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Hyokwang Park, Myeongjin Lee, Xinbiao Wang, Nasir Ali, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Euyheon Hwang, Won Jong Yoo

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[Anisotropic charge transport at the metallic edge contact of ReS2 field effect transistors](https://mdr.nims.go.jp/datasets/71ad30ca-338e-4bd3-8d9e-9c567b7ffd52)

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Anisotropic charge transport at the metallic edge contact of ReS2 field effect transistorscommunicationsmaterials Articlehttps://doi.org/10.1038/s43246-024-00526-zAnisotropic charge transport at themetallic edge contact of ReS2 fieldeffect transistorsCheck for updatesHyokwangPark1,3,MyeongjinLee1,3, XinbiaoWang1,3,NasirAli1,KenjiWatanabe 2, TakashiTaniguchi 2,Euyheon Hwang 1 & Won Jong Yoo 1The in-plane anisotropy of electrical conductance in two-dimensional materials has garneredsignificant attention due to its potential in emerging device applications, offering an additionaldimension to control carrier transport in 2Ddevices.However, previous research hasprimarily focusedon the anisotropy within electrical channel, neglecting the significant impact of anisotropic electricalcontacts of 2D materials. Here, we investigate anisotropic charge transport at the metal contacts ofhBN-encapsulated ReS2 using edge-contacted Field Effect Transistors. We observed the markeddifference in contact resistance between the cross-b and b directions, suggesting that chargetransport from the metal to ReS2 is more efficient along the b direction. This difference in efficiencyresults in a substantial contact anisotropy, reaching ~70 at 77 K. Our findings indicate that themeasured Schottky Barrier Height along the b direction is ~35meV, which is smaller than along thecross-b direction. Moreover, the tunneling probability along the b direction is two times larger thanalong the cross-b direction. Our results indicate that both Schottky Barrier Height and tunnelingamplitude are the primary contributors to the high contact anisotropy of ReS2. This work provides avaluable guideline for understanding how in-plane orientation influences charge transport at metalliccontacts in 2D devices.Since the discovery of monolayer black phosphorus (BP), the interest inanisotropic two-dimensional (2D)materials such as BP, rheniumdiselenide(ReSe2) and other transition metal dichalcogenides (TMDs) has increasedand the extensive study on anisotropic 2Dmaterials has been conducted, asthey introduce an additional degree of freedom to control carrier transportof 2D devices. Among these anisotropic 2D materials, rhenium disulfide(ReS2) standsout as ann-type semiconducting2Dmaterialwith a thickness-independent direct band gap and a high on-off ratio1–7, in addition to itsstrong in-plane anisotropic electrical1,2,8 andoptical properties9–13 dependenton thedifferent crystallographic orientations. These uniquepropertiesmakeanisotropic ReS2 highly promising for various future electronic andoptoelectronic applications, including tunneling field-effect transistors(FETs), inverters, and photodetectors, capitalizing on its intriguing in-planeanisotropic characteristics1,3,4,14–17.Recently, Wang et al. reported the conductance anisotropy controlledby thermionic emission andcarrier drift in low-symmetryReS2 transistors18.On the other hand, our group employed the edge contact method toeliminate out-of-plane conductance, so that precise measurement of theorientation-dependent in-plane conductance of the BP channel can bemade. As a result, we reported a high anisotropy ratio in channel mobility,~7.5, for BP FETs19. However, we have observed that the contact resistancein 2D TMD-based FETs, such as ReS2, is significantly higher than that innarrow bandgap BP, leading to a pronounced dependence of chargetransport anisotropy on the contact resistance, which differs from thebehavior seen inBPFETs. There also have been studies to enhance electricalperformances of 2D devices by using edge contacts, eg. edge termination ofchemical bonds20–23 and in situ edge cleaning by argon (Ar) ion beamtreatment24,25.However, previous research works including ones of our researchgroup have reported mainly on the conductance anisotropy in the channel,not the contact resistance anisotropy, particularlywith edge contact8,18,19.Wefind that studying the contact resistance anisotropy in 2D FETs with edgecontact is very critical for utilizinghigh anisotropy ratio that can be obtainedfrom future asymmetric orientation-dependent FETs. Also, as the role of1SKKU Advanced Institute of Nano Technology, Sungkyunkwan University, Suwon, Gyeonggi-do 16419, Republic of Korea. 2National Institute for MaterialsScience, 1-1 Namiki, Tsukuba 305-0044, Japan. 3These authors contributed equally: Hyokwang Park, Myeongjin Lee, Xinbiao Wang.e-mail: euyheon@skku.edu; yoowj@skku.eduCommunications Materials |            (2024) 5:87 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00526-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00526-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00526-z&domain=pdfhttp://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3269-8856http://orcid.org/0000-0003-3269-8856http://orcid.org/0000-0003-3269-8856http://orcid.org/0000-0003-3269-8856http://orcid.org/0000-0003-3269-8856http://orcid.org/0000-0002-3767-7969http://orcid.org/0000-0002-3767-7969http://orcid.org/0000-0002-3767-7969http://orcid.org/0000-0002-3767-7969http://orcid.org/0000-0002-3767-7969mailto:euyheon@skku.edumailto:yoowj@skku.educontact resistance becomes more significant in nanometer-scale FETs,studying contact anisotropy will become more important to demonstratethe FETs with more design freedom. This aspect has not been adequatelyexplored while the conventional top contact employed in 2D electronicdevices involves out-of-plane charge transport at the metal-2D channelinterface which cannot bematched to in-plane anisotropic charge transportin the 2D channel, rendering the top contact unable tomeasure orientation-dependent contact resistance. Consequently, it becomes highly relevant andsignificant to investigate the influence of anisotropic metal contacts oncharge transport using edge-contacted devices.So, in this work, we present an experimental study on contact aniso-tropy which refers to the anisotropy ratio of contact resistance obtainedfrom different directions in several device designs, for the first time.Moreover, we applied the edge contact method to implement contactresistance dominant devices in which the contact region is reduced to largerthan 100 times. The device structures are devised to eliminate out-of-planecharge transport so as to realize the pristine high contact anisotropy. Weprepared the ReS2 encapsulated by hexagonal boron nitride (hBN) via theidentification of the orientation of metallic contact edges by performingRaman spectroscopy. We extracted contact resistances along different in-plane directions by varying temperature and gate voltage. Additionally, weconducted experimental measurements of Schottky barrier heights (SBHs)and theoretical calculations of tunneling probabilities to elucidate themechanisms underlying contact anisotropy in ReS2 FETs. We further pre-sent energy band diagrams at the interface formed between metal and ReS2for the purpose of revealing charge transport mechanisms dependent oncontact anisotropy in the ReS2 FETs.Results and discussionOrientation differentiation and configuration of ReS2The edge-contacted ReS2 device with four electrodes formed according totheb and cross-bdirections are shown inFig. 1a. Further,we fabricated edge-contacted ReS2 devices with different designs for the purpose of eliminatingpossible parasitic current transport arising from the edge front perpendi-cular to b and cross-b directionswith fully trans-etched channel as shown inSupplementary Fig. 1. Figure 1b illustrates the atomic structure of ReS2,which exhibits a distorted 1T structure with Re chains. The chain directioncorresponds to the b direction, while the direction perpendicular to the bdirection is referred to as the cross-b direction8. Generally a direction and bdirection, which has an angle of ~120o, have been used to analyze theanisotropy of ReS2 based on its crystal structure1. In this study, however, wecompared the transport properties of the b and cross-b directions instead ofthe a and b directions because the largest anisotropy of current is observedalong those directions. In Supplementary Fig. 2, we show the direction-dependent currents of ReS2 and find that the largest difference of currentoccurs between the b and cross-b directions. Also, as shown in Supple-mentary Fig. 2, the cross-b direction allows clearer contact between therhenium chain and metal, resulting in a more refined and precise contactcompared to a direction. Raman spectra of ReS2 encapsulated between topand bottom hBN were measured by rotating the polarizing angle by 15ousing a 532 nm laser. Figure 1c presents a polar plot of the normalizedRaman intensities of A7g as a function of the rotating angle. The normalizedRaman intensities of A7g exhibit a minimum at 0o and a maximum at 90o,corresponding to the cross-b and bdirections ofReS2, respectively.As shownin Supplementary Fig. 3, the Raman peaks of A1g , A6g and A7g for ReS2 arefound at 150 cm−1, 162 cm−1 and 212 cm−1, respectively26. The b and cross-bdirections are determined by theA7g RamanpeakofReS2 as shown inFig. 1c.Also, ReS2 has the direction which is rotated ~119o from the Re chaindirection which is determined by the A1g Raman peak of ReS29,27. Althoughother directions exist in ReS2, we mainly investigate the b and cross-bdirections of ReS2 because the drain current (ID) showed amaximum in theb direction and a minimum in the cross-b direction based on electricalcharacterization results of the angle-resolved edge-contacted ReS2 device asshown in Supplementary Fig. 2. The fabrication process of the devices isillustrated in Supplementary Fig. 4. Figure 1d, e shows schematics of edge-contacted devices oriented along the b and cross-b directions, respectively.Figure 1f shows a cross-sectional high-resolution transmission electronmicroscopy (HRTEM) image of the contact region of the ReS2 devices withedge contact. The HRTEM image reveals a clean van der Waals interfacebetween hBN and ReS2, demonstrating a high-quality heterostructurestacking. Supplementary Fig. 5 illustrates the analyzed electrical dispersivespectroscopy profile, providing clear evidence of the successful formation ofedge-contacted ReS2 FETs and the robust metal contact at the tilted edge ofReS2. Note that our previous paper reported anisotropic channel propertiesFig. 1 | Edge-contacted ReS2 FETs. a ReS2 crystalline structure with Re chainsshowing b and cross-b directions. b Polar plot of normalized Raman peak intensitiesobtained at 212 cm-1 which manifests the b direction at the intensity maximum.c Optical microscopy image of the edge-contacted ReS2 FET in different directions.d, e Schematics of edge-contacted ReS2 FETs along b and cross-b directions. fCross-sectional HRTEM image of the edge-contacted ReS2 consisting of ReS2, hBN, Ti, andAu shown in fake colors.https://doi.org/10.1038/s43246-024-00526-z ArticleCommunications Materials |            (2024) 5:87 2of BP using edge contact which is able to measure in-plane conductanceprecisely without out-of-plane conductance19. However, we found that notonly channel but also contact properties are understood to further influencethe anisotropic behavior significantly.Elucidating the electrical properties of ReS2 through directionaledge contactsTherefore, we investigated the anisotropy of contact resistance of edge-contacted ReS2 device by performing both 2-point probe (2PP) and 4-pointprobe (4PP) electrical characterization28. Figure 2a, b displays thetemperature-dependent 2PP transfer curves obtained from the b and cross-bdirections, respectively, at a drain voltageVD = 1V in the temperature rangeof 77 to 300 K. The drain current increases as temperature increases in bothdirections, indicating that thedevicebehaves as a typical semiconductor.Weextracted contact resistances of edge-contacted ReS2 devices by performingboth 2PP and 4PP electrical characterization. Figure 2c shows the contactresistances obtained from the b and cross-b directions as a function of thegate voltage in the range from−60 to 60 V at 77 and 300 K. Throughout theentire range of gate voltage, the contact resistance along the cross-bdirectionexhibits consistently higher values compared to that along the b direction.Furthermore, as the gate voltage is increased, a noticeable reduction in thecontact resistances is observed for both directions. Figure 2d presents thecontact resistances obtained from the b and cross-b directions as a functionof temperature (from 77 to 300 K) at a fixed gate voltage (VG =−10 and60 V). Throughout the entire temperature range, the contact resistancealong the cross-b direction exhibits a higher value than that along the bdirection and the resistance in both directions decreases as the temperatureincreases. This phenomenon can be ascribed to the thermionic emission ofcharge carriers at elevated temperatures, enabling them to more efficientlyovercome the Schottky barrier at the interface between ReS2 and ametal. InFig. 2e, f, the ratio of contact resistance along cross-b direction to that alongthe b direction is shown as a function of gate voltage and temperature,respectively. The anisotropy of contact resistance between cross-b and bdirections increases as both gate voltage and temperature decrease, reaching~70 at VG =−30V at 77 K as shown in Fig. 2e. This is related to the carriertransport mechanism at the interface between metal and ReS2. In Supple-mentary Fig. 6, we show the device structure and corresponding resistancemodel used to determine the contact anisotropy between b and cross-bdirections. Because our edge-contacted ReS2 devices mainly depend oncontact resistance rather than channel resistance, which is relatively con-sistent as shown in Supplementary Fig. 7, we use contact resistance values inthe calculation of contact anisotropy. Also, we fabricated fully trans-etcheddevices that cover the entire channel width for each direction, as shown inSupplementary Fig. 8. The contact anisotropy of the devices shows themaximum values of ~107 at 300 K and ~225 at 77 K. Supplementary Fig. 9illustrates the Hall bar structure of edge-contacted ReS2 showing a similartrend with data presented in Fig. 2. Supplementary Fig. 10 illustrates theelectrical anisotropy of a fully trans-etched device with uniform widthshowing clear and depressed contact anisotropy after etching the parasiticleakage current.Tofigure out the reason that the contact resistance along thecross-b direction is larger than that along the b direction, we extractedeffective SBH along the b and cross-b directions.Fig. 2 | Electrical performance and contact aniso-tropy of edge-contacted ReS2 FETs. a, bMeasuredI–V characteristics by increasing temperature at bdirection and cross-b direction, respectively. Thedrain voltage is fixed as 1 V. c, dMeasured contactresistance in each direction obtained by 4 PointProbe measurement dependent upon gate voltageand temperature, respectively. e, f Anisotropy ratiosof contact resistance between b direction and cross-bdirection dependent on gate voltage and tempera-ture, respectively.https://doi.org/10.1038/s43246-024-00526-z ArticleCommunications Materials |            (2024) 5:87 3Directional Discrepancy in Schottky Barrier HeightFigure 3a, b shows the experimentally extracted effective SBH along the band cross-b directions as a function of the gate voltage in the range from−60 V to 60 V. In order to extract the effective SBH, the temperature-dependent transfer curves are used as shown in Supplementary Fig. 11. TheSBH is obtained from the thermionic emission equation as shownbelow28,29.I2D ¼ WA�2DT32 exp � qΦSBkT� �expqV2DkT� �ð1ÞΦSB ¼ kq�ΔlnðI2D � T�32ÞΔT�1" #ð2ÞHere,W is the channelwidth,A�2D ismodifiedRichardson constant,q isthe electron charge, ΦSB is the Schottky barrier height, k is the Boltzmannconstant and V2D is the drain voltage. Equation (2) is derived from Eq. (1)under the assumption that the current might be mainly determined by theSchottky barrier formed at the source under high drain voltage. Figure 3c, dshows theArrhenius plots which indicate lnID � T�32 vs. 1000�T−1 while gatevoltage varies from −60 to 60 V. We extracted SBH for a reliable compar-ison atVD=1 V from the negative slope of the linearfit to ln lnI2D � T�32 as afunction of q∙(kT)−1. The extracted effective SBH values are qΦb ~ 35meValong the b direction and qΦcb ~ 46meV along the cross-b direction at theflat-band position (VG =VG0). There have been studies reporting valueshigher than this specific value30, but there have been no papers reportingabout different Schottky barrier heights (SBH) observed along differentdirections.We note that the thermionic current ratio of b direction to cross-b direction is given by eΦcb=Φb , which gives approximately 3.6 times biggerresistivity in the cross-b than in the b direction. As depicted in Supple-mentary Fig. 12, we observed that the SBH of our devices barely changed bythickness, while the contact resistance was found to be highly dependent onthickness. It was initially expected that the SBHwould remain independentof the gate voltages for VG >VG0. However, the extracted effective SBHdecreases gradually with the gate voltage due to the tunneling currentthrough the barrier. AsVG decreases belowVG0, the effective SBH increaseslinearly because the majority carrier current is determined by electrons inour samples. In Fig. 3e-h we show the schematic energy band diagrams atthemetal-ReS2 interface underdifferent gate voltages. Themeasured SBHatVG = 0 indicates the barrier height at the thermal equilibrium and the flatband position (i.e., at VG =VG0) indicates the band structure withoutbending of the conduction band. Similar phenomena may occur in the topcontact, but the value of contact anisotropy is significantly lower comparedto our edge contact, as shown in Supplementary Fig. 13.Directional tunneling barrier thickness and tunneling probabilitydiscrepancyTo understand the SBH difference between b and cross-b directions, weinvestigate the potential profile at the interface between metal and ReS2using the density-functional theory (DFT). In Fig. 4a, b, we show the cross-sectional schematics of the contact region betweenmetal andReS2 along theb and the cross-b directions, respectively. The condition of the simulation isreaveled in Supplementary Fig. 14. When the orientation of 2D materialschanges, the crystal structure of the etched surface also changes. Therefore,the anisotropy of the crystal is closely related to the slope of the etchedsurface31. Due to experimental limitations, this study did not analyze thecrystalline structure formed on the contact surface of edge-contacted ReS2FETs by plasma etching processes. However, according to the referencedliterature, there are differences in etching rates dependingon thedirectionof2D materials, which may lead to differences in the etched crystalline cross-section that are practically impossible to analyze31. In this regard, the atomicarrangement of ReS2 along the b and cross-b directions having differentedges is selected for simulation conditions. Along the b direction, the metalcontacts with both Re and S atoms while it contacts only with sulfur atomsalong the cross-bdirection. These atomic configurations induce the differentpotential profiles at the interface (see Fig. S14). Overall, we find the higherandwider potential barrier along the cross-b direction, i.e., the direct contactof metallic Ti with only sulfur atoms gives rise to the higher and widerSchottky barrier. In Fig. 4c the tunnel barrier width is given as a function ofinter-atomic distance at the interface. While the experimentally obtainedSBHs are closely related to the potential profiles formed at the interface, thedifference of SBH and the barrier width between contact directions plays arole in the observed anisotropy of the contact resistance. Due to the distinctatomic arrangement at the edges along the b and cross-bdirections, not onlySBHbut also the barrierwidth is varied in eachdirection. InFig. 4d,we showthe calculated tunneling probability of electrons through the barrier, whichdetermines the current at low temperatures. The tunneling probability ofFig. 3 | Measured SBHs of ReS2 edge contact FETs. a, b Experimentally extractedSBH at b direction and cross-b direction, respectively. c, d Experimentally measuredArrhenius plot of edge-contacted ReS2 along b direction and cross-b direction,respectively. e, f, g, h Band diagram indicating varying SBH at different gate voltagesat 0 V, high gate voltage, same at built-in-potential and low gate voltage, respectively.https://doi.org/10.1038/s43246-024-00526-z ArticleCommunications Materials |            (2024) 5:87 4carriers can be obtained by 32PTB ¼ expð� 2WTB_ffiffiffiffiffiffiffiffiffiffiffiffiffiffi2mΦTBpÞ ð3ÞwhereWTB is the tunneling width, ℏ is the reduced Planck’s constant, andm is the mass of the free electron. For interlayer distance from 3.77 Å to4.44 Å, both tunnel barrierwidth and tunnel barrier height along the cross-b direction are larger than the ones along the b direction, which results inthe tunneling probability along the cross-b directionmanifesting a smallervalue than along the b direction. And tunneling probability ratio betweencross-b direction and b direction increases as the interlayer distanceincreases. As the distance increases between Ti and ReS2 in the edgecontact structure, the tunnel barrier width increases with thicker tunnelbarrier width at the cross-b direction than the b direction. In this regard,the calculated tunneling probability through metal to semiconductor atthe b direction is higher than at the cross-b direction. As reportedpreviously 33, Fermi level pinning, refers to the phenomenon where theFermi level of a material is fixed at a specific energy level at an interface.Because the Schottky barrier can be formed at the interface although thework function of ReS2 is larger than that of metal. While the difference ofSBH along the b and cross-b directions plays a role in the anisotropy of thetransport, the differences in tunneling probability between the b and cross-b directions seem to give more dominant effects in the highly dopedsituation. In other words, for high positive gate voltages the tunnelingoverwhelmingly affects more than the thermionic emission when thecharge carriers transfer frommetal toReS219,34. The electrons injected frommetal to ReS2 are more along the b direction than along the cross-bdirection due to tunnel barrier width. Also, as the gate voltage increases,the number of electrons transferred from metal to ReS2 by tunnelingmainly increases. For this reason, the anisotropy ratio of contact resistanceis more sensitive to the gate voltage than to the temperature.SummaryIn this study, we have successfully unveiled the underlying mechanismsresponsible for contact anisotropy in 2D ReS2. The marked difference incontact resistance between the cross-b and b directions indicates that chargetransport from the metal to ReS2 is much more efficient along the b direc-tion. The anisotropy of contact resistance between cross-b and b directionsincreases as both gate voltage and temperature decrease, reaching ~70 atVG =−30 V at 77 K. The SBH value measured from the edge-contactedReS2 device was ~35meV along the b direction and ~46meV along thecross-b direction. Additionally, our calculations of tunneling amplitudesacross the edge contact between the metal and ReS2 indicate that theamplitude along the b direction is roughly twice as large as that along thecross-b direction. These findings collectively support the conclusion thatboth the SBH and tunneling amplitude play significant roles in contributingto the observed anisotropic contact resistance.MethodsFabrication of the hBN/ReS2/hBN stackHexagonal boron nitride (hBN) and rhenium disulfide (ReS2) weremechanically exfoliated by scotch tapemethod onto 285 nm thick SiO2/p-Sisubstrate. Thicknesses of the exfoliated hBN and ReS2 were in the range of20–40 nm and 10–20 nm, respectively. Thicknesses of these flakes weredetermined by optical contrast from optical microscopy, and atomic forcemicroscopy. The exfoliated hBN and ReS2 were subjected to a transferprocess to form a hBN/ReS2/hBN stack. The hBN and ReS2 were picked upin order by using polycarbonate (PC) at 353–393 K. The hBN/ReS2 stackwas dropped down on the exfoliated hBN at 503 K. Residues formed by PCwere removed by chloroform.Fabrication of the ReS2 edge-contacted deviceAngle-resolved Raman measurements on hBN/ReS2/hBN hetero-structure were performed to identify the b and cross-b directions ofReS2 using a polarized micro-Raman system equipped with a 532 nmlaser with a spot size of 1 µm and a power of 100mW, and a polarizer.Poly(methylmethacrylate) (PMMA) A6 950 as electron beam resists wasapplied by spin coating at 4000 rpm for 60 s on the wafer with hBN/ReS2/hBN stack. It was hardened at 180 °C for 90 s. Metal patterns weredefined by using electron beam lithography (EBL; JEOL JSM-7001F andRaith ELPHY Plus & Quantum). Electron beam resists were developedby putting in a solution consisting of isopropyl alcohol and deionizedwater (3:1). To completely remove PC and PMMA residues remainingafter the development, UV ozone treatment was carried out for 90 s. ThehBN/ReS2/hBN stack was etched by inductively coupled plasma (ICP) atthe following processing conditions: ICP power of 20W, working pres-sure of 20 mTorr, SF6 and O2 gas flow of 10 and 30 sccm, respectively,Fig. 4 | Schematic of metal-ReS2 interfaces andtunneling properties of edge-contactedReS2 FETs. a, b Cross sectional schematics of thecontact region between metal and ReS2 along bdirection and cross-b direction, respectively. c, dCalculated tunnel barrier width and tunnelingprobability, respectively, showing different dis-tances between Ti and ReS2 in each direction.https://doi.org/10.1038/s43246-024-00526-z ArticleCommunications Materials |            (2024) 5:87 5and time of 60 s. 5 nm Ti/80 nm Au were deposited by an electron beamevaporator (Korea Vacuum, KVE-E2000). The lift-off process was car-ried out in acetone for 1 h after metal deposition.Electrical and TEMmeasurementTheelectricalmeasurements of the fabricateddeviceswereperformedby thesemiconductor parameter analyzer (Agilent 4155C) and the probe station(MSTECH MST-1000B M6VC) with a vacuum level of 10mTorr. Toanalyze ReS2 and metal/ReS2 interfaces, HRTEM was performed. A smallregionof the fabricateddevices including the contactwas isolated by focusedion beammilling andwasmoved to aTEMgrid for cross-sectionalHRTEMand scanning TEM.Calculation methodsTo explore the SBHdifference between the bdirection and cross-b direction,the density-functional theory (DFT) is studied, using the plane-wavepseudopotential approach according to the Cambridge Sequential TotalEnergy Package (CASTEP)35. The study on the exchange-correlationfunction of ReS2 is described by the generalized gradient approximation ofPerdew, Burke, and Ernzerhof parameterization (PBE)36. The electronicwave functions were obtained by using a density-mixing minimizationmethod for self-consistent field calculation. The van derWaals interactionswere taken into account by using the DFT+D method by means ofTkatchenko and Scheffler (TS) corrections to PBE37. Also, we consider non-self-consistent dipole correction in the calculationprocesswith the setting ofthe vacuumof about 25 Å spaces to avoid the neighboring layers’ interactionin the periodic slabs. The valence electronswhich forma chemical bond anddefine the general properties of atoms, were treated by wave functions withthe following electronic configurations: Re 5s2 5p6 5d5 6s2; Ti 3s2 3p6 3d2 4s2and S 3s2 3p4. The ionic core was described by the Vanderbilt ultrasoftpseudopotential38. A plane-wave cut-off energy was chosen at 310 eV. The2 × 2 × 1 and 2 × 3 × 1 Monkhorst-Pack k-mesh were used for cross-bsupercell and b supercell, respectively 39. For ReS2/Ti heterostructures, thereare two different configurations considered, Ti(100) for contact along cross-b direction of ReS2 and Ti(001) for contact along b direction of ReS2. Latticemismatch is less than 3% for both structures. The structural relaxation of thegeometries, due to the Hellmann–Feynman forces, was performed withinthe Broyden, Fletcher, Goldfarb, and Shannon (BFGS) method40. Theoptimization of the studied models was performed until the followingconvergence criteria were reached: the tolerance of the electronic totalenergy convergence was 10−6 eV per atom, the maximum displacement0.001 angstrom, the maximum force 0.03 eV/angstrom, and the maximumpressure 0.05 GPa.Data availabilityAll relevant data are available from the authors.Code availabilityThe DFT code used in this study was available from the CambridgeSequential Total Energy Package (CASTEP).Received: 18 January 2024; Accepted: 21 May 2024;References1. Liu, E. et al. 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Thisworkwassupported by the National Research Foundation of Korea (RS-2024-00346656 and 2021R1A2C1012176). It was also supported by the Ministryof Trade, Industry and Energy (20022369).Author contributionsH.P., M.L., X.W., E.H., W.J.Y. conceived of the research project. E.H. andW.J.Y. supervised the experiment and wrote the manuscript. H.P., M.L.fabricated sandwiched ReS2 structure and characterized the deviceselectrically and optically. X.W. performed a simulation on contact betweenReS2 and Ti. K.W. and T.T. provided hBN samples used in the work. N.A.assisted device measurement and analysis.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s43246-024-00526-z.Correspondence and requests for materials should be addressed toEuyheon Hwang or Won Jong Yoo.Peer review information Communications Materials thanks Antonio DiBartolomeo and the other, anonymous, reviewer(s) for their contribution tothe peer review of this work. Primary Handling Editor: Aldo Isidori. 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To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024https://doi.org/10.1038/s43246-024-00526-z ArticleCommunications Materials |            (2024) 5:87 7https://doi.org/10.1038/s43246-024-00526-zhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/ Anisotropic charge transport at the metallic edge contact of ReS2 field effect�transistors Results and discussion Orientation differentiation and configuration of ReS2 Elucidating the electrical properties of ReS2 through directional edge contacts Directional Discrepancy in Schottky Barrier�Height Directional tunneling barrier thickness and tunneling probability discrepancy Summary Methods Fabrication of the hBN/ReS2/hBN�stack Fabrication of the ReS2 edge-contacted�device Electrical and TEM measurement Calculation methods Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information