Stretchable Thin-Film Transistors Based on Wrinkled Graphene and MoS2 Heterostructures.

Two-dimensional (2D) materials are outstanding candidates for stretchable electronics, but a significant challenge is their heterogeneous integration into stretchable geometries on soft substrates. Here, we demonstrate a strategy for stretchable thin film transistors (2D S-TFT) based on wrinkled heterostructures on elastomer substrates where 2D materials formed the gate, source, drain, and channel and characterized them with Raman spectroscopy and transport measurements. The 2D S-TFTs had initial mobility of 4.9 ± 0.7 cm2/(V s). The wrinkling reduced the strain transferred into the 2D materials by a factor of 50, allowing a substrate stretch of up to 23% that could be cycled thousands of times without electrical degradation. The stretch did not alter the mobility but did lead to strain-induced threshold voltage shifts by ΔVT = -1.9 V. These 2D S-TFTs form the foundation for stretchable integrated circuits and enable investigations of the impact of heterogeneous strain on electron transport.

Exfoliable Transition Metal Chalcogenide Semiconductor NbSe2I2.

As the field of exfoliated van der Waals electronics grows to include complex heterostructures, the variety of available in-plane symmetries and geometries becomes increasingly valuable. In this work, we present an efficient chemical vapor transport synthesis of NbSe2I2 with the triclinic space group P1̅. This material contains Nb-Nb dimers and an in-plane crystallographic angle γ = 61.3°. We show that NbSe2I2 can be exfoliated down to few-layer and monolayer structures and use Raman spectroscopy to test the preservation of the crystal structure of exfoliated thin films. The crystal structure was verified by single-crystal and powder X-ray diffraction methods. Density functional theory calculations show triclinic NbSe2I2 to be a semiconductor with a band gap of around 1 eV, with similar band structure features for bulk and monolayer crystals. The physical properties of NbSe2I2 have been characterized by transport, thermal, optical, and magnetic measurements, demonstrating triclinic NbSe2I2 to be a diamagnetic semiconductor that does not exhibit any phase transformation below room temperature.

Role of Interfacial Interactions in the Graphene-Directed Assembly of Monolayer Conjugated Polymers.

Development of graphene-organic hybrid electronics is one of the most promising directions for next-generation electronic materials. However, it remains challenging to understand the graphene-organic semiconductor interactions right at the interface, which is key to designing hybrid electronics. Herein, we study the influence of graphene on the multiscale morphology of solution-processed monolayers of conjugated polymers (PII-2T, DPP-BTz, DPP2T-TT, and DPP-T-TMS). The strong interaction between graphene and PII-2T was manifested in the high fiber density and high film coverage of monolayer films deposited on graphene compared to plasma SiO2 substrates. The monolayer films on graphene also exhibited a higher relative degree of crystallinity and dichroic ratio or polymer alignment, i.e., higher degree of order. Raman spectroscopy revealed the increased backbone planarity of the conjugated polymers upon deposition on graphene as well as the existence of electronic interaction across the interface. This speculation was further substantiated by the results of photoelectron spectroscopy (XPS and UPS) of PII-2T, which showed a decrease in binding energy of several atomic energy levels, movement of the Fermi level toward HOMO, and an increase in work function, all of which indicate p-doping of the polymer. Our results provide a new level of understanding on graphene-polymer interactions at nanoscopic interfaces and the consequent impact on multiscale morphology, which will aid in the design of efficient graphene-organic hybrid electronics.

Dissipation from Interlayer Friction in Graphene Nanoelectromechanical Resonators.

A unique feature of two-dimensional (2D) materials is the ultralow friction at their van der Waals interfaces. A key question in a new generation of 2D heterostructure-based nanoelectromechanical systems (NEMS) is how the low friction interfaces will affect the dynamic performance. Here, we apply the exquisite sensitivity of graphene nanoelectromechanical drumhead resonators to compare the dissipation from monolayer, Bernal-stacked bilayer, and twisted bilayer graphene membranes. We find a significant difference in the average quality factors of three resonator types: 53 for monolayer, 40 for twisted and 31 for Bernal-stacked membranes. We model this difference as a combination of change in stiffness and additional dissipation from interlayer friction during motion. We find even the lowest frictions measured on sliding 2D interfaces are sufficient to alter dissipation in 2D NEMS. This model provides a generalized approach to quantify dissipation in NEMS based on 2D heterostructures which incorporate interlayer slip and friction.

Buckling-Mediated Phase Transitions in Nano-Electromechanical Phononic Waveguides.

Waveguides for mechanical signal transmission in the megahertz to gigahertz regimes enable on-chip phononic circuitry, which brings new capabilities complementing photonics and electronics. Lattices of coupled nano-electromechanical drumhead resonators are suitable for these waveguides due to their high Q-factor and precisely engineered band structure. Here, we show that thermally induced elastic buckling of such resonators causes a phase transition in the waveguide leading to reversible control of signal transmission. Specifically, when cooled, the lowest-frequency transmission band associated with the primary acoustic mode vanishes. Experiments show the merging of the lower and upper band gaps, such that signals remain localized at the excitation boundary. Numerical simulations show that the temperature-induced destruction of the pass band is a result of inhomogeneous elastic buckling, which disturbs the waveguide's periodicity and suppresses the wave propagation. Mechanical phase transitions in waveguides open opportunities for drastic phononic band reconfiguration in on-chip circuitry and computing.

Tailoring Single- and Double-Sided Fluorination of Bilayer Graphene via Substrate Interactions.

While many technologies rely on multilayer heterostructures, most of the studies on chemical functionalization have been limited to monolayer graphene. In order to use functionalization in multilayer systems, we must first understand the interlayer interactions between functionalized and nonfunctionalized (intact) layers and how to selectively functionalize one layer at a time. Here, we demonstrate a method to fabricate single- or double-sided fluorinated bilayer graphene (FBG) by tailoring substrate interactions. Both the top and bottom surfaces of bilayer graphene on the rough silicon dioxide (SiO2) are fluorinated; meanwhile, only the top surface of graphene on hexagonal boron nitride (hBN) is fluorinated. The functionalization type affects electronic properties; double-sided FBG on SiO2 is insulating, whereas single-sided FBG on hBN maintains conducting, showing that the intact bottom layer becomes electrically decoupled from the fluorinated top insulating layer. Our results define a straightforward method to selectively functionalize the top and bottom surfaces of bilayer graphene.

Author Correction: Ultrasoft slip-mediated bending in few-layer graphene.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Ultrasoft slip-mediated bending in few-layer graphene.

Continuum scaling laws often break down when materials approach atomic length scales, reflecting changes in their underlying physics and the opportunities to access unconventional properties. These continuum limits are evident in two-dimensional materials, where there is no consensus on their bending stiffnesses or how they scale with thickness. Through combined computational and electron microscopy experiments, we measure the bending stiffness of graphene, obtaining 1.2-1.7 eV for a monolayer. Moreover, we find that the bending stiffness of few-layer graphene decreases sharply as a function of bending angle, tuning by almost 400% for trilayer graphene. This softening results from shear, slip and the onset of superlubricity between the atomic layers and corresponds with a gradual change in scaling power from cubic to linear. Our results provide a unified model for bending in two-dimensional materials and show that their multilayers can be orders of magnitude softer than previously thought, among the most flexible electronic materials currently known.

Stochastic Stress Jumps Due to Soliton Dynamics in Two-Dimensional van der Waals Interfaces.

The creation and movement of dislocations determine the nonlinear mechanics of materials. At the nanoscale, the number of dislocations in structures become countable, and even single defects impact material properties. While the impact of solitons on electronic properties is well studied, the impact of solitons on mechanics is less understood. In this study, we construct nanoelectromechanical drumhead resonators from Bernal stacked bilayer graphene and observe stochastic jumps in frequency. Similar frequency jumps occur in few-layer but not twisted bilayer or monolayer graphene. Using atomistic simulations, we show that the measured shifts are a result of changes in stress due to the creation and annihilation of individual solitons. We develop a simple model relating the magnitude of the stress induced by soliton dynamics across length scales, ranging from <0.01 N/m for the measured 5 µm diameter to ∼1.2 N/m for the 38.7 nm simulations. These results demonstrate the sensitivity of 2D resonators are sufficient to probe the nonlinear mechanics of single dislocations in an atomic membrane and provide a model to understand the interfacial mechanics of different kinds of van der Waals structures under stress, which is important to many emerging applications such as engineering quantum states through electromechanical manipulation and mechanical devices like highly tunable nanoelectromechanical systems, stretchable electronics, and origami nanomachines.

Monolayer MoS2 Nanoribbon Transistors Fabricated by Scanning Probe Lithography.

Monolayer MoS2 is a promising material for nanoelectronics; however, the lack of nanofabrication tools and processes has made it very challenging to realize nanometer-scale electronic devices from monolayer MoS2. Here, we demonstrate the fabrication of monolayer MoS2 nanoribbon field-effect transistors as narrow as 30 nm using scanning probe lithography (SPL). The SPL process uses a heated nanometer-scale tip to deposit narrow nanoribbon polymer structures onto monolayer MoS2. The polymer serves as an etch mask during a XeF2 vapor etch, which defines the channel of a field-effect transistor (FET). We fabricated seven devices with a channel width ranging from 30 to 370 nm, and the fabrication process was carefully studied by electronic measurements made at each process step. The nanoribbon devices have a current on/off ratio > 104 and an extrinsic field-effect mobility up to 8.53 cm2/(V s). By comparing a 30 nm wide device with a 60 nm wide device that was fabricated on the same MoS2 flake, we found the narrower device had a smaller mobility, a lower on/off ratio, and a larger subthreshold swing. To our knowledge, this is the first published work that describes a working transistor device from monolayer MoS2 with a channel width smaller than 100 nm.

Nano-electromechanical Drumhead Resonators from Two-Dimensional Material Bimorphs.

Atomic membranes of monolayer 2D materials represent the ultimate limit in the size of nano-electromechanical systems. However, new properties and new functionalities emerge by looking at the interface between layers in heterostructures of 2D materials. Here, we demonstrate the integration of 2D heterostructures as tunable nano-electromechanical systems, exploring the competition between the mechanics of the ultrathin membrane and the incommensurate van der Waals interface. We fabricate electrically contacted 5 or 6 µm circular drumheads of suspended heterostructure membranes of monolayer graphene on monolayer molybdenum disulfide (MoS2), which we call a 2D bimorph. We characterize the mechanical resonance through electrostatic actuation and laser interferometry detection. The 2D bimorphs have resonance frequencies of 5-20 MHz and quality factors of 50-700, comparable to resonators from monolayer or few-layer 2D materials. The frequencies and eigenmode shapes of the higher harmonics display split degenerate modes, showing that the 2D bimorphs behave as membranes with asymmetric tension. The devices display dynamic ranges of 44 dB, with an additional nonlinearity in the dissipation at small drive. Under electrostatic frequency tuning, devices display a small tuning of ∼20% compared with graphene resonators, which have >100%. In addition, the tuning shows a kink that deviates from the tensioned membrane model for atomic membranes and corresponds with a changing in stress of 14 mN/m. A model that accounts for this tuning behavior is the onset of interlayer slip in the heterostructure, allowing the tension in the membrane to relax. Using density functional theory simulations, we find that the change in stress at the kink is much larger than the predicted energy barrier for interlayer slip of 0.102 mN/m in an incommensurate 2D heterostructure but smaller than the energy barrier for an aligned graphene bilayer of 35 mN/m, suggesting a local pinning effect at ripples or folds in the heterostructure. Finally, we observe an asymmetry in tuning of the full width at half-maximum that does not exist in monolayer resonators. These findings demonstrate a new class of nano-electromechanical systems from 2D heterostructures and unravel the complex interaction of membrane morphology versus interlayer adhesion and slip on the mechanics of incommensurate van der Waals interfaces.

Grains and grain boundaries in single-layer graphene atomic patchwork quilts.

The properties of polycrystalline materials are often dominated by the size of their grains and by the atomic structure of their grain boundaries. These effects should be especially pronounced in two-dimensional materials, where even a line defect can divide and disrupt a crystal. These issues take on practical significance in graphene, which is a hexagonal, two-dimensional crystal of carbon atoms. Single-atom-thick graphene sheets can now be produced by chemical vapour deposition on scales of up to metres, making their polycrystallinity almost unavoidable. Theoretically, graphene grain boundaries are predicted to have distinct electronic, magnetic, chemical and mechanical properties that strongly depend on their atomic arrangement. Yet because of the five-order-of-magnitude size difference between grains and the atoms at grain boundaries, few experiments have fully explored the graphene grain structure. Here we use a combination of old and new transmission electron microscopy techniques to bridge these length scales. Using atomic-resolution imaging, we determine the location and identity of every atom at a grain boundary and find that different grains stitch together predominantly through pentagon-heptagon pairs. Rather than individually imaging the several billion atoms in each grain, we use diffraction-filtered imaging to rapidly map the location, orientation and shape of several hundred grains and boundaries, where only a handful have been previously reported. The resulting images reveal an unexpectedly small and intricate patchwork of grains connected by tilt boundaries. By correlating grain imaging with scanning probe and transport measurements, we show that these grain boundaries severely weaken the mechanical strength of graphene membranes but do not as drastically alter their electrical properties. These techniques open a new window for studies on the structure, properties and control of grains and grain boundaries in graphene and other two-dimensional materials.

Energy Transfer from Quantum Dots to Graphene and MoS2: The Role of Absorption and Screening in Two-Dimensional Materials.

We report efficient nonradiative energy transfer (NRET) from core-shell, semiconducting quantum dots to adjacent two-dimensional sheets of graphene and MoS2 of single- and few-layer thickness. We observe quenching of the photoluminescence (PL) from individual quantum dots and enhanced PL decay rates in time-resolved PL, corresponding to energy transfer rates of 1-10 ns(-1). Our measurements reveal contrasting trends in the NRET rate from the quantum dot to the van der Waals material as a function of thickness. The rate increases significantly with increasing layer thickness of graphene, but decreases with increasing thickness of MoS2 layers. A classical electromagnetic theory accounts for both the trends and absolute rates observed for the NRET. The countervailing trends arise from the competition between screening and absorption of the electric field of the quantum dot dipole inside the acceptor layers. We extend our analysis to predict the type of NRET behavior for the near-field coupling of a chromophore to a range of semiconducting and metallic thin film materials.

In-Plane Anisotropy in Mono- and Few-Layer ReS2 Probed by Raman Spectroscopy and Scanning Transmission Electron Microscopy.

Rhenium disulfide (ReS2) is a semiconducting layered transition metal dichalcogenide that exhibits a stable distorted 1T phase. The reduced symmetry of this system leads to in-plane anisotropy in various material properties. Here, we demonstrate the strong anisotropy in the Raman scattering response for linearly polarized excitation. Polarized Raman scattering is shown to permit a determination of the crystallographic orientation of ReS2 through comparison with direct structural analysis by scanning transmission electron microscopy (STEM). Analysis of the frequency difference of appropriate Raman modes is also shown to provide a means of precisely determining layer thickness up to four layers.

Electrical Tuning of Exciton Binding Energies in Monolayer WS_{2}.

We demonstrate continuous tuning of the exciton binding energy in monolayer WS_{2} by means of an externally applied voltage in a field-effect transistor device. Using optical spectroscopy, we monitor the ground and excited excitonic states as a function of gate voltage and track the evolution of the quasiparticle band gap. The observed decrease of the exciton binding energy over the range of about 100 meV, accompanied by the renormalization of the quasiparticle band gap, is associated with screening of the Coulomb interaction by the electrically injected free charge carriers at densities up to 8×10^{12} cm^{-2}. Complete ionization of the excitons due to the electrical doping is estimated to occur at a carrier density of several 10^{13} cm^{-2}.

Fluctuation broadening in carbon nanotube resonators.

We simulated the behavior of suspended carbon nanotube resonators over a broad range of temperatures to explore the physics of semiflexible polymers in underdamped environments. We find that thermal fluctuations induce strong coupling between resonance modes. This effect leads to spectral fluctuations that readily account for the experimentally observed quality factors Q ∼ 100 at 300 K. Using a mean-field approach to describe fluctuations, we analytically calculate Q and frequency shifts in tensioned and buckled carbon nanotubes and find excellent agreement with simulations.

Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist.

Molybdenum disulfide bilayers with well-defined interlayer twist angle were constructed by stacking single-crystal monolayers. Varying interlayer twist angle results in strong tuning of the indirect optical transition energy and second-harmonic generation and weak tuning of direct optical transition energies and Raman mode frequencies. Electronic structure calculations show the interlayer separation changes with twist due to repulsion between sulfur atoms, resulting in shifts of the indirect optical transition energies. These results show that interlayer alignment is a crucial variable in tailoring the properties of two-dimensional heterostructures.

Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide.

Recent progress in large-area synthesis of monolayer molybdenum disulphide, a new two-dimensional direct-bandgap semiconductor, is paving the way for applications in atomically thin electronics. Little is known, however, about the microstructure of this material. Here we have refined chemical vapour deposition synthesis to grow highly crystalline islands of monolayer molybdenum disulphide up to 120 µm in size with optical and electrical properties comparable or superior to exfoliated samples. Using transmission electron microscopy, we correlate lattice orientation, edge morphology and crystallinity with island shape to demonstrate that triangular islands are single crystals. The crystals merge to form faceted tilt and mirror twin boundaries that are stitched together by lines of 8- and 4-membered rings. Density functional theory reveals localized mid-gap states arising from these 8-4 defects. We find that mirror twin boundaries cause strong photoluminescence quenching whereas tilt boundaries cause strong enhancement. Meanwhile, mirror twin boundaries slightly increase the measured in-plane electrical conductivity, whereas tilt boundaries slightly decrease the conductivity.

Valley splitting and polarization by the Zeeman effect in monolayer MoSe2.

We have measured circularly polarized photoluminescence in monolayer MoSe2 under perpendicular magnetic fields up to 10 T. At low doping densities, the neutral and charged excitons shift linearly with field strength at a rate of ∓0.12 meV/T for emission arising, respectively, from the K and K' valleys. The opposite sign for emission from different valleys demonstrates lifting of the valley degeneracy. The magnitude of the Zeeman shift agrees with predicted magnetic moments for carriers in the conduction and valence bands. The relative intensity of neutral and charged exciton emission is modified by the magnetic field, reflecting the creation of field-induced valley polarization. At high doping levels, the Zeeman shift of the charged exciton increases to ∓0.18 meV/T. This enhancement is attributed to many-body effects on the binding energy of the charged excitons.