Fabrication Based on Crystalline Membranes

Bending of thin sheets or ribbons is a ubiquitous phenomenon that impacts our daily lives, from the household thermostat to sensors in airbags. At nanometer-scale thicknesses, the mechanics responsible for bending and other distortions in sheets can be employed to create a nanofabrication approach leading to novel nanostructures. The process and resulting structures have been aptly referred to as “nanomechanical architecture.” In this article, we review recent progress in atomistic simulations that not only have helped to reveal the physical mechanisms underlying this nanofabrication approach, but also have made predictions of new nanostructures that can be created. The simulations demonstrate the importance of the atomic structure of the crystalline membrane and of the intrinsic surface stress in governing membrane bending behavior at the nanoscale and making the behavior fundamentally distinct from that at the macroscale. Molecular dynamics simulations of the bending of patterned graphene (a single-atomic layer film) suggest a new method for synthesizing carbon nanotubes with unprecedented control over their size and chirality. Introduction Mechanical properties of materials en compass at the most fundamental limit parameters such as elastic constants and modulus, and at the empirical end quantities such as strength, hardness, and toughness. Because of the great importance of mechanical properties in the engineering of materials, an immense amount is known for bulk materials and even thin films and materials at the mesoscale, for example, in microelectromechanical systems (MEMS) devices. In nanostructures, the manifestation of a material’s mechanical properties may, however, differ significantly from that in its macroscopic counterparts.1–3 Two limits can be considered. In the limit that the nanostructure is so small that its properties are dominated by surfaces, the fundamental elastic constants themselves may change, producing quite novel mechanical effects. But even if the bulk elastic constants still dominate, many distinctive nanoarchitectures can be fabricated by (1) taking advantage of thinness and other nanodimensions, (2) judiciously combining materials, (3) manipulating the strain, and (4) taking advantage of the anisotropies of the elastic properties.4,5 These nanoarchitectures, ranging from strained flat films to tubes, coils, rings, and “rug wrinkles,” in turn, enable not only significant new nano technologies but also serve to elucidate mechanics at these dimensions. Our focus in this article is on simulations of nanofabrication via nanomechanics, within the overall theme of “atomistic simulations of nanomechanics.” At the foundation of much of nanoarchitecture formation is strain, in particular, differential strain in two materials in contact or that emanate from two sides of a very thin sheet. A common device, the bimetallic-strip switch in a thermostat, illustrates differential strain: the strip bends because of different thermal stress in the two metals, which opens or closes the switch. Similarly, the combination of two thin materials in an epitaxial relationship produces a strained bilayer that bends because of lattice misfit strain in the two layers (even without considering temperature), an effect that is not observable if one of the materials is thick. In fact, when the thicknesses of the two layers are reduced to the nanometer scale, the bending magnitude of the bilayer can be so large that it can roll into tubular shapes with a characteristic radius of curvature that is also nanometer scale. The use of directed lattice misfit strain-induced distortion in bilayers leads to the novel nanomechanical architectures fabrication discussed in this article.1,4,5 The approach has several important technological advantages. It allows for the creation of nanoand microstructures with inexact dimensionality, ranging from microand nanorings (Figure 1a)5 to coils (Figures 1b6 and 1d5), tubes (Figures 1c,7 1e,8 and 1f9), curved sheets,3 or ribbons with odd shapes.10 These different nanoarchitectures can be made based on a priori theoretical designs,5 while their size and shape can be tuned over a wide range by choosing different combinations of materials, varying film dimensions, and applying external forces. The approach is extremely versatile, applicable to most materials combinations, including semiconductors (Figures 1a,5 1d,5 and 1f9), metals (Figure 1b),6 insulators (Figure 1e),8 and polymers (Figure 1c).7 It is also completely compatible with processing methods developed for Si, III–V, or MEMS technologies, and is thus suitable for parallel mass production of identical or different nanostructures (Figure 1f).9 The basic design principle and qualitative behavior of nanoarchitectures can be understood by classical mechanics and continuum theory.5 Nevertheless, atomistic simulations have made significant contributions in revealing the prominent role played by the atomic nature of the membrane structure and by the intrinsic surface stress in governing the bending of nanomembranes. Multiscale modeling Mechanics-Driven Fabrication Based on Crystalline Membranes MRS BULLETIN • VOLUME 34 • MARCH 2009 • www.mrs.org/bulletin 191 that combines atomistic simulation with continuum mechanics theory has resolved discrepancies between recent experiments and classical bending theories, elucidating the difference between the mechanical response of ultrathin films and that of thick films. In addition, molecular dynamics simulations have predicted a unique self-bending mechanism of Si (or Ge) membranes for forming Si (or Ge) nanotubes and have shown the way to synthesizing carbon nanotubes with predefined size and chirality. Modified Timoshenko Formula The effect of lattice misfit strain on the bending of biand multilayer films is described by the classical Timoshenko theory.11 It has been shown that, when the film becomes very thin, the misfit strain can induce novel bending behavior not seen in thick films.1–4,12,13 For example, a bilayer membrane can roll into tubular shapes of multiple rotations (like a rolledup rug) because the radius of bending curvature becomes so small that a long membrane can roll into multiple turns;1,4 roughness induced on a membrane with nanostressors (epitaxial 3D islands) can induce significant localized bending because of the increased compliance of the ultrathin substrate;2,12 or the bending curvature may exhibit an anomalous dependence on the film/substrate thickness ratio because of enhanced strain sharing.13 Most existing theoretical analyses of mechanical bending of nanofilms1,4,5,14–18 are performed within the framework of continuum theory, focusing on the effect of misfit strain. The classical Timoshenko formula,11 for example, has been used to calculate the diameter of rolled-up nano tubes of strained bilayer films, even for films down to only a few monolayers (MLs) or a few Angstroms thick.14,15 But apparent discrepancies exist between this classical theory and experimental results.15–17 Because of the large surface-to-volume ratio, the surface generally plays an important role in determining the mechanical properties of nanostructures. When the film is thinned to the nanometer scale, the effect of film atomic structure and of the intrinsic stress of the solid surface may become significant, something that is not included in the continuum theory. Therefore, the classical Timoshenko formula applies, in principle, only when the effect of surfaces can be neglected. In bending of nanomembranes, the dominant surface effect is expected to be “surface stress.” For ultrathin films, only a few nanometers thick, surface stress due to surface reconstruction (the rearrangement of atoms on the surface from what would be a simple termination of the bulk lattice, driven by the material’s desire to reduce surface energy) or molecular adsorption can affect the film bending behavior significantly.18–20 There are two nanoscale surface stress terms: the intrinsic surface stress due to surface reconstruction (or adsorption) and the additional surface stress induced by large bending. Surface reconstruction can lead to stress because the rearrangement of surface atoms to reduce surface chemical energy can stretch or bend bonds. For the same reason, adsorption leads to stress in the surface. The surface stress of a bilayer film upon bending can be calculated as