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(a) Raman spectrum around the 2D peak along the y-direction highlighted in Figure 3o (at Va = 50 V). (b) ω2D along the y-direction as shown in Figure 3o (see cross for end point) for different applied potentials Va. The black dashed line indicates the maximum strain gradient. (c) Γ2D shows a strong inhomogeneous broadening at the positions where the strain gradient in panel (b) is maximum. (d) To quantify the strain gradient in the grey shaded area in panels (b) and (c), we convolute a piecewise linear function with width d (arrow) with the laser spot. The fit result gives us a width d of 325 nm, which corresponds to a gradient ∂ω2D/∂y = 117 cm −1 /µm or ∂/∂y = 1.4 %/µm at Va = 50 V.
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There are a number of theoretical proposals based on strain engineering of graphene and other two-dimensional materials, however purely mechanical control of strain fields in these systems has remained a major challenge. The two approaches mostly used so far either couple the electrical and mechanical properties of the system simultaneously or intr...
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... pink line shows that the force obtained using the parallel plate approximation for the capacitance is in good agreement with the simulation for displacements up to 10 nm. Please note that 2η = 8.7 ± 0.5 nF/m for these devices, as they had a slightly different design than the devices shown in Supplementary Figure 2 Supplementary Figure 4. Raman pre-characterization. (a) Raman map of the silicon peak area at 521 cm −1 superimposed with a Raman map of the 2D peak area, which has been obtained as follows. ...
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... Many different methods to control strain in 2D materials have been implemented. 7 Examples include controlled wrinkling or buckling, [8][9][10] exfoliating 2D materials onto bendable flexible substrates, 1,11,12 inducing bubbles with differential pressure, 13,14 applying force from scanning probe tips, [15][16][17][18] using microelectromechanical devices (MEMS), [19][20][21] and through applying gate-controllable strain through the use of piezoelectric dielectrics. [22][23][24] Each technique has its unique advantages and disadvantages, but for straintronic devices, we desire a method to apply large-magnitude electric-field controllable nanoscale strain in a scalable device structure. ...
Two-dimensional materials, such as transition metal dichalcogenides, have generated much interest due to their strain-sensitive electronic, optical, magnetic, superconducting, or topological properties. Harnessing control over their strain state may enable new technologies that operate by controlling these materials’ properties in devices such as straintronic transistors. Piezoelectric oxides have been proposed as one method to control such strain states on the device scale. However, there are few studies of how conformal 2D materials remain on oxide materials with respect to dynamic applications of the strain. Non-conformality may lead to non-optimal strain transfer. In this work, we explore this aspect of oxide-2D adhesion in the nanoscale switching of the substrate structural phase in thin 1T′-MoTe 2 attached to a mixed-phase thin-film BiFeO 3 (BFO), a multiferroic oxide with an electric-field induced structural phase transition that can generate mechanical strains of up to 2%. We observe that flake thickness impacts the conformality of 1T′-MoTe 2 to structural changes in BFO, but below four layers, 1T′-MoTe 2 fully conforms to the nanoscale BFO structural changes. The conformality of few-layer 1T′-MoTe 2 suggests that BFO is an excellent candidate for deterministic, nanoscale strain control for 2D materials.
... Moreover, it has been established that anisotropic electronic and optical properties of both SnS and SnSe materials are sensitive to applied inplane strain [27][28][29][30]. In brief, advancement in fabrication of vertical heterojunction [31] and strain engineering are now well adopted for tuning electronic and optical properties of inorganic 2D semiconductor based devices [32][33][34]. ...
Strain engineering of two-dimensional materials provides specific regulation method for the crystal structure, electric transport behavior and hence thermoelectric properties. Since the layer components of the van der Waals heterojunction exhibit discrepant response to strains, it provides a platform for manipulation of emergent electronic and thermoelectric properties. Here, motivated by the promising thermoelectric materials SnSe and its analogue, we design a specific high-promising thermoelectric candidate based on SnSe-SnS heterostructures, focusing on the strain induced asymmetric bonding-transition and its effect on thermoelectric properties. The compressed SnS/SnSe hetero-bilayer shows significantly enhanced anisotropic electrical transport properties, due to depressed carrier scattering rate along the robust weak bonding direction. In this armchair direction, extremely high power factor values (3600 μW/cm·K2 for n-type and 4000 μW/cm·K2 for p-type) are predicted at ∼10²¹ cm⁻³ at 700 K. We obtain a new state-of-the-art thermoelectric material with extremely high thermoelectric power factor and pave the way for strain engineering of thermoelectric van der Waals heterostructures with robust in-plane weak bonding.
... Two-dimensional Raman mapping ( Fig. 2(a), inset) was used to confirm the periodic nature of our strained nanopillar array. The measured 2D Raman peak shift of 85.2 cm -1 is greater than previously reported values for deformed graphene on nanostructured surfaces [14][15][16][17] , confirming the superiority of our strain engineering platform. Local strain distribution based on experimentally determined topographic information is depicted in Figure 2(b). ...
... We will show that above a certain strain level, the energy dissipation starts to be dominated by dislocation dynamics. Tuning strain in a graphene resonator has been done in previous works [7][8][9][10][11][12] . In most works, the tuning is achieved by changing the electrostatic force imposed vertically to the graphene plane 7 . ...
... 1 predicts the resonance frequency approaches zero at very small strain, however, the experiment data begins with a non-zero frequency. The discrepancy comes from the fact that the equation assumes zero bending stiffness of the graphene ribbon, while in reality, as observed in a number of previous works 7,9,18,19 , the edges of free-standing graphene sheets are usually folded like a scroll, which significantly increased the bending stiffness. We find the folded edges also significantly contribute to the energy dissipation during vibration, which we will discuss next. ...
In crystalline materials, the creation and modulation of dislocations are often associated with plastic deformation and energy dissipation. Here we report a study on the energy dissipation of a trilayer graphene ribbon resonator. The vibration of the ribbon generates cyclic mechanical loading to the graphene ribbon, during which mechanical energy is dissipated as heat. Measuring the quality factor of the graphene resonator provides a way to evaluate the energy dissipation. The graphene ribbon is integrated with silicon micro actuators, allowing its in-plane tension to be finely tuned. As we gradually increased the tension, we observed, in addition to the well-known resonance frequency increase, a large change in the energy dissipation. We propose that the dominating energy dissipation mechanism shifts over three regions. With small applied tension, the graphene is in elastic region, and the major energy dissipation is through graphene edge folding; as the tension increases, dislocations start to develop in the sample to gradually dominate the energy dissipation; finally, at large enough tension, graphene layers become decoupled and start to slide and cause friction, which induces the more severe energy dissipation. The generation and modulation of dislocations are modeled by molecular dynamics calculation and a method to count the energy loss is proposed and compared to the experiment.
... A typical strain-engineered graphene nanostructure array and the key concept for the generation of pseudo-magnetic fields are illustrated in Fig. 1a, b. A monolayer graphene sheet was forced to conform to the topography of the nanopillar array using capillary force (see Methods and Supplementary Note 1 for the detailed fabrication procedure) [21][22][23][24][25] . Graphene's excellent mechanical property 4 allows the accumulation of a large tensile strain at the edges of nanopillars 10 . ...
... The measured 2D Raman peak shift of~85.2 cm −1 is larger than other reported values for deformed graphene on nanostructured substrates [22][23][24][25] , demonstrating the excellence of our strain engineering platform (see Supplementary Note 2 for more details on G and 2D peak shift analyses). Figure 2b shows the local strain distribution based on the experimentally obtained topographic information (see Supplementary Note 3 for the strain calculation). ...
The creation of pseudo-magnetic fields in strained graphene has emerged as a promising route to investigate intriguing physical phenomena that would be unattainable with laboratory superconducting magnets. The giant pseudo-magnetic fields observed in highly deformed graphene can substantially alter the optical properties of graphene beyond a level that can be feasible with an external magnetic field, but the experimental signatures of the influence of such pseudo-magnetic fields have yet to be unveiled. Here, using time-resolved infrared pump-probe spectroscopy, we provide unambiguous evidence for slow carrier dynamics enabled by the pseudo-magnetic fields in periodically strained graphene. Strong pseudo-magnetic fields of ~100 T created by non-uniform strain in graphene on nanopillars are found to significantly decelerate the relaxation processes of hot carriers by more than an order of magnitude. Our findings offer alternative opportunities to harness the properties of graphene enabled by pseudo-magnetic fields for optoelectronics and condensed matter physics.
... If the amplitude of the membrane becomes even larger, it can rupture. For this yield strain we take a conservative value of breaking strain [188]: ϵ b = 1.2 %. By rewriting equation (A.2) in terms of an effective deflection induced tension, n eff = 2Yhw 2 c 3R 2 (1−ν) such that F p = 4(n 0 + n eff )w c , and using n eff,b = Yhϵ b /(1 − ν), we obtain as rough estimate for the breaking strain amplitude w c,b : ...
The dynamics of suspended two-dimensional (2D) materials has received increasing attention during the last decade, yielding new techniques to study and interpret the physics that governs the motion of atomically thin layers. This has led to insights into the role of thermodynamic and nonlinear effects as well as the mechanisms that govern dissipation and stiffness in these resonators. In this review, we present the current state-of-the-art in the experimental study of the dynamics of 2D membranes. The focus will be both on the experimental measurement techniques and on the interpretation of the physical phenomena exhibited by atomically thin membranes in the linear and nonlinear regimes. We will show that resonant 2D membranes have emerged both as sensitive probes of condensed matter physics in ultrathin layers, and as sensitive elements to monitor small external forces or other changes in the environment. New directions for utilizing suspended 2D membranes for material characterization, thermal transport, and gas interactions will be discussed and we conclude by outlining the challenges and opportunities in this upcoming field.
... The device was fabricated by an electron-beam lithography (EBL) based structuring of a Cr/Au/Cr hard mask on a silicon-on-insulator substrate consisting of 725 µm silicon, 1 µm SiO 2 and 2 µm highly pdoped silicon followed by a deep reactive ion etching (DRIE) step, as described in detail in [35,36] and in the supplementary note 1 (available online at stacks.iop.org/2DM/8/035039/mmedia). The silicon beam (SB), which also operates as a bottom electrostatic gate for tuning the graphene membrane, was fabricated by interrupting the DRIE step after etching 275 nm deep followed by the deposition of an additional Cr mask before etching completely through the highly p-doped silicon layer. After removal of the Cr layer, a graphene/PMMA stack is transferred on the patterned comb-drive (CD) actuator. ...
... A potential difference V a between the asymmetrically placed fingers of the CD actuator gives rise to an electrostatic force, F a = 1 2 ∂ x C a V 2 a that pulls the suspended comb in the x-direction (see figure 1(d)) and white arrow in figure 1(b). Here, the capacitance C a and ∂ x C a are given by the zeroth and the first order term in the displacement δx of the actuator in a series expansion of the parallel plate approximation for the capacitance between its fingers [35]. ...
... To understand the physical origin of the different resonances, we extract the effective masses and spring constants of the resonances from the tuning of the resonance frequencies with applied electrostatic potentials. Here, we slowly sweep the DC voltages up to a value +V g , V a , then sweep to −V g , V a and then back to 0 V, similarly as in [35]. As we did not see any hysteresis in the measurement presented here, we conclude that slipping at side walls and or clamping points does not play any role. ...
Coupled nanomechanical resonators are interesting for both fundamental studies and practical applications as they offer rich and tunable oscillation dynamics. At present, the coupling in such systems is mediated by a fixed geometric contact or static clamping between the resonators. Here we show a graphene-based electromechanical system consisting of two physically separated mechanical resonators -- a comb-drive actuator and a suspended silicon beam -- that are tunably coupled by an integrated graphene membrane. The graphene membrane, moreover, provides a sensitive electrical read-out for the two resonating systems showing 16 different modes in the frequency range from 0.4 to 24 MHz. In addition, by pulling on the graphene membrane with an electrostatic potential applied to the silicon beam, we control the coupling, quantified by the g-factor, from 20 kHz to 100 kHz. Our results pave the way for coupled nanoelectromechanical systems requiring controllable mechanically coupled resonators.
... Figure 1 shows the design of our silicon-based MEMS device for engineering strain fields in graphene, which is based on the design presented in Refs. [7][8][9]. The actuator consists of two interdigitated combs. ...
... Here, is a constant related to the capacitance of the combs and k is the spring constant of the combined graphene-clamping-silicon geometry. The actuators presented here are improved compared to our previous works [7,8] in two respects: (i) we include additional gold-coated contact areas for multi-terminal transport measurements and (ii) we optimized the clamping geometry (see Figure 2) for creating local strain hot spots and strain gradients, which is imperative for the observation of pseudomagnetic fields and valley-effects [2]. To conduct transport measurements, we also fabricate a local gate, over which the graphene flake is suspended. ...
... The fabrication of these devices follows the procedure previously reported in Refs. [7][8][9]. We start with a silicon-on-insulator (SOI) substrate with a 2 µm thick, chemical vapor deposition-grown, highly doped silicon layer. ...
Here, we present a micro-electromechanical system (MEMS) for the investigation of the electromechanical coupling in graphene and potentially related 2D materials. Key innovations of our technique include: (1) the integration of graphene into silicon-MEMS technology; (2) full control over induced strain fields and doping levels within the graphene membrane and their characterization via spatially resolved confocal Raman spectroscopy; and (3) the ability to detect the mechanical coupling of the graphene sheet to the MEMS device with via their mechanical resonator eigenfrequencies.
... Bubbles have also been applied for 2D material strain engineering because of their versatile fabrication and characterization methods, as detailed earlier. Furthermore, straining atomically thin 2D materials through the inflation or deflation of bubbles is a relatively simple and easy-to-observe process compared with conventional techniques such as point loading by AFM or micro-mechanical loading frames [82,83]. Bulged 2D materials can achieve a considerable strain level, which can be controlled by the degree of inflation [80,84]. ...
When 2D materials are supported by substrates, matter trapped at the interface can coalesce to form nano- and microscale bubbles. These bubbles often negatively impact the performance of 2D material devices as they impede charge/photon/phonon transport across the interface. The difficulties created by these bubbles spurred research to understand how they form, whether their formation can be controlled, and what kind of matter is trapped inside them. These 2D material bubbles have since been exploited for novel chemistry and physics because of their ability to pressurize the trapped matter and strain the confining 2D material. The fabrication, characterization, and applications of 2D material bubbles are summarized in this review.
... However, the impact of local deformations on the global strain is not well understood. A direct way to systematically introduce strain into 2D materials is by generating intrinsic and extrinsic point defects, as strain fields emanate from the distortion in the lattice [14,15]. These * Corresponding author: aitkaliyeva@mse.ufl.edu ...
We investigate the nature of strain in MoS2 and correlate it to defect types and densities, while systematically assessing the tolerance of this low dimensional material to He and Au ion irradiations. Through a series of theoretical predictions and experimental observations, we establish the onset of the crystalline-to-amorphous transition in MoS2 and identify sulfur vacancies as the most favorable defects introduced during irradiation. We note the presence of both tensile and compressive strains, which depend on the types of defects introduced into the lattice and vary with increasing fluence. The results show that defects can be used to tune strain in two-dimensional materials and provide an exciting pathway for using external stimuli to control properties of low dimensional materials.
