Torsional force microscopy of van der Waals moirés and atomic lattices.

In a stack of atomically thin van der Waals layers, introducing interlayer twist creates a moiré superlattice whose period is a function of twist angle. Changes in that twist angle of even hundredths of a degree can dramatically transform the system's electronic properties. Setting a precise and uniform twist angle for a stack remains difficult; hence, determining that twist angle and mapping its spatial variation is very important. Techniques have emerged to do this by imaging the moiré, but most of these require sophisticated infrastructure, time-consuming sample preparation beyond stack synthesis, or both. In this work, we show that torsional force microscopy (TFM), a scanning probe technique sensitive to dynamic friction, can reveal surface and shallow subsurface structure of van der Waals stacks on multiple length scales: the moirés formed between bi-layers of graphene and between graphene and hexagonal boron nitride (hBN) and also the atomic crystal lattices of graphene and hBN. In TFM, torsional motion of an Atomic Force Microscope (AFM) cantilever is monitored as it is actively driven at a torsional resonance while a feedback loop maintains contact at a set force with the sample surface. TFM works at room temperature in air, with no need for an electrical bias between the tip and the sample, making it applicable to a wide array of samples. It should enable determination of precise structural information including twist angles and strain in moiré superlattices and crystallographic orientation of van der Waals flakes to support predictable moiré heterostructure fabrication.

Torsional periodic lattice distortions and diffraction of twisted 2D materials.

Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS2, CrI3, and WSe2/MoSe2.

Resist-Free Lithography for Monolayer Transition Metal Dichalcogenides.

Photolithography and electron-beam lithography are the most common methods for making nanoscale devices from semiconductors. While these methods are robust for bulk materials, they disturb the electrical properties of two-dimensional (2D) materials, which are highly sensitive to chemicals used during lithography processes. Here, we report a resist-free lithography method, based on direct laser patterning and resist-free electrode transfer, which avoids unintentional modification to the 2D materials throughout the process. We successfully fabricate large arrays of field-effect transistors using MoS2 and WSe2 monolayers, the performance of which reflects the properties of the pristine materials. Furthermore, using these pristine devices as a reference, we reveal that among the various stages of a conventional lithography process, exposure to a solvent like acetone changes the electrical conductivity of MoS2 the most. This new approach will enable a rational design of reproducible processes for making large-scale integrated circuits based on 2D materials and other surface-sensitive materials.

Robotic four-dimensional pixel assembly of van der Waals solids.

Van der Waals (vdW) solids can be engineered with atomically precise vertical composition through the assembly of layered two-dimensional materials1,2. However, the artisanal assembly of structures from micromechanically exfoliated flakes3,4 is not compatible with scalable and rapid manufacturing. Further engineering of vdW solids requires precisely designed and controlled composition over all three spatial dimensions and interlayer rotation. Here, we report a robotic four-dimensional pixel assembly method for manufacturing vdW solids with unprecedented speed, deliberate design, large area and angle control. We used the robotic assembly of prepatterned 'pixels' made from atomically thin two-dimensional components. Wafer-scale two-dimensional material films were grown, patterned through a clean, contact-free process and assembled using engineered adhesive stamps actuated by a high-vacuum robot. We fabricated vdW solids with up to 80 individual layers, consisting of 100 × 100 µm2 areas with predesigned patterned shapes, laterally/vertically programmed composition and controlled interlayer angle. This enabled efficient optical spectroscopic assays of the vdW solids, revealing new excitonic and absorbance layer dependencies in MoS2. Furthermore, we fabricated twisted N-layer assemblies, where we observed atomic reconstruction of twisted four-layer WS2 at high interlayer twist angles of ≥4°. Our method enables the rapid manufacturing of atomically resolved quantum materials, which could help realize the full potential of vdW heterostructures as a platform for novel physics2,5,6 and advanced electronic technologies7,8.

Wafer-scale synthesis of monolayer two-dimensional porphyrin polymers for hybrid superlattices.

The large-scale synthesis of high-quality thin films with extensive tunability derived from molecular building blocks will advance the development of artificial solids with designed functionalities. We report the synthesis of two-dimensional (2D) porphyrin polymer films with wafer-scale homogeneity in the ultimate limit of monolayer thickness by growing films at a sharp pentane/water interface, which allows the fabrication of their hybrid superlattices. Laminar assembly polymerization of porphyrin monomers could form monolayers of metal-organic frameworks with Cu2+ linkers or covalent organic frameworks with terephthalaldehyde linkers. Both the lattice structures and optical properties of these 2D films were directly controlled by the molecular monomers and polymerization chemistries. The 2D polymers were used to fabricate arrays of hybrid superlattices with molybdenum disulfide that could be used in electrical capacitors.

Near-equilibrium growth from borophene edges on silver.

Two-dimensional boron, borophene, was realized in recent experiments but still lacks an adequate growth theory for guiding its controlled synthesis. Combining ab initio calculations and experimental characterization, we study edges and growth kinetics of borophene on Ag(111). In equilibrium, the borophene edges are distinctly reconstructed with exceptionally low energies, in contrast to those of other two-dimensional materials. Away from equilibrium, sequential docking of boron feeding species to the reconstructed edges tends to extend the given lattice out of numerous polymorphic structures. Furthermore, each edge can grow via multiple energy pathways of atomic row assembly due to variable boron-boron coordination. These pathways reveal different degrees of anisotropic growth kinetics, shaping borophene into diverse elongated hexagonal islands in agreement with experimental observations in terms of morphology as well as edge orientation and periodicity. These results further suggest that ultrathin borophene ribbons can be grown at low temperature and low boron chemical potential.

Borophene Synthesis on Au(111).

Borophene (the first two-dimensional (2D) allotrope of boron) is emerging as a groundbreaking system for boron-based chemistry and, more broadly, the field of low-dimensional materials. Exploration of the phase space for growth is critical because borophene is a synthetic 2D material that does not have a bulk layered counterpart and thus cannot be isolated via exfoliation methods. Herein, we report synthesis of borophene on Au(111) substrates. Unlike previously studied growth on Ag substrates, boron diffuses into Au at elevated temperatures and segregates to the surface to form borophene islands as the substrate cools. These observations are supported by ab initio modeling of interstitial boron diffusion into the Au lattice. Borophene synthesis also modifies the surface reconstruction of the Au(111) substrate, resulting in a trigonal network that templates growth at low coverage. This initial growth is composed of discrete borophene nanoclusters, whose shape and size are consistent with theoretical predictions. As the concentration of boron increases, nanotemplating breaks down and larger borophene islands are observed. Spectroscopic measurements reveal that borophene grown on Au(111) possesses a metallic electronic structure, suggesting potential applications in 2D plasmonics, superconductivity, interconnects, electrodes, and transparent conductors.

Borophene as a prototype for synthetic 2D materials development.

The synthesis of 2D materials with no analogous bulk layered allotropes promises a substantial breadth of physical and chemical properties through the diverse structural options afforded by substrate-dependent epitaxy. However, despite the joint theoretical and experimental efforts to guide materials discovery, successful demonstrations of synthetic 2D materials have been rare. The recent synthesis of 2D boron polymorphs (that is, borophene) provides a notable example of such success. In this Perspective, we discuss recent progress and future opportunities for borophene research. Borophene combines unique mechanical properties with anisotropic metallicity, which complements the canon of conventional 2D materials. The multi-centre characteristics of boron-boron bonding lead to the formation of configurationally varied, vacancy-mediated structural motifs, providing unprecedented diversity in a mono-elemental 2D system with potential for electronic applications, chemical functionalization, materials synthesis and complex heterostructures. With its foundations in computationally guided synthesis, borophene can serve as a prototype for ongoing efforts to discover and exploit synthetic 2D materials.

Resolving the Chemically Discrete Structure of Synthetic Borophene Polymorphs.

Atomically thin two-dimensional (2D) materials exhibit superlative properties dictated by their intralayer atomic structure, which is typically derived from a limited number of thermodynamically stable bulk layered crystals (e.g., graphene from graphite). The growth of entirely synthetic 2D crystals, those with no corresponding bulk allotrope, would circumvent this dependence upon bulk thermodynamics and substantially expand the phase space available for structure-property engineering of 2D materials. However, it remains unclear if synthetic 2D materials can exist as structurally and chemically distinct layers anchored by van der Waals (vdW) forces, as opposed to strongly bound adlayers. Here, we show that atomically thin sheets of boron (i.e., borophene) grown on the Ag(111) surface exhibit a vdW-like structure without a corresponding bulk allotrope. Using X-ray standing wave-excited X-ray photoelectron spectroscopy, the positions of boron in multiple chemical states are resolved with sub-angström spatial resolution, revealing that the borophene forms a single planar layer that is 2.4 Å above the unreconstructed Ag surface. Moreover, our results reveal that multiple borophene phases exhibit these characteristics, denoting a unique form of polymorphism consistent with recent predictions. This observation of synthetic borophene as chemically discrete from the growth substrate suggests that it is possible to engineer a much wider variety of 2D materials than those accessible through bulk layered crystal structures.

Self-assembly of electronically abrupt borophene/organic lateral heterostructures.

Two-dimensional boron sheets (that is, borophene) have recently been realized experimentally and found to have promising electronic properties. Because electronic devices and systems require the integration of multiple materials with well-defined interfaces, it is of high interest to identify chemical methods for forming atomically abrupt heterostructures between borophene and electronically distinct materials. Toward this end, we demonstrate the self-assembly of lateral heterostructures between borophene and perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA). These lateral heterostructures spontaneously form upon deposition of PTCDA onto submonolayer borophene on Ag(111) substrates as a result of the higher adsorption enthalpy of PTCDA on Ag(111) and lateral hydrogen bonding among PTCDA molecules, as demonstrated by molecular dynamics simulations. In situ x-ray photoelectron spectroscopy confirms the weak chemical interaction between borophene and PTCDA, while molecular-resolution ultrahigh-vacuum scanning tunneling microscopy and spectroscopy reveal an electronically abrupt interface at the borophene/PTCDA lateral heterostructure interface. As the first demonstration of a borophene-based heterostructure, this work will inform emerging efforts to integrate borophene into nanoelectronic applications.

Substrate-Induced Nanoscale Undulations of Borophene on Silver.

Two-dimensional (2D) materials tend to be mechanically flexible yet planar, especially when adhered on metal substrates. Here, we show by first-principles calculations that periodic nanoscale one-dimensional undulations can be preferred in borophenes on concertedly reconstructed Ag(111). This "wavy" configuration is more stable than its planar form on flat Ag(111) due to anisotropic high bending flexibility of borophene that is also well described by a continuum model. Atomic-scale ultrahigh vacuum scanning tunneling microscopy characterization of borophene grown on Ag(111) reveals such undulations, which agree with theory in terms of topography, wavelength, Moiré pattern, and prevalence of vacancy defects. Although the lattice is coherent within a borophene island, the undulations nucleated from different sides of the island form a distinctive domain boundary when they are laterally misaligned. This structural model suggests that the transfer of undulated borophene onto an elastomeric substrate would allow for high levels of stretchability and compressibility with potential applications to emerging stretchable and foldable devices.

Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs.

At the atomic-cluster scale, pure boron is markedly similar to carbon, forming simple planar molecules and cage-like fullerenes. Theoretical studies predict that two-dimensional (2D) boron sheets will adopt an atomic configuration similar to that of boron atomic clusters. We synthesized atomically thin, crystalline 2D boron sheets (i.e., borophene) on silver surfaces under ultrahigh-vacuum conditions. Atomic-scale characterization, supported by theoretical calculations, revealed structures reminiscent of fused boron clusters with multiple scales of anisotropic, out-of-plane buckling. Unlike bulk boron allotropes, borophene shows metallic characteristics that are consistent with predictions of a highly anisotropic, 2D metal.

Electronic and Mechanical Properties of Graphene-Germanium Interfaces Grown by Chemical Vapor Deposition.

Epitaxially oriented wafer-scale graphene grown directly on semiconducting Ge substrates is of high interest for both fundamental science and electronic device applications. To date, however, this material system remains relatively unexplored structurally and electronically, particularly at the atomic scale. To further understand the nature of the interface between graphene and Ge, we utilize ultrahigh vacuum scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) along with Raman and X-ray photoelectron spectroscopy to probe interfacial atomic structure and chemistry. STS reveals significant differences in electronic interactions between graphene and Ge(110)/Ge(111), which is consistent with a model of stronger interaction on Ge(110) leading to epitaxial growth. Raman spectra indicate that the graphene is considerably strained after growth, with more point-to-point variation on Ge(111). Furthermore, this native strain influences the atomic structure of the interface by inducing metastable and previously unobserved Ge surface reconstructions following annealing. These nonequilibrium reconstructions cover >90% of the surface and, in turn, modify both the electronic and mechanical properties of the graphene overlayer. Finally, graphene on Ge(001) represents the extreme strain case, where graphene drives the reorganization of the Ge surface into [107] facets. From this work, it is clear that the interaction between graphene and the underlying Ge is not only dependent on the substrate crystallographic orientation, but is also tunable and strongly related to the atomic reconfiguration of the graphene-Ge interface.

Direct oriented growth of armchair graphene nanoribbons on germanium.

Graphene can be transformed from a semimetal into a semiconductor if it is confined into nanoribbons narrower than 10 nm with controlled crystallographic orientation and well-defined armchair edges. However, the scalable synthesis of nanoribbons with this precision directly on insulating or semiconducting substrates has not been possible. Here we demonstrate the synthesis of graphene nanoribbons on Ge(001) via chemical vapour deposition. The nanoribbons are self-aligning 3° from the Ge〈110〉 directions, are self-defining with predominantly smooth armchair edges, and have tunable width to <10 nm and aspect ratio to >70. In order to realize highly anisotropic ribbons, it is critical to operate in a regime in which the growth rate in the width direction is especially slow, <5 nm h(-1). This directional and anisotropic growth enables nanoribbon fabrication directly on conventional semiconductor wafer platforms and, therefore, promises to allow the integration of nanoribbons into future hybrid integrated circuits.

Silicon growth at the two-dimensional limit on Ag(111).

Having fueled the microelectronics industry for over 50 years, silicon is arguably the most studied and influential semiconductor. With the recent emergence of two-dimensional (2D) materials (e.g., graphene, MoS2, phosphorene, etc.), it is natural to contemplate the behavior of Si in the 2D limit. Guided by atomic-scale studies utilizing ultrahigh vacuum (UHV), scanning tunneling microscopy (STM), and spectroscopy (STS), we have investigated the 2D limits of Si growth on Ag(111). In contrast to previous reports of a distinct sp(2)-bonded silicene allotrope, we observe the evolution of apparent surface alloys (ordered 2D silicon-Ag surface phases), which culminate in the precipitation of crystalline, sp(3)-bonded Si(111) nanosheets. These nanosheets are capped with a √3 honeycomb phase that is isostructural to a √3 honeycomb-chained-trimer (HCT) reconstruction of Ag on Si(111). Further investigations reveal evidence for silicon intermixing with the Ag(111) substrate followed by surface precipitation of crystalline, sp(3)-bonded silicon nanosheets. These conclusions are corroborated by ex situ atomic force microscopy (AFM), transmission electron microscopy (TEM), Raman spectroscopy, and X-ray photoelectron spectroscopy (XPS). Even at the 2D limit, scanning tunneling spectroscopy shows that the sp(3)-bonded silicon nanosheets exhibit semiconducting electronic properties.