Deformation Engineering of Van der Waals Materials
Jin Myung Kim, Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign
SungWoo Nam, Department of Mechanical and Aerospace Engineering, University of California, Irvine
1. Introduction
Materials exhibit drastically different physical and chemical properties as their dimensionality varies.[1] Atomically-thin van der Waals (vdW) materials possess unique mechanical, electrical, optical, and thermal characteristics, originated from quantum confined low-dimensionality and a lack of dangling bond.[2] In particular, strong in-plane covalent bonding and weak interlayer vdW interaction of two-dimensional (2D) vdW materials enable exceptional combination of mechanical properties, such as high Young’s modulus, high in-plane strength, and ultralow bending stiffness at a level of cell membrane.[3] Moreover, mechanical strain can induce modulation of electronic and phononic band structures of 2D vdW materials more effectively due to mechanical resilience and high surface-to-volume ratio. For these reasons, deformation engineering has garnered substantial interest in mechanics and materials communities as a new tuning knob for emerging phenomena and functionalities of 2D vdW materials.[4,5]
In this journal club, we discuss deformation engineering of 2D vdW materials in terms of (1) substrate-induced deformation, (2) buckle delamination and conformal wrinkling, (3) kirigami-inspired structures, (4) interfacial 2D materials, and (5) strain-coupled phenomena, by sharing recent research progress in this field, including our recent work.
2. Substrate-induced deformation of 2D vdW materials
The atomically-thin nature of 2D vdW materials often causes inevitable, uncontrolled out-of-plane deformation in multiple length scale, such as bubbles, blister, or nanotents.[6,7] However, it also allows for exploring deformation engineering in programmable and scalable manners. One of common approaches of 2D deformation engineering is to utilize three-dimensional nano/micro-patterned substrates as a deformation template. There have been a variety of 3D structures developed for tunable strain and properties of 2D vdW materials, such as microcavity,[8] nanogap,[9] nanowires,[10] and nanocones.[11] In the fabrication step, 2D vdW materials are first transferred on top of the pre-patterned nano/micro-structures via dry stamping or wet transfer, and the deformation mode of transferred 2D materials varies with the geometry and aspect ratio of the nano/micro-structure. For instance, 2D materials on high-aspect-ratio nanostructure result in suspended configuration, while conformal deformation occurs when underlying structures are smooth and with low aspect ratio.[12,13] For precisely controlled deformation of 2D materials, it is crucial to achieve improved interfacial integrity and reduced damage of suspended 2D materials on 3D structures. The improved integration of graphene with soft 3D substrate was demonstrated vis swelling, shrinking, and adaptation process (Figure 1a). A poly(dimethyl siloxane) (PDMS) substrate was pre-patterned to have 3D microstructured surface and then swollen with solvent before graphene transfer. Because of the sharp and high-aspect-ratio 3D structure, the as-transferred graphene was suspended over the 3D structure. However, post shrinking led by solvent evaporation allowed graphene to be integrated to the 3D structure surface. Figure 1b shows the scanning electron microscope (SEM) images of the successfully adapted graphene on various 3D structures because of reduced capillary and tensile stress in graphene during the fabrication steps.
Figure 1. (a) Schematic of swelling-shrinking-adaptation for 3D architectured graphene with improved integrity. (b) SEM images of graphene on various 3D structures.
3. Buckle delamination and conformal wrinkling of 2D vdW materials
Buckle delamination and conformal wrinkling are important and versatile methods that enable periodic out-of-plane deformation of 2D vdW materials in multiple length scales.[14-23] In general, shape-memory polymers or prestretched elastomers are used as substrates with a proper skin layer coated, and the prestrain is released after 2D vdW materials are transferred on top of the substrate. Upon the compression, the modulus mismatch between stiff top films (i.e., 2D material, skin layer) and soft substrate leads to surface instability driven buckling or conformal wrinkling, depending on adhesion energy between 2D layer and the substrate.[24] The weak vdW interaction between polymer substrate and 2D materials causes buckle delamination, particularly when high magnitude of prestrain is applied. We demonstrated the shrinkage of a prestrained shape-memory polystyrene (PS) for uniaxial/biaxial deformation of 2D vdW materials (Figure 2a).[25] By heating above the glass transition temperature, shrinkage of graphene/PS resulted in nanoscale buckle structure (Figure 2b). The structural feature can be tailored by changing the number of layers of graphene (i.e., bending stiffness of graphene/graphite). We have demonstrated that the graphene/graphite lateral heterostructures with 70% compressive strain enabled heterogeneous crumple morphology (Figure 2c). In addition to shape-memory polymers, various elastomeric substrates (e.g., very high bond (VHB) film, PDMS) were used for creating buckle delaminated 2D vdW materials.[26-31] A major advantage of using elastomeric substrate is that it enables dynamic tuning and reconfiguring of the crumpled structure and local strain of 2D vdW materials as a function of external stretching/releasing. The mechanical stretchability of the crumpled 2D vdW materials enabled various reconfigurable device applications such as reconfigurable photodetector, radiation control, and strain sensors.[26-31]
Conformal wrinkling of 2D vdW materials with soft substrate is another important approach to enable periodic deformation of 2D materials. Unlike buckle delamination, conformal wrinkling often includes an adhesive stiff layer (i.e., skin layer) in-between 2D materials and elastomeric substrate to enhance the adhesion and restrict delamination of 2D layers. For example, PDMS substrate can be plasma treated by using O2[16,32,33] or CHF3[21,22] to form stiff skin layer (SiOx and CFx). Our research group investigated conformally wrinkled vertical MoS2/WSe2 heterostructure on an elastomeric PDMS substrate coated with thin silicon oxide layer (Figure 2d). The wrinkle structure was formed by prestraining PDMS substrate (20%), performing O2 plasma treatment, transferring 2D heterostructure with encapsulating layer on top of the SiOx/PDMS substrate, and releasing the prestrain (Figure 2e). The photoluminescence (PL) and Raman spectrometry showed that the local strain applied on the heterostructure varied at the peak (tensile strain) and the valley (compressive strain) by up to 1% due to different curvature of the wrinkle geometry (Figure 2f).[16]
Figure 2. Buckle delamination and conformal wrinkling of 2D vdW materials. (a) Schematic illustration of the crumpled graphene on PS substrate. (b) SEM image of uniaxial and biaxial crumples. (c) Crumpled lateral heterostructure of graphene/graphite. (d) Schematic diagram of conformally wrinkled vertical MoS2/WSe2 heterostructure. (e) Optical microscope images of flat and wrinkled heterostructure. (f) Strain-induced photoluminescence energy shift in MoS2/WSe2 heterostructure.
4. Kirigami-inspired structure of 2D vdW materials
Kirigami is an art of paper cutting that enables out-of-plane deformation of thin films to form 3D structures. In particular, kirigami-inspired structures have been adopted for strain-insensitive and reconfigurable means for various applications, including photodetection/imaging, stretchable bioprobes, and motion detection.[34,35] With this approach, highly stretchable kirigami-structured graphene has been demonstrated with maximum stretchability up to 240%.[36] More recently, our group investigated a free-standing kirigami-inspired graphene electrodes to enable strain-insensitive biosensing under mixed strain states (Figure 3a).[37] Our graphene device was encapsulated in thin polyimide layers (2-4 μm) and the assembly was patterned into a kirigami shape. We observed strain-insensitive electrical performance up to 240% stretching and mixed-mode strains, including shear and 720° torsion (Figure 3b). This was primarily realized by desired structuring of graphene, redistributing stress concentrations via out-of-plane buckling at the kirigami notches.
We further extended this work to the creation of strain-insensitive biaxially stretchable graphene field-effect transistor (GFET) sensor arrays, consisting of four separate islands connected to each other and the border contact electrodes with kirigami bridges.[38] Three of the islands each contained three graphene channels, while the fourth island contained a resistive temperature sensor (Figure 3c). The arrays were fabricated in the same manner as the uniaxially stretchable kirigami-inspired GFETs, with a layer of graphene and contact electrodes sandwiched between two polyimide passivation layers. Each island containing graphene channels additionally contained an exposed gate electrode, enabling droplet solution gating on each island. The normalized resistance change of the electrodes and graphene embedded in the structure is smaller than 0.5% and 0.23% under 180° torsion and 100% biaxial strain. To understand the deformation mechanisms of our kirigami structure, we first characterized the mechanical response of a 10 μm-thick kirigami structure under biaxial loading using finite element analysis (FEA) (Figure 3d). The unit cell of kirigami bridges consists of two long plates (P1), two connection plates at the cuts (P2) and one connection plate at the notch (P3). Figure 3d shows the von Mises stress distribution in a kirigami bridge and its deformed structure under nominal stress (σn) of 10 MPa and 50 MPa. The stress was localized near the tip of cuts. Under in-plane loading, the bending of P1 with out-of-plane rotation was predicted. Owing to the out-of-plane bending of P1, the kirigami structure can be elongated in the in-plane direction significantly with a relatively small loading force. Detailed mechanical simulation and experimental results can be found in the reference.[38]
Figure 3. Kirigami-inspired strain-insensitive graphene device. (a) Schematic diagram of the strain-insensitive graphene device. (b) Strain-insensitive electrical performance under stretching and twisting deformation. (c) Photographs of the kirigami-patterned biaxial stretchable sensor in neutral state (left) and 100% biaxially stretched state (right). (d) Schematic diagram of the unit cell of bridges and various geometric parameters (left), and top view and side view of the unit cell structure and stress distribution in the structure under nominal stress of 10 MPa and 50 MPa (right).
5. Interfacial 2D vdW materials for fracture modulation
Thin-film metal electrodes have been ubiquitously used in flexible/wearable electronics because of their high conductivity, integrability, and cost-effectiveness.[39,40] However, practical implementation of thin-film metal based electrode has been limited by a lack of electromechanical robustness during their services under various deformation[41,42] because most of metals fracture at small strains with low cyclic fatigue failures, resulting in rapid surface crack development across the metal and electrical failure of complete disconnection. To overcome this electrical instability with strain led by rapid surface fracture of metals, our research group investigated atomically-thin interlayers of 2D materials including graphene, MoS2, and hBN to modulate fracture modes of metals and the resultant electrical performance of metal-2D electrode system.[43] We first characterized and compared fracture surfaces of thin film gold (Au) with an adhesion layer of titanium on PDMS substrate with and without graphene under bending. As shown in Figure 4a, distinct fracture between a conventional thin film Au/Ti electrode (bare Au) and Au/Ti/graphene electrode (Au/1LG) was observed. Cracks propagated in straight and resulted in debonding fracture failure on bare Au electrodes. In contrast, cracks propagated in local zig-zag fluctuation and led to tortuous extension creating polygonal interconnected fracture domains. Moreover, more gradual increase in crack width was observed with smaller fracture domains with deflected crack edges on Au/1LG electrodes, whereas a rapid increase in crack width with larger isolated fracture domains on bare Au electrodes (Figure 4b). To unveil the underlying mechanism for unique in-plane fracture modes enabled by 2D-interlayers, we investigated spontaneous buckle-network formation using molecular dynamics (MD) simulation and cross-sectional SEM imaging. It was found that spontaneous buckle-network is formed on the as-prepared electrode after the metal deposition owing to thermal residual compressive stress by the different thermal expansion coefficients of the constituent materials, and reduced film adhesion and increased effective modulus modulated by the insertion of 2D-interlayers (Figure 4c-d). Upon bending, multiple cracks favorably initiate at the crest (top) of the formed buckles because of the built-in localized strain at the crest (~1.3%) leading to the susceptibility for the crack initiation compared to other (i.e., non-buckled) areas.
Lastly, strain-dependent electrical characteristics resulting from unique fracture behaviors induced by 2D-interlayers was investigated. First, electrical resistance of metal-2D interlayer electrodes increased gradually upon bending as opposed to the abrupt, many orders-of-magnitude (104~105) soar of resistance observed in bare metal electrodes (Figure 4e). Notably, insertion of additional 2D-interlayers further reduced the magnitude of resistance change upon strain and delayed complete electrical disconnection. The extended plateau region with increased 2D-interlayers demonstrates enhanced ‘plasticity’ of electrical resistance, offering stable electrical resistance locking. We termed this unique strain-resilient electrical functionality enabled by 2D-interlayer as ‘electrical ductility’ where an elongation of electrical conductance of the metal film with strain is analogous to mechanical ductility describing the elongation of deformation with strain.
Figure 4. Fracture behaviors of thin film metal electrodes with 2D interlayers. (a) Crack progression at various bending strains (εb) in bare Au electrode (top) and Au/1LG electrode (bottom). A white arrow indicates Au film debonding from the PDMS substrate. (b) Crack width on bare Au and Au/1LG electrodes as a function of bending stain. (c) Schematic illustration of buckle-guided fracture mechanism and progressive fracture surfaces on Au/1LG electrode during bending (d) Cross-sectional SEM image of a buckled Au/1LG. (e) Electrically ductile behaviors of multilayer-graphene integrated electrodes in response to bending deformation. Scale bar, 10 mm.
6. Strain-coupled phenomena
Another approach to exploit the deformation engineering is to design local strain distribution in the 3D structured 2D materials for emerging functionalities. In particular, the heterogeneity of the strain distribution in deformed 2D materials can modify the electron/phonon band structure with energy gradient over the space.[3,13,44]
One of the example in strain-coupled phenomena in 2D vdW materials is the exciton funneling and single photon emission of strained transition metal dichalcogenides.[9,45] An exciton (i.e., electron-hole pair bound by their Coulomb attraction) in strained 2D vdW materials can drift toward the direction that the strain gradient leads to the local energy minima, resulting in antibunched light emission at low temperature (i.e., single photon emission). We investigated band engineering and single photon generation at a desired position by applying a strain to monolayer WSe2 using a Si3N4 rod structure with a nanogap.[9] Figure 5a shows a schematic illustration of our single photon source. The monolayer WSe2 is placed on top of the dielectric rod structure with a nanogap that induces a local tensile strain. As shown in the schematic of the bandgap of WSe2 (Figure 5b), the nanogap can generate a spatially modulated artificial potential well through a tensile strain-induced perturbation of quantized energy states. Interestingly, the saddle-shaped monolayer WSe2 is formed at the nanogap site (Figure 5c). The dominant direction of elongation is defined according to the nanogap size: the monolayer WSe2 is elongated along the x-axis (y-axis) if the nanogap is relatively narrow (wide). The exciton oscillation occurs along the elongation axis.
To experimentally demonstrate the array of single photon emitters, we first fabricated Si3N4 rod structures with different gaps (d) and widths (w) on an SiO2/Si substrate using electron-beam lithography and reactive ion etching. Figure 5d shows a SEM image of the fabricated Si3N4 rod structures. The value of d gradually changed from 60 nm (upper region) to 140 nm (lower region). Monolayer WSe2 flakes were then transferred to the rod structures using the polydimethylsiloxane (PDMS) stamping method (Figure 5e). The measured PL intensity map of the strained monolayer WSe2 at 4 K showed bright spots at most of the nanogap sites of the Si3N4 rod structures, which exhibited PL intensities >10 times stronger than those of the surrounding areas with no gaps (Figure 5f). The submicron-sized localized emission spot (~200 nm in size) and significant PL enhancement at the nanogap site were due to the exciton confinement resulting from the funneling effect. Next, to verify the single photon feature of the emission, the second-order correlation function g(2)(τ) of a strong emission was measured. g(2)(τ) was measured and fit with a three-level model (Figure 5g). The value of g(2)(0) was 0.108 ± 0.041, which indicates photon anti-bunching.
Figure 5. Strain-coupled single photon source formed by nanogap-suspended 2D WSe2. (a) Schematic of a single photon source consisting of monolayer WSe2 and the dielectric rod structure with a nanogap. (b) Energy bandgap diagram along the x-axis. (c) Schematics of the deformed monolayer WSe2 due to the nanogap. The saddle-shaped deformation occurs along the x-axis (y-axis) for the narrow (wide) nanogap. The exciton oscillation is aligned with the elongation direction. (d) SEM image of the fabricated Si3N4 rod structure array with nanogaps. Scale bar, 10 μm. The inset shows a magnified SEM image of a nanogap. Scale bar, 100 nm. (e) Optical microscope image captured after the monolayer WSe2 flakes were transferred onto the Si3N4 rod structures. The boundary of the monolayer WSe2 is indicated by red dashed lines. Scale bar, 5 μm. (f) Measured PL intensity map for the structure in (e). Scale bar, 5 μm. (g) Measured photon correlation function g(2) of the highest peak at 737.19 nm.
7. Summary and outlook
We have discussed deformation engineering of 2D vdW materials in a variety of morphology, dimensionality, and interfacial characteristics. 2D materials transferred on pre-patterned 3D nano/micro-structured substrate can be either suspended, partially deformed, or conformally contacted to the underlying substrate depending on the geometry and aspect ratio of the 3D structure, while stepwise swelling-shrinking-adaptation can further enhance the interfacial integrity in high aspect ratio structure. In addition, modulus mismatch between 2D material and soft substrate offers opportunities to explore buckle delaminated crumpling or conformal wrinkling of 2D materials. The periodic wrinkle/crumple structures with multiple length scales were highlighted for mechanical stretchability and corresponding electronic, optical, and thermal functionalities. Kirigami-inspired 2D materials are aimed for strain-insensitive electrical performance of 2D electrodes and transistors, while mechanical modeling and calculation is also critical for rational design of strain redistribution across the out-of-plane deformed structure. In addition, we highlighted the interfacial 2D materials in-between flexible substrate and metallic thin film. Inserting 2D vdW layer allowed for modified deformation of metal thin film (i.e., flat to buckle delaminated geometry), which guided the crack propagation and widening behavior under high bending strain. Lastly, we discussed strain-coupled phenomena of 2D vdW materials, with an example of single photon emitters in strained WSe2 on nanogap structure. It was crucial to design the deformation morphology and dimension for deterministic control of position and polarization of the 2D quantum emitters.
In addition to the research progress thus far, there are several perspectives that may enrich future research on deformation engineering of 2D vdW materials. First of all, diversifying the material palettes for deformation engineering beyond graphene and few transition metal dichalcogenides (TMDs) is crucial as it will open up new opportunities for tuning various functionalities beyond optical and electronic applications. Second, extended experimental control over strain and interfacial adhesion in multiple energy and length scales is on demand for more effective and versatile deformation engineering of the 2D vdW materials. Lastly, expanding the capabilities of controlled deformation of 2D materials will also require the development of deformation strategies compatible with varying temperature/pressure conditions, chemical environment (e.g., fluid, reactive gas), and dynamic modulation (e.g., vibration, surface acoustic wave).
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