Optimization of the extraordinary magnetoresistance in semiconductor-metal hybrid structures for magnetic-field sensor applications

Semiconductor-metal hybrid structures can exhibit a very large geometrical magnetoresistance effect, the so-called extraordinary magnetoresistance (EMR) effect. In this paper, we analyze this effect by means of a model based on the finite element method and compare our results with experimental data. In particular, we investigate the important effect of the contact resistance $\rho_c$ between the semiconductor and the metal on the EMR effect. Introducing a realistic $\rho_c=3.5\times 10^{-7} \Omega{\rm cm}^2$ in our model we find that at room temperature this reduces the EMR by 30% if compared to an analysis where $\rho_c$ is not considered.Comment: 4 pages; manuscript for MSS11 conference 2003, Nara, Japa

Quasimodularity and large genus limits of Siegel-Veech constants

Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veech constants. In Part I we connect the geometric definition of Siegel-Veech constants both with a combinatorial counting problem and with intersection numbers on Hurwitz spaces. We introduce modified Siegel-Veech weights whose generating functions will later be shown to be quasimodular. Parts II and III are devoted to the study of the quasimodularity of the generating functions arising from weighted counting of torus coverings. The starting point is the theorem of Bloch and Okounkov saying that q-brackets of shifted symmetric functions are quasimodular forms. In Part II we give an expression for their growth polynomials in terms of Gaussian integrals and use this to obtain a closed formula for the generating series of cumulants that is the basis for studying large genus asymptotics. In Part III we show that the even hook-length moments of partitions are shifted symmetric polynomials and prove a formula for the q-bracket of the product of such a hook-length moment with an arbitrary shifted symmetric polynomial. This formula proves quasimodularity also for the (-2)-nd hook-length moments by extrapolation, and implies the quasimodularity of the Siegel-Veech weighted counting functions. Finally, in Part IV these results are used to give explicit generating functions for the volumes and Siegel-Veech constants in the case of the principal stratum of abelian differentials. To apply these exact formulas to the Eskin-Zorich conjectures we provide a general framework for computing the asymptotics of rapidly divergent power series.Comment: 107 pages, final version, to appear in J. of the AM

Stabilization of colloidal palladium particles by a block copolymer of polystyrene and a block containing amide sidegroups

A block copolymer of polystyrene and poly(tert-butylmethacrylate) was prepared by anionic polymerization. The ester groups of the poly(tert-butylmethacrylate) were hydrolyzed, after wich the remaining carboxyl groups were reacted with pyrrolidine. The resulting block copolymer with amide sidegroups was used for stabilization of a palladium colloid in toluene

Detection of nanoparticles by means of reflection electron energy loss spectroscopy depth profiling

The various studies of nanoparticles are of great importance because of the wide application of nanotechnology. The shape and structure of the nanoparticles can be determined by transmission electron microscopy (TEM) and their chemistry by electron energy loss spectroscopy. TEM sample preparation is an expensive and difficult procedure, however. Surface sensitive, analytical techniques, such as Auger electron spectroscopy (AES) and x-ray photoelectron spectroscopy (XPS) are well applicable to detect the atoms that make up the nanoparticles, but cannot determine whether particle formation occurred. On the other hand, reflection electron energy loss spectroscopy (REELS) probes the electronic structures of atoms, which are strongly different for the atoms being in solution or in precipitated form. If the particle size is in the nm range, plasmon resonance can be excited in it, which appears as a loss feature in REELS spectrum. Thus, by measuring AES (XPS) spectra parallel with those of REELS, besides the atomic concentrations the presence of the nanoparticles can also be identified. As an example, the appearance of nanoparticles during ion beam induced mixing of C/Si layer will be shown

A p-multigrid method enhanced with an ILUT smoother and its comparison to h-multigrid methods within Isogeometric Analysis

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which coarsening is applied in the approximation order p instead of the mesh width h. Since the use of classical smoothers (e.g. Gauss-Seidel) results in a p-multigrid method with deteriorating performance for higher values of p, the use of an ILUT smoother is investigated. Numerical results and a spectral analysis indicate that the resulting p-multigrid method exhibits convergence rates independent of h and p. In particular, we compare both coarsening strategies (e.g. coarsening in h or p) adopting both smoothers for a variety of two and threedimensional benchmarks