Origins of genuine Ohmic van der Waals contact between indium and MoS2

The achievement of ultraclean Ohmic van der Waals (vdW) contacts at metal/transition-metal dichalcogenide (TMDC) interfaces would represent a critical step for the development of high-performance electronic and optoelectronic devices based on two-dimensional (2D) semiconductors. Herein, we report the fabrication of ultraclean vdW contacts between indium (In) and molybdenum disulfide (MoS2) and the clarification of the atomistic origins of its Ohmic-like transport properties. Atomically clean In/MoS2 vdW contacts are achieved by evaporating In with a relatively low thermal energy and subsequently cooling the substrate holder down to ~100 K by liquid nitrogen. We reveal that the high-quality In/MoS2 vdW contacts are characterized by a small interfacial charge transfer and the Ohmic-like transport based on the field-emission mechanism over a wide temperature range from 2.4 to 300 K. Accordingly, the contact resistance reaches ~600 Ω μm and ~1000 Ω μm at cryogenic temperatures for the few-layer and monolayer MoS2 cases, respectively. Density functional calculations show that the formation of large in-gap states due to the hybridization between In and MoS2 conduction band edge states is the microscopic origins of the Ohmic charge injection. We suggest that seeking a mechanism to generate strong density of in-gap states while maintaining the pristine contact geometry with marginal interfacial charge transfer could be a general strategy to simultaneously avoid Fermi-level pinning and minimize contact resistance for 2D vdW materials.


INTRODUCTION
Layered semiconducting transition-metal dichalcogenides (TMDCs) such as MoS 2 , WSe 2 , and MoTe 2 have been extensively studied for the future development of low-power and highperformance electronic and optoelectronic applications [1][2][3] . However, establishing a reliable Ohmic contact between metals and TMDCs remains a critical challenge 4,5 . For instance, in reducing the Schottky barrier height (ϕ SB ) for TMDCs, efforts to identify metals with appropriate work functions Φ metal (e.g. Φ Sc ≈ 3.5 eV for Sc and Φ Ti ≈ 4.3 eV for Ti) based on the electron affinity of monolayer (1L) and few-layer TMDCs (e.g. monolayer MoS 2 : χ 1L MoS2 % 4 eV, multilayer MoS 2 : χ ML MoS2 % 4.3 eV) have not been effective because of the strong Fermi-level pinning (FLP) effect 6,7 . While various approaches have been explored to overcome this problem, including molecular doping 8 , tunnel-barrier insertion 9,10 , fabrication of graphene contacts 11,12 , and TMDC phase changes 13 , recent studies have shown that the formation of an ideal or defect-free metal-TMDC van der Waals (vdW) contact through the transfer of atomically flat metal thin films significantly improves the contact properties [14][15][16] . In these advances, it was important to recognize that the conventional thermal evaporation process of metals typically introduces crystalline defects in TMDCs and leads to an uncontrollable ϕ SB (or FLP) and high contact resistance 7,14 . Meanwhile, several groups overcame the challenge and showed that the thermal-evaporation process of indium (In) can lead to clean vdW-type contacts for TMDCs with very low contact resistance values [17][18][19] . However, regarding our initial report on the achievement of Ohmic-like three-dimensional (3D) In-2D MoS 2 contact 18 , question was raised in that the origins of the low contact resistance through the In-MoS 2 vdW contact are unclear.
Here, we prepare an ultraclean vdW contact between In and MoS 2 using an improved evaporation method, and clarify through extensive transport measurements and computations the nature and origins of Ohmic transport characteristics from In/MoS 2 vdW contacts. We prepare the high-quality vdW In/MoS 2 interface by lowering the temperature (T) of the substrate holder to~100 K during the metal deposition process and utilizing the relatively low In evaporation T of~530°C. The In/MoS 2 interface is then characterized by the transmission electron microscope (TEM) and Raman measurements as well as density functional theory (DFT) calculations. DFT calculations show that in comparison with the Au/MoS 2 counterpart, the In/MoS 2 contact induces an order of magnitude smaller charge transfer, which is consistent with the Raman spectroscopy data. For both mono-and few-layer MoS 2 devices prepared through our approach, we find that the contact resistance decreases with decreasing T from room temperature to T = 100 K and 2.4 K, reaching to 1 kΩ μm and 0.6 kΩ μm, respectively. This behavior indicates the Ohmic-like character at the In/MoS 2 contact and the field emission is the dominant charge transport mechanism at the In/MoS 2 contact. We finally identify from DFT calculations large in-gap states originating from the hybridization between MoS 2 conduction-band-edge and In Fermilevel states, which provides a mechanism to achieve an Ohmic contact in spite of the marginal interfacial charge transfer.

RESULTS AND DISCUSSION
Characterizations of the ultraclean In/MoS 2 interface We fabricated MoS 2 field-effect transistors (FETs) on hexagonal boron nitride (h-BN) flakes, where the h-BN flakes were deposited onto a 300-nm-thick SiO 2 /Si substrate by mechanical exfoliation. We then transferred a few-layer MoS 2 flake (HQ-graphene, Inc.) onto a selected h-BN flake 12,20 . For the electrical measurements, we deposited 100-nm-thick In electrodes across the MoS 2 channel, where the substrate holder was kept at~100 K by flowing liquid nitrogen through it (see Fig. 1a). The substrate cooling process leads to an important result, namely a highly uniform surface morphology of In film. This contrasts strongly with the usage of a room-temperature holder that produces a segregated granular film for at least up to~70 nm thickness, as reported in our previous work (also see Supplementary Fig. 1) 21 . The upper panel of Fig. 1b shows a cross-sectional TEM image of the In/few-layered MoS 2 junction, which clearly shows an atomically separated interface between In and MoS 2 layers without any metal invasion into the MoS 2 layers. Whereas crystal-lattice disorders that cause defect-induced gap states and FLP typically occur during the hightemperature deposition process of evaporated metal atoms with high thermal energy 7,14 , the In deposited at a relatively low thermal energy could apparently provide a clean vdW interface without disorder or defect. For instance, whereas the evaporation temperature of Au at 10 −7 Torr is~860°C, only~530°C is required for the evaporation of In at the same pressure. For comparison, we prepared an Au/few-layered MoS 2 junction, where the substrate holder was also kept at~100 K during Au deposition. The lower panel of Fig. 1b shows a TEM image of the Au/MoS 2 junction, where we observe that the invasion of Au atoms during the deposition process produces atomic defects at the first and second layers from the MoS 2 interface, like previous studies 14 .
To further characterize the quality of In/MoS 2 interface, we applied the Raman spectroscopy for both the pristine and Incovered MoS 2 regions to estimate doping effect at the metal contacts. It is known that the A 1g phonon peak of MoS 2 exhibits a red shift and its width broadens with electron doping 22,23 . Figure 2a, b shows the optical images of, respectively, 1L-and bilayer (2L)-MoS 2 (indicated by regions bounded with dashed black lines) prepared on SiO 2 and partially covered with 5-nmthick In (indicated by regions bounded with dashed white lines). Figure 2c, d shows the A 1g energy maps for the 1L-and 2L-MoS 2 , respectively. The In-covered region shows a relatively lower energy than the non-covered region, i.e., Δω ≈ −0.3 and −1 cm −1 for the 1L-and 2L-MoS 2 , respectively (see Supplementary Fig. 2 for representative Raman spectra for a 1L-MoS 2 ). In the upper panel of Supplementary Fig. 2a, we also show the E 1 2g energy map of the 1L-MoS 2 , which indicates relatively negligible difference between the In-covered and non-covered regions. For the biaxial strain, the red shift of the E 1 2g Raman mode corresponding to the in-plane vibration is more sensitive than the A 1g mode (out-of-plane vibration) 24,25 . For the in-and out-of-plane compressive strains, both modes should show blue shifts 26 . In our case, however, we observed a relatively strong red shift of the A 1g mode than that of the E 1 2g mode, which has been interpreted as a doping effect 22 . For instance, Chakraborty et al. 22 reported that the A 1g mode softens with doping at a rate of~0.2 cm −1 per 10 12 cm −2 for 1L-MoS 2 , whereas the E 1 2g mode is relatively insensitive to the doping. We thus conclude that the 1L-MoS 2 region covered by In was doped by electrons at a density of~+1.5 × 10 12 electrons cm −2 (electron accumulation in MoS 2 ). The full-width at half-maximums, Γ, in Fig. 2e, f also show consistent results. For instance, the In-covered region shows a relatively broader Γ than the non-covered region for both 1L-and 2L-MoS 2 , implying electron doping. This In-to-MoS 2 electron transfer feature will be further discussed below based on DFT calculations and shown to be another strong indication of ultraclean vdW contacts.
Charge redistribution at the In/MoS 2 interface To extract the atomistic information of the In/MoS 2 vdW contact and contrast them with those of the Au/MoS 2 counterpart, we carried out DFT calculations for the vertical In/MoS 2 and Au/ MoS 2 interface models and applied several analysis methods 27,28 . In Fig. 3a, b top panels, we show the fully optimized In/MoS 2 and Au/MoS 2 contact models, respectively (see details in Supplementary Figs. 3, 4 and Table 1). First, compared to the Au/MoS 2 case, we find in the optimized In/MoS 2 atomic structure negligible structural distortions at the rightmost metal atomic layer (see also Supplementary Fig. 3). As supported by the DFT-estimated binding energy 29,30 as well as the explicit experimental demonstration for the transferred Au electrode 14 , Au is a representative metal that forms vdW-type interactions with MoS 2 . Accordingly, the comparatively smaller In contactinduced structural perturbations consistently seen in our experiment and simulation indicate that In forms even more ideal vdW interactions with MoS 2 than Au.
To quantify this conclusion, we calculated the real-space charge density differences (Δρ) at the metal/MoS 2 interfaces according to and overlaid the results on the atomic structures in Fig. 3a, b top panels. The plane-averaged ΔρðzÞ for the In/MoS 2 and Au/MoS 2 contact cases are also presented in Fig. 3a, b middle panels, respectively. A positive (negative) Δρ indicates a gain (loss) in electron density, and we find stronger charge redistributions in the Au/MoS 2 contact compared with the In/MoS 2 counterpart. Examining the distribution of Δρ between the surface metal layers and the interfacial S layer ① of MoS 2 , we further note that due to the "push-back" effect arising from Pauli repulsion there appear charge-depleted (negative Δρ) 2D plane regions close to the metal surfaces (denoted by vertical dotted lines) 28,30 .
Using the minimum-Δρ layers as the reference planes (z = 0), we calculated along the MoS 2 direction the position-dependent and displayed the results in Fig. 3a, b bottom panels. Note that a positive (negative) Q indicates a metal-to-MoS 2 (MoS 2 -to-metal) electron transfer upon establishing the metal/MoS 2 interface 27 . We then find that In induces a marginal electron transfer of +5.0 × 10 12 electrons cm −2 to MoS 2 (left blue arrow in Fig. 3a bottom panel), which is in good quantitative agreement with the above-described estimate of~1.5 × 10 12 electrons cm −2 from Raman measurement (see Fig. 2). The marginal electron transfer leads to a weakened FLP, compared to an Au case. For the Au/ MoS 2 case, the direction of charge transfer is reversed (electron depletion in MoS 2 ), and its magnitude is significantly enhanced to −1.7 × 10 13 electrons cm −2 (left blue arrow in Fig. 3b  The multiple electrodes for the six-layer (6L) MoS 2 flake with different intervals between two neighboring electrodes were designed to measure the contact resistance via the transfer-length method (TLM) 13 , i.e., four FETs with different channel lengths (L 1 = 0.5 μm, L 2 = 1 μm, L 3 = 1.5 μm, and L 4 = 2 μm from the left channel in the region indicated by a dashed box) with a fixed metal contact length (L c ) as 1 μm. Here, the widths (W) of all channels were nearly identical at 2 μm. Figure 4c shows the twoprobe conductance as a function of the back-gate voltage (G-V G ) of the L 2 -FET with a source-drain voltage (V SD ) of 30 mV at various temperatures. The conductance decreased for negatively increasing V G and reached zero near V G ≈ 0 V throughout the investigated temperature range, which indicates that the electrical carriers are electrons. The two-probe conductance increased with decreasing T at a given V G for V G > 10 V, i.e., the device exhibited a metallic behavior. However, the opposite behavior was observed near a depletion region of 0 < V G < 10 V (see the inset of Fig. 4c), representing an insulating character. These behaviors are consistent with the current-voltage (I-V SD ) curves for various V G values at T = 2.5 K in Fig. 4d. For instance, the I-V SD curves for V G > 10 V and 0 < V G < 10 V show linear and nonlinear characteristics, respectively. We consider that the linearity and non-linearity originate from the field and thermionic emission through a Schottky barrier, respectively. The fourprobe measurements for the L 2 channel also showed a similar V G value for the metal-insulator crossover location (see Supplementary Fig. 9). This result indicates that the transport in the MoS 2 channel near the conduction-band edge also contributes to the crossover behavior, as well as the Schottky barrier. We also extracted the on/off ratio of~10 5 and 10 3 -10 5 of other monolayer (1L-#1) and 6L (6L-#2) devices, respectively, as shown in Supplementary section 5. The ratios satisfy a condition for logic gate applications. On the other hand, the on-current densities of 1L-#1 MoS 2 and 6L-#2 MoS 2 devices reached~60 μA μm −1 and~200 μA μm −1 , respectively. The 6L-#2 MoS 2 device also showed a stability against aging at least for 40 days for −1 V < V SD < 1 V (see Supplementary Fig. 11d).
In Fig. 4e, we show the field-effect mobility (μ) of the 6L-#1 MoS 2 device as a function of T obtained from the two-probe (open squares) and four-probe (closed squares) measurement schemes. The mobility was obtained at the local maximum location in the μ-V G curves (see Supplementary Fig. 12). For T > 100 K, in both cases, the data were fitted with a relation of μ T ð Þ ¼ μ 0 T Àα with α = 2.2 as shown by the dashed red line. This value is close to the expected value for bulk MoS 2 (α = 2.6) with the optical phonon scattering as a dominant scattering mechanism 12,32,33 . At room T, μ~50 cm 2 V −1 s −1 values were obtained for both cases. However, the two-probe and four-probe μ values were saturated with decreasing temperature in the region T < 20 K at 1200 and 3200 cm 2 V −1 s −1 , respectively. The saturation behavior in low-T regions is known to occur when the impurity scattering assumes a dominant role while the phonon-scattering effect is suppressed 34 . By contrast, the mobility for two different 1L MoS 2 devices (1L-#1 and 1L-#2; see Supplementary Figs. 10c, 13, respectively) displayed in Fig. 4f show a T dependence with α = 1.1 for T > 100 K, which is close to the prediction of the acoustic phonon scattering becoming a dominant scattering mechanism for a monolayer MoS 2 (ref. 33 ).
For comparison, we also fabricated MoS 2 devices with In contacts covered with Au, where the sample holder was a copper block prepared without a liquid-nitrogen cooling process. In this case, we found that the reproducibility was not high enough to obtain the consistent Ohmic-like behavior in the I-V SD curves, confirming the critical role of our substrate cooling technique (see Supplementary Fig. 14).
Schottky barrier height at In/MoS 2 contacts We evaluated ϕ SB at the In/MoS 2 interface because this parameter plays a critical role in determining the contact resistance between a metal and a semiconductor 4 . For this purpose, it is necessary to measure the activation energy (ϕ AE ) at the contacts in the thermionic emission region 6 . Here, because the V G range for the insulating region is larger than that of the 6L-#1 MoS 2 device (see Fig. 4c), we used the 1L-#2 MoS 2 device with the L = 1 μm channel shown in Supplementary Fig. 13a. Figure 5a shows the resulting G-V G curves for various temperatures obtained by the twoprobe measurement. In this case, the crossover V G between the insulating and metallic regions was located at a relatively higher V G (~65 V) than that of the 6L-#1 MoS 2 device, as indicated by an arrow.
The G values increased with increasing T for T < 130 K at V G < 65 V and decreased for T > 200 K in the examined V G range. When the thermionic emission is dominant, the current crossing a metal/2D system is described by the relation where A * is the Richardson constant, e is the elementary charge, k B is the Boltzmann constant, and η is the ideality factor that accounts for a lower barrier height due to image charging 12 . Figure 5b shows lnðI=T 3=2 Þ as a function of 1=k B T at V SD = 0.5 V for various V G values from 0 V to 70 V with 5 V spacing (from bottom to top). The slopes of lnðI=T 3=2 Þ À1=k B T curves are related to ϕ AE as ϕ AE ¼ V SD =η À slope. After obtaining the slopes corresponding to representative V SD values, we plotted the slope as a function of V SD for various V G (5 V to 70 V with 5 V spacing from bottom to top) to obtain ϕ AE at V SD = 0 V, as shown in Fig. 5c. Finally, we plotted ϕ AE vs. V G to obtain ϕ SB , as blue squares in Fig. 5d. Near the depletion region, ϕ AE is linearly lowered with increasing V G when the thermally activated transport is dominant and changes its slope when the field-emission transport is accounted at the Schottky barrier. Thus, the crossover point between them occurs when the band flattens, where, the value of ϕ AE becomes equal to the value of ϕ SB 6 . To find V G making the band flat, we plotted two linear blue lines on the blue squares in Fig. 5d. The two curves meet at V G ≈ 10 V, where the flat band is believed to form, and we estimated ϕ SB ≈ 7 meV at the corresponding ϕ AE for the In/MoS 2 (n = 1) contact. In addition, we also obtained a similar value for the L = 1.5 μm channel as indicated by green squares and green fit lines in Fig. 5d (see also Supplementary Fig. 13a). This value is in a similar range obtained from a Co/h-BN contact with a monolayer MoS 2 (ref. 10 ). Such a low ϕ SB at the In/MoS 2 contact could allow the field-emission to play a dominant role for the transport across the In/MoS 2 contact.

Contact resistance at In/MoS 2 contacts
On the basis of the TLM measurements (see Supplementary Fig.  15) with multiple channels (see Fig. 4a), we extracted the contact resistance (R c W) as a function of n e of the 6L-#1 MoS 2 device at representative temperatures; the results are shown in Fig. 6a (solid squares; see also Supplementary Table 2). Here, n e was estimated from the relation n e ¼ eμR sh ð Þ À1 . We note that, for the consistency, the sheet resistance R sh as well as mobility μ were obtained from the four-probe data, although R sh could have been extracted from the TLM method. The obtained contact resistance includes serial resistances of In and Ti/Au electrodes (see supplementary Fig. 16). At a given T, R c W decreased with increasing n e . The contact which is only valid for L c ≫L T . Here, ρ c is the specific contact resistivity and L T (= ffiffiffiffiffiffiffiffiffiffiffiffiffi ρ c =R sh p ) is the transfer length, which represents the average distance that charge carriers flow in a semiconductor beneath the contact before they completely transport to the electrode. Supplementary Fig. 15c shows that our device satisfied this condition with L c ≈ 1 μm and L T ≈ 0.1 μm. Equation (4) implies that R c W decreases with increasing n e because both R sh and ρ c generally decrease with increasing n e . At a fixed n e , the thermionic emission charge transport mechanism across the Schottky barrier predicts that R c W will increase with decreasing T because the thermionic emission will be suppressed with lowering T 35 . On the other hand, R c W in our measurements decreased with decreasing T, as shown by scattered red diamonds in Fig. 6b for the case measured at n e = 3.4 × 10 12 cm −2 . The contact resistance decreased from 2.3 to 0.6 kΩ μm when T was decreased from room temperature to 2.4 K. This behavior, which has been reported in several previous works such as graphene/ MoS 2 (ref. 12 ) and Pd/graphene contacts 36 , is considered as an evidence for the non-dominant role of thermionic emission for the transport across a contact. Scattered squares in Fig. 6b also show R sh as a function of T at n e = 3.4 × 10 12 cm −2 , where R sh decreased with decreasing T because the phonon scattering is reduced. Sheet resistance vs. specific contact resistivity We further analyzed the mechanism of charge transport across In/ MoS 2 contacts with experimental data in detail. We first examined which component between R sh and ρ c predominantly determines the contact resistance of the In/MoS 2 contact. For comparison, we included in Fig. 6a other values reported in the literature; graphene(Gr)/four-layer (4L)-MoS 2 contact 12 , Au/4L-MoS 2 (ref. 35 ) and Au/In/few-layer MoS 2 (ref. 17 ). In the case of Gr/4L-MoS 2 , the graphene functions as a work-function-controllable contact material, which leads to a lower contact resistance, i.e., R c W ≈ 1 kΩ μm at n e > 4 × 10 12 cm −2 and T = 12 K (see the red curve in Fig. 6a). Although both the Gr-and In-contact MoS 2 devices gave a similar minimum R c W at cryogenic temperatures, we conclude that the transport mechanisms at the contacts rather differ from each other. For the In/MoS 2 contact case, R c W decreased with decreasing T in the examined n e range, representing the field emission (or tunneling) for all examined T and n e ranges. However, the R c W−n e curves obtained at T = 12 and 250 K for the Gr/4L-MoS 2 device suggest that the left and right sides with respect to n e ≈ 2 × 10 12 cm −2 followed the thermionic and field emissions at the contact, respectively. At T = 12 K for the Gr/4L-MoS 2 device, although the R c W of~1 kΩ μm was relatively insensitive to the variation of n e in the range from 4 × 10 12 to 7 × 10 12 cm −2 , it rapidly changed from 1 kΩ μm to 6 kΩ μm when n e decreased from 3 × 10 12 cm −2 to 1.5 × 10 12 cm −2 . In the case of the Au/4L-MoS 2 contact, on the other hand, R c W was increased with decreasing T representing the thermionic emission for n e < 4 × 10 12 cm −2 . While the Au/In/few layer-MoS 2 contact provides a relatively low-R c W level for n e > 1.5 × 10 12 cm −2 at T = 300 K, it is hard to judge the transport mechanism for the In contact because of the absence of the T-dependence of R c W in the experiment. Then, for the In/6L-#1 MoS 2 device, the R c W was lowered with decreasing T at a given n e for 1 × 10 12 cm −2 < n e < 1 × 10 13 cm −2 , representing an Ohmic-like behavior based on the field-emission mechanism in the examined n e region. In our In/6L-MoS 2 device (see Fig. 7a), R sh varies in the range from 1 to 80 kΩ when ρ c only varies from 5 × 10 −6 to 5 × 10 −7 Ω cm 2 , as shown by two dashed lines, for R c W changing from 0.6 to~3 kΩ μm. This result indicates that R sh plays a dominant role in determining R c W in the fieldemission region.
We also obtained R c W from the 1L-#2 MoS 2 device on a 40-nmthick h-BN flake (see Fig. 7b and Supplementary Fig. 13 for the thickness profile). In Fig. 7b, the R c W values were extracted via the TLM with three channels (L = 0.5, 1, 1.5 μm) as shown in Supplementary Fig. 13a. For three V G-th conditions of 35, 40, and 45 V, R c W decreased with decreasing T in the range 250 ≥ T ≥ 100 K, representing the field emission. Here, V G−th = V G − V th and V th is a threshold voltage. At V G−th = 45 V, R c W reached~1 kΩ μm at T = 100 K as the minimum value obtained from the 1L-MoS 2 device. Although this value is similar to that obtained from the 6L-MoS 2 device at a similar T range (see Fig. 6a), the contact resistance for the monolayer MoS 2 is higher than that of multilayer MoS 2 . The reason could be related to the relatively low affinity energy in the monolayer MoS 2 . Interestingly, R c W increased with decreasing T for T < 100 K under all V G−th conditions. In this region, the MoS 2 channel also exhibited an insulating behavior in G-V G curves for various temperatures of Fig. 5a for V G < 60 V and T < 100 K. Thus, it indicates that the increase of R sh with decreasing T in the insulating phase plays a dominant role in determining the contact resistance at T < 100 K. We note that this non-Ohmic behavior could not be improved by the contact engineering because the behavior originates from the intrinsic property of MoS 2 itself. This implies that the manipulation of the metalinsulator crossover gate voltage could be crucial to get a better contact property in a mono-layer MoS 2 device. In Fig. 7a (see also  Supplementary Table 2), we compared the lowest achievable contact resistance as a function of R sh from previous reports with ours. For the In/MoS 2 device, the contact resistance decreased with decreasing R sh and reached~0.6 kΩ μm as the lowest value at R sh~1 kΩ and T = 2.4 K. At T = 300 K, on the other hand, the Au/ In/few layer-MoS 2 device showed the lowest value of~0.6 kΩ μm at R sh~6 0 kΩ. In addition, for monolayer cases, our In/1L-#2 MoS 2 contact provided 0.9-4 kΩ μm at R sh~5 0 kΩ, which are comparable to those obtained from the Au/In/1L-MoS 2 contact that showed~3 kΩ μm at R sh~4 0 kΩ.
Atomistic origins of the field emission-dominated charge transport across In/MoS 2 contacts Analyzing the electronic structures of the In/MoS 2 and Au/MoS 2 interfaces obtained from DFT calculations, we finally identify the atomistic mechanisms of the experimentally observed Ohmiclike charge transport behavior. It should be noted that, while there exist in the literature several theoretical studies that examined the Schottky barriers in metal/TMDC interfaces 30,[37][38][39][40] , the In/TMDC case has been rarely treated 41 . We show the calculated band structures at the In/MoS 2 and Au/MoS 2 contacts in Fig. 8a, b, respectively, and particularly display the projected bands of Mo-4d (green circles in Fig. 8a, b), In-5p z (wine filled circles in Fig. 8a), and Au-6s (orange circles in Fig. 8b) orbitals. From the band structures, one could determine the electron ϕ SB by measuring the energy level difference between the conduction band minimum (CBM) edge (upper solid purple line) and the Fermi level E F (dashed purple line) of metal/MoS 2 contacts. However, the comparison of the two bands indicate that identifying the electron ϕ SB in the In/ MoS 2 contact is a non-trivial matter due to the strong density of in-gap states appearing below and around the MoS 2 CBM region (green circles between CBM and E F in Fig. 8a; note the absence of such in-gap states in the Au/MoS2 contact in Fig. 8b). To circumvent this difficulty, we first extracted the hole ϕ SB from the In/MoS 2 junction band structure (see also Supplementary Fig.  5). Next, calculating the band structure of the pristine monolayer MoS 2 using the simulation cell of the corresponding In/MoS 2 junction model ( Supplementary Fig. 6), we determined the electron ϕ SB by subtracting the hole ϕ SB from the calculated band gap of monolayer MoS 2 (1.94 eV) (Supplementary Fig. 7). The obtained electron ϕ SB values were 0.31 eV and 0.72 eV for the In/ MoS 2 and Au/MoS 2 junctions, respectively. The In/MoS 2 electron, ϕ SB value of 0.31 eV is comparable to a previous estimate of 0.47 eV 41 and much larger than the experimentally identified marginal ϕ SB values. We thus conclude that the experimentally observed ϕ SB is an effective ϕ SB that has been significantly reduced from the intrinsic ϕ SB by strong density of in-gap states.
Having been identified as the distinguishing feature, the large in-gap states arising in the In/MoS 2 contact should be the source of the marginal effective ϕ SB and Ohmic-like transport and deserve further attention. Disregarding this factor, for example, can lead to the conclusion that Au would form a better contact than In for MoS 2 41 , but the in-gap states of the In/MoS 2 contact remains unexplored 37,38 . To examine the nature of in-gap states in the In/MoS 2 interface in comparison with that of the Au/MoS 2 counterpart, we show in Fig. 8c, d how the In-5p z (pink filled line) and Au-6s (orange filled line) projected density of states (PDOS) evolve into the metal-contacting ① S-3p layer, ② Mo-4d layer, and ③ the outer S-3p layer PDOS of MoS 2 for the In/MoS 2 and Au/MoS 2 contacts, respectively. It is immediately notable that, while the Au-6s PDOS are uniformly distributed across the MoS 2 bandgap (Fig. 8d first panel), the In-5p z PDOS show energetically very asymmetric distribution such that they start from a negligible level near the MoS 2 VBM region and increase significantly toward the MoS 2 CBM region ( Fig. 8c first panel). The MoS 2 VBM and CBM PDOS are mostly composed of Mo-4d orbitals (compare the second/fourth panels with the second panels in Fig. 8c, d). Then, we find for the In/MoS 2 contact case that very strong density of ingap states are formed between E F and MoS 2 CBM position ( Fig. 8c third panel). As schematically depicted by the thick arrow in Fig. 8c, electrons injecting from In into these MoS 2 in-gap states then should result in the experimentally observed field-emissiontype charge transport accompanied by a negligible effective ϕ SB . On the other hand, the corresponding Mo-4d PDOS around E F for the Au contact case are relatively marginal, making such a charge injection mechanism ineffective (schematically represented by a thin arrow in Fig. 8d). In Fig. 8e, f, we additionally visualized in real space the E F -region In-MoS 2 and Au-MoS 2 hybridized DOS, respectively. The stronger hybridization between In and MoS 2 states than that between Au and MoS 2 states then provides an intuitive explanation how the Ohmic-like charge transport is achieved for the In/MoS 2 interface in spite of the very small interfacial charge transfer (see Fig. 3).
In summary, carrying out a combined experimental and theoretical investigation for an ultraclean vdW contact between an elemental metal In (without alloying) and semiconductor MoS 2 , we revealed the mechanism of Ohmic charge transport across the In/MoS 2 vdW interface. For the single-and few-layer MoS 2 devices, the contact resistance decreased with decreasing temperatures for 100 ≤ T ≤ 300 K, indicating the field-emission mechanism for the Ohmic-like contact transport. The contact resistance was sensitive to the change of sheet resistance of MoS 2 , rather than that of the specific contact resistivity within the field-emission region. For the monolayer MoS 2 case, we achieved the contact resistance of~1 kΩ μm at T = 100 K, which is the lowest value achieved by metal evaporations on MoS 2 to date. Our experimental findings were corroborated by DFT calculations, which showed that the In/MoS 2 contact has a weakened FLP due to the marginal interfacial charge transfer. Importantly, in spite of the weak interface dipole formation, we found that strong density of in-gap states are formed around MoS 2 CBM states and enable an Ohmic-like charge transport across the In/MoS 2 interface. Related with this identified mechanism, we comment that one of us previously predicted for semiconducting carbon nanotubes that a highly efficient charge injection across vdW metal contacts could be achieved via large in-gap states generated from topological defects within the sp 2 carbon network 28 . We thus suggest that seeking a mechanism of introducing strong density of in-gap states while maintaining the ideal contact geometry with weak charge transfer could prove to be a general strategy to simultaneously avoid FLP and minimize contact resistance for low-dimensional vdW materials 42 .

Device fabrication
We fabricated MoS 2 FETs on h-BN flakes, where the h-BN flakes were deposited onto a 300-nm-thick SiO 2 /Si substrate by mechanical exfoliation. We then transferred a few-layer MoS 2 flake (HQ-graphene, Inc.) onto a selected h-BN flake 12,20 . For the electrical measurements, we deposited 100-nm-thick In electrodes across the MoS 2 channel, where the substrate holder was kept at~100 K by flowing liquid nitrogen through it. The substrate cooling process leads to an important result; a uniform surface morphology of In film is achieved, which contrasts strongly with the usage of a room-temperature holder that produces a segregated granular film for at least up to~70 nm thickness, as reported in our previous work (also see Supplementary Fig. 1) 21 .

Raman spectroscopy
The Raman measurements were performed in a backscattering geometry at room temperature. An incident laser light with a wavelength of 514.5 nm was focused on the sample surface through an optical microscope objective lens (100×/0.9 NA). An excitation laser power was maintained less than 0.4 mW to avoid any laser-induced heating effects. Scattered light from the sample was dispersed through a monochromator with a 1200 grooves mm −1 grating and was collected using a thermoelectrically cooled charge-coupled device detector. For mapping measurements, Raman spectra were taken at the step of 0.5 μm over the area of 15 × 15 μm 2 .

DFT calculations
We performed DFT calculations within the local density approximation (LDA) 43 using the SIESTA software 44 . The atomic cores were replaced by norm-conserving nonlocal pseudopotentials of the Troullier-Martins type 45 , and double ζ-plus-polarization-level numerical atomic orbital basis sets were employed. Geometry optimizations were performed until the Hellmann-Feynman ionic forces were below 0.02 eV Å −1 . To check the reliability of geometries and electronic structures obtained within LDA in terms of vdW interactions, we also carried out DFT calculations using the DFT-D3 (ref. 46 ) exchange-correlation functional. As in our earlier work 47 , we obtained consistent results from LDA and DFT-D3 calculations (see Supplementary Figs. 3, 4 and Table 1).

DATA AVAILABILITY
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request. All data generated or , ① metal-contacting S-3p (second panels), ② Mo-4d (third panels), and ③ outer S-3p (fourth panels) orbitals. In the second, third, and fourth panels, the upper and lower solid lines indicate the MoS 2 CBM and VBM levels, respectively. The arrows schematically show that the charge transport across the In/MoS 2 contact is much more efficient than that across the Au/MoS 2 counterpart, and the Ohmic-like charge transport is mediated by the large in-gap states formed around E F of the In/MoS 2 interface. The local DOS in the range between E F and E F +0.2 eV overlaid over the e In/MoS 2 and f Au/MoS 2 interface models. The iso-surface level is 2.5 × 10 −4 states eV −1 Å −3 .