Physics Letters A 378 (2014) 1321–1325

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Physics Letters A

www.elsevier.com/locate/pla

Transport properties of graphene/metal planar junction

Caihua Shen a, Juan Liu a, N. Jiao a, C.X. Zhang b,∗, Huaping Xiao b, R.Z. Wang c, L.Z. Sun a,∗∗a Department of Physics, Xiangtan University, Xiangtan 411105, Hunan, Chinab Hunan Provincial Key Laboratory of Micro-Nano Energy Materials and Devices, Xiangtan University, Xiangtan 411105, Hunan, Chinac College of Materials Science and Engineering, Beijing University of Technology, Beijing 100124, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 1 September 2013Received in revised form 1 March 2014Accepted 6 March 2014Available online 15 March 2014Communicated by R. Wu

Keywords:Graphene/metal planar junctionFirst-principles calculationTransmission minimumWork function differenceElectrostatic potential

The transport properties of graphene/metal (Cu(111), Al(111), Ag(111), and Au(111)) planar junctionare investigated using the first-principles nonequilibrium Green’s function method. The planar junctioninduce second transmission minimum (TM2) below the Fermi level due to the existence of the Diracpoint of clamped graphene. Interestingly, no matter the graphene is p- or n-type doped by the metalsubstrate, the TM2 always locates below the Fermi level. We find that the position of the TM2 is not onlydetermined by the doping effect of metal lead on the graphene, but also influenced by the electrostaticpotential of the metal substrate and the work function difference between the clamped and suspendedgraphene.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Graphene [1,2] has attracted much attention as a fascinatingcandidate for nanoelectronics and spintronics [3–6] due to its ex-cellent properties. Lots of prototypic graphene based devices, suchas high-speed graphene photodetector [7] and field effect tran-sistors [8], have been fabricated in experiments. Either used aselectrode or channel, the interface between graphene and othermaterials is an important part for graphene based nano-device.Consequently, lots of experimental [9–11] and theoretical [12–16]works have focused on the properties of graphene-based planarjunction, because the performance of nano device is significantlyaffected by the contact.

The advent of epitaxially grown graphene on the metal, such asCu [17], facilitates the fabrication of graphene based nano-device.The graphene/metal planar junction (metal-covered graphene) isthe most popular electrode, so physical understanding of the trans-port properties of graphene/metal planar junction is essentiallyimportant. Previous studies indicated that the interaction betweengraphene and metals can be divided into two types [16]: (I)chemisorption, the interaction between graphene and metals, suchas Co, Ni, and Pd, is so strong that the electronic characteristics ofgraphene are undermined; (II) physisorption, the metals, such as

* Corresponding author. Tel.: +86732 58292195; fax: +86732 58292468.

** Corresponding author. Tel.: +86732 52665818; fax: +86732 58292468.E-mail addresses: zhangchunxiao@xtu.edu.cn (C.X. Zhang), lzsun@xtu.edu.cn

(L.Z. Sun).

http://dx.doi.org/10.1016/j.physleta.2014.03.0080375-9601/© 2014 Elsevier B.V. All rights reserved.

Ag, Au, Cu, Pt, and Al, only slightly influence the electronic charac-teristics of graphene. In case (II), the graphene’s linear dispersionbands and Dirac cone are preserved.

The effects of the metal leads on the electronic transport werealso studied for the planar junction made up of graphene sand-wiched by Ni(111), Co(111) [18] or Cu(111) [19] and that madeup of graphene contacted underneath by metal lead [20–22]. Twotransmission minima are found in the transmission spectra dueto the vanishing density of states (DOS) at the Dirac point forgraphene/Cu(111) and graphene/Al(111) junction where graphenephysically absorbs no metal leads. The position of the transmissionminimum (TM) originating from clamped graphene on the metallead is qualitatively attributed to the doping effects of metal leadson graphene [19,20]. However, there is work function differencebetween clamped and suspended graphene in a device with pla-nar junction. The work function difference can induce the chargetransfer between clamped and suspended regions and influencethe position of TM. At the same time, the electrostatic potentialof the metal lead acting on the graphene also affects the potentialprofile of graphene and then the position of TM.

To this end, we study the transport properties of the graphene/metal (Cu, Al, Ag, Au) planar junction in details. Our finding in-dicates that the metal lead induces a TM (denoted as TM2) inaddition to the TM at the Fermi level (TM1) because of weakhybridization between the graphene and metal lead. More interest-ingly, the TM2 is always below the Fermi level independent of thedoping type of graphene. The position of the TM2 is determinedby the doping effect of the metal on graphene, the electrostatic

1322 C. Shen et al. / Physics Letters A 378 (2014) 1321–1325

Fig. 1. Schematic of the device with graphene/Au planar junction (a). The most sta-ble configuration of graphene on Cu with 1 × 1 supercell (b) and graphene with2 × 2 supercell on Au, Ag, Al (111) surface with

√3 × √

3 supercell (c). The pink,yellow and orange represent the metal atoms on “A”, “B” and “C” site, respectively.(d) is the LDOS at Fermi level of the device constructed by graphene/Au planar junc-tion. (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

potential of the metal lead, and the work function difference be-tween suspended and clamped graphene in the device.

2. Computational methods and models

To investigate the transport properties of graphene/metal(111)planar junctions, we construct two-probe systems in which theleft and right leads are composed by graphene/metal(111) planarjunctions and free-standing graphene, respectively. The model con-structed by graphene/Au(111) planar junction is shown in Fig. 1(a).The center scattering region contains 8 unit-cells of graphene (thelength is about 20 Å) and 2 surface layers of metal for the leftlead. The most stable configurations of the graphene/metal(111)planar junction are following the results of previous report [16].The top-fcc adsorption geometry is the most favorable one forgraphene/Cu(111) as shown in Fig. 1(b). The most favorable con-figuration for graphene/metal(111) (metal = Au, Ag, and Al) is√

3 × √3 metal supercell matching 2 × 2 graphene supercell, as

shown in Fig. 1(c).The atomic coordinates are optimized using VASP [23,24], a

density functional theory (DFT) [25] package, until the residualforces are less than 0.01 eV/Å and the total energies are convergedto 10−5 eV. The local density approximation (LDA) [26] is used forthe exchange–correlation functional. In the graphene/metal leads,six atom layers of Au(111), Ag(111), Cu(111), and Al(111) areadopted as substrate. Only the carbon atoms as well as the fourtop layers of the metal substrate are allowed to relax without sym-metric constraint. In the calculation, a vacuum space of ∼10 Å isset in the perpendicular direction of the graphene to avoid the in-teraction between neighboring images and the Dipole correctionis applied to eliminate the interaction between the asymmetricsurfaces of adjacent images. On the basis of our calculation, thedistance between the graphene and the metal substrates is around3.3 Å indicating the physisorption of graphene on these metal sub-strates, which agrees with the results in previous work [16].

The quantum transport is calculated using the real-spacenonequilibrium Green’s function (NEGF) method implemented inthe Atomistix ToolKit (ATK) package [27]. Such package com-bines the NEGF technique with DFT to realize the simulation ofelectronic or spin-polarized quantum transport in the molecularconductors under nonequilibrium situations. The Hamiltonian andoverlap matrices employed in the NEGF calculation of the trans-mission are obtained from the self-consistent potential derived

from the numerical linear combination of atomic orbital (LCAO)method implemented in SIESTA [28]. The voltage transmissionspectrum is calculated by the standard equation

T (E, V ) = Tr[ΓL(E, V )G(E, V )ΓR G†(E, V )

](1)

where G is the Green’s function of the contact region, ΓL/R is thecoupling matrix, and V is the applied voltage bias. The electriccurrent as a function of the applied voltage is obtained by the in-tegration of the transmission spectrum. The electric current can becalculated from the corresponding Green’s function and the self-energies using the Landauer–Büttiker formula:

I(V ) = 2e

h

+∞∫

−∞dE

[f L(E − μL) − f R(E − μR)

]T (E, V ) (2)

where μL and μR are the electrochemical potentials for the twoelectrodes and T (E, V ) is the transmission coefficient at energy Eand bias voltage V . The details of this method can be found inRef. [27]. In present study, we use a single-ζ polarization as ba-sis set, LDA.PZ, for exchange–correlation energy, and 250 Ry forthe mesh cutoff. The total energies are converged to 10−5 Ry. Con-verged k-meshes are adopted in our calculation. It is worth notingthat before we performed the calculations combined two differ-ent method, we have tested the compatibility of the two codes,VASP and ATK. Our results indicate that the transmission spec-tra are almost the same by different relaxation methods. In ourpresent work, we choose VASP for relaxation due to its powerfulcomputational capability in relaxation and less time consumption.

3. Results and discussions

Fig. 2(a) shows the transmission conductance (T ) versus energy(E) along zigzag direction under zero bias. Perpendicular to trans-port orientation, the width of the unit cell in graphene/Cu is onlyhalf of that in graphene/Al, graphene/Ag, and graphene/Au. Forcomparison purpose, we calculate the T of graphene/Cu2 with twographene orthogonal unit cells perpendicular to transport orienta-tion. The results in Fig. 2(a) indicate that the T of graphene/Cu2 issimilar to that of graphene/Al, graphene/Ag, and graphene/Au. TheT of graphene/Cu2 is almost twice intensity as that of graphene/Cudue to the double transport channels. The T results of graphene/Cuand graphene/Al in our present work agree well with previous re-ports [19,20].

All the devices show two transmission minima originating fromthe vanishing DOS at the Dirac points of left and right leads. TheTM at E = 0 (TM1) and TM below the Fermi level (TM2) are de-rived from the Dirac point of the freestanding graphene (rightlead) and the graphene on the metal lead (left lead), which can beconfirmed by the distribution of the eigenstates of the molecularprojected self-consistent Hamiltonian (MPSH) shown in the insetsof Fig. 2(a). From the insets, one can see that the TM2 is derivedfrom the Dirac point of the clamped region of graphene sittingon the metal lead for the n-type doping graphene/Al and p-typedoing graphene/Au planar junction. The transmission around TM2shows non-zero characteristics, especially, there are apparent twoor more minima for Au and Pt cases as shown in Fig. 3 and Fig. S1in the Supplementary Data. Such phenomenon derives from thecoupling between graphene and the metal which admixes metalstates into the states around the Dirac point producing nonzeroDOS around the Dirac cone and further producing nonzero trans-mission. When the coupling between graphene and metal becomestronger, the dispersion splitting will be induced around the Diracpoint [16]. Such band splitting will produce two or more minimain the transition around the TM2, such as the cases of Au and Pt.

C. Shen et al. / Physics Letters A 378 (2014) 1321–1325 1323

Fig. 2. (a) Transmission spectra of the devices with graphene/metal planar junc-tion. The insets are the MPSH of the molecule orbital around the TM2 for thedevices with graphene/Au and graphene/Al metal planar junction, respectively.(b) Schematic of Ed and �EW for isolated systems. Left and right panels representthe isolated graphene on metal substrate and freestanding graphene, respectively.(c) Schematic of the relative position between Dirac points of clamped and sus-pended regions (�) in two-probe system.

The results are in good agreement with the report of Barraza-Lopez [20]. Interestingly, the TM2 locates below the Fermi levelat −0.77 eV, −0.88 eV, −0.91 eV and −0.76 eV for graphene/Cu2,graphene/Al, graphene/Ag and graphene/Au, respectively. Grapheneis n-type doped on Cu(111), Al(111), and Ag(111) substrates, whileis p-type doped on the Au(111) substrate. [11] The doping effectsinduce charge transfer between the graphene and the metal leads,and shift the Dirac cone of graphene relative to the Fermi level.Based on the DFT calculation, the Dirac cone is lowered to belowthe Fermi level in the n-doped graphene planar junctions, while itis raised to beyond the Fermi level in the p-doped graphene pla-nar junctions. However, the TM2 is below the Fermi level for allthe devices with these four kinds of planar junctions. To confirmthat the TM2 is below the Fermi level for the two-probe systemwith graphene/Au, we calculate the T of two-probe system with16 unit cells of graphene and 4 surface layers of Au in central re-gion, as shown in Fig. 3. We find that the transmission spectraalmost remains unchanged with the increase of the surface lay-ers and central region, except slight fluctuation away from theFermi level. For comparison purpose, we also calculate the equi-librium transmission, effective potential, and I–V characteristics of

Fig. 3. Transmission spectra of the devices with graphene/Au planar junction. Theblue and wine lines represent the graphene/Au with 2 and 4 surface layers of Auin the scattering region. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

the device with graphene/Pt(111) planar junction. The results areshown in Fig. S1 in the Supplementary Data. Similar to the caseof graphene/Au, graphene is p-type doped on Pt(111) substrates intwo-dimensional planar junction. The results as shown in Fig. S1(a)indicate that the TM2 originated from the Dirac point of clampedgraphene also locates at −0.70 eV below the Fermi level. Con-sequently, there are other important factors that determines therelative position between TM1 and TM2 besides the doping effects.

Besides the doping effects, the electrostatic potential of themetal lead and the work function difference between the sus-pended and clamped graphene determine the relative position be-tween TM1 and TM2. When graphene is adsorbed on the metalsubstrates, the weak hybridization between the graphene and thesubstrate induces a net charge transfer producing the doping effectfor the graphene. The doping effect determines relative position(Ed) of the Dirac cone to the Fermi level in the two-dimensionalgraphene/metal (corresponding to the clamped regions in Fig 2(b)).On the basis of DFT calculation, we find that graphene is n-typedoped on Cu(111), Al(111) and Ag(111), and their Ed is nega-tive as −0.16 eV, −0.54 eV, and −0.37 eV, respectively, whereasgraphene is p-type doped on Au(111) and its Ed is positive as0.19 eV. Although the doping effect determines the relative po-sition of the Dirac cone to the Fermi level in isolated clampedregions, the electrostatic potential of the metal lead depresses theabsolute position of the electronic states of the clamped graphenein a two-probe system. As shown in Fig. 4, the electrostatic po-tential of clamped region is significantly lower than that of thesuspended one. The electrostatic potential difference (E P ) betweenclamped and suspended regions is −0.67 eV, −0.98 eV, −0.48 eVand −0.60 eV in the devices with Cu, Al, Ag, and Au lead, re-spectively. The electrostatic potential difference depresses the TM2relative to TM1 in the energy. In addition, owing to the inter-action between graphene and metal lead, the work function ofthe clamped graphene in left lead (4.46 eV, 4.04 eV, 4.20 eV and4.85 eV for the graphene no Cu, Al, Ag and Au respectively, whichagree with Ref. [16]) is not equal to that of the freestanding one(4.48 eV) in right lead. The work function difference between sus-pended and clamped graphene tunes the relative position of theFermi level when put graphene/planar junction and suspendedgraphene together into a two-probe system, as shown in Fig. 2(b)and (c). The difference between TM2 and TM1 induced by workfunction difference (denoted as �EW ) is 0.02 eV, 0.44 eV, 0.28 eV,and −0.37 eV for graphene/Cu2, graphene/Al, graphene/Ag, and

1324 C. Shen et al. / Physics Letters A 378 (2014) 1321–1325

Fig. 4. Electrostatic potential profile of graphene/metal devices along the transportdirection. The potential profile of graphene/Cu is same to that of graphene/Cu2.

graphene/Au, respectively. Consequently, the energy difference ofDirac cones � between the clamped and suspended regions is thesum of Ed , �EW , and E P as −0.81,−1.08,−0.57, and −0.78 forCu2, Al, Ag, and Au systems, as shown in Fig. 2(c). � determinesthe relative position between TM1 and TM2. When TM1 is setto the Fermi level, TM2 locates below the Fermi level. In partic-ular, for graphene/Au and graphene/Pt, although the Au(111) andPt(111) lead induce p-type doping effect on the clamped graphene,both work function difference and electrostatic potential of themetal substrate depress the Dirac cone of the clamped region,resulting in that the TM2 locates below the Fermi level in thegraphene/Au and graphene/Pt two-probe system.

We also consider the dependence of the transport properties onthe orientation of graphene. The results indicate that the two Tsare related by a constant scaling factor and the ratio of the trans-mission between zigzag and armchair orientation is equal to theratio of the width of the super-cell used for transport. The resultsare in good agreement with previous report [19]. Moreover, the po-sitions of the two TM points are also independent of the transportorientation. As for graphene/Au, the TM2 is below the Fermi levelfor both zigzag and armchair transport orientations. Such resultsfurther confirm the conclusion that the TM2 depends not onlyon the doping effect but also on the electrostatic potential of themetal lead and the work function difference between the clampedand suspended regions. It is worth mentioning that the slight po-sition difference between the TM2 (determined in two probe sys-tem) and the absolute position of the Dirac cone of clamped region(rely on perfect two dimensional system) is produced by the com-plicated edge effect of the metal lead on the graphene. From thelocal density of states (LDOS) as shown in Fig. 1(d), which qual-itatively represents the distribution of transport channels at realspace, one can obviously see the heterogeneity of the distributionof the electron channels between the clamped and suspended re-gions induced by the edge effect of the metal lead.

The I–V characteristics of all the graphene/metal systems un-der low applied bias are shown in Fig. 5. The I–V curve of thedevice with graphene/Cu agrees well with previous report [19],and its current is only half of that of other four systems. Moreover,the I–V curves of the device with graphene/Cu2, graphene/Al,graphene/Ag, and graphene/Au planar junction show similar char-acteristics, which is derived from the similar transmission in thebias window [−0.5 eV,0.5 eV]. The differential conductancesin bias windows [0.2 V,0.5 V] and [−0.5 V,−0.2 V] obtainedby linearly fitting the I–V curves are shown in the inset ofFig. 5. The results indicate that the differential conductance of the

Fig. 5. I–V characteristics of graphene/metal devices. The inset is the differentialconductance of each device when bias windows are 0.2 ∼ 0.5 V, −0.5 ∼ −0.2 Vand corresponding asymmetric ratio.

graphene/metal devices under forward bias is smaller than thatunder reverse bias. We define the asymmetric ratio of the differ-ential conductance (η) as |Gn − G p |/G p , where Gn and G p presentthe differential conductance under reverse bias and forward bias,respectively. The asymmetric ratios are about 40.7% (38.3%), 44.9%,39.2% and 54.5% for graphene/Cu2 (graphene/Cu), graphene/Al,graphene/Ag, and graphene/Au, respectively. The results indicatethat there is a Schottky barrier at the contact area produced by thesharp electrostatic potential step at the edge of the planar junc-tion. The η of graphene/Cu2 and graphene/Cu shows similar valueswhich indicates that the asymmetric differential conductance is in-dependent of the transverse size of the systems. In comparisonwith the case of graphene/Au, the hybridization between clampedgraphene and Pt is much stronger in graphene/Pt(111) as shown inFig. S1, as a result, its asymmetric ratio of the differential conduc-tance is only 1.6%. The details can be found in the SupplementaryData. It is worth mentioning that when the bias is in the range of[−0.1 V,0.1 V], the low current only originates from the TM1 inthe transmission. The effects of TM2 on the current do not emergebecause TM2 locates beyond the bias window in our calculationswhich will induce negative differential resistance as pointed outby previous report [19].

4. Conclusion

We studied the transport properties of the nanodevices withgraphene/metal planar junction. Two transmission minima appearin the transmission spectra for all metal planar junctions, whichderive from the Dirac cones of clamped and freestanding grapheneof the device. The position of TM2 derived from the clamped re-gion is determined not only by the doping effect introduced by themetal lead, but also by the mismatch of the work function betweenclamped and freestanding regions as well as the electrostatic po-tential around the clamped region. The I–V curves of all systemsshow asymmetric due to the sharp electrostatic potential step atthe edge of the metal lead.

Acknowledgements

This work is supported by the National Natural Science Foun-dation of China (Grant Nos. 11274262, 11274029, 10874143,11304263, and 11304264), the Program for New Century Excel-lent Talents in University (Grant No. NCET-10-0169), the Scien-tific Research Fund of Hunan Provincial Education Department

C. Shen et al. / Physics Letters A 378 (2014) 1321–1325 1325

(No. 13B117) and Hunan Provincial Natural Science Foundation ofChina (Grant No. 13JJ4046).

Appendix A. Supplementary data

Supplementary material related to this article can be found on-line at http://dx.doi.org/10.1016/j.physleta.2014.03.008.

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