Quantitative convergence analysis of multi-agent systems

We introduce a characterization of contraction for bounded convex sets. For discrete-time multi-agent systems we provide an explicit upperbound on the rate of convergence to a consensus under the assumptions of contractiveness and (weak) connectedness (across an interval.) Convergence is shown to be exponential when either the system or the function characterizing the contraction is linear. Copyright © 2007 IFAC.

Hydrogen-induced morphotropic phase transformation of single-crystalline vanadium dioxide nanobeams.

We report a morphotropic phase transformation in vanadium dioxide (VO2) nanobeams annealed in a high-pressure hydrogen gas, which leads to the stabilization of metallic phases. Structural analyses show that the annealed VO2 nanobeams are hexagonal-close-packed structures with roughened surfaces at room temperature, unlike as-grown VO2 nanobeams with the monoclinic structure and with clean surfaces. Quantitative chemical examination reveals that the hydrogen significantly reduces oxygen in the nanobeams with characteristic nonlinear reduction kinetics which depend on the annealing time. Surprisingly, the work function and the electrical resistance of the reduced nanobeams follow a similar trend to the compositional variation due mainly to the oxygen-deficiency-related defects formed at the roughened surfaces. The electronic transport characteristics indicate that the reduced nanobeams are metallic over a large range of temperatures (room temperature to 383 K). Our results demonstrate the interplay between oxygen deficiency and structural/electronic phase transitions, with implications for engineering electronic properties in vanadium oxide systems.

Atom probe tomography for advanced metallization

In microelectronics, the increase in complexity and the reduction of devices dimensions make essential the development of new characterization tools and methodologies. Indeed advanced characterization methods with very high spatial resolution are needed to analyze the redistribution at the nanoscale in devices and interconnections. The atom probe tomography has become an essential analysis to study materials at the nanometer scale. This instrument is the only analytical microscope capable to produce 3D maps of the distribution of the chemical species with an atomic resolution inside a material. This technique has benefit from several instrumental improvements during last years. In particular, the use of laser for the analysis of semiconductors and insulating materials offers new perspectives for characterization. The capability of APT to map out elements at the atomic scale with high sensitivity in devices meets the characterization requirements of semiconductor devices such as the determination of elemental distributions for each device region. In this paper, several examples will show how APT can be used to characterize and understand materials and process for advanced metallization. The possibilities and performances of APT (chemical analysis of all the elements, atomic resolution, planes determination, crystallographic information...) will be described as well as some of its limitations (sample preparation, complex evaporation, detection limit, ...). The examples illustrate different aspect of metallization: dopant profiling and clustering, metallic impurities segregation on dislocation, silicide formation and alloying, high K/metal gate optimization, SiGe quantum dots, as well as analysis of transistors and nanowires. © 2013 Elsevier B.V. All rights reserved.