Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

High power pulsed magnetron sputtering (HPPMS) is an emerging technology that has gained substantial interest among academics and industrials alike. HPPMS, also known as HIPIMS (high power impulse ...

High power pulsed magnetron sputtering: A review on scientific and engineering state of the art

BACKGROUND Light trapped at the nanoscale, deep below the optical wavelength, exhibits an increase in the associated electric field strength, which results in enhanced light-matter interaction. This leads to strong nonlinearities, large photonic forces, and enhanced emission and absorption probabilities. A practical approach toward nanoscale light trapping and manipulation is offered by interfaces separating media with permittivities of opposite signs. Such interfaces sustain hybrid light-matter modes involving collective oscillations of polarization charges in matter, hence the term polaritons. Surface plasmon polaritons, supported by electrons in metals, constitute a most-studied prominent example. Yet there are many other varieties of polaritons, including those formed by atomic vibrations in polar insulators, excitons in semiconductors, Cooper pairs in superconductors, and spin resonances in (anti)ferromagnets. Together, they span a broad region of the electromagnetic spectrum, ranging from microwave to ultraviolet wavelengths. We discuss polaritons in van der Waals (vdW) materials: layered systems in which individual atomic planes are bonded by weak vdW attraction (see the figure). This class of quantum materials includes graphene and other two-dimensional crystals. In artificial structures assembled from dissimilar vdW atomic layers, polaritons associated with different constituents can interact to produce unique optical effects by design. ADVANCES vdW materials host a full suite of different polaritonic modes with the highest degree of confinement among all known materials. Advanced near-field imaging methods allow the polaritonic waves to be launched and visualized as they travel along vdW layers or through multilayered heterostructures. Spectroscopic and nanoimaging experiments have identified multiple routes toward manipulation of nano-optical phenomena endowed by polaritons. A virtue of polaritons in vdW systems is their electrical tunability. Furthermore, in heterostructures assembled from dissimilar vdW layers, different brands of polaritons interact with each other, thus enabling unparalleled control of polaritonic response at the level of single atomic planes. New optoelectronic device concepts aimed at the detection, harvesting, emission, propagation, and modulation of light are becoming feasible as a result of combined synthesis, nanofabrication, and modeling of vdW systems. The extreme anisotropy of vdW systems leading to opposite signs of the in-plane and out-of-plane permittivities of the same layered crystal enables efficient polaritonic waveguides, which are instrumental for subdiffractional focusing and imaging. In addition to near-field optical probes facilitating nanoimaging, coupling to polaritons can be accomplished via electrical excitation and nonlinear wave mixing. OUTLOOK Potential outcomes of polariton exploration in vdW heterostructures go beyond nano-optical technologies. In particular, images of polaritonic standing and traveling waves contain rich insights into quantum phenomena occurring in the host material supporting polaritons. This line of inquiry into fundamental physics through polaritonic observations constitutes an approach toward optics-based materials research. In particular, the strong spatial confinement exhibited by vdW polaritons involves large optical-field gradients—or equivalently, large momenta—which allows regions of the dispersion relations of electrons, phonons, and other condensed-matter excitations to be accessed beyond what is currently possible with conventional optics. Additionally, polaritons created by short and intense laser pulses add femtosecond resolution to the study of these phenomena. Alongside future advances in the understanding of the physics and interactions of vdW polaritons, solutions to application challenges may be anticipated in areas such as loss compensation, nanoscale lasing, quantum optics, and nanomanipulation. The field of vdW polaritonics is ripe for exploring genuinely unique physical scenarios and exploiting these new phenomena in technology. van der Waals (vdW) materials consist of individual atomic planes bonded by weak vdW attraction. They display nearly all optical phenomena found in solids, including plasmonic oscillations of free electrons characteristic of metals, light emission/lasing and excitons encountered in semiconductors, and intense phonon resonances typical of insulators. These phenomena are embodied in confined light-matter hybrid modes termed polaritons—excitations of polarizable media, which are classified according to the origin of the polarization. The most studied varieties are plasmon, phonon, and exciton polaritons. In vdW materials, polaritons exhibit extraordinary properties that are directly affected by dimensionality and topology, as revealed by state-of-the-art imaging of polaritonic waves. vdW heterostructures provide unprecedented control over the polaritonic response, enabling new quantum phenomena and nanophotonics applications.

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Polaritons in van der Waals materials

Graphene plasmons were predicted to possess ultra-strong field confinement and very low damping at the same time, enabling new classes of devices for deep subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. While all of these great prospects require low damping, thus far strong plasmon damping was observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphene with other atomically flat materials. In this letter we exploit near-field microscopy to image propagating plasmons in high quality graphene encapsulated between two films of hexagonal boron nitride (h-BN). We determine dispersion and particularly plasmon damping in real space. We find unprecedented low plasmon damping combined with strong field confinement, and identify the main damping channels as intrinsic thermal phonons in the graphene and dielectric losses in the h-BN. The observation and in-depth understanding of low plasmon damping is the key for the development of graphene nano-photonic and nano-optoelectronic devices.

Highly confined low-loss plasmons in graphene-boron nitride heterostructures

Celebrating the 100th anniversary of the Stoney equation for film stress: Developments from polycrystalline steel strips to single crystal silicon wafers

We report on nano-infrared (IR) imaging studies of confined plasmon modes inside patterned graphene nanoribbons (GNRs) fabricated with high-quality chemical-vapor-deposited (CVD) graphene on Al2O3 substrates. The confined geometry of these ribbons leads to distinct mode patterns and strong field enhancement, both of which evolve systematically with the ribbon width. In addition, spectroscopic nanoimaging in the mid-infrared range 850-1450 cm(-1) allowed us to evaluate the effect of the substrate phonons on the plasmon damping. Furthermore, we observed edge plasmons: peculiar one-dimensional modes propagating strictly along the edges of our patterned graphene nanostructures.

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Edge and Surface Plasmons in Graphene Nanoribbons.

Young’s modulus of free-standing polycrystalline Al, Au, and W films with submicron thickness has been studied using a dynamic bulge-testing technique. For Au and Al films a clear frequency dependence of the modulus is observed at room temperature in the range 1×10−4–0.5 rad/s. The values of the moduli are considerably smaller than the corresponding values of bulk material. The modulus of W films measured under the same conditions does not depend on frequency and is equal to the bulk value. The origin of the behavior found in the Al and Au films is anelastic grain boundary sliding. As a consequence of the relatively small grain size of thin polycrystalline films this phenomenon is observable at room temperature in films with a relatively low melting point.

Young’s modulus measurements and grain boundary sliding in free-standing thin metal films

In the absence of thermal stress, tensile stress in hard metal films is caused by grain boundary shrinkage and compressive stress is caused by ion peening. It is shown that the two contributions are additive. Moreover tensile stress generated at the grain boundaries does not relax by ion bombardment. In polycrystalline hard metal films the grain structure evolves during growth, leading to wider grains higher up in the film. The tensile component of the stress in the film is generated at the grain boundaries and therefore depends on film thickness. The effect of ion bombardment is independent of grain size, therefore compressive stress does not depend on film thickness. As a result in polycrystalline films deposited under a bias voltage a stress gradient exists from tensile at the interface to compressive at the top of the film.

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Stress in hard metal films

Thin films on substrates are usually in a stressed state. An important, but trivial, contribution to that stress stems from the difference in thermal expansion coefficient of substrate and film. Much more interesting are the intrinsic stresses, resulting from the growth and/or microstructure of the film. Intrinsic compressive stress was explained by d’Heurle in 1970. Intrinsic tensile stress for recrystallizing metal films was treated succesfully by Doljack and Hoffman in 1972. In the present letter we explain the occurrence of tensile stress in nonrecrystallizing metal films. The explanation is based on modern grain growth models and accurate stress measurements. The key ingredient to the explanation is the proof of the existence of a stress gradient in nonrecrystallizing metal films.

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Tensile stress in hard metal films

We developed a bulge-test setup which enables measurement of the elastic and plastic properties of free-standing thin film samples between room temperature and at least 300 °C. Mechanical stress is applied to the film by a differential gas pressure across the sample and the bulge height is measured by a scanning laser beam technique. To prevent sample oxidation the pressure cell containing the sample is mounted in a vacuum chamber. The correct operation of the setup is demonstrated by measurement of the thermal expansion of free-standing Al films. Creep experiments and tensile tests demonstrate measurement of the plastic deformation of these films at temperatures up to 200 °C.

G. C. A. M. Janssen

Papers

Edge and Surface Plasmons in Graphene Nanoribbons.

Young’s modulus measurements and grain boundary sliding in free-standing thin metal films

Stress in hard metal films

Tensile stress in hard metal films

High-temperature bulge-test setup for mechanical testing of free-standing thin films