Intrinsic Electronic Transport Properties of High. Information

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1 Intrinsic Electronic Transport Properties of High Quality and MoS 2 : Supporting Information Britton W. H. Baugher, Hugh O. H. Churchill, Yafang Yang, and Pablo Jarillo-Herrero Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 2139, United States bwhb@mit.edu Fabrication The devices presented here were fabricated starting from mined, naturally-grown, ake MoS 2 acquired from SPI Supplies. MoS 2 was exfoliated from the bulk material down to atomic layers using a mircomechanical cleavage process standard for graphene. 1 The akes were deposited onto highly doped silicon substrates with a 285 nm, thermally-grown, siliconoxide dielectric layer. s and bilayers were identied by optical contrast 2 using a Zeiss Axio-Imager microscope. Optical identication was calibrated and checked with AFM measurements (Fig. S1). Step heights from the substrate to the ake were often found to be slightly larger than the predicted inter-layer spacing for MoS 2 (.62 nm). 3 As is common with graphene depositions on SiO 2, the discrepancy was reduced after thermal annealing in To whom correspondence should be addressed 1

2 Ar/H 2, though the step would still remain marginally higher than expected. Layer to layer measurements, however, match very well with predicted inter-layer spacing (Fig. S1). (a) AFM 2 nm Height (nm) Step Height.67 nm.85 nm Distance (µm) Figure S1: MoS 2 ake AFM and step heights. (a) Atomic force micrograph of an MoS 2 ake containing both monolayer and bilayer regions deposited on an SiO 2 substrate. The light blue (monolayer) and dark blue (bilayer) lines added show the position of the step heights in. Scale bar is 2 µm. Inset: Optical image of the ake in (a) showing the color contrast change with layer number. Scale bar is 2 µm. Step height for monolayer (light blue) and bilayer (dark blue) regions of an MoS 2 ake. Once identied, candidate akes were contacted using PMMA masks patterned with e-beam lithography and developed in cold ( 5 C) MIBK:IPA, 1:1. Contacts were then deposited using either e-beam or thermal evaporators, with gold contacts 5-1 nm thick, and titanium sticking layers nm thick (Table S1). After annealing, device B2 was annealed in an Ar/H 2 environment at 35 C for 3 hours, though this procedure did not seem to have a substantial eect on quality. Device B2 was also etched into a Hall bar pattern using oxygen plasma. All other devices reported on in the main text were unetched. All of the devices were annealed in situ at high temperatures ( 12 C) in vacuum ( 1 6 mbar) for 5-2 hours. This procedure caused a substantial drop in two terminal resistivity (Fig. S2) and the elimination of Schottky behavior in the contacts down to 4 K. 2

3 (a) 1 7 Annealing T=12 o C 5 V 1 12 R (Ω) 1 6 R (Ω) After Before Time (hours) 1 3 T=2 o C V (V) Figure S2: Eect of annealing on two-terminal resistance of MoS 2 devices. (a) Two-terminal resistance change over time for monolayer (yellow) and bilayer (blue) devices being annealed at 12 C in vacuum. Back-gate sweeps of a monolayer device before and after vacuum annealing. Data from devices M1 and B1. Table S1: Device Fabrication Parameters Device Length Width Sticking Layer (Ti) Contact Metal (Au) Vacuum Annealing M1 4. µm 2.6 µm.3 nm 1 nm 12 C, 2 hours M2 3.5 µm 4.2 µm.3 nm 6 nm 12 C, 1 hours M3 3.5 µm 3.2 µm.3 nm 6 nm 12 C, 1 hours B1 4.6 µm 5.1 µm.3 nm 1 nm 12 C, 1 hours B2 5. µm.6 µm 3.5 nm 5 nm 1 C, 5 hours Metal Insulator Transition The Ioe-Regel condition for two-dimensional semiconductors states that k F λ 1 at a metal-insulator transition, 4 for the Fermi wave vector, k F = 2πn and the mean free path, λ = k F σ/ne 2. This leads to the expectation that the critical resistivity, ρ c, will be of order h/e 2. Our results match this condition, though the mean, h/2e 2, is slightly below the predicted value. 3

4 Table S2: Metal Insulator Transition Device Critical Resistivity, ρ c (h/e 2 ) M1.9 M2.8 M3.7 B1.4 B2.3 Table S2: Resistivity of monolayer and bilayer MoS 2 at the metal insulator transition. Four-terminal critical resistivity, ρ c, of monolayer and bilayer devices. The values mark the resistivity at which the lowest temperature traces of ρ vs. V cross. Hall Measurements Density, n, and Hall mobility, µ H, were calculated from Hall measurements performed in a magnetic eld. The current was sourced longitudinally along the device from one of the outer contacts. The transverse voltage, V xy, was then measured across the sample. The Hall resistance was calculated as R xy = I ds /V xy. Fitting a linear trend to R xy as it varies with magnetic eld yields the Hall coecient, R H = dr xy /db. (Fig. S3). There was a nonzero transverse resistance at zero eld due to imperfections in contact alignment and sample inhomogeneities. This oset was subtracted from the data as it was small and irrelevant to our t of the slope. 4

5 (a) R xy (Ω) V 75 V T=1K 1 1 B (T) n (cm 2 ) Density 5 V 25 V V 5 V 25 V V T (K) Figure S3: Hall measurements of MoS 2. (a) Hall resistance of a monolayer MoS 2 device. Hall resistance, R xy, of a monolayer device as a function of magnetic eld, B, measured at 1 K. Traces shown are at back-gate voltages of 25 (blue) and 75 (yellow). The dotted lines show linear ts to the traces. Density as a function of temperature for monolayer and bilayer MoS 2 at, 25, and 5 V, colored from dark to light. Data from devices M1 and B2. Mobility If µ H varies linearly with density, the eld-eect mobility will vary with density with twice the slope. To show this, we write µ H = A n + C, where A and C are constants. Then µ F E = µ H + n dµ H /dn = A n + C + n (A) = 2A n + C. Then dµ F E /dn = 2A = 2 dµ H /dn, as stated in the main text. 5

6 (a) ρ (Ω/ ) 1 5 R c (Ω) 1 6 T=5K V (V) 1 4 5K 5K 1K 2K 1 3 3K V (V) ρ (Ω/ ) V -25 V V 25 V 5 V T (K) 1 3 Figure S 4: Contact resistance and four-terminal resistivity of monolayer device M 1. (a) Four-terminal resistivity of device M1 as a function of V. Curves colored from red to black show measurements at 3, 2, 1, 5, and 5 K, respectively. Inset: Contact resistance, R c, to device M1 as a function of V at 5 Kelvin. Resistivity of device M1 as a function of temperature. The curves, from black to orange, correspond to V = -5, -25,, 25, and 5 V. (a) 15 Room Temp. Mobility T=2 o C 4 Leakage µ (cm 2 /Vs) 1 5 µ FE µ H µ FE µ H V (V) I leak (na) M1 B1 M2 B2-5 5 V (V) Figure S 5: Room temperature mobilities and leakage current. (a) Hall and eld eect mobilities for monolayer and bilayer devices at room temperature. Data from devices M 1 and B2. Representative leakage currents measured for each device presented in the text. 6

7 References (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 24, 36, (2) Benameur, M. M.; Radisavljevic, B.; Heron, J. S.; Sahoo, S.; Berger, H.; Kis, A. Nanotechnology 211, 22, (3) Wang, T.; Liu, W.; Tian, J.; Shao, X.; Sun, D. Polymer Composites 24, 25, (4) Gurvitch, M. Phys. Rev. B 1981, 24,