructures as well as 2D/bulk material heterostructures.

Methods Monolayer graphene is grown on copper foils using CVD. For both the side contact and the vertical tunneling structures, a n++ Si substrate with a dopant concentration of 1019 cm3

is used as the substrate and as the contact electrode, and a 300 nm field oxide is deposited using

the LOCOS process around each contact region to define the injection area and isolate individual 15 ACS Paragon Plus Environment

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devices. The Si substrate is subsequently treated with HF, immediately followed by the wet transfer of the graphene. The monolayer graphene is etched into many disks with a diameter slightly larger than the contact region using oxygen plasma, followed by photo-lithography and e-beam evaporation of the side and top contacts (Cr/Au 10/100 nm). The temperature dependent J-V characteristics and ETS spectrums are measured in a physical properties measurement system (PPMS, Quantum Design, Inc.). To directly measure the first and second derivatives of current as a function of the applied voltage, an AC voltage with a DC offset is applied to the device under test using a function generator (Agilent 3250). The amplitude of the AC oscillation is set to 2 mV. The current signal for the device is converted to a voltage signal using a current preamplifier (SR570) and fed into two lock-in amplifiers (SR 830) to measure the 1st and 2nd derivatives simultaneously. The impedance spectroscopy data is collected in room temperature using an Agilent 4284A Precision LCR meter with the oscillation amplitude set to 10 mV.

ASSOCIATED CONTENT Supporting information Electron tunneling spectroscopy measurements of graphene as an electrode to collected injected carriers through the vdW gap are discussed in detail in this section. Details of the transport behavior of the vertical structure with and without graphene, theoretical analysis on the capacitance model of vertical tunneling across graphene, and experimental determination of the capacitance-voltage characteristics are also given. This material is available free of charge via the Internet at http://pubs.acs.org.


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AUTHOR INFORMATION Corresponding Author * Email: [email protected], [email protected] Author Contributions +

These authors contributed equally to this work.

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS We would like to acknowledge the support of National Science Foundation (EFMA-1433541). We would also like to acknowledge the collaboration of this research with King Abdul-Aziz City for Science and Technology (KACST) via The Centre of Excellence for Green Nanotechnologies (CEGN). This work was supported in part by FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA. We thank M.A.Zurbuchen for discussions and comments on this work. J.Liu and Y.Wang thanks the support of the National Science Foundation of China (51390474, 11234011) and National 973 Program of China (2013CB934600).


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