Strain-Tuning Atomic Substitution in Two-Dimensional Atomic Crystals

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Strain-Tuning Atomic Substitution in Two-Dimensional Atomic Crystals Honglai Li, Hongjun Liu, Linwei Zhou, Xueping Wu, Yuhao Pan, Wei Ji, Biyuan Zheng, Qinglin Zhang, Xiujuan Zhuang, Xiaoli Zhu, Xiao Wang, Xiangfeng Duan, and Anlian Pan ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b01646 • Publication Date (Web): 24 Apr 2018 Downloaded from http://pubs.acs.org on April 24, 2018

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Strain-Tuning Atomic Substitution in Two-Dimensional Atomic Crystals Honglai Li,†,‡,⊥ Hongjun Liu, ‡,⊥ Linwei Zhou,§,⊥Xueping Wu,‡ Yuhao Pan,§ Wei Ji,*,§ Biyuan Zheng,‡ Qinglin Zhang,‡ Xiujuan Zhuang,‡ Xiaoli Zhu,‡ Xiao Wang,‡ Xiangfeng Duan,*,∥ and Anlian Pan*,†,‡ †

Key Laboratory for Micro-Nano Physics and Technology of Hunan Province, State Key Laboratory

of Chemo/Biosensing and Chemometrics, and College of Materials Science and Engineering, Hunan University, Changsha, Hunan 410082, P. R. China ‡

School of Physics and Electronics, Hunan University, Changsha 410082, P. R. China

§

Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials

and Micro-Nano Devices, Renmin University of China, Beijing 100872, China ∥

Department of Chemistry and Biochemistry, University of California, Los Angeles, CA

90095, USA

ABSTRACT: Atomic substitution offers an important route to achieve composition engineered two-dimensional nanostructures and their heterostructures. Despite the recent research progress, the fundamental understanding of the reaction mechanism has still remained unclear. Here we reveal the atomic substitution mechanism of two dimensional atomic layered materials. We found that the atomic substitution process is depending on the varying lattice constant (strain) in monolayer crystals, dominated by two strain-tuning (self-promoted and self-limited) mechanisms using density functional theory calculations.

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These mechanisms were experimentally confirmed by the controllable realization of graded substitution ratio in the monolayers through controlling the substitution temperature and time, and further theoretically verified by kinetic Monte Carlo simulations. The strain-tuning atomic substitution processes are of generality to other two-dimensional layered materials, which offers an interesting route for tailoring electronic and optical properties of these materials. KEYWORDS: stain, atomic substitution, mechanism, two dimensional material, composition engineering The design and preparation of materials with precisely controlled atomic structure and electronic properties is a long lasting scientific quest for material scientists.1−3 The energy barrier on the surface of solids can be explored for fine controlling the atomic substitution during the growth.4,5 A fundamental understanding of the atomic substitution mechanism in solid-state materials is essential for the precise control of their chemical structure and physical properties. Nevertheless, how the substituting atoms find the appropriate positions and how the reaction proceeds are still ambiguous. The recent discoveries of atomically thin two-dimensional (2D) layered semiconductors6−10 provide a fascinating model system for exploring such atomic control at the limit of single or few-atomic thickness. 2D layered semiconductors, notably transitional metal dichalcogenides (TMDs),11−13 have recently attracted significant attention as the next generation of atomically thin semiconductors for flexible field-effect transistors,14 photovoltaics,15 light emitting diodes16 and sensors17. The devices based on pristine TMD nanosheets are insufficient to meet the


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increasing performance requirements, and advanced materials with specific structures and tailored properties are desired.18−24 To explore 2D semiconductors for tunable and broadband optoelectronic devices, atomic substitution has been broadly used to prepare TMD alloys25−29 or heterostructures30−35 with variable chemical compositions, electronic structures and properties. However, a fundamental understanding of the detailed substitution process, which is essential for controlling the atomic structure, defect density and electronic properties, remains largely elusive. Herein we report a systematic investigation of Se/S-substitution in MoS2/MoSe2 monolayers, and found that the substitution rate in MoS2 (MoSe2) is gradually decreased (increased) from the edge to the center in the atomic crystals. Density functional theory (DFT) calculations and kinetic Monte Carlo (KMC) simulations further support that the substitution initiates from the peripheral edge and propagates towards the center, driven by the strain between the substituted and host lattices, resulting in the self-promoted and self-limited substitution processes in MoS2 and MoSe2, respectively. Our studies reveal important insight regarding the kinetic process of atomic diffusion and exchange at the limit of single atomic thickness, which represents a major step to synthetic control of these atomically thin materials and offers valuable insight for controlling 2D alloys and heterostructures with atomic precision. RESULTS Experimental investigation of atomic substitution in 2D atomic crystals. The experimental investigation of atomic substitution of monolayer MoS2 by Se was carried out at 1013 K. Both the pre-grown monolayer MoS2 and the substituted one have the same 3 ACS Paragon Plus Environment

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triangular morphology (Fig. 1A) and thickness (0.68 nm), indicating the basic structure and morphology of the monolayer remained intact during the substitution (Fig. S2). The micro-PL and micro-Raman measurements were performed at five selected positions from the corner to the center of the MoS2 triangular domain (Fig. 1A), and the corresponding normalized spectra are shown as dashed lines in Fig. 1B and Fig. 1C, respectively. Before the substitution process, all PL spectra show single emission peak with identical full width at half maximum. The peak wavelengths of all PL spectra are located at 675 nm (pure MoS2), indicating no obvious structural change from the corner to the center of the domain. The Raman spectra taken from the five different locations show essentially identical features, with two prominent peaks locating at 403.1 cm−1 and 378.6 cm−1, corresponding to the A1g and E2g vibration modes of MoS2, respectively (Fig. 1C), further confirming the quality and uniformity of the as-grown MoS2 sample. After the atomic substitution process, the PL spectra show a gradual shift from 703 nm at the corner to 675 nm at the center (solid line in Fig. 1B), suggesting that the successful chemical substitution occurred and the concentration of Se gradually decreased from the corner to the center in the substituted sample19,20. This composition difference was also confirmed by the decreasing Raman intensity of the A1g mode of MoSe2 (Fig. 1C). The gradual decrease of A1g mode of MoSe2 collected from position 1 (outer) to position 3 (inner), and even to zero at positions 4 and 5, indicates the gradient change of the composition Se from the corner to the center of the triangular domain. Furthermore, the PL mapping was performed on the sample to further confirm the concentration gradient of Se in the substituted MoS2 domain (Fig. S3). To further verify the gradient composition changing in the substituted MoS2 domain, the 4 ACS Paragon Plus Environment

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atomic arrangement of a typically substituted monolayer is clearly resolved in high angle annular dark field (HAADF)−STEM imaging. Figure 1D−F gives the HAADF−STEM images taken from three representative positions from the edge to the center of one representative substituted nanosheet (points 1 to 3 in Fig. S4A), along with the atom-by-atom reconstruction in Fig. 1G−I. Depending on the vertical bi-chalcogen planes in the sandwich structure of TMDs, we labeled three types of chalcogen atoms, S2, SSe, and Se2, corresponding to the three different intensity sites observed in monolayer MoS2(1-x)Se2x alloy.21 Obviously, the spots corresponding to Se2 atoms are mainly located at the edge of the nanosheet, while those corresponding to S2 atoms are mostly located at the center of the sheet. Overall, the Se atoms in the edge of the 2D structure are significantly more than that of the center, which clearly demonstrates that the substitution rate is gradually decreased from the edge to the center of the sheet. In addition，the energy-dispersive X-ray spectroscopy (EDX) line profile also reveals the continuously gradient change for the concentrations of both S and Se across the sample (Figure S5). Density Function Theory Calculations. The formation of composition gradient from corner to center suggests that the substitution may occur more readily at the edge than in the planar surface of MoS2, which may be governed by several likely processes. At the very beginning of the substitution, Se atoms absorb on the surface of MoS2 likely at some specific preferred sites. Since it is difficult to directly probe such sites experimentally, we conducted density function calculations (DFT) to explore the Se adsorption energy of various representative sites. To this end, we adopted a triangular model with dimerized S Klein edge (Fig. 2A), which represents energetically most stable configuration based on our calculation results. 5 ACS Paragon Plus Environment

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Figure 2B shows the calculated adsorption energy of a Se atom on a pristine MoS2 nanosheet from the outermost site to inner sites, which suggests an incoming Se atom prefers to adsorb at the outermost site of a MoS2 sheet, with the adsorption energy being at least 0.2 eV lower than that at other sites. The adsorption site preference is consistent with the previously found chemical activity that the edges may act as active sites for a variety of chemical reactions.36 In terms of inner sites, the outermost one InS1, has a slightly lower total energy of 30 meV, indicating that Se atoms prefer to adsorb at the periphery of a MoS2 nanosheet where initial substitution occurs. This mechanism is, however, not fully responsible for the observed composition gradient since the adsorption preference decays rather fast and is nearly quenched with few nanometers from the edge or corner of the MoS2 domain. In addition to the adsorption site preference, the substitution energy barrier height may vary at different sites, which substantially affects the substitution rate. Figure 2C shows the initial-, transition- and final-state of the most likely pathway for the Se-S substitution process, which were revealed by nudged elastic band (NEB) calculations among six possible pathways (see Figures S6−8 for other five possible pathways). It was found that a Se atom first adsorbs on a surface S atom, and then moves towards to a neighboring S atom of the adsorbed S atom. The Se atom lifts up the neighboring S atom from the surface. The substitution process thus reaches to its transition state (TS) where the Se and S atoms are nearly at the same vertical level. The process continues to develop so that the Se atom takes the original position of the neighboring S atom, pushing it to the next neighboring S-top site. The whole pathway needs 2.81 eV to activate (Fig. 2D), corresponding to a thermal energy of 1080 K if assuming a typical pre-factor of 1013 in the Arrhenius Law. Similar to the adsorption energy preference, 6 ACS Paragon Plus Environment

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this barrier might also be spatially dependent. Figure 2E shows the barriers at positions InS1and InS2 are only 1.90 and 2.52 eV, respectively. Although the substitution barrier at the periphery is much lower than those at the inner positions, it increases rapidly and nearly reaches the bulk value at site InS3, i.e. 2.75 eV versus 2.81 eV. In light of this, such a barrier variation cannot be the sole reason to explain the long-range gradient found in the experimental studies. In addition, we considered likely differences in diffusion barriers of Se on bare or substituted MoS2 (Figure S9 and Table 1). It turns out the barriers are too small, in a range from 0.92 to 1.42 eV, which cannot induce an appreciable substitution gradient at the synthesis temperatures. MoSe2 has a 4% lattice mismatch with MoS2 because of larger atomic size of Se. The substitution process thus expands the original MoS2 lattice parameter, from 3.16 Å eventually up to 3.30 Å. Initial substitution process always occurs at the periphery of a MoS2 nanosheet due to lower adsorption energy and substitution barrier there, which results in expanded MoS2 lattice, and effectively produces a tensile strain to the edges and corners of the nanosheet. It is easier for strain relaxation at the periphery than at inner regions, which leads to a long-range strain field from the corner or edge to the center (Fig. 3A). As a result of the strain field, the MoS2 lattice constant forms a long-range size gradient, namely the outer the position of the nanosheet, the larger the size of the lattice. Figure 3B shows the evolution of the effective lattice constant and barrier height as a function of Se occupancy ratio. The in-plane lattice constant of MoS2 enlarges from 3.16 Å to 3.23 Å when the occupancy of Se increases from 0 to 80%. This expanded lattice constant leads to significantly reduced substitution barriers, dropping from 2.81 eV in the original lattice to roughly 2.3 eV in the 80% 7 ACS Paragon Plus Environment

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substituted lattice. The substitution barrier decreases with the increasing occupation, indicating a continually enhanced substitution rate (self-promoted). Given this strain-driven substitution mechanism, a consistent model can be developed to explain the observed concentration gradient. The initial Se-substitution takes place at the periphery of a nanosheet. The incoming Se atoms enlarge the lattice constant of the replaced unit cells, gradually lowering the adsorption energy and substitution barriers. In other words, the more the S atoms are replaced in an area, the easier the substitution process occurrs near that area (see Fig. S10). Here, one may argue that substituted Se atoms do diffuse in the sheet giving a diffusion driven gradient. However, our calculations show that the barrier height for in-plane diffusion was so high (~5 eV) that this diffusion processes are unlikely under the experimental conditions (see Fig. S6). Kinetic Monte Carlo Simulations. We have further performed KMC simulation to verify our model. The barrier of 2.52 eV for site InS2 corresponds to an activation temperature of 970 K and 1080 K for 2.81 eV. We infer the substitution occurs in between these two temperatures and thus simulated the process from 990 K to 1020 K with a step of 10 K. Figure 4A plots the substitution ratio with respect to the position in a nanosheet under different reaction time and temperatures. At 990 K, the gradient is only observable around the corners/edges of the sample, and it needs sufficient substitution time to achieve, which is consistent with the kinetics governed substitution mechanism and the lower barrier at the corners or edges. If the temperature goes slightly higher, the substitution rate increases substantially, which further lowering the barrier and leading to even higher substitution rate. As a result of this self-promoted process, the most pronounced gradient was found at 1010 K. 8 ACS Paragon Plus Environment

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If the temperature goes further higher (e.g., 1020 K), the thermal activation energy can easily surmount the barrier height across the entire nanosheet (even at the center). In this case, the difference of barrier heights is less meaningful. Thus, the randomness largely dominates the substitution, leading to lower gradient at 1020 K, especially for longer substitution time periods. One may also argue whether the initial substitution and the induced strain at periphery are of crucial importance to the observed gradient. We carried out a similar KMC simulation without initial substitution at periphery, which explicitly shows that the gradient no longer exists; on the other hand, if a constant external force is applied to the periphery, the gradient emerges again (Fig. S11). These studies strongly support the mechanism of long-range strain field and the effective initial strain model, which is responsible for the self-promoted process. Furthermore, the KMC simulation predicted tendencies are well verified with our massive experimental data taken at different temperatures (Fig. 4B). There is no appreciable substitution occurring at or below 1003 K, comparable with the theoretically activation temperature of 970 K (not shown). At 1013 K, the activated substitution process leads to the gradient observable at the corner; while at 1023 K, the gradient starts to enhance and the steepest gradient was achieved at 1033 K owing to the self-promoted mechanism, which is the calculated critical temperature and the largest gradient found theoretically. At even higher temperature (e.g., 1043 K), the thermal energy can overcome the barrier at the center, so that statistics largely governs the substitution process, leading smaller gradient, which is consistent with general picture that high temperature vanishes kinetic governed process. To verify our proposed strain-driven mechanism, we have also investigated 9 ACS Paragon Plus Environment

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S-substitution in MoSe2 monolayers. The initial substitution at the periphery is still valid in the MoSe2 case (Fig. 5A) that the substitution barrier at outermost sites is appreciably lower than that at inner sites, which can be verified from the STEM image in Fig. S12. The lattice constant and substitution barrier also varies, but they are opposite to that in MoS2 with increasing substitution (Fig. 5B). Particularly, the in-plane lattice parameter decreases from 3.30 Å to 3.23 Å at the S-occupancy of 80%, which shrinks the original lattice due to smaller size of S compared with Se. In analogy to the MoS2 case, the smaller lattice gives rise to increased substitution energy barrier. The smaller atomic size of S results in a compression of the lattice at edges and corners in a periphery-substituted MoSe2 nanosheet. It thus builds a long-range compressive strain field from the corner or edge to the center, similar but opposite to the case of MoS2. As a result of the strain field, the size of the MoSe2 lattice forms an increasing long-range gradient from outer to inner positions. Given the inversely proportional relationship between the substitution energy barrier and the size of lattice as shown in Fig. 5C, the substitution barrier at the periphery of the nanosheet is larger than that at the center, suppressing the continued substitution at the periphery and relatively more S-substitution at the inner region. In contrast to the self-promoted process of Se replacing S in MoS2, the S-substitution of MoSe2 is thus a self-limited process. It would be thus interesting to double check this mechanism with KMC simulation. The barrier of S-substitution of MoSe2 is at least 0.6 eV smaller than that of the MoS2 case, ascribed to higher reactivity and smaller atomic size of S in comparison with Se. The substitution temperature drops by roughly 130 K from the MoS2 case since it is directly relevant to the barrier height. Figures 5D and 5E show the simulated and experimental results, namely the spatially 10 ACS Paragon Plus Environment

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resolved occupancies at different substitution temperatures and time periods. The features found in both plots are surprisingly consistent that larger occupations were found at inner positions, but smaller ones at outer positions. In addition, the data points in each plot seem nearly linear and continuous spanning different temperatures. Unlike the self-promoted process in MoS2, the initial substitution cannot accelerate subsequent substitutions but slows them down. The substitution ratio, therefore, tends to exhibit a uniform spatial distribution, giving rise to a rather smooth slope of the occupancy gradient. All these features compellingly support the periphery substitution induced long-range strain field and the self-limited substitution mechanism in MoSe2. CONCLUSIONS In summary, we found that the Se-substitution barrier, thus the substitution rate, in MoS2 monolayers, is highly correlated with their local strain built around the substituted S atom, which well explains the experiment observations that S atoms are gradually substituted from the edge to the center of the nanosheets. The observed inverse gradient in S-substituted monolayer MoSe2 further confirms this strain-driven substitution mechanism, which could be universally applicable in all 2D atomic crystals since it is not relevant to the specific electronic structure. This revealed atomic substitution mechanism offers valuable insight into the kinetic process of atomic diffusion and exchange in the nearly free-standing atomic layer crystals, and is fundamentally important in precise preparation of composition engineered 2D nanostructures and heterostructures.

METHODS


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Experimental investigation. The monolayer MoS2 nanosheets were substituted by a homemade traditional chemical vapor deposition (CVD) furnace (OTF-1200X). Two boats loaded with selenium powder and Si/SiO2 wafer (adhering pre-grown MoS2 nanosheets), respectively, were placed at the upstream of the furnace, and the boat loaded with wafer can be shifted by a pull rod driven by a step motor through magnetic force during the course of the experiment (Fig. S1). Before heating, Ar mixed with 5% H2 gas was first introduced into the system to ensure a favorable circumstance for the substitution, and the pressure was kept at about 8 Torr. The furnace was then rapidly heated to the substitution temperature. Then the boat loaded with Si/SiO2 wafer was rapidly pushed to the heating zone of the furnace. After reacting for a certain time, the boat was then rapidly pulled back, and the furnace was naturally cooled to room temperature. Micro-photoluminescence and micro-Raman measurements excited with a 488 nm argon ion laser were performed to characterize the spatially structural and optical modulation of the sheet. For S-substitution in monolayer MoSe2, the method is almost the same except that the selenium powder was changed to sulfur powder.

Density functional theory calculation. Density functional theory (DFT) calculations were carried out using the generalized-gradient-approximation (GGA) for exchange-correlation potentials, the projector augmented waves (PAW) method37 and a plane-wave basis set with the kinetic energy cutoff up to 500 eV as implemented in the Vienna Ab-initio Simulation Package (VASP).38 Van der Waals forces were considered at the self-consistent vdW-DF39 level which includes of the non-local correlation functional combined with optB86b for the exchange functional (optB86b-vdW).40 This functional was found suitable for energetic properties of layered two-dimensional materials and their homo- and hetero-structures .41−43

The lattice constant of MoS2 unit cell is 3.164 Å and 3.295 Å for MoSe2, highly consistent with the experiment values of 3.166 Å and 3.292 Å. Two supercells, i.e. a 3×3 and a 9×9 one, were employed for


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revealing the relationship of varied lattice constant versus substitution occupation and unveiling the substitution or diffusion barrier, respectively. Another large triangular MoS2 sheet was adopted to evaluate the adsorption preference of Se adatoms on MoS2. Each edge of this sheet contains eight units of MoS2 lattice and the space between two images is at least 15 Å. A vacuum layer of 20 Å was used to simulate the two-dimensional nature of these materials. In revealing the lattice-occupation relationship, a k-mesh of 5×5×1 was adopted to sample the surface Brillouin-zone of the 3×3 supercell, in which we only replace S atoms with Se atoms one by one in the top sublayer. Both ionic positions and lattice shape and volume were fully relaxed until the residual force on every ion and the lattice is less than 0.005 eV/Å. For adsorption preference calculations, the force criterion was set to 0.01 eV/Å. Only the Gamma point was used in the 9×9 supercell for the nudged elastic band (NEB) theory calculation,44 with force criterion of 0.02 eV/Å. To model the doping concertation from 0% to 100%, the lattice constant enlarges from the pristine value of 3.164 Å to the fully Se-doped values of the 3.243 Å. A plane-wave energy cut-off of 300 eV was adopted for NEB calculations to balance the huge computation demand and accuracy requirement.

Kinetic Monte Carlo simulation. In our model for KMC simulation, a triangular MoS2 (MoSe2) nanosheet was adopted. Each edge of these sheets contains 600 units of MoS2. Since Mo atoms were not appreciable involved in the substitution process, only S or Se atoms, denoted X atom below, were considered on our KMC grid.45 Therefore, each X atom is located on a grid point. In light of this we assume an X atom is connected with its neighbors with springs. These springs should originally represent the X-Mo-X bonds. Lattice relaxation was considered by applying a simple Hooke’s law: F=k(l−l0) to evaluated the strain F of each atom, where l represents real distance between two linked X atom and l0 represents theirs equilibrium separation. Here, l0 of S-S or Se-Se are the equilibrium lattice constant of pure MoS2 or MoSe2 layer, and l0 of S-Se is the lattice constant of MoS2-xSex when the occupation of Se is 50%,


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noticed that the lattice constant increased linearly with the growth of occupation. In order to simplify the process, we assume that all of those “springs” have a same Young’s modulus k. Given these parameters, we applied Newton’s law to relax the whole system to equilibrium, which usually gives rise to a varied local lattice constant.

As we discussed in the main text, we first set outermost X atoms being substituted as the initial configuration shown in Fig. 3A. In each loop of the simulation, we carry out the relaxation and tolerant force of each atom is rkl, r=0.001. The substitution barrier is relevant with the local lattice constant. Here, we used the averaged distance of the six nearest site to reveal the local lattice constant of an atom. Given a local lattice constant, the corresponding substitution barrier Ei can be obtained from the fitting curve shown in Fig. 3B and the substitution rate is thus derived by D=Aexp[−Ei /(kBT)], where kB is the Boltzmann constant, T is temperature, A is the attempt frequency which fix to a typical value of atomistic processes of 1.0×1013/s. The substitution possibility of the ith atom (grid point) should, therefore, be

ri = A exp(− Ei /(k BT )) / ∑ A exp(− Ei /(k BT )) . At a certain grid point (atom) i, possibility ri governs i

whether the substitution process occurs. If the process happened, the ith atom on the grid point was replaced by a coming atom. The time interval between two substitution processes lies in

∆t = − ln(s ) / ∑ A exp(− Ei / k BT ) , where s is a random number between 0 and 1. The loop will go on i

until the total simulation time T reaches the setting simulation time.

The sampling method used to unveil substitution concentration is comparable to what adopted in the experiment. In particular, we chose five points from the corner to the center with equal distances. The sampling diameter for each point is 1.5 times the inter-point distance, which gives a balanced inter-point overlap and sufficient sample size. There are three corner-center lines in a triangle grid. We averaged the


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data along these three lines to get the final results. Substitution atoms around the edges were not included in our statistics.

ASSOCIATED CONTENT Supporting Information The Supporting Information including the schematic setup for the substitution, AFM and TEM (STEM) characterizations, wavelength-dependent PL mapping, other calculated pathways for the Se-S substitution process, spatial distribution of substitution barriers, verification of stain-tuning mechanism, and position-dependent PL spectra is available free of charge via the Internet at http://pubs.acs.org. The authors declare no competing financial interest.

AUTHOR INFORMATION Corresponding Authors Wei Ji*, Email: [email protected] Xiangfeng Duan*, Email: [email protected] Anlian Pan*, Email: [email protected] Author Contributions ⊥

These authors contributed equally to this work.

ACKNOWLEDGMENT The authors are grateful to the National Natural Science Foundation of China (Nos. 51525202, 61574054, 51672076, 61505051, 61674171, 51772084, and 11622437), the Aid Program for 15 ACS Paragon Plus Environment

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Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province, Joint Research Fund for Overseas Chinese, Hong Kong and Macau Scholars of the National Natural Science Foundation of China (No. 61528403), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grant No. 16XNLQ01). Calculations were performed at the Physics Laboratory for High-Performance Computing of Renmin University of China and at the Shanghai Super computer Center.

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Figure 1. Characteristics of Se-substitution in monolayer MoS2 nanosheets. (A−C) The optical image of a monolayer MoS2 nanosheet and PL, Raman spectra of MoS2 at different positions marked in (A) before substitution reaction (dashed lines) and after the substitution (solid lines). All the Raman and PL spectra show no position-dependence before the substitution, while they show the gradient after the substitution. (D1−D3) HAADF−STEM images taken from three representative positions from the edge to the center of one typical nanosheet (scale bars: 1 nm). (E1−E3) Atomic models corresponding to the structures in panels D1−D3.


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Figure 2. The calculation binding energies and energy barrier for the substitution of MoS2 with Se. (A) shows the atomic model for MoS2. (B) The corresponding binding energies for the positions marked with red open ring. (C) lists the models for Se atom adsorbed on different positions of monolayer MoS2, and the corresponding binding energies are shown in below. (D) The binding energies for different transition models are calculated and that of the TS model has the lowest binding energy. (E) The substitution barrier at different positions of monolayer MoS2. The energy barrier for the positions near the edge is much lower than that in the center of the monolayer.


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Figure 3. (A) The lattice constant in different position while the outermost S atoms are substituted by Se atoms. A clear gradient is observed. (B) The calculated results for the relations between the occupation of the substituted Se atoms, lattice constant and substitution barrier. With the increase of the occupation, the lattice constant increases and the energy barrier decreases.


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Figure 4. The KMC simulation and experimental evolution of the Se-substitution of monolayer MoS2. (A) The KMC simulation results for the substitution of MoS2 with Se and the corresponding experimental results are listed in (B) at various temperatures. The occupation increases with the increasing temperature and decreases with the increasing distance to edge.


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Figure 5. The theoretical calculation and experimental evolution of the S-substitution in monolayer MoSe2. (A) The energy barrier for the positions near the edge is much lower than that in the center, as same as MoS2 monolayer. (B) The calculated results for the relations between the occupation of the substituted S atoms, lattice constant and substitution barrier. (C) The lattice constant-dependent substituted energy barrier of the substituted MoSe2. (D) The KMC simulation results for the substitution of MoSe2 with S and the corresponding experimental results are listed in (E) at various temperatures. The occupation increases with the increasing temperature and the increasing distance to edge.


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Strain-Tuning Atomic Substitution in Two-Dimensional Atomic Crystals

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