Quantum Transport in Two-Dimensional WS_2 with High-Efficiency Carrier Injection Through Indium Alloy Contacts
Chit Siong Lau, Jing Yee Chee, Yee Sin Ang, Shi Wun Tong, Liemao Cao, Zi-En Ooi, Tong Wang, Lay Kee Ang, Yan Wang, Manish Chhowalla, Kuan Eng Johnson Goh
QQuantum Transport in Two-Dimensional WS with High-Efficiency CarrierInjection through Indium Alloy Contacts Chit Siong Lau † , Jing Yee Chee † , Yee Sin Ang , Shi Wun Tong , LiemaoCao , Zi-En Ooi , Tong Wang , LayKee Ang , Yan Wang , Manish Chhowalla , Kuan Eng Johnson Goh † These authors contributed equally to this work.* [email protected]
Abstract
Two-dimensional transition metal dichalcogenides (TMDCs) have properties attractive for optoelectronic andquantum applications. A crucial element for devices is the metal-semiconductor interface. However, high contactresistances have hindered progress. Quantum transport studies are scant as low-quality contacts are intractable atcryogenic temperatures. Here, temperature-dependent transfer length measurements are performed on chemicalvapour deposition grown single-layer and bilayer WS devices with indium alloy contacts. The devices exhibit lowcontact resistances and Schottky barrier heights ( ∼
10 kΩ µ m at 3 K and 1.7 meV). Efficient carrier injection enableshigh carrier mobilities ( ∼
190 cm V − s − ) and observation of resonant tunnelling. Density functional theorycalculations provide insights into quantum transport and properties of the WS -indium interface. Our results revealsignificant advances towards high-performance WS devices using indium alloy contacts. Keywords:
2D materials, contacts, quantum transport, WS , transition metal dichalcogenides Introduction
Two-dimensional transition metal dichalcogenides (TMDCs) have been widely studied for their exceptionalmechanical and optoelectronic properties, with most of the attention centered on single-layer MoS . [3, 28, 34, 41, 42]Another intriguing member of the TMDC family is WS . [1, 5, 14, 16, 25, 30, 37, 39, 43] Theoretical calculations suggestthat WS is expected to have higher carrier mobility due to its lower effective mass compared to MoS , raisinginteresting prospects for device applications. [20, 46] Yet, significantly fewer studies have been made relative to MoS .It can be challenging to achieve effective contacts in CVD WS as the conduction band edge in WS is located ata higher energy compared to MoS , which can result in larger Schottky barriers. [1, 18] In particular, quantumtransport studies in WS have been limited due to the lack of high quality devices with good contacts at cryogenictemperatures. [2, 15, 36] While promising strategies for room temperature contacts to 2D TMDCs have recently beenrealized, [6, 7, 12, 26, 27, 44, 45] the viability of such contacts at cryogenic temperatures down to 4 K and theunderstanding of charge injection and transport remain elusive. This poses a major obstacle for the development ofquantum devices in 2D TMDCs. 1/13 a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b igure 1. a) Optical image of the WS single-layer (SL) and bilayer (BL) devices with channel widths 10 µ m and 5 µ m respectively. (b) Schematics of single-layer WS device and crystal structure of bilayer WS . Transfer curves forthe WS (c) single-layer ( L = 2 µ m, W = 10 µ m) and (d) bilayer devices ( L = 1 µ m, W = 5 µ m) on linear (blue,right) and logarithmic (black, left) scales. The solid red lines represent the linear fits to the transconductances forextracting V TH and µ FE . Transfer length method measurements of device resistance as a function of length for the (e)single-layer and (f) bilayer devices. The solid blue lines represent the linear fits to the data.Furthermore, most reports on WS devices show large variance in number of layers, preparation methods, i.e. exfoliated vs CVD, and with poorly defined device geometries, leading to inconsistent results. Understandinglow-temperature carrier injection and transport is thus of critical importance for better design and control of TMDCbased quantum devices. This will require characterization of scalable devices with properly defined geometries andhigh quality contacts operable at cryogenic temperatures.Here, we present our work on Transfer Length Method (TLM) devices fabricated on single-layer and bilayer CVDgrown WS using indium alloy contacts. We extract key parameters including contact resistances and Schottkybarrier heights, and identify the carrier transport and injection regimes for different temperature and bias ranges.Importantly, our experimental data and Density Functional Theory (DFT) calculations allow us to uncover valuableinsights into the nature of low temperature transport and carrier injection in CVD grown single-layer and bilayerWS . Results and discussion
Field-Effect Transport and Carrier Mobility
Figure 1a shows an optical image of our fabricated CVD single-layer (SL) and bilayer (BL) WS TLM devices. TheSL WS device schematic and crystal structure of BL WS are shown in Figure 1b. Atomic force micrograph isshown in the Supporting Information (Figure S1).We determine the electrical quality of the indium alloy contacts and our WS devices through field effect andTLM measurements. Our devices exhibit typical n- type semiconducting behavior with high on/off ratios ( > /10 for SL/BL), as estimated from the transfer curves measured at 10 K (Figure 1c and 1d). We also show in theSupporting Information (Figure S6) measurements of our control device where the WS was grown from the samebatch as the manuscript device and processed in parallel, but with Ti/Au contacts instead of In/Au. 2/13hile a widely used technique in literature, the field effect mobility µ FE is an underestimation as it ignores thecontribution from the contact resistance R C . A more accurate value for the carrier mobility can be extracted usingTLM measurements. [48] TLM is also the standard method for determining the contact resistance R C , related to thechannel resistance R CH and sheet resistance R S by the following equation: R CH ( L ) = R S LW + 2 R C W . (1)A linear fit of device R CH with lengths L at specific net gate voltages V G − V TH , i.e . specific carrier densities n ,yields the width W normalized R S and 2 R C from the slope and y-intercept respectively (Supporting InformationFigure S2). From the sheet resistance R S , we calculate the carrier mobility µ TLM using: µ TLM = 1 qn ( V G − V TH ) R S ( V G − V TH ) . (2)We show the temperature dependence of µ TLM for SL and BL in Figure 2c,d, plotted for source-drain voltages V DS =0.1 and 1 V. The measured µ TLM at 10 K ( V DS = 1 V) for SL (23 ± V − s − ) and BL (187 ±
33 cm V − s − )are among some of the highest reported values for CVD grown WS . These values are comparable even to devicesmade from exfoliated flakes, highlighting the excellent quality of our CVD grown material. At higher temperatures >
200 K, µ TLM scales as T − γ , with γ = 1.61 (SL) and γ = 1.51 (BL), consistent with reports for other WS andMoS devices. The values are close to those predicted for MoS , where γ ≈ <
70 K, the behaviour of µ TLM differs between the SL and BL devices. For SL, µ TLM decreases with decreasing temperature at V DS = 0.1 Vbut for V DS = 1 V, µ TLM instead saturates at low temperatures. For the BL, V DS = 0.1 V and 1 V both lead toconsistent saturation values for µ TLM at low temperatures.
Variable Range Hopping and Disorder
While mobility degradation at low temperatures is commonly interpreted as due to scattering from chargeimpurities, [33] it could also be due to the invalidity of applying the mobility equation since the device is operating ata non-linear region. Another possible origin is the underestimation of mobility due to Schottky barriers at smallV DS . [25] At small V DS , the mobility can be underestimated due to Schottky barriers, whereas contact resistancebecomes negligible when V DS is increased. The saturation of µ TLM ( V DS = 1 V) at low temperatures for both the SLand BL devices point to effective damping of the Coulomb scattering from charged impurities. [33] To betterunderstand the nature of the low-temperature transport, we use the variable range hopping (VRH) model: G = G ( T ) exp( − T /T ) / . (3)Here, G is the conductance, T the correlation energy scale and G = AT m with m ≈ V G − V TH for the (a) SL and (b) BL devices. We find two distinct regimes, (1) 30 < T <
130 K and (2)
T <
30 K.For regime (1), the data agrees very well with the VRH transport model, suggesting that transport in WS occursover a wide band of localized states. [9, 33] For regime (2), the weakening of G with T points to the transitiontowards a strongly localized regime. Such transport behaviour in 2D materials was previously attributed to thepresence of a disordered potential landscape. [9, 13] Indeed, the high resolution differential conductance curves takenat 3 K, shown in Figure 2d (SL) and 2e (BL), exhibit stable reproducible peaks across a range of V DS . These peaksare indicative of resonant quantum tunnelling through localized states in a disordered potential landscape, consistentwith the low temperature behaviour of our VRH model in Figure 2a,b.The extracted T values are shown in Figure 2c. We find that T decreases with increasing carrier densities,expected for strongly localized 2D electron systems where the Fermi energy lies in the conduction band tail. [10, 32]Notably, values of T for all 14 devices lie within a single order of magnitude. This strongly suggests that the originof the disordered potential landscape is extrinsic, for instance carrier traps in the substrate/interface, rather thanintrinsic, such as structural defects/chemical impurities. [9, 13] A disordered potential landscape is consistent with thelarger SL T values as SL devices are more strongly influenced by substrate induced disorder compared to BL devices.The higher variance for T in BL devices suggests that intrinsic disorder such as random impurities and defects plays3/13 igure 2. Fits to the Variable Range Hopping (VRH) transport model for (a) single-layer and (b) bilayer devices.At lower temperatures below 30 K, the data deviates from the model, indicating the onset of resonant tunnellingthrough localized states. (c) Extracted correlation energy scale T for single-layer (red) and bilayer (blue) devices.We find little variation between the single-layer devices with different lengths, while T decreases with increasingdevice lengths for bilayer. High resolution differential conductance curves taken at 3 K for (d) single-layer ( L =2 µ m)and (e) bilayer ( L =1 µ m). Reproducible peaks suggesting resonant tunnelling through localized states are clearlyvisible in both devices across a range of V DS . 4/13 igure 3. (a) Temperature dependence of the contact resistances R C . Schottky barrier heights Φ B vs gate voltage V G for (b) single-layer (length= 2.0 µ m) and (c) bilayer (length= 1.0 µ m) as determined from the Richardson plots(Supporting Information Figure S3). The gate voltage where Φ B tends away from the linear fit is the flatbandcondition for which the true Schottky barrier height is determined. (d) Schottky barrier heights Φ B for the differentdevice lengths.a more prominent role compared to substrate disorder. This implies that transport in the BL devices occur primarilythrough the indium-contacted top layer with partial screening from the bottom layer, consistent with ourfirst-principle DFT calculations (discussed below).Furthermore, we find that T generally decreases with increasing length for BL devices, suggesting a greaterdensity of defects in the shorter channel devices. Considering that the contact regions constitute a greater proportionof the system for shorter channel devices, this indicates that the bulk of the disorder lies close to themetal-semiconductor interfaces. Indeed, such disorder at the metal/semiconductor interface was shown to be causedby lattice damage during metal deposition or increased polymer residue from resist development duringfabrication. [26, 44] The further reduction of evaporation rate during metal deposition can mitigate these destructiveeffects. [44] Temperature Dependence of Contact Resistance and Schottky Barrier
Having established the nature of low temperature transport through our devices, we now discuss the contacts. Weestimate the influence of the width normalized contact resistances R C through the TLM measurements usingEquation 2. The temperature dependence of R C is shown in Figure 3a. We find that R C tends to saturate at lowtemperatures for both SL and BL devices, with R C = 28 ±
45 (SL) and 9.9 ± µ m at 10 K (SupportingInformation Figure S2). These values compare favorably with literature reported values, indicating the excellentmetal-semiconductor contact between indium alloy and WS . [2, 6, 12, 27, 31, 44] For a metal/semiconductor contact5/13ith sizable Schottky barrier height, the charge injection is dominated by thermionic emission and the contactresistance decreases exponentially with temperature as R C ∝ exp (Φ B /k B T ). The weak temperature dependence of R C in our devices suggests that charge injection across the metal/semiconductor contact is not limited by thermionicemission, and the Schottky barrier height is expected to be small.To further assess the nature of our contacts, we extract the Schottky barrier heights Φ B of our devices bymeasuring the activation energy in the thermionic emission region at low gate voltages. Here the current I DS isdetermined by: I DS = A ∗ T / exp (cid:18) − Φ B k B T (cid:19) (1 − exp (cid:18) − qV DS k B T (cid:19) , (4)where A ∗ is the Richardson constant, V DS the bias, T the temperature and k B the Boltzmann’s constant. With thisequation, the Richarson plot, ln( I DS /T / ) ≈ T (Supporting Information Figure S3), yields Φ B as a function ofgate voltage which is shown in Figure 3b (SL) and 3c (BL). The true Φ B is extracted using the flat band voltagecondition, determined as the gate voltage at which Φ B tends away from the linear fit, and shown in Figure 3d for alldevice lengths. We find that the BL devices generally exhibit lower Schottky barrier heights, with Φ B = (BL) 1.7 ± ± >
100 meV). [8, 17, 38, 47] The low Φ B values further confirm the quality of our indium alloy contacts and are consistent with our interpretation of themobility µ TLM curves (Figure 2c,d). At Φ B ≈ ≈
70 K, close to the temperature at which µ TLM begins to diverge for different V DS in the case of the SL(Supporting Information Figure S4). For the BL device, the lower Φ B and R C at low temperatures compared to theSL device result in little difference between the µ TLM curves for V DS = 0.1 V and 1 V.We now discuss the relation between Schottky barrier heights and R C in our devices. The contact resistance of ametal/2D-semconductor interface is not solely determined by the metal/semiconductor Schottky barrier, but acombination of (i) thermionic charge injection over Schottky barrier heights; and (ii) carrier scattering in the 2Dsemiconductor under the metal contact region. [7] As the Schottky barrier heights exhibit an exceptionally low value,the contact resistance is expected to be dominated by the carrier scattering in the metal contacted WS region,rather than by thermionic carrier injection across the metal/semiconductor interface. The temperature dependence of R C offers an obvious signature to distinguish the charge injection and transport mechanism across a Schottky contact.In thermionic-limited transport, R C is expected to decrease rapidly with temperature as thermionic charge injectionis approximately exponentially promoted at elevated temperatures. However, such strong temperature dependence of R C is absent in our device (Figure 3a), suggesting that thermionic charge injection is not a limiting transport processacross the metal/semiconductor contacts, in agreement with the measured ultra-low Schottky barrier heights (Figures3c and 3d). As demonstrated in our DFT simulations (Figure 5), the strong metallization between In and WS canlead to the generation of substantial defect sites that leads to higher R C . We suspect that these carrier scatteringeffects are the dominant contributor of R C in our devices. Charge Injection Mechanism at Indium/WS Interface
We now investigate the charge injection and transport mechanisms in the SL and BL devices. Across ametal/semiconductor contact, charge injection occurs via three distinct pathways (see Figure 4a-c): (i) directtunneling (DT) at low V DS ; [40] (ii) Richardson-Schottky (RS) thermionic injection at moderate V DS ; [4, 35] and (iii)field-induced Fowler-Nordheim (FN) tunneling at high V DS [29] where the current-voltage scaling relations aregoverned, respectively, by ln (cid:18) I DS V (cid:19) ∝ ln (cid:18) V DS (cid:19) & , DT (5)ln ( I DS ) ∝ V / & , RS emission (6)ln (cid:18) I DS V (cid:19) ∝ − V DS & , FN tunneling (7)6/13 igure 4. Schematics showing the charge injection mechanisms for (a) direct tunnelling (DT), (b) Richardson-Schottky (RS) emission and (c) Fowler-Nordheim (FN) tunnelling. Current signatures for the different models for(d-f) single-layer (g-i) and bilayer devices. Insets show the thermionic Arrhenius plots In( I DS /T / ) ∝ -1/ T at thedifferent bias regimes. Full-sized figures of the insets are available in the Supporting Information (Figure S5). 7/13n Figure 4d-g, we show the DT, RS and FN plots for the SL (length = 2 µ m) and BL (length = 2 µ m) devices atdifferent temperatures and V G = -50 V (Supporting Information Figure S7 shows ln( I DS ) vs ln( V DS ) plots). These SLand BL devices exhibit contrasting transport behavior. For the SL device, the best linear fit for the ohmiccurrent-voltage relation in Equation 5 (Figure 4d) spans the entire measured bias voltage range. While there is somelinear behavior for the RS plot at intermediate to high bias voltages (Figure 4e), the thermionic Arrhenius plots ofIn( I DS /T / ) ∝ -1/ T (insets of Figure 5d-f) do not exhibit any negative slope trends. This rules out interfacialthermionic-based injection as a dominant transport mechanism over the temperature range 3 K ≤ T ≤
110 K.Charge transport across the device is determined by both the charge injection across the contact and the chargeconduction in the bulk. Because of the ultra-low Schottky barrier heights in SL device, the lower µ TLM compared toBL suggests that transport in SL device is more strongly influenced by the channel, compared to the contact. Ascharge conduction across the SL channel also exhibits ohmic behavior ( i.e . the bulk current I bulk ≈ neµV s /L ) withthe same current-voltage scaling relation as Equation 5, the conduction in the SL device is likely bulk-limited ratherthan injection-limited . This is further supported by the absence of FN tunneling in the high-bias regime of the FNplot in Figure 4f.In contrast, the BL device (Figure 4g-i) exhibits injection-limited conduction. Due to the substantially higher µ TLM ≈
187 cm V − s − in BL device (compared to µ TLM ≈
23 cm V − s − for SL device), charge injection acrossthe contact plays a relatively more prominent role in limiting the device output characteristics. The injection-limitednature of the charge transport in BL device is confirmed by the thermionic Arrhenius plot which exhibits a negativeslope at temperature T ≥
30 K, a signature of thermionic charge injection across the metal/semiconductor interface(Figure 4g).From small to intermediate bias voltages, linear behavior is observed for both the DT and RS models (right regionof Figure 4g and left region of Figure 4h). At higher bias voltages, the DT plots deviates from linear behaviour as thecharge injection mechanism transits towards FN emission, confirmed by the signature negative slopes of the FNmodel (Figure 4i). With increasing temperatures at
T >
50 K, we find that the FN plot no longer exhibits a negativeslope, indicating the dominance of thermionic emission. This is further corroborated by the thermionic Arrhenius plotat high-bias regime, which exhibits the signature negative-slope trend at
T >
50 K (inset of Figure 4i).The charge injection and transport mechanisms in Figure 4 thus reveal fundamentally different charge transportmechanisms between the SL and BL devices, despite both having similarly low values of R C and Φ B . Density Functional Theory Simulation
To validate our experimental findings and gain further insights on the electronic properties of the WS -indiumcontact, we turned to DFT calculations (Figure 5). Because the WS devices are fabricated using conventionaldeposition of indium, the metal/2D-semiconductor interface can be non-ideal and more prone to defects, strain andchemical bonding. [26] For completeness, we performed DFT calculations on indium-contacted WS SL and BL withtwo distinct contact types [19]: (i) ‘clean’ contact with an optimized indium/WS corresponding to anatomically-sharp Van der Waals metal/2D-semiconductor interface fabricated via mechanical transfer of metal onto2D semiconductor [26]; and (ii) covalent-bonded contact corresponding to a non-ideal contact fabricated usingconventional methods of metal deposition. DFT calculations for MoS /indium are also available in the SupportingInformation (Figure S8).From the band structure diagrams in Figure 5a-d, we find substantial metallization in both type (i) and (ii)contacts. The overlap of WS and indium electronic states around the Fermi level reveals the absence of Schottkybarriers at the indium/WS interfaces. This is consistent with our exceptionally low experimental values of Φ B ( < B measured in our devices is likely to originate from imperfections and defects at theindium/WS interface.In Figure 5e and 5f, the calculated charge density variation, ∆ ρ , of the bilayer-WS /indium interface indicatessignificant amount of charges transferred from indium into metal-contacted top layer WS . We thus expect themetal-contacted top layer WS to play an importantly role in both the charge injection and transport in our devices.To elucidate the layer-contrasting metallization and transport, we calculate separately the density of states (DOS)of indium and WS (Figure 5g), and the top layer (indium-contacted) WS and the bottom layer WS (Figure 5h),for type (i) and (ii) (see Figure 5i and 5j) contacts. By inspecting the DOS around the Fermi level, the bottom layerWS remains semiconducting, while the metal-contacted top layer becomes highly metallic. 8/13 igure 5. Density functional simulations of indium/WS contact. Projected band structure of (a,b)/(c,d) single-layer(SL)/bilayer(BL) WS contacted by indium with (a,c) type (i) contact of indium/WS (separation d = 2.99 (cid:6) A(SL) and d = 2.98 (cid:6) A (BL)); and (b,d) type (ii) contact of indium/WS (separation d = 1 . (cid:6) A). Charge transfer, ∆ ρ in bilayer WS with (e) type (i) and (f) type (ii) contact. Calculated partial density of states (DOS) of the (g)/(i) type(i)/type(ii) bilayer WS /indium contact, and the (h)/(j) type (i)/type(ii) top layer indium-contacted WS (denoted as1st WS ) and the bottom layer WS (denoted as 2nd WS ). Schematic drawings of the charge injection mechanismsacross the (k) single-layer and (i) bilayer WS /indium contacts.Importantly, the top and the bottom WS is separated by a large transport barrier of about 0.4 eV (Figure 5j and5h). We thus expect that the domination of the top-layer carriers is not limited to carrier injection at themetal/semiconductor interface, but that subsequent carrier transport in the 2D channel is also concentrated in thetop indium-contacted WS layer. This effect is further amplified at low temperatures where inter-layerthermal-assisted carrier injection and phonon-assisted scattering are strongly suppressed.The layer-dependent metallization and carrier transport predicted by our DFT simulations are thus in unison withthe T extracted at the low-temperature regime of 30 < T <
130 K (Figure 2c), where the lower variance of the T values for BL device can be attributed to the dominant role of top layer indium-contacted WS as the primary carriertransport channel (see Figure 5k and 5l for the schematic drawings of the carrier injection and transport in SL andBL WS /indium contact, respectively). Conclusion
To conclude, we performed temperature dependent electrical measurements on single-layer and bilayer CVD grownWS transistors with indium alloy contacts. We find that the high quality of the indium alloy contacts persists downto 3 K leading to excellent performance in our devices. We used DFT calculations to unravel hitherto unexplainedcarrier injection and transport mechanisms. These results represent an important advance for the study of quantumtransport in 2D TMDCs and the development of scalable TMDC based quantum devices, where progress had beenlimited by poor contacts and low quality of scalable TMDC materials. Experimental
Device Growth and Fabrication.
We first cleaned the growth substrates (SiO /Si) with acetone, isopropanol andDI water under 10 min ultrasonication. The pre-cleaned SiO /Si substrates were then treated with oxygen plasma for20 seconds in Harrick Plasma Expanded Plasma Cleaner at fixed RF power (30W) and oxygen flow rate of 8 sccm.9/13e next prepared the W-based precursor solution by dissolving 3 mg sodium tungstate dihydrate (Na WO · O) in10 ml DI water. After spin coating the precursor solution on the plasma-treated substrates at 3500 rpm for 40 s, weannealed at 130 ◦ C for 10 min. We performed the atmospheric pressure growth in a fused quartz tube at 800 ◦ Cunder 60 sccm of N gas. A crucible filled with 1500 mg of sulfur powder (99.999 %) was placed upstream and heatedto a temperature of 200 ± ◦ C. After 10 min growth, we cooled the furnace to room temperature under 300 sccmN gas flow.The grown flakes were wet transferred onto a 290 nm SiO /Si substrate that also serves as a back-gate for tuningthe overall carrier densities in our devices. PMMA was spun onto the surface of the growth SiO substrate which wasthen etched using dilute HF (5%) to detach the PMMA/WS film. We rinsed the film in a series of 3 DI water baths.Finally, the film was transferred onto the target substrate (also dipped in dilute HF (5%) and rinsed) and driedovernight before PMMA removal with Microposit Remover 1165.Next, we patterned the source/drain electrodes using standard e-beam lithography and subsequently deposited3/40 nm of In/Au at 0.5/1.0 (cid:6) A / s. The channel geometries were then defined using e-beam lithography and etchedwith SF plasma. [21] Finally, we annealed the devices at 200 ◦ C in 10% H /Ar forming gas to remove resist residualand further improve the contacts. Transport measurements were performed in a closed-cycle Janis cryostat usingKeithley 2450 sourcemeters. Computational Details.
The density functional theory (DFT) calculations were performed by Vienna
Ab Initio simulation package (VASP). [22, 23] We adopted the Perdew-Burke-Ernzerhof (PBE) functional of the generalizedgradient approximation (GGA) to describe the exchange correlation interaction. [24] The (1 × √
3) unit cells of In in(101) orientation were adjusted to match the (1 × √
3) unit cell of WS . The k-point sampling was set to 9 × × × − . The DFT-D3method of Grimme was used to describe the interlayer van der Waals interaction. [11] The dipole correction was alsoadded, and the forces on all atoms were less than 0.01 eV/ (cid:6) A for the structural relaxation. A 15 (cid:6)
A vacuum layer waschosen along the z direction to avoid the artificial interactions between adjacent layers.
Supporting Information
Supporting information is available at http://pubs.acs.org.
Acknowledgments
This research was supported by the Agency for Science, Technology and Research (A*STAR) under its A*STARQTE Grant No. A1685b0005 and CDA Grant No. A1820g0086. Y.S.A., L.C. and L.K.A. acknowledge the supportsof Singapore MOE Tier 2 Grant (2018-T2-1-007) and USA ONRG grant (N62909-19-1-2047). All the calculationswere carried out using the computational resources provided by the National Supercomputing Centre (NSCC)Singapore. The authors thank C.H.K. Goh for assistance with indium evaporation in device fabrication.
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