An axiomatic approach to the non-linear theory of generalized functions and consistency of Laplace transforms

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of Colombeau type in the sense that it contains a copy of the space of Schwartz distributions. We study the uniqueness of the objects we define and the consistency of our axioms. Next, we identify an inconsistency in the conventional Laplace transform theory. As an application we offer a free of contradictions alternative in the framework of our algebra of generalized functions. The article is aimed at mathematicians, physicists and engineers who are interested in the non-linear theory of generalized functions, but who are not necessarily familiar with the original Colombeau theory. We assume, however, some basic familiarity with the Schwartz theory of distributions.Comment: 23 page

Expanding impulsive gravitational waves

We explicitly demonstrate that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a "cut and paste" method may be considered to be impulsive limits of the Robinson-Trautman vacuum type N solutions. We extend these results to all the generically distinct subclasses of these solutions in Minkowski, de Sitter and anti-de Sitter backgrounds. For these we express the solutions in terms of a continuous metric. Finally, we also extend the class of spherical shock gravitational waves to include a non-zero cosmological constant.Comment: 11 pages, LaTeX, To appear in Class. Quantum Gra

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

Doping and Mobility Profiles in Defect-Engineered Ultra-shallow Junctions: Bulk and SOI

ABSTRACTSilicon on insulator (SOI - Smartcut®) wafers were implanted with 1MeV and 300keV silicon ions to doses of 3.8x1015 cm−2 and 3x1014 cm−2, respectively, in order to modify the vacancy concentration in a controlled way. Boron was then implanted at 2keV to a dose of 1×1015 cm−2 into the near-surface part of the vacancy-engineered region. Atomic profiles were determined using SIMS and electrical profiles were measured using a novel Differential Hall Effect (DHE) technique, which enables profiling of electrically active dopants with a nanometer depth resolution. The electrical profiles provide pairs of carrier concentration and mobility values as a function of depth. The buried oxide (BOX) is proven to restrict the back diffusing interstitials positioned below the BOX from entering the silicon top layer and interacting with the boron profile. Also an increase of ∼50% in boron activation is achieved when a co-implant is used. However, SOI shows a reduced degree of activation when compared to bulk silicon, with or without a co-implant.</jats:p

Diffusion and activation of ultrashallow B implants in silicon on insulator: End-of-range defect dissolution and the buried Si∕SiO2 interface

The fabrication of preamorphized p-type ultrashallow junctions in silicon-on-insulator (SOI) has been investigated. Electrical and structural measurements after annealing show that boron deactivation and transient enhanced diffusion are reduced in SOI compared to bulk wafers. The reduction is strongest when the end-of-range defects of the preamorphizing implant are located deep within the silicon overlayer of the SOI silicon substrate. Results reveal a very substantial increase in the dissolution rate of the end-of-range defect band. A key player in this effect is the buried Si/SiO2 interface, which acts as an efficient sink for interstitials competing with the silicon surface.</p

Vacancy-engineering implants for high boron activation in silicon on insulator

The formation of boron interstitial clusters is a key limiting factor for the fabrication of highly-conductive ultrashallow doped regions in future silicon-based device technology. Optimized vacancy engineering strongly reduces boron clustering, enabling low-temperature electrical activation to levels rivalling what can be achieved with conventional pre-amorphization and solid-phase epitaxial regrowth. An optimized 160-keV silicon implant in a 55/145nm silicon-on-insulator structure enables stable activation of a 500eV boron implant to a concentration ~ 5x1020cm-3