Supporting Information

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1 Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, Supporting Information for Adv. Funct. Mater., DOI: /adfm Tuning the Excitonic States in MoS 2 /Graphene van der Waals Heterostructures via Electrochemical Gating Yang Li, Cheng-Yan Xu,* Jing-Kai Qin, Wei Feng, Jia-Ying Wang, Siqi Zhang, Lai-Peng Ma, Jian Cao, Ping An Hu, Wencai Ren, and Liang Zhen*

2 Supporting Information Title Tuning the excitonic states in MoS 2 /graphene van der Waals heterostructures via electrochemical gating Yang Li, Cheng-Yan Xu*, Jing-Kai Qin, Wei Feng, Jia-Ying Wang, Siqi Zhang, Lai-Peng Ma, Jian Cao, PingAn Hu, Wencai Ren, and Liang Zhen* This file includes: 1. Raman spectra of graphene on MoS 2 at different gate bias 2. First-principle calculation of band structures of MoS 2 /graphene heterostuctures at external electric field 3. The reproducibility of PL spectra of monolayer or bilayer MoS 2 /graphene after stability 4. AFM topographies of SAMs on MoS 2, and surface potential of monolayer MoS 2 on Pt substrate 5. PL intensities, peak positions of excitons and trions, Raman spectra and carrier densities of MoS 2 in MoS 2 /C8-OTS/graphene and MoS 2 /C18-OTS/graphene heterostructures as a function of gate bias 6. PL spectra of bilayer MoS 2 /graphene heterostructures at different gate bias 1

3 1. Raman spectra of graphene on MoS 2 at different gate bias Figure S1. Raman (a) and PL (b) spectra of separate monolayer MoS 2 on Si/SiO 2 substrate. The peak distance between the Raman modes E 1 2g and A 1g is around 16.3 cm -1. The PL spectrum of pristine MoS 2 can be fitted by three Lorentzen peaks, corresponding to A exciton (1.83 ev), B exciton (1.95 ev) and A - trion (1.79 ev), as shown in Figure S1b. The trion/exciton intensity ratio is about 1.2. Figure S2. (a) Raman spectra of graphene on monolayer MoS 2 at gate bias from 3.6 to 2 V. (b) The dependence of graphene Raman G-band frequency on gate bias from 3.6 to 2 V. 2. First-pinciple calculation of band structures of MoS 2 /graphene heterostuctures at external electric field In order to clarify the effect of Schottky barrier at the hetero-interface between graphene and MoS 2 on PL tuning in monolayer MoS 2 /graphene heterostructures, we calculated the band structure of MoS 2 /graphene heterostructures at perpendicular external electric field. In our calculation process, the electronic structures of MoS 2 /graphene heterostructures under electric field are calculated by using density functional theory(dft) as implemented in the VASP code. The generalized gradient approximation (GGA) was adopted for the exchange and correlation potential, and the projector augmented wave potential (PAW) was applied to deal with the ion-electron interactions. [1] The kinetic energy cutoff of electron wave functions is 420 ev. The number of k-points was set to be according to the Monkhorst- 2

4 Pack scheme. All the structures were relaxed until all the atomic forces on each ion were smaller than 0.02 ev/å. The simulated structure containing up to 98 atoms was modeled, which consists of a monolayer graphene supercell of 5 5 and a MoS 2 supercell of 4 4 with 1.9% lattice mismatch. To simulate the electronic structure of MoS 2, the lattice of MoS 2 supercell is fixed to be Å, which has been optimized in isolated monolayer MoS 2. The energetic and electronic structure in MoS 2 /graphene with different kinds of configurations has been investigated in previous reports. [2] In our work, only one representative arrangement is adopted to simplify the calculated procedures. As shown in Figure S3-1, C atom of graphene is fixed on top of S atom and the distance at the hetero-interface is set to be 3.32 Å. An external electrical field perpendicular to the system is applied to the system to change the Fermi level of graphene and electronic structure of MoS 2, in order to modulate the Schottky barrier at the interface and electronic coupling between MoS 2 and graphene. It needs to be noted that in order to compensate the lattice mismatch, graphene is stretched, resulting in a slight bandgap opening of 5 mev, as depicted in Figure S3-2. We believe that such a small value would not take influence on the band structure in MoS 2 /graphene hybrid system when subjected to external field. In order to avoid the interactions between different MoS 2 /graphene hybrid layers along the Z direction, the vacuum layer upon graphene and below MoS 2 is set to be 10 and 13 Å, respectively. Figure S3-1. Side and top views of the arrangements of graphene on MoS 2. The brown, purple and yellow balls represent C, Mo and S atoms, respectively. 3

5 Figure S3-2. (a) The projected band structure of MoS 2 /graphene heterostructures without electric field. (b) The enlarged area of graphene close to the Dirac point. A small bandgap opening in graphene is observed due to the stretch of graphene. The. projected band structure of MoS 2 /graphene heterostructures without gate bias is depicted in Figure S3-2. The band structure of graphene and MoS 2 are well preserved separately, meaning that there is weak electronic coupling between layers, which is consistent with previous reports. [2-4] The slight band gap opening of graphene is resulted from the stretch of the graphene lattice to compensate the lattice mismatch at the pristine setting. The ideal metal/semiconductor contact model was used to estimate the Schottky barrier height, that is φ B = W (gra) χ (MoS2), where W F(gra) and χ (MoS2) are work function of graphene and electron affinity of MoS 2, respectively. [5-7] According to Figure S3-2a, φ B is estimated to be ev. Figure S3-3. The energetic band structures of MoS 2 /grpahene heterostructures under the perpendicular electric field of (a) 0.1V/Å (~ 0.5 V) and (b) 0.3 V/Å (~ 1.5 V). It is noted that considering the effective thickness of ion-gels (~0.5 nm), [8] the electric field is approximate to be changed from -0.7 to 0.4 V/Å, when the applied gate bias in our experiments ranges from 3.6 to 2 V. Figure S3-3 presents the band structures of MoS 2 /graphene hybrid system under external electric field of 0.1 and 0.3 V/Å. At finite doping (p-doping), the Fermi level of graphene (E F(gra) ) is downshifted away from the Dirac point, which changes the magnitude of the Schottky barrier height (φ B ). In this case, we use 4

6 the ideal metal/semiconductor contact model (Schottky limit) to estimate φ B, [5-7] that is the barrier is given by the difference between the Fermi level of the hybrid system and the conduction band minimum of MoS 2 at the k-point in the Brillouin zone. It is observed that by increasing the negative electric field from zero to 0.3 V/Å, the Schottky barrier height φ B increases from to ev. Figure S3-4. The energetic band structures of MoS 2 /grpahene heterostructures under the perpendicular electric field of (a) 0.1 V/Å (~ 0.5 V) and (b) 0.3 V/Å (~ 1.5 V). Similar to the case applied with negative electric field, Figure S3-4 presents the energetic band structures of MoS 2 /graphene hybrid system applied with positive electric field. Graphene is n-doped, the Fermi level E F(gra) is upshifted away from the Dirac point, leading to the decrease of Schottky barrier height (φ B ). It is observed that the band structures of MoS 2 still preserves, and the Schottky barrier decreases to ev after the electric field of 0.3 V/Å is applied. Table S1. The number of orbital electrons without and with electric field of ± 0.3 V/Å Number of orbital electrons Monolayer MoS 2 Graphene Without electric field Electric field of 0.3 V/Å Electric field of 0.3 V/Å Next, we evaluate the charge transfer between MoS 2 and graphene after applying negative or positive gate bias. The orbital electrons are counted to clarify the charge transfer efficiency. According to Table S1, MoS 2 /graphene hybrid system contains up to 584 orbital electrons, including 384 for MoS 2 and 200 for graphene without electric field. The total number of electrons in MoS 2 decreases by with applying electric field of 0.3 V/Å, while it increases by with electric field of 0.3 V/Å. The electronic coupling between MoS 2 and graphene may enhance the complex many-body interactions in MoS 2 /graphene heterostructures, which may affect the behavior of quasiparticles (such as 5

7 trion binding energy). This would motivate further experimental and theoretical studies for more thoroughly understanding the coupling between MoS 2 and graphene, and its effect on many-body interaction in MoS 2 /graphene or other vdws heterostructures. 3. The reproducibility of PL spectra of monolayer or bilayer MoS 2 /graphene after stability Figure S4. The reproducibility of PL spectra of monolayer MoS 2 /graphene and bilayer MoS 2 /graphene at gate bias of 1 V after 15 to 20 minutes for equilibrium. Since electric double layer in the ion-gels needs to take equilibrium after the gate bias is applied, we conducted the PL measurements after 15 to 20 minutes. From Figure S4, it is observed that the ratio of maximum and minimum PL intensity of monolayer MoS 2 /graphene and bilayer MoS 2 /graphene at the gate bias of 1 V approaches to 85% and 83% after several number of measurements, respectively, indicating the high reproducibility of the PL spectra in our work. 6

8 4. AFM topographies of SAMs on MoS 2, and surface potential of monolayer MoS 2 on Pt substrate Figure S5. AFM topographies of (a and b) pristine MoS 2, (c and d) C8-OTS modified and (e and f) C18-OTS modified MoS 2. As shown in Figure S5, the roughnesses of pristine MoS 2, C8-OTS modified and C18-OTS modified MoS 2 are 0.273, and nm, respectively. Figure S6. (a) AFM topography and (b) enlarged topography of monolayer MoS 2 on Pt substrate. (c) The corresponding surface potential mapping of monolayer MoS 2 on Pt 7

9 substrate. (d) The surface potential difference obtained from (c). (e) I-V curve of Pt/tip. (f) SEM image of Co/Cr tip. The diameter is about 80 nm. To demonstrate the formation of tunneling barrier between MoS 2 and SAMs, Pt/MoS 2 and Pt/MoS 2 /SAMs were prepared, and measured by conductive AFM. Figure S6a and b shows AFM topography of monolayer MoS 2 on Pt substrate. Figure S6c shows the corresponding surface potential mapping, and the potential difference between MoS 2 and Pt is about 21±10 mv, indicating that the work function difference between MoS 2 and Pt is only 21±10 mev in our experiment, indicating that the barrier between Pt and monolayer MoS 2 in our experiments is much small. Therefore, according to F-N tunneling models used in Main Text, the calculated tunneling barrier φ B is represented to that in MoS 2 /SAMs. 5. PL intensities, peak positions of excitons and trions, Raman spectra and carrier densities of MoS 2 in MoS 2 /C8-OTS/graphene and MoS 2 /C18-OTS/graphene heterostructures as a function of gate bias Figure S7. The peak positions, intensities of trion and exciton, and the intensity ratio of trion and exciton in MoS 2 /C8-OTS/graphene at V g from 2.7 to 2 V. 8

10 Figure S8. (a) Raman spectra of MoS 2 in MoS 2 /C8-OTS/graphene at gate bias from 2.7 to 2V. (b) The enlarged Raman spectra of graphene G-band in MoS 2 /C8-OTS/graphene at gate bias from 2.7 to 2 V. It is difficult to observe the shift of A 1g mode in MoS 2 at the measured gate bias due to the relatively lower carrier density variation. The shift of graphene Raman G- band dependent on gate bias indicates that the ion-gel dielectric takes effects upon applying gate bias. Figure S9. The peak positions, intensities of trion and exciton, and the intensity ratio of trion and exciton in MoS 2 /C18-OTS/graphene at V g from 2.7 to 2 V. 9

11 Figure S10. Raman spectra of MoS 2 in MoS 2 /C18-OTS/graphene at gate bias from 2.7 to 2V. It is difficult to observe the shift of A 1g mode in MoS 2 at the measured gate bias due to the relatively lower carrier density variation. Carrier density (n MoS2 ), cm MoS 2 /graphene MoS 2 /C8-OTS/graphene 1.0 MoS 2 /C18-OTS/graphene Gate bias (V) Figure S11. The calculated carrier densities of MoS 2 in MoS 2 /C8-OTS/graphene and MoS 2 /C18-OTS/graphene at V g < 0. According to the electric displacement distribution models analyzed in the Main Text, we calculated the carrier densities of MoS 2 by Gauss law, and the results are shown in Figure S11. The carrier density (n) was estimated to be n 0 and n 0 in MoS 2 /C8-OTS/graphene and MoS 2 /C18-OTS/graphene, respectively. n 0 is the carrier density of MoS 2 in MoS 2 /graphene heterostructures. 10

12 6. PL spectra of bilayer MoS 2 /graphene heterostructures at different gate bias. Figure S12. (a) Optical image of a bilayer MoS 2 /graphene heterostructure. (b) The corresponding AFM topography of bilayer MoS 2 on Si/SiO 2 subsrate. (c) The height profile of bilayer MoS 2 in Figure b. The height is 1.8 nm, indicating the bilayer characteristic of MoS 2. (d) Raman spectra of bilayer MoS 2 /graphene heterostructure covered with ion-gels. The inset shows the enlarged Raman spectra of bilayer MoS 2. The peak distance between two Raman modes E 1 2g and A 1g is 21.8 cm -1, also demonstrates that MoS 2 is bilayer. Figure S13. PL spectra of bilayer MoS 2 /graphene heterostructure at the gate bias from 4 to 2.4 V. 11

13 As show in Figure S11, the PL intensity of bilayer MoS 2 /graphene heterostructure decreases significantly at the positive gate bias, and it almost quenches at the gate bias of 2.4 V. However, unlike monolayer MoS 2 /graphene, the PL intensity of bilayer graphene increase slightly at the positive gate bias when the gate bias increases up to 4 V. This may be due to the lower intrinsic photoluminescence efficiency of bilayer MoS 2 itself. References [S1] J. Padilha, A. Fazzio, A. J. da Silva, Phys. Rev. Lett. 2015, 114, [S2] Y. Ma, Y.Dai, M. Guo, C. Niu, B. Huang, Nanoscale 2011, 3, [S3] S. Han, H. Kwon, S. K. Kim, S. Ryu, W. S. Yun, D. Kim, J. Hwang, J.-S. Kang, J. Baik, H. Shin, Phys. Rev. B 2011, 84, [S4] H.-P. Komsa, A. V. Krasheninnikov, Phys. Rev. B 2013, 88, [S5] L. Yu, Y.-H. Lee, X. Ling, E. J. Santos, Y. C. Shin, Y. Lin, M. Dubey, E. Kaxiras, J. Kong, H. Wang, T. Palacios, Nano Lett. 2014, 14, [S6] Y. Du, L. Yang, J. Zhang, H. Liu, K. Majumdar, P. D. Kirsch, P. D. Ye, IEEE Electron Devices Letters 2014, 35, 599. [S7] E. Rhoderick, IEE Proceedings I (Solid-State and Electron Devices) 1982, 129, 1. [S8] Y. Zhou, J. Park, J. Shi, M. Chhowalla, H. Park, D. A. Weitz, S. Ramanathan, Nano Lett. 2015, 15,