Theory of Scanning Probe Microscopy of Carbon Nanostructures
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Theory of Scanning Probe Microscopy of Carbon Nanostructures Vincent Meunier1, Sergei Kalinin2, and Philippe Lambin3 1 Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367, U.S.A. 2 Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, U.S.A. 3 Department of Physics, Facultés Universitaires Notre-Dame de la Paix, Namur, B-5000, Belgium ABSTRACT Experimental techniques for SPM imaging and spectroscopy of low-dimensional systems have significantly progressed in recent years. At the same time, new simulation methods and computational techniques have allowed the development of a theoretical basis to the interpretation and understanding of the measurements. In this contribution, we concisely review two state-of-the-art modeling methods for scanning probe microscopy, as applied to carbon nanostructures. INTRODUCTION When carbon nanotubes were discovered1, they initiated a spectrum of opportunities in the science and technology of novel materials and devices at the nanoscale. Single-walled carbon nanotubes can be thought of as the result of the curling up of a graphene sheet into a cylinder where the carbon lattice is joined seamlessly along the circumference. Nanotubes are conveniently characterized by their length, diameter and helicity. The latter is a measure of the orientation of the graphene sheet as it is folded to form nanotubes. Following the conventional notation2, the structure of a nanotube is described by a pair of integers (n,m), which gives the coordinates of the circumference vector in the basis of the primitive lattice vectors of graphene. The helicity is the most important feature that determines both their mechanical and electrical properties3. Carbon nanotubes are often found in a non-pristine state: defects in single-wall carbon nanotubes are conventionally classified as atomic vacancies, chemical impurities, or topological defects. The latter are typically made up of carbon rings that are not perfect sp2bonded hexagons. Usually, topological defects consist of at least a pair of defective rings, e.g. squares, pentagons, heptagons, etc. Topological defects may be formed during growth, or they may be induced via photon and ion bombardment 4, or tensile stress—both in the absence5 and presence6 of carbon adatoms. Controlled production and purification processes are important concerns to be managed in the quest for opening a new era of a nano-carbon based industry. Along with their availability and quality, the ultimate goal envisioned by the emerging nano-industry can only be met with the help of state-of-the-art characterization techniques. In that respect, local probe techniques such as scanning tunneling microscopy (STM), spectroscopy (STS), and scanning gate microscopy (SGM) are among the very few descriptive techniques that allow for an accurate depiction of structural (topographical) and electronic (spectroscopy and transport) characteristics7.
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First, STM and STS have provided an abundance of information about
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