Supporting information for. Direct imaging of kinetic pathways of atomic diffusion in. monolayer molybdenum disulfide

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1 Supporting information for Direct imaging of kinetic pathways of atomic diffusion in monolayer molybdenum disulfide Jinhua Hong,, Yuhao Pan,, Zhixin Hu, Danhui Lv, Chuanhong Jin, *, Wei Ji, *, Jun Yuan,,*, Ze Zhang State Key Laboratory of Silicon Materials and School of Materials Science and Engineering, Zhejiang University, Hangzhou, Zhejiang , China Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-Nano Devices, Department of Physics, Renmin University of China, Beijing , China Department of Physics, University of York, Heslington, York, YO10 5DD, United Kingdom These authors contributed equally to this work. *Correspondence and request for materials should be addressed to C.J. W.J. or J.Y. Figure S1. Example of the hopping of Mo vacancy. (a-e) Time series of Mo vacancy migrating within monolayer MoS 2. Scale bar: 0.5 nm. Time interval: 3s.

2 Figure S2. Example of the hopping of Mo vacancy. (a-f) Time series of Mo vacancy migrating within monolayer MoS 2. Scale bar: 0.5 nm. Time interval: 3s. Figure S3. Trajectories of Mo vacancy hopping. Different independent examples assemble in one picture to show their random motion. Circles are the starting sites of the vacancies and arrows point to final sites.

3 Figure S4. Random hopping of defects. (a) Cumulative travel distance of Mo adatom and Mo vacancy with the observation time. Both cases are collections of their independent examples. They show almost linear relation, indicating an average migration speed. (b) Displacements of hopping defects from their initial sites. They behave as an almost-linear function of square root of the number of steps, in accordance with the characteristic of Brownian particle motion. Figure S5. Quantitative comparison of the experimental and simulated adatom images. (a) Atomically resolved ADF-STEM image of typical Mo adatom T Mo. Scale bar: 0.5 nm. (b) Corresponding simulation image. The green and red dashed arrowed lines indicate both the path and direction for line profile analysis of the intensity. (c) Comparison of intensity line profiles extracted from experimental and simulated images respectively, with the highest peaks in both curves corresponding to the Mo adatom on top of the Mo site in MoS 2 monolayer.

4 Figure S6. Intensity fluctuation of Mo sites and S 2 sites in ADF images of monolayer MoS 2. (a) A typical example of experimental ADF-STEM image. (b) Histogram of the intensity distribution of each atomic site, all normalized with respect to the average intensity of the Mo sites. The peak centered at a relative intensity of 0.5 can be assigned to the intensity distribution of S 2 sites. The small peak with an average intensity of 2.2 is due to Mo adatoms on top of Mo sites (T Mo ). As a result, the adatom can be easily distinguished from the monolayer MoS 2 substrate due to their brighter contrast. The image intensity of this defect site is a little more than twice of the image intensity of single atom, which may reflect the strong atomic lens focusing effect and is not an artifact.

5 Figure S7. Example of the random hopping of Mo adatoms. (a-l) Time series of a Mo adatom migrating on the surface of monolayer MoS 2. Scale bar: 0.5 nm. Time interval: 3s. Figure S8. DFT relaxed Mo atom adsorption structure. Top view and side view of Mo adatom

6 on top of Mo site (T Mo ), at hollow site (or hexagon center, H), and on top of S site (T S ) show their different three dimensional geometry. In DFT calculation, adatoms at hollow sites can have two distinct configurations: hollow-high and hollow-low (H), as can be clearly seen in the side views. A Mo adatom has an adsorption energy ev at hollow-low (H) site and -0.83eV at hollow-high site, indicating that the hollow-low site (H) is more stable. Figure S9. Comparison of experimental/simulated ADF-STEM images. (a,b) Simulated and experimental ADF image of T S, respectively. (c,d) Simulated and experimental ADF image of T Mo, respectively. (e) Comparison of the intensity line profiles along the long sides of the dashed rectangles in the ADF images in a-d.

7 Figure S10. Migration pathway for T Mo T S transition. (a) DFT calculated energy barrier. (b) Detailed atomic process in the migration from ground state T Mo to metastable state T S. Figure S11. Comparison of bond reorganization of transition states. (a) DFT relaxed perfect monolayer with Mo-S bond length 2.41Å. (b) Transition state (TS) of a Mo vacancy during its migration. The central Mo-S bonds are reconstructed and far from the bond length of perfect MoS 2. (c) Transition state (TS) of a Mo adatom. Note all the values are real bond length in 3D space, not projected length on the atomic plane. For TS of vacancy in b, the central mobile Mo atom is

8 coordinated with four S atoms; and for TS of adatom in c, the mobile adatom Mo is only coordinated with two S atoms. Much less freedom in the out-of-plane direction, more coordinations and other constraints within Mo atomic plane for the structure relaxation make the TS state of Mo vacancy suffer from more local strain and give rise to its much higher energy barrier than TS of adatom. Figure S12. Trajectories of Mo adatom hopping. Different independent examples of adatom migrations assemble in one picture to better illustrate their random motion. Dots indicate their initial site and arrows are their migration directions.

9 Figure S13. Schematic diagram for probability estimation. This is to demonstrate nearest-neighboring hopping and second-nearest-neighboring hopping from the initial site located at origin. Here the central red dot is the initial site 0 (T Mo ) for adatom hopping and green dots are the first three equivalent H sites (1) that can be assessed. The three black arrows indicate the elementary T Mo H or 0 1 hopping. The purple circle crosses the six equivalent final sites 2 that can be reached via two successive elementary hopping (namely nearest-neighboring hopping) from initial site 0. For each site 2, another two successive elementary hopping yields the red circle crossing site 3 (second-nearest-neighboring hopping, two equivalent such sites), site 4 (only one such site), site 2 (two equivalent such sites) and site 0 (origin, only one site). Here the terminology equivalent is always relative to the initial site (site 0, origin).

10 Figure S14. Spin-polarized density of states (DOS). (a,b) DOS of Mo adatom T Mo with structure relaxation shown in b. (c,d) DOS of Mo adatom H with relaxed structure in d. Note the symbol of T Mo and H denote the central adatom, S n is the S atom neighboring the central Mo adatom. Pure Mo and pure S are corresponding to normal sublattices far from the adatom. From Fig a,c one can conclude the spin-up state is highly concentrated within the central Mo adatom, and neighboring S atom has a minor contribution. The total magnetic moments of T Mo and H are 4μ B and 2μ B, respectively.

11 Figure S15. Knock-on displacement mechanism. (a) Maximum transfer energy to Mo and S atom at different acceleration voltages. (b) The knock-on cross section 1 as a function of the displacement energy E d of the target atom Mo. The two pairs of arrows indicate the knock-on cross section of Mo vacancy is almost one order of magnitude smaller than that of Mo adatom. Figure S16. Comparison of knock-on effect and thermal activation. (a) Displacement rate caused by knock-on beam effect and thermal activation. Thermal displacement rate is estimated by 2 R ν exp ( E / kt) where ν is adatom vibration frequency~10 11 Hz. The knock-on th d displacement rate is derived from the integration of Rutherford cross section whose angular range is determined by transfer energy being larger than the displacement energy E d. (b) The contribution to the atomic displacement from thermal activation. Threshold displacement energy E d ~0.7eV signify the critical point determining the relative importance of the knock-on effect and thermal activation.

12 Figure S17. Filtering process of ADF-STEM images. (a,c) Original experimental ADF images. Scale bar: 2nm. (b,d) Corresponding filtered images to enhance the signal-to-noise ratio. The well-known wiener filtering is used for the image processing.

13 Figure S18. Areal density of S vacancy. (a-f) Example of time lapsed observation of S vacancy at a probe current of 60 pa. (g,h) The change of S vacancy density with exposure time, where M-52 and M-63 are two different slices (containing 52 frames and 63 frames respectively) we have recorded. The initial S vacancy density is as low as 0.04 nm -2. This indicates that only one or two S vacancy reside in a supercell. Significant beam-induced increase in the S vacancy density is observed after about 100s exposure. Figure S19. Areal density and neighboring distance of S vacancy. (a) The change of S vacancy density with time. (b) The distance of the observed adatom to the nearest neighboring S vacancy. On average, this distance is larger than 2nm.

14 Note 1. Relative probability estimation. As shown in Supplementary Fig. S13, the Mo site (site 0, red circle) is the origin for adatom hopping. One basic hopping is from T Mo to three (C 3 1 =3) equivalent neighboring hollow sites H (site 1, green circle). If the second basic hopping occurs, adatoms at site 1 (3 equivalent green circle) will continue to hop: one way is to jump back onto site 0 (only 1 choice), another way is to jump onto site 2 (2 choices for one green circle). Hence, we can derive: If atomic hopping consists of only one basic hopping, adatom at the origin (site 0) have C 3 1 =3 paths to reach site 1; we set this hopping probability as p. If atomic hopping consists of two successive basic hopping, adatom at the origin (site 0) have 3 1=3 ways to return to site 0, and 3 2=6 ways to nearest neighbor sites (6 equivalent site 2). This is easy to understand with the aid of purple circle centered on site 0 in Supplementary Fig. S13. As there are altogether 6 equivalent site 2 located on the circle, the probability of nearest sublattice hopping (site 0 2) relative to that of basic hopping is probability of returning to site 0 is 1 p. 3 6 p p, and the If atomic hopping consists of four successive elementary hopping steps, we can consider it as another two-consecutive hopping following the previous case of double hopping. For the 3 ways back to site 0, these adatoms have 3 3=9 ways to back to site 0 and 3 6=18 ways to site 2; for the 6 equivalent site 2 on the purple circle, these adatoms have 6 3=18 ways to back to site 2, and 6 6=36 ways to reach Mo sites on red circle. Among the 36 sites on all equivalent red circles, 6 2=12 sites (site 2) are on both red and purple circles, 6 1=6 back to site 0, 6 2=12 to site 3, and 6 1=6 to the farthest site 4. Hence after four successive hopping, adatoms at site 0 have =48 ways to site 2, 12 ways to site 3. Then the relative ratio of the hopping probability of site 0 3 to that of site 0 2 is 12/48=1/4. The relative ratio of the hopping probability of site 0 3 hopping to that of elementary hopping is site 0 4 hopping to that of basic hopping is p p p p. The relative ratio of probability of Following our statistical analysis of the hopping probabilities, the hopping step statistics shown in Fig. 5d can be understood as follows: the first peak is due to site 0 1 hopping (the elementary hopping step), the second peak is due to site 0 2 hopping (Fig.5d inset), and the third for site 0 3 hopping with their probabilities in the ratio of 1: 2 3 : 1. With the ratio of the areas of 6 the calculated Gaussian peaks set to 1: 2 3 : 1, the calculated probability distribution as shown in 6 Fig.5d is well consistent with our experimental statistics. Low-probability 0 4 site hopping, involvement of less energetically favorable pathway T Mo T S, and limited counts of long-range

15 hopping contribute to the discrepancy between calculated and experimental distributions of the peak 3 in Fig. 5d of our interest. Note 2. Beam effect. In principle, both elastic and inelastic electron-atom scattering may induce atom s movement. To quantitatively address this beam effect on defect migration, elastic knock-on model has been widely employed. It is also worth mentioning that the actual temperature rise due to beam irradiation is at most several and can also be neglected 2. The elastic knock-on displacement rate can be derived from Rutherford cross section 1 : R J / e e E t Ed d / d 2 sin d where J is the current density, e the electron charge, and the integration is limited by the transfer energy E t larger than the characteristic displacement energy E d. We further calculate the transfer energy (Supplementary Figure. S15) and atom displacement rate as a function of displacement energy E d (Supplementary Figure. S16). On the other hand, the thermal displacement rate can be given approximately by R exp( E / kt) where is adatom vibration th frequency~ Hz 2. The comparison of beam-induced and thermally-activated displacement rates in Supplementary Figure. S16 shows that for the elementary low-energy hopping T Mo H (0.62eV), the natural thermal activated effect dominates, while for the higher-energy migration T Mo T S (1.1eV) and vacancy migration V Mo V Mo, thermal activation can be neglected and the beam induced effect dominates the atomic motion. It is worth mentioning that in the STEM mode, the beam is not always chasing the adatom, hence the knock-on effect on adatom is a pulse-like interaction. The percentage of beam-adatom dwelling time to the time for one frame is ~10-4, accounting for the low displacement rate in ADF-STEM imaging. This is to say, after the beam scans over the adatom to gives an initial kick, in the most remaining time the adatom relaxes naturally as if the beam far away is absent. This makes a difference from the continuous electron bombardment in the TEM imaging mode. The creation of S vacancies is also considered: the areal density of S vacancy is quite low ~0.04 nm -2 (Supplementary Fig. S18) and the shortest distance between the considered adatom and S vacancies is>2 nm (Supplementary Fig. S19). Hence we don t consider the effect of S vacancy on Mo adatom diffusion. d

16 One may expect to derive energy barriers through variable-temperature experiments like the case in graphene. Unfortunately, we find that at elevated temperature 500 the S sublimation is much more severe to create S monovacancy or multivacancy more easily under the beam radiation. While at room temperature, S vacancy increases only after a period of beam radiation. To exclude the complex effect of S monovacancy or divacancy to the largest extent, our time-sequential observation of Mo adatom and vacancy are all conducted at room temperature and very low probe current. Supplementary references 1. Reimer, L.; Kohl, H. Transmission Electron Microscopy-Physics of Image Formation, Springer, Egerton, R. F.; Malac, P. Li, M. Micron 2004, 35, 399