Watching Dynamic Self-Assembly of Web Buckles in Strained MoS2

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Watching Dynamic Self-Assembly of Web Buckles in Strained MoS2 Thin Films

Hongtao Ren,†,‡,# Zixin Xiong,§,# Enze Wang,†,# Zhiquan Yuan,† Yufei Sun,† Kunlei Zhu,† Bolun Wang,† Xuewen Wang,† Hanyuan Ding,†,‡ Peng Liu,∥ Lei Zhang,*,‡ Junqiao Wu,⊥ Shoushan Fan,∥ Xiaoyan Li,*,§ and Kai Liu*,†

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State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China ‡ MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Science, Xi’an Jiaotong University, Xi’an 710049, China § Center for Advanced Mechanics and Materials, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China ∥ Department of Physics and Tsinghua-Foxconn Nanotechnology Research Center, Tsinghua University, Beijing 100084, China ⊥ Department of Materials Science and Engineering, University of California, Berkeley, California 94720, United States S Supporting Information *

ABSTRACT: Thin films with large compressive residual stress and low interface adhesion can buckle and delaminate from relatively rigid substrates, which is a common failure mode of film/substrate interfaces. Current studies mainly focused on the geometry of various buckling patterns and related physical origins based on a static point of view. However, fundamental understanding of dynamic propagation of buckles, particularly for the complicated web buckles, remains challenging. We adopt strained two-dimensional MoS2 thin films to study the phenomenon of web buckling because their interface adhesion, namely van der Waals interaction, is naturally low. With a delicately site-controlled initiation, web buckles can be triggered and their dynamic propagation is in situ observed facilely. Finite element modeling shows that the formation of web buckles involves the propagation and multilevel branching of telephone-cord blisters. These buckled semiconducting films can be patterned by spatial confinement and potentially used in diffuse-reflective coatings, microfluidic channels, and hydrogen evolution reaction electrodes. Our work not only reveals the hidden mechanisms and kinematics of propagation of web buckles on rigid substrates but also sheds light on the development of semiconducting devices based on buckling engineering. KEYWORDS: MoS2 thin films, web buckling, dynamic propagation, finite element modeling, multilevel branching recently.17 It was also shown by phase field modeling how complex morphologies of expansion ridges can appear due to competitive elastic interactions26 and how the buckles may develop different kinds of patterns.27 However, most of the previous studies mainly focused on static and final (or staged) morphologies of various buckles. Predictions of dynamic propagations of versatile buckles still remain great challenges due to the difficulties in both in situ observation and kinematic simulation. Recently, the propagation of a single telephone cord has been studied by finite-element modeling involving mixed-mode interface fracture and damage.25 A sag was found

uckling-driven delamination of thin film systems on rigid substrates is frequently observed1−4 and has been extensively studied for several decades.5−9 When an intrinsic or growth-induced residual stress in a thin film exceeds a critical value, it can delaminate the film from the rigid substrate, leading to failure of the film-based device. The buckles often start at defective sites or around the edge of the film and propagate along branching buckling fronts, forming versatile shapes of straight-sided,10−14 circular,15−17 telephone cord,17−19 or web blisters.16,20,21 In the buckling process, multiple instabilities are involved, which can be analytically described by nonlinear thin plate theory.22−24 The Föppl−von Kármán plate model has provided valuable insights into a variety of blisters.17,21−25 On the basis of this model, a 3Ddetailed profile of telephone cord blisters has been probed very

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© XXXX American Chemical Society

Received: November 4, 2018 Accepted: February 13, 2019

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DOI: 10.1021/acsnano.8b08411 ACS Nano XXXX, XXX, XXX−XXX

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Figure 1. Formation of large-area web buckles. (A) Schematic illustration of the growth of a MoS2 thin film with a polymer-assisted deposition and the triggering of buckles by a probe touching. (B−G) In situ observation of large area web buckles formed on an as-grown MoS2 thin film with a thickness of 370 nm. Scale bar, 100 μm. (H, I) Propagating distances and velocities of buckles along four different branches as labeled in Figure 1G, as a function of time, respectively. (J) AFM 3D topography of a buckled MoS2 thin film with a thickness of 230 nm. Scale bar, 20 μm. (K) Two height-profile lines crossing the middle of a telephone cord (line A) and a node position (line B) as shown in the inset. (L, M) Statistical histograms of lengths and widths of buckles (bars) that fit Gaussian distributions (dotted lines).

to appear immediately when the telephone cord rotation changed direction, followed by a counter-rotating branch that emerges from the buckling front pinned by the sagged area.25 The pinning mechanism reveals the mode mixity of the interface fracture. In contrast to the propagation of a single telephone-cord buckle, the dynamic propagation of web buckles is much more complicated and remains largely unknown because it sweeps over a wide area and involves multiple transient branching and configurational instability. Interfacial adhesion is one of the key factors to determine the morphology of buckles as well as their propagations. A relatively low adhesion is necessary for the initiation and propagation of buckles. So far, various buckles have been investigated on thin films of single-layer metal,17,24,25,28 multilayer metal,16,18,19 carbon,3,29,30 and amorphous silicon31 deposited on glass, silicon, or other rigid substrates. While web buckles of telephone cords are often observable, their formation is usually transient, thereby hindering the analysis of kinematics. Materials selection and interfaces design are of vital importance to build a buckling system of thin films, where a buffer layer is sometimes needed to weaken the interfacial adhesion. In recent years, the two-dimensional (2D) layered materials provide perfect platforms to study the buckling phenomena because their interfacial adhesion, namely van der Waals interaction, is naturally low owing to their layered structures without dangling bonds. Some postbuckling micro-

or nanostructures have been observed in several 2D materials and their heterostructures.7,8,10−14,21,32−36 In this study, we employ large-scale MoS2 thin films with a thickness ranging from 60 to 440 nm to study the dynamic propagation of web telephone-cord buckles. The films grown by a polymer-assisted approach are originally flat with a residual compressive stress. A point load applied by a probe can initiate several branches of telephone-cord buckles that propagate forward on the flat films. Each cord front will branch into two daughter cords after a certain distance of propagation, forming web buckles with lots of node positions. This sitecontrolled, point-initiated buckling therefore offers an ideal approach to in situ observations of buckling propagation from an origin. Finite-element simulations reproduce the kinematics of web telephone-cord buckles, in good agreement with experimental observations. It indicates that the dynamic propagation of web buckles is associated with the mixedmode interface fracture. The experimental and simulation results also show the strong dependence of geometry of buckled patterns on film thickness. Moreover, the potential applications are verified for the buckled semiconducting thin films in diffuse-reflective coatings and microfluidic channels.

RESULTS AND DISCUSSION MoS2 thin films are synthesized by a polymer-assisted deposition (PAD) which includes a spin coating of B


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Figure 2. Characterization of as-grown MoS2 thin films. (A, B) Typical MoS2 films before and after buckling, indicating a mirror- and diffusive-reflection, respectively. Scale bars, 3 mm. (C) AFM 3D topography of a MoS2 thin film grown at 850 °C. (D) High-resolution TEM image of the MoS2 thin film. The inset shows the selected area electron diffraction (SAED) pattern. Scale bars, 10 nm (D); 5.0 nm−1 (inset of D). (E) TEM image of a MoS2 thin film and the corresponding elemental mapping of Mo and S by an energy-dispersive spectrometer (EDS), respectively. Scale bars, 500 nm. (F) XPS spectra of Mo 3d and S 2p peaks for the MoS2 thin film grown at 850 °C. (G) Raman spectra of asgrown (clamped, strain-existing without buckling) and as-released MoS2 films (released, strain-free). The clamped sample was characterized from the back side before buckling, with the laser passing through the transparent sapphire substrate. The sample was then peeled off the substrate, thoroughly releasing the interface strain, and characterized by the Raman spectroscope at the same side.

starts to buckle along two branches of short telephone cords at the initial stage (Figure 1B). Each buckle front propagates forward for a certain distance and then branches into two daughter telephone cords at a node position (Figure 1C). The node is not pinned there immediately after its formation but remains somewhat mobile for a short time with the propagation of the buckle fronts (Figure 1B−D, also see movie S1). Overall, some major buckle fronts always propagate forward along different directions, while other minor fronts will stop when they approach adjacent buckles and can slightly reshape these buckles (Figure 1D−F). The buckling sweeps the entire visual field, finally forming a web buckles throughout the sample (Figure 1G). These buckles follow a style of meandering, rather than straight path, in the film plane (movie S1), which is similar to the case of telephone cords. The propagation velocities of buckles are estimated to be in the range of 50−80 μm/s along different directions, as shown in Figure 1H,I. Such velocity reflects the competition between the residual elastic strain energy (driving force) and the interface fracture energy

molybdenum-contained polymer solution on a substrate followed by a sulfurization of the coating film in a tube furnace at a growth temperature ranging from 550 to 850 °C (Figure 1A and Figure S1; see also details in the Materials and Methods). The as-grown MoS2 films are flat and continuous, with a thickness varying from 60 to 440 nm. We found that without sulfurization the as-grown product is a cracked, islandlike membrane (Figure S2). The formation of a continuous MoS2 film is actually indispensable for studying the buckling phenomenon, as the van der Waals interaction between MoS2 and the substrate is naturally weak, which facilitates the propagation of buckling. The MoS2 film can remain flat in ambient environment for several days and then could buckle due to the disturbance in temperature or moisture. A more intriguing way to dynamically initiate buckles is by touching. A tungsten probe is used (with a tip diameter of ∼ 20 μm) to approach, touch, and finally push the MoS2 film (movie S1), applying a point load on the film with both compressive and shear components. Once the probe is put into contact with the film, the originally flat MoS2 film C


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Figure 3. Mechanisms and kinematics of buckle propagation. (A) Finite-element modeling for buckling and delamination of a thin film from a rigid substrate. A geometrically nonlinear plate on a rigid substrate with cohesive elements for interface adhesion. Tn, Tt1, and Tt2 represent the normal and two tangential components of the interface traction T, respectively. (B) SEM image of a buckle observed in our experiments. Scale bar, 5 μm. (C−F) Corresponding snapshots from finite-element simulations. The film are colored by the out-of-plane displacement. These snapshots are rotated for a certain degree for comparison with the experimental observations. Scale bar, 100 μm. (G−J) Snapshots of buckle propagation and branching process of a 370 nm thick film in the experiments. Scale bar, 100 μm.

which indicates that a tiny amount of carbon may exist due to the decomposition and carbonization of polymers. However, the stronger signals of Mo and S in the as-grown sample suggest that MoS2 is the major composition of our film. X-ray photoelectron spectroscopy (XPS) confirms the atomic ratio of S to Mo to be exactly 2:1 in the as-grown film at 850 °C (Figure 2F and Table S1), but the S content in the film grown at 550 °C is found to be slightly higher (Table S1). Previous studies showed that mechanical properties and residual stress of films are key factors to determine the buckling process. The residual compressive stress/strain in as-grown MoS2 films is attributed to the mismatch in the thermal expansion coefficients of MoS2 film and the substrate (sapphire). Because both the MoS2 film and the substrate are structurally isotropic, the residual strain ε0 should be biaxial and can be expressed as ε0 = (αf − αs)ΔT, where ΔT is the temperature change from growth to room temperature, and αf and αs are the thermal expansion coefficients of MoS2 film and sapphire substrate, respectively. Substituting αf = 1.9 × 10−6/ °C,37 αs = 7.3 × 10−6/°C,38 the growth temperature (550−850 °C), and the room temperature (20 °C) into the above equation, it is found that the estimated residual strain in the MoS2 films is compressive, in the range of 0.29−0.45%. The Raman spectrum is also used to probe the residual stress/strain in the as-grown MoS2 film. As the MoS2 film is grown on optically transparent sapphire, its Raman signal at the film− substrate interface can be detected from the back side of the sample. Figure 2G shows Raman spectra for the as-grown MoS2 films on the substrate and those released from the substrate. The in-plane Raman mode E12g and out-of-plane mode A1g can be clearly identified. Compared with the fully released one without any residual stress, the as-grown MoS2 film clamped by the substrate has a blue shift of ∼ 1.9 cm−1 in

(damping/resistance force) and, thus, is mainly related to the residual stress/strain in thin film and the interface fracture energy between film and substrate. The nearly consistent velocities reveal an isotropic propagation of the buckles. The AFM 3D image further verifies that the buckles are blisters which are parts of films detached from the substrate (Figure 1J). The height of a node position is up to ∼2.0 μm, while the height at the middle of a cord that bridges adjacent nodes is ∼1.5 μm (Figure 1K). The distance between two adjacent nodes (length) is measured to be 48 ± 10 μm and the width of buckles 32 ± 5 μm, as shown in Figure 1L,M. This dynamic, isotropic propagation of buckles is related to the intrinsic features of as-grown MoS2 films. The as-grown films are found to be very flat and uniform and become rough after buckling (Figure 2A,B). A 400 nm-thick film grown at 850 °C has a surface roughness (Ra) of merely ∼1.0 nm, as revealed in Figure 2C; the roughness is even lower for the film grown at 550 °C (Figure S3A). These roughness values are distinctly lower than normal metal films deposited by e-beam evaporation or sputtering. The selected-area electron diffraction (SAED) pattern under transmission electron microscope (TEM) reveals distinct diffraction rings and/or bright, ambiguous areas, indicating the existence of both poly crystalline and amorphous components in the as-grown film at 850 °C (Figure 2D and inset) or amorphous component alone for the film grown at 550 °C (Figure S3B). The two diffraction rings in the inset of Figure 2D correspond to the lattice spacing of 0.271 and 0.158 nm, consistent with the (100) and (110) planes of MoS2, respectively. Elemental mapping characterized by energy dispersive spectrometer (EDS) shows that both Mo and S elements are distributed uniformly in the as-grown film (Figure 2E). As shown in Figure S4, there are weak carbon signals from the as-grown sample, D


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Figure 4. Dependence of buckled 3D features on film thickness. (A) Experimental observations of buckled patterns in the films with thicknesses of 79, 196, and 263 nm, respectively. Scale bars, 50 μm. (B) Buckled patterns obtained from finite-element simulations for the films with the same thicknesses as those in the experiments. Scale bars, 50 μm. (C) Length between adjacent nodes and width of buckles as a function of film thickness. (D) Heights at the node and in the middle of buckle as a function of film thickness. In (C) and (D), there are two simulation cases with different tangential stiffnesses.

E12g (Figure 2G), suggesting that a residual compressive stress/ strain exists in the as-grown film. According to the experimental results under a biaxial strain in literature (−5.2 cm −1 /%), 39 this Raman shift corresponds to ∼0.37% compressive strain, comparable to the values (0.29−0.45%) estimated from the thermal coefficient mismatch. The elastic modulus of the MoS2 film was tested by an indentation approach, deriving a result of ∼29 and ∼23 GPa for the films grown at 850 and 550 °C, respectively (Figure S5). To reveal both kinematic details and underlying mechanisms of buckle propagation, a finite-element modeling is performed to simulate the dynamic propagation of telephone-cord buckles using the software ABAQUS. As shown in Figure 3A, the simulated model includes a thin film (modeled as geometrically nonlinear plate) and a rigid substrate and well describes the real shape of a buckle that has an arc shape in the cross section (Figure 3B). Similar to previous simulations on the propagation of a single telephone-cord buckle,25 the mixedmode cohesive zone model is used to describe the interface damage and fracture (Figure S6). Therefore, the cohesive elements with zero thickness are inserted between the thin film

and the rigid substrate. To generate the biaxial compressive residual stress in thin film, a uniform thermal expansion is applied to the film. To track the propagation of buckle front, the film is colored using the out-of-plane displacement of elements. More details of finite-element modeling are supplied in the Materials and Methods. Parts C−F of Figure 3 capture a sequence of snapshots of propagation of web telephone-cord buckles, which are very similar to the corresponding experimental observation as shown in Figure 3G−J. At the initial stage of simulation, a straight-sided blister first forms from a small adhesion-free domain and then transforms into a telephone-cord buckle due to the secondary buckling instability. Subsequently, each propagating front of this blister bifurcates into two branches, and each branch moves forward for a certain distance and then separates into two branches again. Such a branching process repeats itself until the propagating front reaches the boundary of model. During the buckling propagation, two daughter branches from different mother branches encounter and then connect, leading to the formation of closed hexagons. In this way, the final buckled E


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match with the experimental measurements. Such theoretical analysis indicates that the formation of hexagonal buckling pattern is intrinsically determined by the minimization of total energy per area in overall film. In our simulations, the propagation of buckles leads to the delamination of thin films from rigid substrates, which is dominated by the mode I interface fracture with a fracture energy of 0.25−0.3 J/m2 used in our simulations (Table S5). Under similar conditions, our simulations reproduce nearly identical kinematics and 3D geometry of web telephone-cord buckles as in the experiments (Figure 4C,D). It suggests that the interface adhesion energy between MoS2 and sapphire is on the same order of magnitude as the facture energy used in our simulations. The results shown in Figures 3 and 4 are from finite-element simulations, where the buckles initiated from a small rectangular adhesion-free domain. Furthermore, we simulated the buckling of films with initial circular adhesion-free domains to investigate the influence of the shape of initial adhesion-free domain on the final buckle pattern. During these simulations, we introduced a small circular adhesion-free domain at the center of the film as the initial perturbation. More details of simulation are given in the Materials and Methods. Figure S10A shows the buckled patterns of films with different thicknesses. These buckles initiate from the circular adhesionfree domains. Both the shape and size of buckles are very similar to those from our experiments and finite-element simulations with the rectangular domains. The dependencies of 3D features of web buckles on the film thickness from these simulations are in good agreement of those from our experiments, as shown in Figure S10B,C. The results from these simulations with the initial circular domains agree well with those from previous simulations with the initial rectangular domains. It indicates that the final web buckles are independent of the shape of initial adhesion-free domain. Furthermore, we investigated the influence of touching force intensity on the buckling of MoS2 films on a substrate. We buckled a MoS2 film by applying three different touching forces (44, 164, and 274 mN) with a probe, where the touching forces were calibrated by an electronic balance. As shown in Figure S11A−F, the geometry of the buckles appears to be very similar under these three touching forces. The lengths of the formed buckles are 54 ± 7, 55 ± 8, and 56 ± 8 μm, respectively, which shows a very slight deviation under different touching forces (Figures S11G−I). Both widths and heights of the buckles seem also independent of the intensity of the driving force. We also performed a series of finiteelement simulations to further validate the independency of static morphologies on driving force. In our experiments, the touching force generates a perturbation, which further triggers the buckling and delamination of the film. Different touching force induces the perturbation with different intensities. Therefore, we used initial adhesion-free domains with different sizes (Table S4) in simulations to equate the intensity of perturbation. Parts A and B of Figure S12 show the simulated buckled patterns initiated from strips with different sizes in the films with thicknesses of 79, 196, and 263 nm. These results are in good agreement with those from both experimental observations and our previous simulations shown in Figure 4A,B. The 3D features of web buckles agree well with the experimental measurements, as evidenced by Figure S12C,D. These results indicate that the 3D geometry features of weblike telephone cord buckles are independent of the intensity of

pattern is an arrangement of many hexagons bounded by undulated buckles. Our experiments and simulations show that the formation of web buckle is due to the propagation and branching of telephone-cord blisters. Notably, multilevel branching plays an important role in the formation of web buckles. Therefore, the underlying mechanisms for the multilevel branching is further explored. Parts A−C of Figure S7 show a sequence of snapshots of first-, second-, and third-level branching, respectively. During the first-level branching, the buckle front is first pinned by two points A1 and B1, which is evidenced by the unchangeable distance between A1 and B1. Then the front separates into two branches around point C1. The separated branches propagate forward while the buckling heights increase. Points C1 and D1 become new pinning points, leading to further propagation and upheaving of branches. During the second- and third-level branching, three pinning points are also observed, respectively. The pinning points (A2, B2) and (A3, B3) constrain the width of buckle, while the pinning points C2 and C3 induce the bifurcation of the propagating front. The emergence of these pinning points originates from the coupling of the instability and mode mix dependent adhesion.25 Therefore, to some extent it reflects the occurrence of mixed-mode fracture at propagating fronts. Our simulations elucidated the pinning mechanism responsible for multilevel branching during buckle propagation. The similar mechanism has also been reported in previous simulations of branching of single telephone-cord blister.40 The ultimate 3D feature of web buckles also depends on the thickness of MoS2 film. Figure 4A shows a series of buckling experiments on 79, 196, and 263 nm thick MoS2 films. With the increase of the thickness of films, the blisters experience a 3D enlargement in length, width, and height, generally forming isolated rootlike, quasi-connected hexagonal or isolated hexagonal shapes (Figure 4A). Both of the shapes and sizes of blisters fit well with the results obtained by the finiteelement simulations (Figure 4B). These results indicate that the dynamic propagation and the 3D geometry of web buckles are highly dependent on film thickness. It should be noted that in the finite-element simulations, closed hexagons are dominant buckled patterns, while a few branches in the experimental patterns are isolated and do not form closed hexagons, which might be attributed to the smaller in-plane size of thin films and more symmetrical and realistic conditions used in the simulations. Because of the identical growth temperature, the residual stress/strain in these films should be similar. Previous studies showed that the critical stress for various buckling increases sharply with the film thickness.41 It means that when the buckling occurs, the released elastic strain energy per area for buckling generally increases with the film thickness. Therefore, under a given residual stress/strain, if the film buckles due to the configurational instability, the 3D geometrical features of web blisters will increase as the film thickens. Such a phenomenon for web blisters in the current studies is similar to those of single straight and telephone-cord blisters.17,41 To further demonstrate the dependence of web blisters’ characteristic length on film thickness, a quantitative analysis is made by minimizing total energy per area (including bending energy, stretching energy and surface energy of buckled/delaminated parts, and in-plane elastic strain energy of undelaminated parts) stored in the overall film. The relevant details of theoretical analysis are supplied in text S1. As shown in Figure S9B, the predictions from this theoretical analysis F


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Figure 5. Patterns of buckled MoS2 films made by spatial confinement. (A) Optical image of buckles in different zones on the same substrate. Scale bar, 500 μm. (B, C) Zoomed-in images of buckles shown in A in the free zone and in the confined zone, respectively. Scale bars, 100 μm. (D) Statistical histograms of buckle lengths in free- and confined-zones. The dotted lines indicate Gaussian fits of data.

Figure 6. Buckled MoS2 films as diffusive-reflection coatings and capillary channels. (A) Illustration of mirror- and diffusive-reflection in flat and buckled MoS2 films. (B) Optical images of bare sapphire substrate and MoS2 films with different thicknesses on sapphire. Scale bars, 2 mm. (C) Reflectance spectra of buckled and flat (in inset) MoS2 films. (D) Illustration of water flow in buckled MoS2 microchannels. (E) In situ observation of water flow through a section of microchannel. The red arrows indicate the flowing front and the flowing direction with the elapse of time. Scale bar, 50 μm. (F) Velocity of water flow in the microchannel (main panel) as well as the contact angles of water on sapphire substrate, top-side MoS2, and back-side MoS2 (inset).

initial perturbation, which is induced by the touching force in the experiments.

The feature of web blisters is further found to be related to spacial boundary conditions of MoS2 films in local area. To G


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50 μL) are put on the top of it (Figure 6D). The transportation of water inside the buckles is observed from the back side of the sample through the sapphire substrate at a distance (∼ 2 mm) away from the water-dropping site (Figure 6E). Contact angles are measured to be ∼45° for the inside MoS2 and ∼69° for the substrate after release of MoS2 (Figure 6F), revealing that the buckled channels are hydrophilic which can benefit the transportation of water inside. The velocity of water transportation was measured to be 99 ± 10 μm/s independent of the time, which suggests that the buckled MoS2 film may offer itself as potential microfluidic channels. Lastly, we tested hydrogen evolution reaction (HER) properties of buckled MoS2 films. As shown in Figure S15, a buckled MoS2 film shows a lower overpotential (566 mV at 10 mA·cm−2) and a lower charge-transfer resistance compared to a flat one (718 mV at 10 mA·cm−2). However, the Tafel slope of the buckled film is slightly higher than the flat one, which indicates that there is no significant improvement of intrinsic HER activity for the buckled film. From Figure S15D, the value of electrochemical double-layer capacitances (Cdl) can be estimated according to the slope of the fitted line. The Cdl of buckled and flat films are ∼0.269 and ∼0.195 mF·cm−2, respectively, which means that the buckled film has more active sites. Actually, the buckles increase the outer surface area of the film to enhance HER, and meanwhile, the inner surface at the buckles can also be permeated with electrolyte and contributes to HER. Due to these two factors, the active sites for HER increase, which makes the buckled film have better HER capability compared to the flat one.

show that, the nonpatterned, free-boundary zone, whose size is much larger than the feature size of blisters, and the patterned, confined-boundary zone, which is divided by many etched trenches, are fabricated on the same substrate by UVphotolithography and dry etching techniques, as shown in Figure 5A. The trenches in the confined zone are designed with a uniform length of 140 μm but with different widths (2− 10 μm) and separated with two pitch sizes of 15 and 60 μm. As shown in Figure 5B, the MoS2 film is found to buckle at the free-boundary zone. At the confined zone, however, the buckles only form at the pitch area with the size of 60 μm. Eventually, it leads to the formation of a connected, squared mesh of blisters (Figure 5C). The length of the blisters is slightly larger at the free-boundary zone than that at the confined zone (Figure 5D), while the width exhibits an opposite behavior (Figure S13). The MoS2 film remains flat at the pitch zone with the smaller size (15 μm), which is less than both the length and width of buckles at free-boundary zone (∼25 and 16 μm, respectively). It suggests that the adjacent trenches confine the extension of blisters in length and width directions, leading to the inactivation of buckling in the confined zone. Our method provides a strategy to the controlled modulation of buckles on rigid substrates, which might have practical applications in morphable microelectronic devices with specific patterns. The buckled thin films on rigid substrates have found their applications as antiglare surface, shock absorber, microlens array, etc.21,35,36 The configuration of web blisters of MoS2 film, together with its intrinsic band gap as a semiconducting material, gives rise to emerging applications in optics and microflow. Figure 6A illustrates that after buckling, the reflection of an incident light will be changed from mirror to diffuse type. The buckled films thus become visibly colorful by altering the thickness of the buckled films. As the film thickness increases from 80 to 265 nm, the color of the buckled films changes from dark brown to dark cyan (Figure 6B) because the reflected light shifts its peak to blue in the reflectance spectra (Figure 6C). The almost identical reflection spectra of both flat and buckled films suggest that the color change is mainly attributable to the intrinsic absorption of MoS2 films and the optical interferences at the multilayer interfaces. This phenomenon makes the buckled MoS2 films a highly promising candidate for colorful diffusive-reflection coatings. Photoluminescence (PL) of the buckled MoS2 film is also measured. We found that the PL intensity at the strained buckles is lower than that at the flat area (Figure S14). This result is different from the reported enhanced PL at the strained MoS2 film due to the funneling effect.42 We attribute the weakening of the PL to the geometry of our MoS2 buckles. In our experiments, the size of buckles is much larger than that of the laser spot, which can have the entire incident laser reflected by the curved MoS2 surface and deviated from the incident direction at buckled zones. In this situation, most of the excited PL will also emit outside and cannot be collected by the spectrometer, inducing a weakened PL intensity measured at the buckled MoS2 zones. The web blisters with underneath hollow structures appear like the capillary web in the human blood circulation system. A preliminary test is carried out to transport water inside the buckled channels. As shown in Figure 3A,B, these channels consist of parts of arc-shaped MoS2 and flat substrate. To guide water flow inside the channels, a small hole is made on the buckled part of a MoS2 film, and several droplets of water (∼

CONCLUSION In summary, we study the dynamic propagation of web telephone-cord buckles in MoS2 films on rigid substrates, combining in situ experiments and finite-element modeling. In situ experiments show the multilevel branching process during buckle propagation and 3D morphologies of web buckles. Considering both geometrically nonlinear deformation of the film and mixed-mode interface fracture, finite-element modeling is employed to reproduce the nearly identical processes of buckle propagation. These results show that the dynamic propagation and 3D morphologies (including geometry parameters and pattern) of web buckle are highly dependent on film thickness, and they also reveal the pinning mechanisms for multilevel branching. Moreover, our study demonstrates that the buckled semiconducting films can find potential applications as diffusive reflection coatings and capillary microchannels. Our present work not only provides a fundamental understanding of dynamic propagation of web buckles in thin films on rigid substrates but also sheds light on the development of emerging semiconducting devices based on buckling engineering. MATERIALS AND METHODS Specimen Synthesis. Molybdenum disulfide (MoS2) films were prepared by polymer-assisted deposition (PAD) of ammonium molybdate tetrahydrate, ethylene imine polymer (PEI, 99%), and ethylenediaminetetraacetic acid (EDTA, 99.99%) followed by a sulfurization in a furnace. To prepare Mo-polymer solution, 2 g of (NH4)6Mo7O24·4H2O was dissolved to a solution containing 1 g of EDTA and 40 mL of ultrapure water, and then 2 g of ethylene imine polymer was added into the mixed solution. After stirring, the solution was purified by Amicon Ultra Centrifugal Filters with a 10000 molar weight-off membrane. The solution was spin-coated on (0001) R-cut sapphire substrates with different spinning rates to obtain films with H


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In finite-element simulations, quadrilateral shell elements are used to model the film. The Green−Lagrange strain tensor was used to characterize the large nonlinear deformation of film. The simulated film has a thickness, t, varying from 79 to 391 nm. For these thin films, their element size is about 5 times the corresponding film thickness, which ensures that tens of elements are contained in one buckle width. The in-plane sizes of films with different thicknesses are given in Table S2. Quadrilateral cohesive elements with zero thickness are used to characterize interface behaviors. The size of cohesive element is about one-third of that of the shell element. The substrate is modeled as a rigid body. The lower nodes of the cohesive elements are fixed since the substrate is rigid, while the upper nodes are tied to the film. To avoid the interpenetration between film and substrate after the cohesive elements are removed, a normally hard and tangentially frictionless contact is imposed on the shell elements. During simulations, uniform thermal expansion is applied to the film with an eigenstrain, i.e., εxx = εyy = ε0, εxy = 0.40 At equilibrium, an equi-biaxial compressive stress state of σxx = σyy = −ε0E/(1 − ν) = −σ0, σxy = 0 (where E and ν are the Young’s modulus and Poisson’s ratio of film) is generated in the film due to the constraints of rigid substrate on the film. The eigenstrain ε0 used in our simulations is taken as 1.0%, which is comparable to those (about 0.20−0.45%) estimated by our Raman spectrum and theoretical predictions. A small rectangular strip is introduced to the center of model. Its length is parallel to the y axis in Figure 3A. Such a strip is initially adhesion-free to trigger buckling and delamination. The in-plane sizes of strips in the films with different thicknesses are given in Table S2. To address the influence of the shape of initial domain on the final buckle, we also introduced circular adhesion-free domains and compared associated results with those from the rectangular adhesion-free domains. The in-plane sizes of circular domains in the film with different thicknesses are listed in Table S3. Due to the simultaneous presence of geometrical nonlinear deformation and cohesive law, the quasi-static analysis with ABAQUS/Explicit is adopted to ensure both efficiency and accuracy of calculations.40 Thus, the kinetic energy always remains very small compared with the strain energy in the elements. During simulations, the film is considered as an isotropic and homogeneous elastic material. Its Young’s modulus was taken as 24.5 GPa, which is close to experimental measurements (25.0 GPa) via nanoindentation, and the Poisson’s ratio was set as 0.27.37 For the traction-separation law of cohesive elements, the parameters in two tangential directions were set to be identical for the sake of simplicity, i.e., Kt1 = Kt2, T0t1 = T0t2, δ0t1 = δ0t2 and δft1 = δft2. Table S5 summarizes the values of the relevant parameters (such as stiffness and maximum traction) for their traction-separation law. For each film with a thickness of 79, 196, or 263 nm, two different values for tangential stiffness Kt1 and Kt2 were obtained. In our simulations, the energy release rate GCn for mode I fracture are 3 orders of magnitude higher than those GCt1 andGCt2 for mode II fracture, which is similar to that for the previous simulations.25

different thicknesses. The coated substrates were gradually heated in a tube furnace from room temperature to a target temperature (550− 850 °C) and kept at that temperature for 30 min under an atmosphere of 10% H2 mixed in Ar. A sulfur (99.998%) source in a quartz boat was placed at the entrance of the quartz tube and maintained at 180 °C during the growth for the sulfurization of the films. Structure Characterizations. Buckled patterns of MoS2 thin films were observed under ambient conditions using an optical microscope (OLYMPUS BX51M), scanning electron microscope (SEM, FEI Sirion 200 microscope, 5 kV), and atomic force microscope (AFM, Bruker Multimode 8). Raman spectra were obtained by a confocal Raman microscope (Horiba HR800) with an excitation laser line of 514 nm and PL spectra by a Horiba HR550 with an excitation wavelength of 532 nm. Transmission electron microscopy (TEM, FEI Tecnai G2F20 microscope) and selected area electron diffraction (SAED) were carried out at 200 kV to determine the crystalline structures. X-ray photoelectron spectroscopy (XPS) experiments were conducted on a Thermal Fisher ESCALAB 250Xi spectrometer. Reflection spectra were measured at variant wavelengths under a CRAIC 308 UV−vis−NIR microscope spectrophotometer. Finite Element Modeling. We performed the finite-element simulations to investigate the dynamic propagation of buckle of MoS2 thin film on the rigid substrate via software ABAQUS. As shown in Figure 3A, the used model contains a geometrically nonlinear film and a rigid substrate. To describe interface adhesion and debonding, a mixed-mode cohesive zone model which considered both modes I and II interface fracture was used. Thus, the cohesive elements are inserted between the plate and substrate. Their constitutive relationships are described by a bilinear traction-separation law (Figure S6). The separation and traction of cohesive elements can be resolved into the normal component (δn, Tn) and two tangential components (δt1, Tt1) and (δt2, Tt2) (Figure 3A), which characterize the modes I (opening) and II (shearing) interface fracture, respectively. The constitutive relationship is linearly elastic before the traction reaches the peak value. After the peak traction is attained, the traction linearly decreases with the increase of separation, indicating the interface fracture. When the separation reaches the maximum, the cohesive elements are removed, meaning a complete interface rupture. For the mixed-mode loadings, the following criterion is used to characterize the damage initiation l o o ⟨Tn⟩ Tt1 Tt2 | maxo m 0 , 0, 0o }=1 o o Tn Tt1 Tt2 o o n ~ T0n

(1) T0t1

T0t2

is the maximum normal tractions, and are the where maximum tangential tractions along the first and second shear directions, respectively, and ⟨ ⟩ denotes the Macaulay bracket, indicating that compression does not initiate damage. Once the traction reaches the peak value, the cohesive element starts to damage by reducing the stiffness by a factor of 1 − D, where D is a damage variable and is defined as43 f

D=

ASSOCIATED CONTENT

S Supporting Information *

0

δ (δ − δ ) f

0

δ(δ − δ )

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.8b08411. Schematic illustration of the growth of MoS2 films by polymer-assisted deposition; optical images of as-grown products with and without sulfurization; characterization of MoS2 films grown at 550 °C; EDS mapping of carbon element for as-grown MoS2 film; XPS elemental analysis of MoS2 films grown at different temperatures; moduli of MoS2 films measured by the indentation approach; mixed-mode traction-separation law of cohesive elements; multilevel branching during buckle propagation in the thin film on rigid substrate; hexagonal buckling pattern described by eq (S3); theoretical analysis based on the minimization of energy and comparison between

(2)

where δ = δn2 + δt12 + δt22 is the separation magnitude, δ0 is the separation corresponding to the peak traction, and δf is the complete separation. The following fracture criterion is used to reflect the dependence of fracture energy on the mode mix ji G zy ji G zy jij Gn zyz jj C zz + jjj t1C zzz + jjj t2C zzz = 1 jG z jG z jG z k n{ k t1 { k t2 { 2

2

2

(3)

where Gn, Gt1, and Gt2 are the energy release rates in the normal and two tangential directions, respectively, and GCn , GCt1, and GCt2 represent their corresponding critical fracture energies. These critical fracture energies are the areas under the corresponding traction-separation curves. I


Article

ACS Nano

University, and the Instrument Analysis Center of Xi’an Jiaotong University.

theoretical prediction and experimental measurements; theoretical analysis on the dependence of characteristic length of web-like blister on film thickness; in-plane sizes of thin films and initial adhesion-free strip; finiteelement modeling of buckled patterns initiating from circular adhesion-free domains; in-plane sizes of initial adhesion-free circular domains introduced in MoS2 films with different film thicknesses; buckled MoS2 thin films triggered by different touching forces; in-plane sizes of initial adhesion-free strips in films with different thicknesses; finite-element modelings of buckled patterns propagated from different sizes of adhesion-free strips; stiffness and maximum traction for cohesive law; statistical histograms of widths of buckles in free- and confined-zones as shown in Figure 5A; photoluminescence spectra of MoS2 web buckles under an excitation wavelength of 532 nm; hydrogen evolution reaction (HER) properties of flat and buckled MoS2 films (PDF) Dynamic propagation of web buckles of a MoS2 film, triggered by a tungsten probe (AVI) Finite-element simulation of dynamic propagation of web buckles in a MoS2 film 391 nm thick on a rigid substrate (AVI)

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AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. ORCID

Peng Liu: 0000-0002-1860-5126 Junqiao Wu: 0000-0002-1498-0148 Xiaoyan Li: 0000-0002-2953-9267 Kai Liu: 0000-0002-0638-5189 Author Contributions #

H.R., Z.X., and E.W. contributed equally to this work. K.L., X.L., and L.Z. designed the research. H.R. synthesized and characterized the samples and measured the optical and microfluidic properties of the samples. Z.X. and X.L. performed the finite element modeling and theoretical analysis. Z.Y. and Y.S. carried out the AFM measurements. E.W. measured the wetting properties, photoluminescence, and HER performance of the samples. Z.X., H.R., X.L., and K.L. wrote the paper. All authors analyzed the data, discussed the results, and commented on the manuscript. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS K.L. acknowledges support from the National Key R&D Program of China (2018YFA0208400), Basic Science Center Project of NSFC under Grant No. 51788104, National Natural Science Foundation of China (Grant Nos. 11774191 and 51602173), Fok Ying-Tong Education Foundation (161042), and Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics (KF201603). X.L. acknowledges financial support from National Natural Science Foundation of China (Grant Nos. 11522218, 11720101002, and 51420105001). L.Z. acknowledges support from the National Natural Science Foundation of China (Grant No. 11774279), the Young Talent Support Plan of Xi’an Jiaotong J


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K


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