atomistic insight into the formation of metal-graphene one
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Atomistic Insight into the Formation of Metal-Graphene One-Dimensional Contacts
Kretz, Bernhard; Pedersen, Christian Søndergaard; Stradi, Daniele; Brandbyge, Mads; Garcia-Lekue,Aran
Published in:Physical Review Applied
Link to article, DOI:10.1103/PhysRevApplied.10.024016
Publication date:2018
Document VersionPublisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):Kretz, B., Pedersen, C. S., Stradi, D., Brandbyge, M., & Garcia-Lekue, A. (2018). Atomistic Insight into theFormation of Metal-Graphene One-Dimensional Contacts. Physical Review Applied, 10(2).https://doi.org/10.1103/PhysRevApplied.10.024016
PHYSICAL REVIEW APPLIED 10, 024016 (2018)
Atomistic Insight into the Formation of Metal-Graphene One-DimensionalContacts
Bernhard Kretz,1 Christian S. Pedersen,2 Daniele Stradi,2 Mads Brandbyge,2 andAran Garcia-Lekue1,3,*
1Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, E-20018 San Sebastian, Spain2Center for Nanostructured Graphene (CNG), Department of Micro- and Nanotechnology (DTU Nanotech),
Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark3IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
(Received 16 February 2018; revised manuscript received 27 April 2018; published 14 August 2018)
Motivated by the need to control the resistance of metal-graphene interfaces, we have simulated thestructural and transport properties of edge contacts upon their formation. Our first-principles calculationsreveal that the contacts evolve in a nontrivial way depending on the type of metal and the chemical con-tamination of the graphene edge. In particular, our results indicate that the origin of the low experimentalresistance of chromium-graphene edge contacts is related to their weaker variation upon contaminationand defect formation. In summary, by analyzing the distance dependence of the graphene-metal inter-action and the relation between the reactivity and forces at the graphene edge, we shed new light on themechanisms responsible for the diverse performance of experimentally fabricated graphene edge contacts.
DOI: 10.1103/PhysRevApplied.10.024016
I. INTRODUCTION
The idea of using graphene in electronic components,such as interconnects, comes naturally due to the mate-rial’s small volume and excellent electrical and thermalproperties [1,2]. However, many of the envisioned applica-tions involve the formation of contacts between grapheneand metallic electrodes [3–7], which will necessarily alterthe electrical characteristics of graphene near the contactregion [8–10]. Accordingly, huge efforts are being madeto design metal-graphene (M-Gr) interfaces with minimalcontact resistance [11–16].
Achieving a good contact performance has been provendifficult to achieve with conventional on-top contactschemes, in which the large overlap between the grapheneπ -system and the metal often yields a large contact resis-tance [17–21]. An alternative approach is to use edgecontacts, where the graphene edge is directly connected tothe metal, forming a one-dimensional (1D) metal-grapheneinterface [22]. Within this new contact scheme, the spatialoverlap between the graphene and the metal is reduced to aminimum and, ideally, a covalent bond is formed betweenthe metal atoms and the graphene. This leads to substan-tially lower resistance in edge contacts as compared toon-top contacts [22–28].
Despite their outstanding potential, understanding andcontrolling the transport properties of edge contactsremains a challenging task, mainly due to the difficulty
of obtaining statistically reproducible M-Gr 1D contactgeometries. Indeed, considerable device-to-device resis-tance variations have been observed [15,22,26], which canbe ascribed to the use of different fabrication strategies.For instance, before electrode deposition the graphene isoften shaped by reactive ion or plasma etching. This tech-nique is efficient in exposing graphene edges and removingresidues [15,22,25,29,30], but might also significantly alterthe structural and chemical conformation of the contact.
A few first-principle calculations have already discussedthe influence of chemical contamination by foreign atomicspecies in graphene edge contacts, but assuming chemi-cally abrupt M-Gr interfaces at equilibrium bonding con-ditions [22,31]. Yet, the final properties of the contacts aremost likely governed by electrochemical processes involv-ing both graphene (clean or contaminated) and metal.Additionally, the chemical reactivity during the contactformation will also depend on the metal of choice. Thiscomplex atomic-scale scenario is not accessible experi-mentally, which indicates an urgent need for a systematictheoretical study.
In this work, we investigate the formation of M-Gredge contacts using different contaminants and metal elec-trodes. Special attention is paid to the reactivity of themetal and the graphene edges, a relevant question so farneglected in the study of this type of contact. Based onour first-principles calculations, we elucidate the complexdependence of the graphene edge-contacts resistance onboth the termination chemistry of graphene and the metalwork function [32,33].
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B. KRETZ et al. PHYS. REV. APPLIED 10, 024016 (2018)
II. METHODS
The electronic structures and geometries of 1D metal-graphene contacts upon their formation are calculatedusing density-functional theory (DFT), as implemented inthe SIESTA code [34]. To describe the model graphene edgecontact schematically depicted in Fig. 1(a), we use a super-cell made up of a metallic slab containing five layers ofNi(111), Cr(110), Ti(0001), or Au(111), and a graphenesheet containing 40 C rows. The graphenic subsystem ispassivated with H at the edge furthest from the contactregion, and unpassivated or functionalized with F, F2, orO at the edge facing the metal surface. This choice ofcontaminants is based on stability calculations of differ-ent graphene edge functionalizations, performed using theVASP [35–38] code (for details see Ref. [39]).
In order to determine the relevant contact configura-tions, we first calculate the total system energy as afunction of the separation distance between both subsys-tems (metal, and pristine or contaminated graphene sheet)at frozen geometries. This allows us to approximatelyestimate the minimum-energy and maximum-force separa-tions, from where all the atoms of the graphenic subsystem(C, H, and contaminant atoms) as well as the three topmostmetal layers are allowed to relax (for more details aboutmetal-graphene distances see Ref. [39]). The optimizedinterface geometries obtained in this way are referred toas minimum-energy and maximum-force contact confor-mations throughout the paper. It is worth mentioning thatmore realistic interface structures might be obtained usingmodern stochastic methods [40,41]. However, this wouldpose a challenging task that falls outside the scope ofthe present work. Thus, herein we focus on the optimizedstructures obtained by standard DFT, which might indeedserve as excellent starting points for future studies basedon stochastic approaches.
Based on the relaxed contact geometries, we com-pute the elastic transmission with TRANSIESTA [42,43],which combines DFT with nonequilibrium Green’s func-tion methods. The scattering region is constructed byconnecting the metal and graphene electrodes at the left-hand and right-hand sides of the contact region, aimingto prevent spurious effects related to the graphene chan-nel length. Due to the asymmetric arrangement of the twoelectrodes, a buffer region of 16 C atom rows is intro-duced. Regarding the termination of the graphene edge,it is found to have a minor influence on the resistance ofthe uncontaminated contacts (see Ref. [39]). Although thescenario is likely to change in the case of contaminatedgraphene edges, to allow direct comparisons between dif-ferent contacts to the same metal, here we have decidedto consider only zigzag-edged graphene both for uncon-taminated and chemically modified cases. Moreover, sincethe metal contacts used experimentally are not crystallineand thus difficult to simulate, we have chosen one single
zx
z
xy
(b)
(a)
FIG. 1. (a) Side (left) and top (right) view of a model M-Gredge contact. (b) Calculated contact resistance at 300 K as afunction of gate voltage (VG) for different graphene edge con-tacts with different metals, namely Ni (orange), Cr (brown), Ti(brown), and Au (cyan). The intrinsic resistance of free-standinggraphene is included as reference (black curve). A gate voltageof VG = ±0.2 V corresponds to a doping level of approximately4 × 1012 cm−2.
crystalline orientation for each of the metals considered.This approach allows us to focus on trends, making ourresults for different systems fairly comparable.
For all the calculations, a Monkhorst-Pack k-point gridwith 23 × 3 × 1 k-points is used for the Brillouin zonesampling and the mesh cutoff is set to 400 Ry. A double-ζpolarized basis set is utilized with 0.02 Ry energy shift tocontrol the cutoff radii of the basis orbitals. The exchange-correlation energy is approximated by the Perdew-Burke-Ernzerhof (PBE) [44] flavor of the generalized gradientapproximation (GGA). Structures are relaxed until forcesare smaller than 0.01 eV/Å. The transmission functions aresampled over 767 × 5 × 1 k-points.
Based on the first-principles transport results, the effectof gate voltage is modeled by a rigid shift of the Fermilevel. The thermally averaged resistance as a function ofthe gate voltage (VG) is then obtained from the calculatedtransmission curve T(E) as follows [26]:
1RC
= G0
L
∫T(E)
e(E−(EF+eVG))/kBT
(1 + e(E−(EF+eVG))/kBT)2
dEkBT
, (1)
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where L is the transverse length of the contact along theperiodic x direction, G0 is the quantum of conductance,and T is the temperature.
III. RESULTS AND DISCUSSION
A. Conductance properties of clean contacts
To examine whether the wide range of resistance val-ues reported for different metals can be attributed to theirintrinsic different nature [22,26], we first study clean M-Grcontacts at equilibrium. Figure 1(b) shows the calculatedresistance of uncontaminated edge contacts to a represen-tative set of metal surfaces [31], i.e., Cr(110), Ti(0001),Ni(111), and Au(111). Unexpectedly, the maximum resis-tance is obtained when contacting graphene to Ti. In fact,the performance is even worse than with the more inertAu electrode. The origin of such poor electronic transmis-sion across the Ti-Gr interface is the mismatch between theFermi level states of the metal and those at the grapheneedge, as was reported to occur for epitaxial graphene on Ti[45]. In any case, despite small variations, all four metalsexhibit contact resistances of the same order of magnitude,within roughly a factor of two from the ideal contact resis-tance of graphene. Our calculated resistances are in qual-itative agreement with those reported in Ref. [46], despitesome numerical discrepancies which can be attributed tomethodological issues (in particular, to the short channellength employed in their studies). Remarkably, this indi-cates that the experimental orders-of-magnitude disparityin the resistance of edge contacts can not be solely dueto the use of different metal electrodes. For this reason,in the following we turn our attention to the influence ofgraphene’s chemical termination.
B. Interface reactivity of contaminated contacts
The plasma employed to etch graphene is usually gen-erated from a mixture of gases containing fluorine (F) oroxygen (O) [22,25,26,47] and, thus, we consider such ele-ments as possible edge contaminants. According to ourenergetics considerations (see details in Ref. [39]), mono-and difluorination [48], and mono-oxidation are found tobe the most favorable chemical edge modifications. Foreach of these contaminant groups, we mimic the exper-imental fabrication process by investigating the contactformation upon approach of the metal to the graphenicsystem (see the details in the Methods section). Particularfocus is placed on the maximum total attractive force con-formation, as this corresponds to the separation at whichmetal and graphene will be most reactive.
Figure 2 shows the forces in the z direction (perpendic-ular to the metal surface) on the atoms of the clean or con-taminated graphene sheet, at a distance of maximum totalattractive force. The following representative systems arestudied: (i) three Ni-based contacts, composed of Ni(111)
(d)
Forces on C atoms at interface
(a) (b)
(c)
z
x
FIG. 2. Forces in the z direction on the atoms of the graphenicsubsystem, for four selected contacts at maximum-force confor-mation. Blue (red) shades indicate forces pointing towards (awayfrom) the metal surface. The forces for the following contacts areshown: (a) Ni-Gr, (b) Ni-O-Gr, (c) Ni-F-Gr, and (d) Cr-F-Gr.
and clean, O-contaminated, or F-contaminated graphene(Ni-Gr, Ni-O-Gr, and Ni-F-Gr, respectively); (ii) a Cr-based contact composed of Cr(110) and F-contaminatedgraphene (Cr-F-Gr). Blue (red) shades indicate forces onthe individual atoms pointing towards (away from) themetal surface. To allow direct comparisons, the forcesfor the contaminated graphene contacts are rescaled withrespect to those for clean graphene. The arrows in Fig. 2indicate the magnitude and direction of the forces on theatoms closest to the metal, i.e., on the first C row for theclean Ni-graphene contact, and on the F or O atoms forthe contaminated contacts. In all cases, the net forces onthe edges of the graphenic subsystems are pointing towardsthe metal surface, i.e., graphene feels an attractive forceexerted by the metal. We see how the magnitude of theforce strongly depends both on the chemical terminationof graphene as well as on the metal of choice. For the Nielectrode we find that the attraction is maximum for theclean metal-graphene interface, the attractive force alwaysbeing reduced upon contamination. However, the degreeto which the force is quenched depends on the type ofcontaminant: for the oxidized case the forces remain quitelarge [Fig. 2(b)], while in the fluorinated case they becomeextremely small [Fig. 2(c)]. Interestingly, if one substi-tutes Ni by Cr, the force on the fluorinated graphene edgeincreases significantly [Fig. 2(d)], while it remains almostconstant upon contamination with O (see Fig. S7 in [39]).
In addition, we investigate to which degree the interfaceevolution depends on the specific contacting site betweenthe metal and the graphenic system. With this aim, we
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(a) (b)
FIG. 3. (a),(b) Side and top views of two Ti-F2-Gr interfaceswith different contacting sites (marked with horizontal dashedlines). Top panels: maximum-force conformations before struc-tural optimization. Lower panels: contact geometry upon relax-ation, together with the corresponding resistance at T = 300 Kand VG = 0 V.
consider a Ti(0001) electrode and a difluorinated graphenesheet, which are brought into contact at two different rela-tive positions, as shown in Fig. 3. Both systems are fullyrelaxed from their maximum-force conformation (upperfigures) and, interestingly, the equilibrium structures areremarkably different (lower figures). For the initial con-tact configuration of Fig. 3(a), only one of the F atomsgets stripped off from the graphene edge and bonds to themetal. For the contact geometry in Fig. 3(b) instead, bothF atoms are removed from the edge and adsorbed onto themetal substrate. In the latter case, the graphene eventuallyforms a clean contact to Ti and the contact resistance isthus significantly reduced.
C. Resistance characteristics of 1D contacts
The results presented in the previous section clearlyindicate that an appropriate interpretation of experimen-tal results requires more realistic considerations of thecomplex interplay between the interface structure and itsreactivity. Accordingly, we carry out a systematic analysisof the structural and chemical changes of the 1D contactsupon their formation, for all the possible combinationsof metal electrodes (Au, Ni, Cr, and Ti) and grapheneterminations (clean, and F-, F2-, or O-contaminated) con-sidered in this work. We find that, when transition metalsare used, the final contacts always fall in one of the threeconformations schematically depicted in Fig. 4(a). Thus,the F2 modification of the graphene edge, despite beingenergetically more favorable for isolated graphene [48],
MOOO
MFFF
M
102
103
104
105 Ni(b)
(a)
RC (
Ωμm
)
Cr Ti AuCleanOF
FIG. 4. (a) Schematic illustration of the three equilibrium con-formations for transition-metal-based contacts. (b) Histogram ofthe contact resistance at T = 300 K and VG = 0 V, as obtainedfor different metals (Ni, Cr, Ti, and Au) and graphene edgecontaminations (O, F).
is not likely to occur under the influence of transition-metal electrodes in edge-contacted topology. When Au isused, instead, the graphene edges (clean or contaminated)are not modified by the interaction with the metal. Thereason behind this is the low reactivity of Au and the subse-quent weak interplay between the metal and the grapheneedge, which might also explain the bad performance ofexperimentally fabricated Au-based 1D contacts [22].
Having determined the structural and chemical con-formation of the 1D contacts, we now focus on theirconductance properties. The calculated zero gate volt-age resistances of the different interfaces studied hereare compiled in Fig. 4(b). From our results, it is clearthat, regardless of the metal, the presence of contaminantsreduces the efficiency of electron transmission across thecontacts. However, the degree to which the contaminationreduces the conductance and, thus, deteriorates the con-tact performance depends on the chemical species at thegraphene edge. Oxygen contamination does not signifi-cantly alter the contact resistance for Ni, Cr, and Ti. Incontrast, when graphene is terminated with fluorine, theresistance is always drastically enlarged (by at least anorder of magnitude). There are two intertwined factors thatplay a role in this increase of contact resistance upon F con-tamination. The first is that F can only form one covalentbond and, therefore, the contact between the metal elec-trode and the graphene edge is quite weak. The second is
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102
103
104
105
106
107 d1 d2 d3(a) (b) (c)
F
O
F
d1,Rc1
d2,Rc2
d3,Rc3 FO
Ni-Gr contacts Cr-Gr contacts
RCn
(Ωμm
)102
103
104
105
106
107 d1 d2 d3
RCn
(Ωμm
)COFF2
COFF2FFFFFFFFFFFFFFFFFFF
OOOOOOOOOOFFFFFFFFFFFFFFF
OOOOOOOOOOOOOOOOOOOOOO
FIG. 5. (a) Schematic model of a corrugated metal-graphene 1D contact. The distances d1, d2, and d3 denote metal-graphene distancesat minimum energy, maximum force, and maximum force distance plus 1 Å, respectively. The corresponding resistances are denotedby R1
C, R2C, and R3
C. (b),(c) show the histograms of contact resistance at T = 300 K and VG = 0 V for the clean (gray), O- (red),F- (blue), and F2- (light blue) contaminated Ni and Cr electrodes.
the larger separation distance between the metal and the F-contaminated graphene edge as compared to the clean one(see Table S1 in [39]). As expected from its inert charac-ter, these two effects are magnified for Au, giving rise to acontact resistance more than an order of magnitude largerthan for other metals.
The contacts employed in our simulations, made upof perfect crystalline metals and graphene with straightedges, are highly idealized structures. Experimental con-tacts will deviate in different ways from these theoreticalsystems, e.g., structural defects are expected and chemicalcontamination is most likely not uniform. Figure 5(a) dis-plays a schematic model of a corrugated metal-graphenejunction, which contains an irregular graphene edge withinhomogeneous fluorine and oxygen contamination. In thismodel, we consider the following representative distancesfrom the metal to the graphene edge (clean or contam-inated): d1 (distance of minimum energy), d2 (distanceof maximum force), and d3 (distance of maximum forceplus 1 Å). Taking this model as a reference, and usingNi and Cr as representative metals, transport calculationsfor each distance and different graphene edge terminations(clean, oxidized, mono- or difluorinated) are carried outseparately. The realistic system can be viewed as a com-bination of the different simulated scenarios and, thus, wecan extract a range of values for the resistance of the modelcontact in Fig. 5(a) from the calculations reported in thefollowing.
Figures 5(b) and 5(c) show the zero-gate-voltage resis-tance for clean, oxidized, and mono- or difluorinatedgraphene sheets at different distances from the Ni and Crmetal electrodes (additional results in [39]). As expected,the resistance rises as the graphenic subsystem gets furtherfrom the metal. However, the degree at which the qual-ity of the contact is deteriorated depends on the type ofmetal. For Ni contacts, the resistance smoothly increases asthe graphene sheet is moved further away. The increase ismore pronounced for contaminated interfaces, particularly
for fluorinated ones. At d3, the resistance of Ni-F-Gr ismore than two orders of magnitude larger than at theequilibrium distance.
Interestingly, the situation is quite different for Cr(110).When connected to clean graphene, we find that the con-tact resistance does not depend much on the Cr-Gr sep-aration distance. This behavior can be ascribed to therelatively short bond distance, both at minimum-energyand maximum-force conformations. Furthermore, whenthe graphene edge is contaminated, either with F or O,increasing the distance to the Cr electrode yields a lowerrelative variation of the resistance as compared to Ni [31].In other words, the quality of Cr-based contacts is lessdamaged upon contamination. We can thus conclude thatCr is the best candidate to form 1D graphene contacts, inagreement with the experimental observations reported byWang et al. [22].
D. Spin polarization at contaminated interfaces
Finally, the spin-polarization character of the electrontransport across 1D M-Gr contacts is addressed, using Cr-F-Gr and Ni-F-Gr as illustrative systems. Figure 6 showsthe spin-resolved density of states projected onto the inter-face atoms of a Cr-F-Gr contact, at the representativeseparation distances described above. At the distance ofminimum energy (d1), the coupling to the metal destroysthe spin-polarized attributes of the graphene zigzag edge,and the corresponding projected density of states (PDOS)exhibits spin-unpolarized behavior. As the graphenic sub-system is detached from the Cr surface, the interaction withthe metal is weakened and a net spin polarization rapidlybuilds up. Indeed, at d3 the PDOS on the first C row is com-parable to that for isolated hydrogen-passivated zigzag-edged graphene. In the case of Ni-F-Gr, instead the elec-tronic properties exhibit strong spin-polarization characterat any separation distance, which can be attributed to theintrinsic spin-polarized nature of Ni (see Fig. S10 in [39]).
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-1.0 -0.5 0.0 0.5 1.0E–EFermi (eV)
-0.3
0.0
0.3C1F x4Gr
-0.3
0.0
0.3 d2
d3
-0.3
0.0
0.3 d1PD
OS
(sta
tes/
eV)
PDO
S(s
tate
s /eV
)PD
OS
( sta
tes/
eV)
FIG. 6. Spin-up (↑) and spin-down (↓) calculated density ofstates projected onto the interface atoms of the Cr-F-Gr contact,at distances d1 (top panel), d2 (middle panel), and d3 (bot-tom panel). In the bottom panel the corresponding PDOS of agraphene zigzag edge is shown for comparison. For visualizationpurposes, the PDOS of F has been multiplied by 4.
The spin-polarization properties studied above willeventually manifest in the conductance across the con-tacts. In fact, as shown in Table I, the Ni-based contactexhibits a large spin-filtering efficiency at any separationdistance. In contrast, when Cr is used as electrode mate-rial, the spin polarization of the conductance predicted atlarge separation distances is completely quenched whenthe graphene is bound to the metal. Hence, the spin-polarization properties of the contact might be greatlymodified both by contamination and by the use of differentmetallic electrodes.
IV. CONCLUSIONS
In summary, we investigate the role of atomic-scalechemical reactivity on the formation and resistance
TABLE I. Spin-filtering efficiency, defined as (G ↑ − G ↓)/
(G ↑ + G ↓), at zero gate voltage and different separationdistances.
Spin-filtering efficiency %
d1 d2 d3
Ni-F-Gr −74.4 −89.0 −92.8Cr-F-Gr −0.4 −32.5 −86.1
performance of metal-graphene 1D contacts. We demon-strate that the final interface configuration depends on adelicate interplay between the type of metal, the contami-nation of the graphene edge, and the contacting site. More-over, structural defects and chemical inhomogeneities arefound to induce significant changes in the conductanceproperties and even the appearance of spin-filtering effects.Interestingly, we find that Cr-based contacts exhibit thelowest dependence on contamination and structural irreg-ularities, which explains why 1D contacts fabricated usingCr electrodes have the lowest interface resistance.
All in all, our results allow us to conclude that the useof different metals and etching agents is crucial to produce1D contacts with resistance values suitable for their use inreal applications. Of course, the actual resistance of a 1DM-Gr contact depends on the density and distribution ofdefects and contaminants, which in turn is conditioned bythe exact fabrication process. This kind of information isvery difficult to extract experimentally and, thus, a quan-titative assessment of measured resistances is out of thescope of this work. Nevertheless, our atomistic simula-tions are very valuable for understanding the origin of thedevice-to-device variations and, more importantly, mightbe helpful for guiding the future design of metal-graphenecontacts.
ACKNOWLEDGMENTS
This work was supported by the Spanish Ministeriode Economía y Competitividad (MINECO) (Grant No.MAT2016-78293-C6-4-R) and the Basque Dep. de Edu-cación and UPV/EHU (Grants No. IT-756-13 and PI-2016-1-0027). The Center for Nanostructured Graphene (CNG)is sponsored by the Danish Research Foundation, ProjectNo. DNRF103. D.S. acknowledges support from the HCØDTU-COFUND program. We thank Dr. B. S. Jessen foruseful comments on our manuscript and Prof. P. Bøggildfor helpful discussions.
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