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

## Abstract

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 MoS2, WSe2, and MoTe2 have been extensively studied for the future development of low-power and high-performance electronic and optoelectronic applications1,2,3. However, establishing a reliable Ohmic contact between metals and TMDCs remains a critical challenge4,5. For instance, in reducing the Schottky barrier height (ϕSB) for TMDCs, efforts to identify metals with appropriate work functions Φmetal (e.g. ΦSc ≈ 3.5 eV for Sc and ΦTi ≈ 4.3 eV for Ti) based on the electron affinity of monolayer (1L) and few-layer TMDCs (e.g. monolayer MoS2: $${\upchi}_{1{\mathrm{L}}\,{\mathrm{MoS}}_2} \approx$$ 4 eV, multilayer MoS2: $${\upchi}_{{\mathrm{ML}}\,{\mathrm{MoS}}_2} \approx$$ 4.3 eV) have not been effective because of the strong Fermi-level pinning (FLP) effect6,7. While various approaches have been explored to overcome this problem, including molecular doping8, tunnel-barrier insertion9,10, fabrication of graphene contacts11,12, and TMDC phase changes13, 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 properties14,15,16. 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 ϕSB (or FLP) and high contact resistance7,14. 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 values17,18,19. However, regarding our initial report on the achievement of Ohmic-like three-dimensional (3D) In-2D MoS2 contact18, question was raised in that the origins of the low contact resistance through the In–MoS2 vdW contact are unclear.

Here, we prepare an ultraclean vdW contact between In and MoS2 using an improved evaporation method, and clarify through extensive transport measurements and computations the nature and origins of Ohmic transport characteristics from In/MoS2 vdW contacts. We prepare the high-quality vdW In/MoS2 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/MoS2 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/MoS2 counterpart, the In/MoS2 contact induces an order of magnitude smaller charge transfer, which is consistent with the Raman spectroscopy data. For both mono- and few-layer MoS2 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/MoS2 contact and the field emission is the dominant charge transport mechanism at the In/MoS2 contact. We finally identify from DFT calculations large in-gap states originating from the hybridization between MoS2 conduction-band-edge and In Fermi-level 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/MoS2 interface

We fabricated MoS2 field-effect transistors (FETs) on hexagonal boron nitride (h-BN) flakes, where the h-BN flakes were deposited onto a 300-nm-thick SiO2/Si substrate by mechanical exfoliation. We then transferred a few-layer MoS2 flake (HQ-graphene, Inc.) onto a selected h-BN flake12,20. For the electrical measurements, we deposited 100-nm-thick In electrodes across the MoS2 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 MoS2 junction, which clearly shows an atomically separated interface between In and MoS2 layers without any metal invasion into the MoS2 layers. Whereas crystal-lattice disorders that cause defect-induced gap states and FLP typically occur during the high-temperature deposition process of evaporated metal atoms with high thermal energy7,14, 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 MoS2 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/MoS2 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 MoS2 interface, like previous studies14.

To further characterize the quality of In/MoS2 interface, we applied the Raman spectroscopy for both the pristine and In-covered MoS2 regions to estimate doping effect at the metal contacts. It is known that the A1g phonon peak of MoS2 exhibits a red shift and its width broadens with electron doping22,23. Figure 2a, b shows the optical images of, respectively, 1L- and bilayer (2L)-MoS2 (indicated by regions bounded with dashed black lines) prepared on SiO2 and partially covered with 5-nm-thick In (indicated by regions bounded with dashed white lines). Figure 2c, d shows the A1g energy maps for the 1L- and 2L-MoS2, 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-MoS2, respectively (see Supplementary Fig. 2 for representative Raman spectra for a 1L-MoS2). In the upper panel of Supplementary Fig. 2a, we also show the $$E_{2g}^1$$ energy map of the 1L-MoS2, which indicates relatively negligible difference between the In-covered and non-covered regions. For the biaxial strain, the red shift of the $$E_{2g}^1$$ Raman mode corresponding to the in-plane vibration is more sensitive than the A1g mode (out-of-plane vibration)24,25. For the in- and out-of-plane compressive strains, both modes should show blue shifts26. In our case, however, we observed a relatively strong red shift of the A1g mode than that of the $$E_{2g}^1$$ mode, which has been interpreted as a doping effect22. For instance, Chakraborty et al.22 reported that the A1g mode softens with doping at a rate of ~0.2 cm−1 per 1012 cm−2 for 1L-MoS2, whereas the $$E_{2g}^1$$ mode is relatively insensitive to the doping. We thus conclude that the 1L-MoS2 region covered by In was doped by electrons at a density of ~+1.5 × 1012 electrons cm−2 (electron accumulation in MoS2). 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-MoS2, implying electron doping. This In-to-MoS2 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/MoS2 interface

To extract the atomistic information of the In/MoS2 vdW contact and contrast them with those of the Au/MoS2 counterpart, we carried out DFT calculations for the vertical In/MoS2 and Au/MoS2 interface models and applied several analysis methods27,28. In Fig. 3a, b top panels, we show the fully optimized In/MoS2 and Au/MoS2 contact models, respectively (see details in Supplementary Figs. 3, 4 and Table 1). First, compared to the Au/MoS2 case, we find in the optimized In/MoS2 atomic structure negligible structural distortions at the rightmost metal atomic layer (see also Supplementary Fig. 3). As supported by the DFT-estimated binding energy29,30 as well as the explicit experimental demonstration for the transferred Au electrode14, Au is a representative metal that forms vdW-type interactions with MoS2. Accordingly, the comparatively smaller In contact-induced structural perturbations consistently seen in our experiment and simulation indicate that In forms even more ideal vdW interactions with MoS2 than Au.

To quantify this conclusion, we calculated the real-space charge density differences (Δρ) at the metal/MoS2 interfaces according to

$$\Delta \rho = \rho _{{\mathrm{metal}}/{\mathrm{MoS}}_2} - \left( {\rho _{{\mathrm{MoS}}_2} + \rho _{{\mathrm{metal}}}} \right)$$
(1)

and overlaid the results on the atomic structures in Fig. 3a, b top panels. The plane-averaged $$\Delta \bar \rho (z)$$ for the In/MoS2 and Au/MoS2 contact cases are also presented in Fig. 3a, b middle panels, respectively. A positive (negative) ∆$$\bar \rho$$ indicates a gain (loss) in electron density, and we find stronger charge redistributions in the Au/MoS2 contact compared with the In/MoS2 counterpart. Examining the distribution of $$\Delta \bar \rho$$ between the surface metal layers and the interfacial S layer of MoS2, we further note that due to the “push-back” effect arising from Pauli repulsion there appear charge-depleted (negative $$\Delta \bar \rho$$) 2D plane regions close to the metal surfaces (denoted by vertical dotted lines)28,30.

Using the minimum-$$\Delta \bar \rho$$ layers as the reference planes (z = 0), we calculated along the MoS2 direction the position-dependent accumulated interfacial charge transfers according to

$$Q\left( z \right) = \mathop {\int}\nolimits_0^z \Delta \bar \rho (z^\prime )dz^{\prime} ,$$
(2)

and displayed the results in Fig. 3a, b bottom panels. Note that a positive (negative) Q indicates a metal-to-MoS2 (MoS2-to-metal) electron transfer upon establishing the metal/MoS2 interface27. We then find that In induces a marginal electron transfer of +5.0 × 1012 electrons cm−2 to MoS2 (left blue arrow in Fig. 3a bottom panel), which is in good quantitative agreement with the above-described estimate of ~1.5 × 1012 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/MoS2 case, the direction of charge transfer is reversed (electron depletion in MoS2), and its magnitude is significantly enhanced to −1.7 × 1013 electrons cm−2 (left blue arrow in Fig. 3b bottom panel). These opposite MoS2 doping characters of In and Au can be understood in terms of the alignment of the MoS2 charge neutrality level $$\phi _{1{\mathrm{L}}\,{\mathrm{MoS}}_2}^ \ast \approx$$ 4.78 eV with respect to the metal work functions ΦIn ≈ 4.1 eV and ΦAu ≈ 5.1 eV31, as schematically shown in Fig. 3c, d, respectively (see Supplementary Figs. 5, 6, and 7).

### Electrical properties of a MoS2 FET

Figure 4a and b shows a photograph of a MoS2 FET on a 22-nm-thick h-BN flake and schematic for the electrical measurement configuration, respectively. The number of MoS2 layers was estimated to be six (6L-#1 MoS2; see Supplementary Fig. 8). The multiple electrodes for the six-layer (6L) MoS2 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 (L1 = 0.5 μm, L2 = 1 μm, L3 = 1.5 μm, and L4 = 2 μm from the left channel in the region indicated by a dashed box) with a fixed metal contact length (Lc) as 1 μm. Here, the widths (W) of all channels were nearly identical at 2 μm. Figure 4c shows the two-probe conductance as a function of the back-gate voltage (GVG) of the L2-FET with a source–drain voltage (VSD) of 30 mV at various temperatures. The conductance decreased for negatively increasing VG and reached zero near VG ≈ 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 VG for VG > 10 V, i.e., the device exhibited a metallic behavior. However, the opposite behavior was observed near a depletion region of 0 < VG < 10 V (see the inset of Fig. 4c), representing an insulating character. These behaviors are consistent with the current–voltage (IVSD) curves for various VG values at T = 2.5 K in Fig. 4d. For instance, the IVSD curves for VG > 10 V and 0 < VG < 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 four-probe measurements for the L2 channel also showed a similar VG value for the metal–insulator crossover location (see Supplementary Fig. 9). This result indicates that the transport in the MoS2 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 ~105 and 103–105 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 MoS2 and 6L-#2 MoS2 devices reached ~60 μA μm−1 and ~200 μA μm−1, respectively. The 6L-#2 MoS2 device also showed a stability against aging at least for 40 days for −1 V < VSD < 1 V (see Supplementary Fig. 11d).

In Fig. 4e, we show the field-effect mobility (μ) of the 6L-#1 MoS2 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 μVG curves (see Supplementary Fig. 12). For T > 100 K, in both cases, the data were fitted with a relation of $$\mu \left( T \right) = \mu _0T^{ - \alpha }$$ with α = 2.2 as shown by the dashed red line. This value is close to the expected value for bulk MoS2 (α = 2.6) with the optical phonon scattering as a dominant scattering mechanism12,32,33. At room T, μ ~ 50 cm2 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 cm2 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 suppressed34. By contrast, the mobility for two different 1L MoS2 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 MoS2 (ref. 33).

For comparison, we also fabricated MoS2 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–VSD curves, confirming the critical role of our substrate cooling technique (see Supplementary Fig. 14).

### Schottky barrier height at In/MoS2 contacts

We evaluated ϕSB at the In/MoS2 interface because this parameter plays a critical role in determining the contact resistance between a metal and a semiconductor4. For this purpose, it is necessary to measure the activation energy (ϕAE) at the contacts in the thermionic emission region6. Here, because the VG range for the insulating region is larger than that of the 6L-#1 MoS2 device (see Fig. 4c), we used the 1L-#2 MoS2 device with the L = 1 μm channel shown in Supplementary Fig. 13a. Figure 5a shows the resulting G–VG curves for various temperatures obtained by the two-probe measurement. In this case, the crossover VG between the insulating and metallic regions was located at a relatively higher VG (~65 V) than that of the 6L-#1 MoS2 device, as indicated by an arrow. The G values increased with increasing T for T < 130 K at VG < 65 V and decreased for T > 200 K in the examined VG range. When the thermionic emission is dominant, the current crossing a metal/2D system is described by the relation

$$I_{\mathrm{d}} = {{A}}^ \ast T^{3/2}{\mathrm{exp}}\left( {\frac{{ - e\phi _{{\mathrm{AE}}}}}{{k_{\mathrm{B}}T}}} \right)\left[ {{\mathrm{exp}}\left( {\frac{{eV_{{\mathrm{SD}}}}}{{\eta k_{\mathrm{B}}T}}} \right) - 1} \right],$$
(3)

where A* is the Richardson constant, e is the elementary charge, kB is the Boltzmann constant, and η is the ideality factor that accounts for a lower barrier height due to image charging12. Figure 5b shows $${\mathrm{ln}}(I/T^{3/2})$$ as a function of $$1/k_{\mathrm{B}}T$$ at VSD = 0.5 V for various VG values from 0 V to 70 V with 5 V spacing (from bottom to top). The slopes of $${\mathrm{ln}}(I/T^{3/2})$$ $$-1/k_{\mathrm{B}}T$$ curves are related to ϕAE as $$\phi _{{\mathrm{AE}}} = V_{{\mathrm{SD}}}/\eta - {\mathrm{slope}}$$. After obtaining the slopes corresponding to representative VSD values, we plotted the slope as a function of VSD for various VG (5 V to 70 V with 5 V spacing from bottom to top) to obtain ϕAE at VSD = 0 V, as shown in Fig. 5c. Finally, we plotted ϕAE vs. VG to obtain ϕSB, as blue squares in Fig. 5d. Near the depletion region, ϕAE is linearly lowered with increasing VG 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 ϕAE becomes equal to the value of ϕSB6. To find VG making the band flat, we plotted two linear blue lines on the blue squares in Fig. 5d. The two curves meet at VG ≈ 10 V, where the flat band is believed to form, and we estimated ϕSB ≈ 7 meV at the corresponding ϕAE for the In/MoS2 (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 MoS2 (ref. 10). Such a low ϕSB at the In/MoS2 contact could allow the field-emission to play a dominant role for the transport across the In/MoS2 contact.

### Contact resistance at In/MoS2 contacts

On the basis of the TLM measurements (see Supplementary Fig. 15) with multiple channels (see Fig. 4a), we extracted the contact resistance (RcW) as a function of ne of the 6L-#1 MoS2 device at representative temperatures; the results are shown in Fig. 6a (solid squares; see also Supplementary Table 2). Here, ne was estimated from the relation $$n_{\mathrm{e}} = \left( {e\mu R_{{\mathrm{sh}}}} \right)^{ - 1}$$. We note that, for the consistency, the sheet resistance Rsh as well as mobility μ were obtained from the four-probe data, although Rsh 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, RcW decreased with increasing ne. The contact resistance is given by4,5

$$R_{\mathrm{c}}W(n_{\mathrm{e}},T) = \sqrt {R_{{\mathrm{sh}}}(n_{\mathrm{e}},T)\rho _{\mathrm{c}}(n_{\mathrm{e}},T)} ,$$
(4)

which is only valid for LcLT. Here, ρc is the specific contact resistivity and LT (= $$\sqrt {\rho _{\mathrm{c}}/R_{{\mathrm{sh}}}}$$) 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 Lc ≈ 1 μm and LT ≈ 0.1 μm. Equation (4) implies that RcW decreases with increasing ne because both Rsh and ρc generally decrease with increasing ne. At a fixed ne, the thermionic emission charge transport mechanism across the Schottky barrier predicts that RcW will increase with decreasing T because the thermionic emission will be suppressed with lowering T35. On the other hand, RcW in our measurements decreased with decreasing T, as shown by scattered red diamonds in Fig. 6b for the case measured at ne = 3.4 × 1012 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/MoS2 (ref. 12) and Pd/graphene contacts36, 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 Rsh as a function of T at ne = 3.4 × 1012 cm−2, where Rsh 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/MoS2 contacts with experimental data in detail. We first examined which component between Rsh and ρc predominantly determines the contact resistance of the In/MoS2 contact. For comparison, we included in Fig. 6a other values reported in the literature; graphene(Gr)/four-layer (4L)-MoS2 contact12, Au/4L-MoS2 (ref. 35) and Au/In/few-layer MoS2 (ref. 17). In the case of Gr/4L-MoS2, the graphene functions as a work-function-controllable contact material, which leads to a lower contact resistance, i.e., RcW ≈ 1 kΩ μm at ne > 4 × 1012 cm−2 and T = 12 K (see the red curve in Fig. 6a). Although both the Gr-and In-contact MoS2 devices gave a similar minimum RcW at cryogenic temperatures, we conclude that the transport mechanisms at the contacts rather differ from each other. For the In/MoS2 contact case, RcW decreased with decreasing T in the examined ne range, representing the field emission (or tunneling) for all examined T and ne ranges. However, the RcWne curves obtained at T = 12 and 250 K for the Gr/4L-MoS2 device suggest that the left and right sides with respect to ne ≈ 2 × 1012 cm−2 followed the thermionic and field emissions at the contact, respectively. At T = 12 K for the Gr/4L-MoS2 device, although the RcW of ~1 kΩ μm was relatively insensitive to the variation of ne in the range from 4 × 1012 to 7 × 1012 cm−2, it rapidly changed from 1 kΩ μm to 6 kΩ μm when ne decreased from 3 × 1012 cm−2 to 1.5 × 1012 cm−2. In the case of the Au/4L-MoS2 contact, on the other hand, RcW was increased with decreasing T representing the thermionic emission for ne < 4 × 1012 cm−2. While the Au/In/few layer-MoS2 contact provides a relatively low-RcW level for ne > 1.5 × 1012 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 RcW in the experiment. Then, for the In/6L-#1 MoS2 device, the RcW was lowered with decreasing T at a given ne for 1 × 1012 cm−2 < ne < 1 × 1013 cm−2, representing an Ohmic-like behavior based on the field-emission mechanism in the examined ne region. In our In/6L-MoS2 device (see Fig. 7a), Rsh varies in the range from 1 to 80 kΩ when ρc only varies from 5 × 10−6 to 5 × 10−7 Ω cm2, as shown by two dashed lines, for RcW changing from 0.6 to ~3 kΩ μm. This result indicates that Rsh plays a dominant role in determining RcW in the field-emission region.

We also obtained RcW from the 1L-#2 MoS2 device on a 40-nm-thick h-BN flake (see Fig. 7b and Supplementary Fig. 13 for the thickness profile). In Fig. 7b, the RcW values were extracted via the TLM with three channels (L = 0.5, 1, 1.5 μm) as shown in Supplementary Fig. 13a. For three VG-th conditions of 35, 40, and 45 V, RcW decreased with decreasing T in the range 250 ≥ T ≥ 100 K, representing the field emission. Here, VG−th = VG − Vth and Vth is a threshold voltage. At VG−th = 45 V, RcW reached ~1 kΩ μm at T = 100 K as the minimum value obtained from the 1L-MoS2 device. Although this value is similar to that obtained from the 6L-MoS2 device at a similar T range (see Fig. 6a), the contact resistance for the monolayer MoS2 is higher than that of multilayer MoS2. The reason could be related to the relatively low affinity energy in the monolayer MoS2. Interestingly, RcW increased with decreasing T for T < 100 K under all VG−th conditions. In this region, the MoS2 channel also exhibited an insulating behavior in GVG curves for various temperatures of Fig. 5a for VG < 60 V and T < 100 K. Thus, it indicates that the increase of Rsh 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 MoS2 itself. This implies that the manipulation of the metal-insulator crossover gate voltage could be crucial to get a better contact property in a mono-layer MoS2 device. In Fig. 7a (see also Supplementary Table 2), we compared the lowest achievable contact resistance as a function of Rsh from previous reports with ours. For the In/MoS2 device, the contact resistance decreased with decreasing Rsh and reached ~0.6 kΩ μm as the lowest value at Rsh ~ 1 kΩ and T = 2.4 K. At T = 300 K, on the other hand, the Au/In/few layer-MoS2 device showed the lowest value of ~0.6 kΩ μm at Rsh ~ 60 kΩ. In addition, for monolayer cases, our In/1L-#2 MoS2 contact provided 0.9–4 kΩ μm at Rsh ~ 50 kΩ, which are comparable to those obtained from the Au/In/1L-MoS2 contact that showed ~3 kΩ μm at Rsh ~ 40 kΩ.

### Atomistic origins of the field emission-dominated charge transport across In/MoS2 contacts

Analyzing the electronic structures of the In/MoS2 and Au/MoS2 interfaces obtained from DFT calculations, we finally identify the atomistic mechanisms of the experimentally observed Ohmic-like 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 interfaces30,37,38,39,40, the In/TMDC case has been rarely treated41. We show the calculated band structures at the In/MoS2 and Au/MoS2 contacts in Fig. 8a, b, respectively, and particularly display the projected bands of Mo-4d (green circles in Fig. 8a, b), In-5pz (wine filled circles in Fig. 8a), and Au-6s (orange circles in Fig. 8b) orbitals. From the band structures, one could determine the electron ϕSB by measuring the energy level difference between the conduction band minimum (CBM) edge (upper solid purple line) and the Fermi level EF (dashed purple line) of metal/MoS2 contacts. However, the comparison of the two bands indicate that identifying the electron ϕSB in the In/MoS2 contact is a non-trivial matter due to the strong density of in-gap states appearing below and around the MoS2 CBM region (green circles between CBM and EF 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 ϕSB from the In/MoS2 junction band structure (see also Supplementary Fig. 5). Next, calculating the band structure of the pristine monolayer MoS2 using the simulation cell of the corresponding In/MoS2 junction model (Supplementary Fig. 6), we determined the electron ϕSB by subtracting the hole ϕSB from the calculated band gap of monolayer MoS2 (1.94 eV) (Supplementary Fig. 7). The obtained electron ϕSB values were 0.31 eV and 0.72 eV for the In/MoS2 and Au/MoS2 junctions, respectively. The In/MoS2 electron, ϕSB value of 0.31 eV is comparable to a previous estimate of 0.47 eV41 and much larger than the experimentally identified marginal ϕSB values. We thus conclude that the experimentally observed ϕSB is an effective ϕSB that has been significantly reduced from the intrinsic ϕSB by strong density of in-gap states.

Having been identified as the distinguishing feature, the large in-gap states arising in the In/MoS2 contact should be the source of the marginal effective ϕSB 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 MoS241, but the in-gap states of the In/MoS2 contact remains unexplored37,38. To examine the nature of in-gap states in the In/MoS2 interface in comparison with that of the Au/MoS2 counterpart, we show in Fig. 8c, d how the In-5pz (pink filled line) and Au-6s (orange filled line) projected density of states (PDOS) evolve into the metal-contacting S-3p layer, Mo-4d layer, and the outer S-3p layer PDOS of MoS2 for the In/MoS2 and Au/MoS2 contacts, respectively. It is immediately notable that, while the Au-6s PDOS are uniformly distributed across the MoS2 bandgap (Fig. 8d first panel), the In-5pz PDOS show energetically very asymmetric distribution such that they start from a negligible level near the MoS2 VBM region and increase significantly toward the MoS2 CBM region (Fig. 8c first panel). The MoS2 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/MoS2 contact case that very strong density of in-gap states are formed between EF and MoS2 CBM position (Fig. 8c third panel). As schematically depicted by the thick arrow in Fig. 8c, electrons injecting from In into these MoS2 in-gap states then should result in the experimentally observed field-emission-type charge transport accompanied by a negligible effective ϕSB. On the other hand, the corresponding Mo-4d PDOS around EF 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 EF-region In-MoS2 and Au-MoS2 hybridized DOS, respectively. The stronger hybridization between In and MoS2 states than that between Au and MoS2 states then provides an intuitive explanation how the Ohmic-like charge transport is achieved for the In/MoS2 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 MoS2, we revealed the mechanism of Ohmic charge transport across the In/MoS2 vdW interface. For the single- and few-layer MoS2 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 MoS2, rather than that of the specific contact resistivity within the field-emission region. For the monolayer MoS2 case, we achieved the contact resistance of ~1 kΩ μm at T = 100 K, which is the lowest value achieved by metal evaporations on MoS2 to date. Our experimental findings were corroborated by DFT calculations, which showed that the In/MoS2 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 MoS2 CBM states and enable an Ohmic-like charge transport across the In/MoS2 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 sp2 carbon network28. 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 materials42.

## Methods

### Device fabrication

We fabricated MoS2 FETs on h-BN flakes, where the h-BN flakes were deposited onto a 300-nm-thick SiO2/Si substrate by mechanical exfoliation. We then transferred a few-layer MoS2 flake (HQ-graphene, Inc.) onto a selected h-BN flake12,20. For the electrical measurements, we deposited 100-nm-thick In electrodes across the MoS2 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 μm2.

### DFT calculations

We performed DFT calculations within the local density approximation (LDA)43 using the SIESTA software44. The atomic cores were replaced by norm-conserving nonlocal pseudopotentials of the Troullier-Martins type45, 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 work47, 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 analyzed during this study are included in this published article (and its Supplementary Information).

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## Acknowledgements

We acknowledge Prof. E. Hwang and Dr. J.-S. Park for fruitful discussion. This work was supported by the Korea Research Institute of Standards and Science (KRISS-2020-GP2020-0001) and the National Research Foundation of Korea (NRF) (Grant Nos. 2018R1A2A1A05078440, SRC2016R1A5A1008184, 2020R1F1A1075216, 2019R1A2C1003366, 2017R1A2B3009872, 2016M3A7B4024133, 2013M3A6B1078881, and 2017R1A4A1015400). Growth of hexagonal boron nitride crystals was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant Number JPMXP0112101001, JSPS KAKENHI Grant Number JP20H00354 and the CREST (JPMJCR15F3), JST. Computational resources were provided by the KISTI Supercomputing Center (KSC-2018-C2-0032).

## Author information

Authors

### Contributions

M.-H.B., J.-J.K, and Y.-H.K. conceived the research project. K.W. and T.T. grew the bulk h-BN. D.-H.C. and B.-K.K. fabricated the devices. D.-H.C. performed the TEM analysis. B.-K.K. performed the electrical measurements and analyzed the data with M.-H.B. H.K. and H.R. performed the Raman spectroscopy. T.-H.K. and Y.-H.K. performed the DFT calculations. M.-H.B, B.-K.K, T.-H.K., Y.-H.K., and J.-J.K. wrote the manuscript. All authors discussed the results and commented on the manuscript. B.-K.K., T.-H.K., and D.-H.C. contributed equally to this work.

### Corresponding authors

Correspondence to Ju-Jin Kim or Yong-Hoon Kim or Myung-Ho Bae.

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### Competing interests

The authors declare no competing interests.

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Kim, BK., Kim, TH., Choi, DH. et al. Origins of genuine Ohmic van der Waals contact between indium and MoS2. npj 2D Mater Appl 5, 9 (2021). https://doi.org/10.1038/s41699-020-00191-z

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