Supporting Information:

Supporting Information: Low-temperature Ohmic contact to monolayer MoS 2 by van der Waals bonded Co/h-BN electrodes Xu Cui, En-Min Shih, Luis A. Jauregui, Sang Hoon Chae, Young Duck Kim, Baichang Li, Dongjea Seo, ǂ Kateryna Pistunova, Jun Yin, Ji-Hoon Park, Heon-Jin Choi, ǂ Young Hee Lee, Kenji Watanabe, Takashi Taniguchi, Philip Kim, Cory R. Dean,* James C. Hone* These authors contributed equally to this work. Email: James C. Hone: jh2228@columbia.edu (212) 854-6244 Cory R. Dean: cd2478@columbia.edu (212) 854-3189 S1

Contents S1 MoS 2 contact strategies summary S2 Contacts with low work-function metals S3 Material characterization S4 Samples S5 Device from CVD h-bn and CVD MoS 2 S6 XPS S7 Room temperature I sd -V sd output curve S8 Low temperature I sd -V sd output curve at small bias S9 Schottky barrier extraction S10 Disorder S11 Hall measurement S12 Hall mobility vs T S13 h-bn/co Contact deposited at different pressure S2

S1 MoS 2 contact techniques summary MoS 2 layer number Contact strategy Contact resistance Carrier density Temperature Reference 1-2 L Ti/Au+annealing ~ 30 kω.µm 1-2 10 13 /cm 2 1.7-300 K 1 4 L Sc 2-probe 100-500 kω / 100-300 K 2 1 L Al 1-10 MΩ.µm 4-6 10 12 /cm 2 300 K 3 1L CVD CVD graphene 2-probe 600-2000 kω 4-6 10 12 /cm 2 80-330K 4 1 L graphene ~ 10 kω.µm 1 10 13 /cm 2 0.3 K 3L graphene ~ 5 kω / 4 K 5 6 6.8 nm Nb doped MoS 2 p-contact 2-probe ~1.1kohm / 5-300 K 7 2-3 L Ionic-liquid gating ~ 50-100 kω.µm very high 230-300 K 8 1-3 L 1T phase engineering ~ 0.3 kω.µm >1 10 13 /cm 2 300 K 9 S3

Few-layer Selective etching + Ti/Au 0.5 kω.µm 8.8 10 12 /cm 2 2 K 10 9 L Selective etching + Ti/Au + annealing 12h 0.25 kω.µm / 2-300 K 11 1L MgO + Co 2-probe ~ 190 kω / 155-300 K 12 10 nm TiO 2 + Co 2-probe ~ 10 kω / 200-300 K 13 4-5 L BN + Ni 1.8 kω.µm / 77-300 K 14 1L BN + Co 3 kω.µm 5.3 10 12 /cm 2 1.7 K This work Table S1 MoS 2 contact techniques summary. S4

S2 Contacts with low work-function metals S2.1 low work function contact We have made devices contact with Sc (Φ = 3.5 ev). At room temperature, the devices showed promising contact behavior with low contact resistance and linear output I-V curve (Figure S1a, b). However, the contacts showed high resistance and non-linear output curve at low temperature (Figure S1c, d), which indicate the contacts are non-ohmic in nature. Sc contact: S5

Figure S1. Transfer curves and output curves of a Sc contact device. (a) Transfer curve at 300 K with V sd = 100 mv. (b) Linear output curve at 300 K at different back gate voltage from -20 V to 80 V. (c) Transfer curve at 50 K with V sd = 100 mv. (d) Non-linear output curve at 50 K at different back gate voltage from -20 V to 80 V. S6

S2.2 Other metal contacts with monolayer h-bn insertion layer Other metals (Sc, Al, Ti, Ag) with monolayer h-bn insertion layer do not provide Ohmic contact to monolayer MoS 2, as shown in Figure S2-5. All devices showed high resistance and non-linear output curves at either 300 K or low temperature. Sc with 1L BN insertion: Figure S2. Transfer curves and output curves of a Sc contact with monolayer h-bn insertion. (a) Transfer curves at 300 K and 20 K with V sd = 1 V. (b) non-linear output curve at 300 K and 20 K with 80 V back-gate voltage. S7

Al with 1L BN insertion: Figure S3. Transfer curves and output curves of an Al contact with monolayer h-bn insertion. (a) Transfer curve at 300 K with V sd = 100 mv. (b) Linear output curve at 300 K with different back gate voltage from -80 V to 80 V. (c) Transfer curve at 15 K with V sd = 100 mv. (d) Nonlinear output curve at 15 K with different back gate voltage from -80 V to 80 V. S8

Ti with 1L BN insertion: Figure S4. Transfer curves and output curves of Ti contacts with monolayer h-bn insertion. (a) Transfer curve at 300 K with V sd = 100 mv. (b) Linear output curve at 300 K with different back gate from 40 V to 80 V. (c) Transfer curve at different low temperature with V sd = 1 V. (d) Nonlinear output curve at 80 V back-gate at different temperatures. S9

Ag with 1L BN insertion: Figure S5. Transfer curves and output curves of a Ag contact with monolayer h-bn insertion. (a) Transfer curve at 300 K with V sd = 100 mv. (b) Non-linear output curve at 300 K with back gate voltage 80 V. S3 Material characterization S3.1 monolayer h-bn Figure S6a shows the optical micrograph of a exfoliated monolayer h-bn flake with contrast enhanced by LUT (Lookup Table) image processing. The Raman spectrum of the flake has the E 1g peak centered at 1375.2 cm -1, which is 4.7 cm -1 higher than bulk flakes, indicating it is S10

monolayer 15 (Figure S6b). We further characterize monolayer h-bn with AFM, which shows clean smooth surface (Figure S6c). The step heights (Figure S6d) relative to SiO 2 substrate are often found to be higher than the predicted monolayer h-bn thickness (0.33 nm). However, after we transfer monolayer h-bn onto a h-bn substrate, we always get the predicted thickness value (Figure S6b). S11

Figure S6. Monolayer h-bn identification and characterization. (a) Optical micrograph of the monolayer h-bn flake with contrast enhanced by LUT. Scale bar is 5 µm. (b) Raman spectra of the monolayer h-bn flake and another bulk BN flake with 532 nm laser and 1800 gr/mm grating. The E 2g peak is centered at 1375.2 cm -1 for monolayer and 1370.5 cm -1 for bulk. (c) AFM measurement of the monolayer h-bn flake and (d) the height (0.55 nm) of the flake relative to the SiO 2 substrate. S3.2 monolayer MoS 2 We identify monolayer MoS 2 with optical contrast and further confirm with PL (Figure S7a) and Raman (Figure S7b) spectra. The single sharp peak at around 1.8 ev of PL spectrum and E 1 2g and A 1g peak separation of ~18 cm -1 of Raman spectrum give reliable identification of monolayer MoS 2. S12

Figure S7. Monolayer MoS 2 characterization. (a) PL spectrum of the monolayer MoS 2 flake. (b) Raman spectrum of the monolayer MoS 2 flake. The E 1 2g and A 1g peak separation is 18.8 cm -1. S4 Sample fabrication Figure S8a shows the steps to invert a stack from PPC. One sample image after stacking, inverting and annealing is shown in Figure S8b. The monolayer h-bn is hard to see from the optical image but can be identified with AFM (Figure S8c). The monolayer h-bn laying on thick h-bn substrate smoothly and its thickness can be measured accurately to be 0.34 nm. S13

Figure S8. Inverting process and the image of stack after being inverted and annealed. (a) the process from left to right are: picking up the stack with the dry Van der Waals transfer method, peeling the PPC off from the PDMS, Putting the peeled stack on a clean SiO 2 /Si substrate, and annealing the stack to remove the PPC. (b) Optical micrograph and (c) AFM image of a inverted stack of monolayer h-bn, monolayer MoS 2, thick BN from top to bottom. Scale bar is 5 µm. S14

S5 Device from CVD MoS 2 and CVD h-bn Figure S9a shows a schematic of the device from CVD MoS 2 and CVD h-bn, and figure S9b shows an optical image. After Poly(methyl methacrylate) (PMMA A4, Chem) was spin-coated onto the as-grown CVD MoS 2, the PMMA and MoS 2 were detached from the SiO 2 /Si substrate by floating the PMMA/MoS 2 /SiO 2 /Si, with the PMMA side up, in a hot 2 M NaOH solution. 16 The bubbling-based transfer method (applying voltage: ~ 5V) was used to transfer monolayer h- BN film onto MoS 2 /SiO 2 /Si substrate. 17 Once the samples transferred onto target substrates, the PMMA was removed by flowing acetone (1 min) and IPA. The transport behavior for this structure is similar to exfoliated MoS 2 and BN and output curve is linear at small bias down to low temperature. This shows promise that this technique can be applied to large scale application. S15

Figure S9. CVD MoS 2 and CVD h-bn device and transport characterization. (a) Device schematic for CVD MoS 2 /CVD h-bn Co contact. (b) Optical image of the device. Scale bar 5 µm. (c) Transfer curve from 300 K to 20 K, V sd = 10 mv. (d) Linear output curve at 20 K, with gate voltage from 0 V to 80 V. S16

S6 XPS data Figure S10. Fermi edge. The work-function is determined by the energy difference between the cut-off and Fermi edge subtracted from the source energy (hv = 1486.6 ev), thus 1L h-bn/co work-function (Φ) = 3.3eV. S17

S7 Room temperature I sd -V sd output curve At room temperature, both cobalt contact device with and without monolayer h-bn show linear I-V curve. Figure S11. Room temperature output curve of (a) cobalt contact with monolayer h-bn insertion and (b) cobalt directly contact to monolayer MoS 2. S18

S8 Low temperature I sd -V sd output curve at small bias Figure S12. Output curve at small source-drain bias and conductance as a function of bias for exfoliated 1L h-bn (a, b) and CVD 1L h-bn (c, d). S19

S9 Schottky barrier extraction The Arrhenius plots mentioned in main text are shown in Figure S13a, d. At low doping (gating), the charge injection to the MoS 2 channel mainly through thermionic emission and can be modeled by equation: 18 J A T exp (1) Where J is current density, A * is the Richardson constant, k B is the Boltzmann constant and E A is the total activation energy that charge carriers must overcome to access the channel. The activation energy can be extracted from the slope of the Arrhenius plots, and the Schottky barrier height can be extracted at the flat-band condition as described in the main text. Above the flatband voltage, however, equation (1) no longer holds true, since there is current contributed from tunneling effect and the slope we got from Arrhenius plot will not reflect the true activation energy. To get the flat-band voltage, we notice that as long as V g < V FB, the activation energy depends linearly on Vg: where C ox is the gate oxide capacitance and C it is the interface trap capacitance. The linearity assumes C it to be a constant over the range of gate voltage below V FB. This assumption seems to (2) S20

be true for our devices as can be seen on Fig S13(b)(e). In fact, previous reports from STM measurement also showed linear response between E F and V g. 19,20 The factor also can be extract from the subthreshold swing from SS= γ -1 ln(10)kt/q, and the values extracted from two methods are consistent. It is worth noting that γ is smaller for devices without 1L BN insertion, which means it has larger trap density. This indicate the monolayer BN still screen the extrinsic disorder to some degree. In the data for monolayer BN insertion device (Fig S13a), we can measure Arrhenius behavior down to 100 K (8.6 mev). Below 100 K the data points deviate from linear relationship, which might due to disorder induced band edge smearing (as calculated below). The measured Schottky barrier value 16 mev is close to this disorder scale, so we might have reached the limit of small Schottky barrier height, at which the Schottky barrier can t be measured easily. S21

Figure S13. Arrhenius plots, activation energy and transfer curves of cobalt contacts with (a, b, c) and without (d, e, f) monolayer h-bn. S22

S10 Disorder We calculate the disorder range as below: For 2D system, the band-edge density of states (DOS) is given by, where g s, g v are the spin and valley degeneracy respectively, m* is the band-edge effective mass, ħ is the reduced Planck constant. The 2D carrier density in the conduction band (CB) is described as: where E c is the band-edge energy of CB. The occupation probability is the Fermi-Dirac distribution (3) with k B is Boltzmann constant, T the absolute temperature, and E f the Fermi level. From above equations, the electron density in the CB is (4) Under thermal equilibrium, the Fermi energy is thus (5) (the above derivation is from 21 ) (6) S23

From the letter Fig. 3a, c, the MoS 2 start to transit from metallic to insulator, or the mobility start to decrease at low temperature at charge density 3.5x10 12 cm -2. We can calculate the Fermi level respective to CB at this density and at 1.7 K using the formula above (with g s = 2, g v = 2, m* = 0.46 m 22,23 0 ). Hence, we got E f - E c = 9.1 mev, which is the disorder range in our system. S11 Hall measurement We performed Hall measurement at room temperature (300 K) to low temperature (1.7 K) as shown in Figure S14. The calculated carrier density shows linear behavior with back-gate and matches well with the capacitance of 285 nm SiO 2. We conclude there is no significant doping effect introduced during the fabrication process. S24

Figure S14. R xy and carrier density characterization. (a) R xy as a function of small magnetic field -1 T - 1T at room temperature 300 K. (b) Calculated carrier density as a function of back-gate. The linear fit extrapolates to the band edge around -2.3 V. (c) R xy as a function of small magnetic field -1 T - 1T at room temperature 1.7 K. (d) Calculated carrier density as a function of backgate. The linear fit extrapolates to the band edge around 3 V. S25

S12 Hall mobility vs Temperature Figure S15 shows the Hall mobility as a function of temperature for different carrier densities. At high carrier densities above 4 10 12 /cm 2, the mobility increases as we decrease the temperature. 5 With Ohmic h-bn/co contact, we can measure at carrier densities even below 4 10 12 /cm 2. At low carrier density, the mobility decreases below 100 K, indicating an insulating and disorderly behavior. 24 Figure S15. Hall mobility as a function of temperature (300 K to 1.7 K) at three different densities. S26

S13 h-bn/co Contact deposited at different pressure We also investigated effect of the depositing pressure on the contact resistance (Figure S16). The contact deposited in UHV (ultra-high vacuum, 10-10 torr) is about 3-5 times better than deposited at normal condition (10-8 torr) which is consistent to other literature using Au contact. 25 Figure S16. Contact resistance of h-bn/co deposited at different pressure 10-10 and 10-8 torr. S27

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