Boron-doped silicon nanowires (SiNWs) grown by the vapor-liquid-solid growth mechanism using silicon tetrachloride (SiCl4) as the silicon precursor and trimethylboron (TMB) as the boron source were studied to understand the axial and radial doping uniformity. TMB-doped SiNWs with diameters up to 400 nm and lengths > 7.5 μm were integrated into a global back-gated test structure with multiple electrodes for electrical characterization. From gate modulated measurements, the SiNWs were confirmed to be heavily doped p-type. Multiple four point resistivity measurements across a total length of 7.5 μm were taken on as-grown SiNWs. Resistivity, corrected for surface charge, was determined to be 0.01 +/− 0.002 Ω cm along the entire length of the as-grown boron doped SiNWs. This was also observed in the axial direction for etched SiNWs, with corrected resistivity of 0.01 +/− 0.003 Ω cm, therefore confirming the uniform p-type doping of SiNWs using TMB and SiCl4 as precursors.

Directed assembly of two-dimensional (2D) layered materials, such as transition metal dichalcogenides, holds great promise for large-scale electronic and optoelectronic applications. Here, we demonstrate controlled placement of solution-suspended monolayer tungsten disulfide (WS2) sheets on a substrate using electric-field-assisted assembly. Micrometer-sized triangular WS2 monolayers are selectively positioned on a lithographically defined interdigitated guiding electrode structure using the dielectrophoretic force induced on the sheets in a nonuniform field. Triangular sheets with sizes comparable to the interelectrode gap assemble with an observed preferential orientation where one side of the triangle spans across the electrode gap. This orientation of the sheets relative to the guiding electrode is confirmed to be the lowest energy configuration using semianalytical calculations. Nearly all sheets assemble without observable physical deformation, and postassembly photoluminescence and Raman spectroscopy characterization of the monolayers reveal that they retain their as-grown crystalline quality. These results show that the field-assisted assembly process may be used for large-area bottom-up integration of 2D monolayer materials for nanodevice applications.

Tungsten diselenide (WSe2) is a two-dimensional material that is of interest for next-generation electronic and optoelectronic devices due to its direct bandgap of 1.65 eV in the monolayer form and excellent transport properties. However, technologies based on this 2D material cannot be realized without a scalable synthesis process. Here, we demonstrate the first scalable synthesis of large-area, mono and few-layer WSe2 via metal-organic chemical vapor deposition using tungsten hexacarbonyl (W(CO)6) and dimethylselenium ((CH3)2Se). In addition to being intrinsically scalable, this technique allows for the precise control of the vapor-phase chemistry, which is unobtainable using more traditional oxide vaporization routes. We show that temperature, pressure, Se:W ratio, and substrate choice have a strong impact on the ensuing atomic layer structure, with optimized conditions yielding >8 μm size domains. Raman spectroscopy, atomic force microscopy (AFM), and cross-sectional transmission electron microscopy (TEM) confirm crystalline monoto-multilayer WSe2 is achievable. Finally, TEM and vertical current/voltage transport provide evidence that a pristine van der Waals gap exists in WSe2/graphene heterostructures.

The stacking of two-dimensional layered materials, such as semiconducting transition metal dichalcogenides (TMDs), insulating hexagonal boron nitride (hBN), and semimetallic graphene, has been theorized to produce tunable electronic and optoelectronic properties. Here we demonstrate the direct growth of MoS2, WSe2, and hBN on epitaxial graphene to form large-area van der Waals heterostructures. We reveal that the properties of the underlying graphene dictate properties of the heterostructures, where strain, wrinkling, and defects on the surface of graphene act as nucleation centers for lateral growth of the overlayer. Additionally, we show that the direct synthesis of TMDs on epitaxial graphene exhibits atomically sharp interfaces. Finally, we demonstrate that direct growth of MoS2 on epitaxial graphene can lead to a 10(3) improvement in photoresponse compared to MoS2 alone.

Heterogeneous engineering of two-dimensional layered materials, including metallic graphene and semiconducting transition metal dichalcogenides, presents an exciting opportunity to produce highly tunable electronic and optoelectronic systems. In order to engineer pristine layers and their interfaces, epitaxial growth of such heterostructures is required. We report the direct growth of crystalline, monolayer tungsten diselenide (WSe2) on epitaxial graphene (EG) grown from silicon carbide. Raman spectroscopy, photoluminescence, and scanning tunneling microscopy confirm high-quality WSe2 monolayers, whereas transmission electron microscopy shows an atomically sharp interface, and low energy electron diffraction confirms near perfect orientation between WSe2 and EG. Vertical transport measurements across the WSe2/EG heterostructure provides evidence that an additional barrier to carrier transport beyond the expected WSe2/EG band offset exists due to the interlayer gap, which is supported by theoretical local density of states (LDOS) calculations using self-consistent density functional theory (DFT) and nonequilibrium Green's function (NEGF).

Electric-field-assisted deterministic assembly is used to position arrays of p+-i-n+ In0.53Ga0.47As nanowires on a Si substrate for de-vice integration. Forces induced on the solution-suspended wires by a spatially varying, nonuniform electric field determines the po-sition of each wire with respect to lithographic features on the sub-strate. The electrical properties of the sub-50 nm diameter In0.53Ga0.47As junctions with a 100 nm thick unintentionally doped channel were characterized after adding source and drain contacts. The junctions showed clear rectification, with a forward bias ideal-ity factors as low as 1.8, and reverse leakage current as small as 20 pA at a -1 V bias. This represents an important step towards demonstrating an In0.53Ga0.47As-based nanowire tunnel transistor.

We have studied frustrated kagome arrays and unfrustrated honeycomb arrays of magnetostatically-interacting single-domain ferromagnetic islands with magnetization normal to the plane. The measured pairwise spin correlations of both lattices can be reproduced by models based solely on nearest-neighbor correlations. The kagome array has qualitatively different magnetostatics but identical lattice topology to previously-studied 'artificial spin ice' systems composed of in-plane moments. The two systems show striking similarities in the development of moment pair correlations, demonstrating a universality in artificial spin ice behavior independent of specific realization in a particular material system.

We study permalloy nanorings that are lithographically fabricated with narrow gaps that break the rotational symmetry of the ring while retaining the vortex ground state, using both micromagnetic simulations and magnetic force microscopy (MFM). The vortex chirality in these structures can be readily set with an in-plane magnetic field and easily probed by MFM due to the field associated with the gap, suggesting such rings for possible applications in storage technologies. We find that the gapped ring edge characteristics (i.e., edge profile and gap shape) are critical in determining the magnetization switching field, thus elucidating an essential parameter in the controls of devices that might incorporate such structures.

We have studied the moment correlations within triangular lattice arrays of single-domain co-aligned nanoscale ferromagnetic islands. Independent variation of lattice spacing along and perpendicular to the island axis tunes the magnetostatic interactions between islands through a broad range of relative strengths. For certain lattice parameters, the sign of the correlations between near-neighbor island moments is opposite to that favored by the pair-wise interaction. This finding, supported by analysis of the total correlation in terms of direct and convoluted indirect contributions across multiple pairwise interactions, indicates that indirect interactions and/or those mediated by further neighbors can be tuned to be dominant, with implications for the wide range of systems composed of interacting nanomagnets.

We report a magneto-optical Kerr effect study of the collective magnetic response of artificial square spin ice, a lithographically defined array of single-domain ferromagnetic islands. We find that the anisotropic interisland interactions lead to a nonmonotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.

We have studied the magnetic-moment configurations of different geometry clusters of single-domain nano-scale ferromagnetic islands. The clusters consisted of four islands arranged in geometries taken from the square lattice of artificial spin ice. The magnetic-moment configurations were imaged by magnetic force microscopy after effectively annealing through ac demagnetization. We then compared the results for cluster geometries with and without frustration of the magnetostatic interactions between the island moments. We found that nonfrustrated clusters achieve their lowest energy states more readily than do frustrated clusters. This behavior suggests the presence of a kinetic barrier associated with frustration of the magnetostatic interactions.

We study the impact of geometry on magnetostatically frustrated single-domain nanomagnet arrays. We examine square and hexagonal lattice arrays, as well as a brickwork geometry that combines the anisotropy of the square lattice and the topology of the hexagonal lattice. We find that the more highly frustrated hexagonal lattice allows for the most thorough minimization of the magnetostatic energy, and that the pairwise correlations between moments differ qualitatively between hexagonal and brickwork lattices, although they share the same lattice topology. The results indicate that the symmetry of local interaction is more important than overall lattice topology in the accommodation of frustrated interactions.

Frustrated arrays of interacting single-domain nanomagnets provide important model systems for statistical mechanics, as they map closely onto well-studied vertex models and are amenable to direct imaging and custom engineering. Although these systems are manifestly athermal, we demonstrate that an effective temperature, controlled by an external magnetic drive, describes their microstates and therefore their full statistical properties.

As a measure of disorder, entropy is a central concept of statistical mechanics. In practice, however, it is typically determined thermodynamically, that is, by measuring heat. However, in arrays of interacting submicrometre-sized magnetic islands—known as artificial spin ice—entropy can be determined directly by ‘counting’ the microstate of the system. From thermodynamic origins, the concept of entropy has expanded to a range of statistical measures of uncertainty, which may still be thermodynamically significant1,2. However, laboratory measurements of entropy continue to rely on direct measurements of heat. New technologies that can map out myriads of microscopic degrees of freedom suggest direct determination of configurational entropy by counting in systems where it is thermodynamically inaccessible, such as granular3,4,5,6,7,8 and colloidal9,10,11,12,13 materials, proteins14 and lithographically fabricated nanometre-scale arrays. Here, we demonstrate a conditional-probability technique to calculate entropy densities of translation-invariant states on lattices using limited configuration data on small clusters, and apply it to arrays of interacting nanometre-scale magnetic islands (artificial spin ice)15. Models for statistically disordered systems can be assessed by applying the method to relative entropy densities. For artificial spin ice, this analysis shows that nearest-neighbour correlations drive longer-range ones.

We study ac demagnetization in frustrated arrays of single-domain ferromagnetic islands, exhaustively resolving every (Ising-like) magnetic degree of freedom in the systems. Although the net moment of the arrays is brought near zero by a protocol with sufficiently small step size, the final magnetostatic energy of the demagnetized array continues to decrease for finer-stepped protocols and does not extrapolate to the ground-state energy. The resulting complex disordered magnetic state can be described by a maximum-entropy ensemble constrained to satisfy just nearest-neighbor correlations.

We study the configuration of magnetic moments on triangular lattices of single-domain ferromagnetic islands, examining the consequences of magnetostatic interactions in this frustrated geometry. By varying the island-island distance along one direction, we are able to tune the ratios of different interactions between neighboring islands, resulting in a corresponding variation in the local correlations between the island moments. Unlike other artificial frustrated magnets, this lattice geometry displays regions of ordered moment orientation, possibly resulting from a higher degree of anisotropy leading to a reduced level of frustration.

We analyze the rotational demagnetization of artificial spin ice, a recently realized array of nanoscale single-domain ferromagnetic islands. Demagnetization does not anneal this model system into its antiferromagnetic ground state: the moments have a static disordered configuration similar to the frozen state of the spin ice materials. We demonstrate that this athermal system has an effective extensive degeneracy and we introduce a formalism that can predict the populations of local states in this icelike system with no adjustable parameters.

We report a study of demagnetization protocols for frustrated arrays of interacting single domain permalloy nanomagnets by rotating the arrays in a changing magnetic field. The most effective demagnetization is achieved by not only stepping the field strength down while the sample is rotating, but by combining each field step with an alternation in the field direction. By contrast, linearly decreasing the field strength or stepping the field down without alternating the field direction leaves the arrays with a larger remanent magnetic moment. These results suggest that non-monotonic variations in field magnitude around and below the coercive field are important for the demagnetization process.