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.

Material-Dependent Evolution of Mechanical Folding Instabilities in Two-Dimensional Atomic Membranes.

Inducing and controlling three-dimensional deformations in monolayer two-dimensional materials is important for applications from stretchable electronics to origami nanoelectromechanical systems. For these applications, it is critical to understand how the properties of different materials influence the morphologies of two-dimensional atomic membranes under mechanical loading. Here, we systematically investigate the evolution of mechanical folding instabilities in uniaxially compressed monolayer graphene and MoS2 on a soft polydimethylsiloxane substrate. We examine the morphology of the compressed membranes using atomic force microscopy for compression from 0 to 33%. We find the membranes display roughly evenly spaced folds and observe two distinct stress release mechanisms under increasing compression. At low compression, the membranes delaminate to generate new folds. At higher compression, the membranes slip over the surface to enlarge existing folds. We observe a material-dependent transition between these two behaviors at a critical fold spacing of 1000 ± 250 nm for graphene and 550 ± 20 nm for MoS2. We establish a simple shear-lag model which attributes the transition to a competition between static friction and adhesion and gives the maximum interfacial static friction on polydimethylsiloxane of 3.8 ± 0.8 MPa for graphene and 7.7 ± 2.5 MPa for MoS2. Furthermore, in graphene, we observe an additional transition from standing folds to fallen folds at 8.5 ± 2.3 nm fold height. These results provide a framework to control the nanoscale fold structure of monolayer atomic membranes, which is a critical step in deterministically designing stretchable or foldable nanosystems based on two-dimensional materials.

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.

Tailoring Surface Properties via Functionalized Hydrofluorinated Graphene Compounds.

A new compound material of 2D hydrofluorinated graphene (HFG) is demonstrated whose relative hydrogen/fluorine concentrations can be tailored between the extremes of either hydrogenated graphene (HG) and fluorinated graphene (FG). The material is fabricated through subsequent exposures to indirect hydrogen plasma and xenon difluoride (XeF2 ). Controlling the relative concentration in the HFG compound enables tailoring of material properties between the extremes offered by the constituent materials and in-plane patterning produces micrometer-scale regions with different surface properties. The utility of the technique to tailor the surface wettability, surface friction, and electrical conductivity is demonstrated. HFG compounds display wettability between the extremes of pure FG with contact angle of 95° ± 5° and pure HG with contact angle of 42° ± 2°. Similarly, the HFG surface friction may be tailored between the two extremes. Finally, the HFG electrical conductivity tunes through five orders of magnitude when transitioning from FG to HG. When combined with simulation, the electrical measurements reveal the mechanism producing the compound to be a dynamic process of adatom desorption and replacement. This study opens a new class of 2D compound materials and innovative chemical patterning with applications for atomically thin 2D circuits consisting of chemically/electrically modulated regions.

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.

Author Correction: Atomically precise graphene etch stops for three dimensional integrated systems from two dimensional material heterostructures.

The original version of this Article contained an error in the second sentence of the second paragraph of the 'Electrical properties of fluorinated graphene contacts' section of the Results, which incorrectly read 'The mobility was calculated by the Drude model, µ = ne/σ where µ, n, e, and σ are the carrier mobility, carrier density, electron charge, and sheet conductivity, respectively'. The correct version states 'µ = σ/ne ' in place of 'µ = ne/σ '. This has been corrected in both the PDF and HTML versions of the Article.

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.

Atomically precise graphene etch stops for three dimensional integrated systems from two dimensional material heterostructures.

Atomically precise fabrication methods are critical for the development of next-generation technologies. For example, in nanoelectronics based on van der Waals heterostructures, where two-dimensional materials are stacked to form devices with nanometer thicknesses, a major challenge is patterning with atomic precision and individually addressing each molecular layer. Here we demonstrate an atomically thin graphene etch stop for patterning van der Waals heterostructures through the selective etch of two-dimensional materials with xenon difluoride gas. Graphene etch stops enable one-step patterning of sophisticated devices from heterostructures by accessing buried layers and forming one-dimensional contacts. Graphene transistors with fluorinated graphene contacts show a room temperature mobility of 40,000 cm2 V-1 s-1 at carrier density of 4 × 1012 cm-2 and contact resistivity of 80 Ω·µm. We demonstrate the versatility of graphene etch stops with three-dimensionally integrated nanoelectronics with multiple active layers and nanoelectromechanical devices with performance comparable to the state-of-the-art.

Correction: Eu2+-Eu3+ valence transition in double, Eu-, and Na-doped PbSe from transport, magnetic, and electronic structure studies.

Correction for 'Eu2+-Eu3+ valence transition in double, Eu-, and Na-doped PbSe from transport, magnetic, and electronic structure studies' by Bartlomiej Wiendlocha et al., Phys. Chem. Chem. Phys., 2017, 19, 9606-9616.

Eu2+-Eu3+ valence transition in double, Eu-, and Na-doped PbSe from transport, magnetic, and electronic structure studies.

The Eu atoms in Pb1-xEuxSe have long been assumed to be divalent. We show that p-type doping of this magnetic semiconductor alloy with Na can modify the effective Eu valence: a mixed, Eu2+-Eu3+ state appears in Pb1-x-yEuxNaySe at particular values of y. Magnetization, carrier concentration, resistivity, and thermopower of Pb1-x-yEuxNaySe are reported for a number of samples with different x and y. A pronounced increase in thermopower at a given carrier concentration was identified and attributed to the presence of enhanced ionized impurity scattering. A strong decrease in the hole concentration is observed in Pb1-yNaySe when Eu is added to the system, which we attribute to a Eu2+-Eu3+ self-ionization process. This is evidenced by magnetization measurements, which reveal a significant reduction of the magnetic moment of Pb1-xEuxSe upon alloying with Na. Further, a deviation of magnetization from a purely paramagnetic state, described by a Brillouin function, identifies antiferromagnetic interactions between the nearest-neighbor Eu atoms: a value of Jex/kB = -0.35 K was found for the exchange coupling parameter. The conclusion of a Eu2+-Eu3+ self-ionization process being in effect is supported further by the electronic structure calculations, which show that an instability of the 4f7 configuration of the Eu2+ ion appears with Na doping. Schematically, it was found that the Eu 4f levels form states near enough to the Fermi energy that hole doping can lower the Fermi energy and trigger a reconfiguration of a 4f electronic shell.

TRRUST: a reference database of human transcriptional regulatory interactions.

The reconstruction of transcriptional regulatory networks (TRNs) is a long-standing challenge in human genetics. Numerous computational methods have been developed to infer regulatory interactions between human transcriptional factors (TFs) and target genes from high-throughput data, and their performance evaluation requires gold-standard interactions. Here we present a database of literature-curated human TF-target interactions, TRRUST (transcriptional regulatory relationships unravelled by sentence-based text-mining, http://www.grnpedia.org/trrust), which currently contains 8,015 interactions between 748 TF genes and 1,975 non-TF genes. A sentence-based text-mining approach was employed for efficient manual curation of regulatory interactions from approximately 20 million Medline abstracts. To the best of our knowledge, TRRUST is the largest publicly available database of literature-curated human TF-target interactions to date. TRRUST also has several useful features: i) information about the mode-of-regulation; ii) tests for target modularity of a query TF; iii) tests for TF cooperativity of a query target; iv) inferences about cooperating TFs of a query TF; and v) prioritizing associated pathways and diseases with a query TF. We observed high enrichment of TF-target pairs in TRRUST for top-scored interactions inferred from high-throughput data, which suggests that TRRUST provides a reliable benchmark for the computational reconstruction of human TRNs.