Phase transformation of Ni-B, Ni-P diffusion barrier deposited electrolessly on Cu interconnect

In this paper, we report that the phase transformation of Ni-B, Ni-P diffusion barriers deposited electrolessly on Cu, for the reason that the Ni-P layer is a more effective diffusion barrier than the Ni-B layer. The Ni₃B crystallized was decomposed to Ni and B₂O₃ above 400 °C and the Ni₃P crystallized was decomposed to Ni and P₂O₅ above 600 °C respectively in Ar atmosphere. Also, the Ni₃B was decomposed to Ni and free B above 400 °C and the Ni₃P was decomposed to Ni and free P above 600 °C respectively in H₂ atmosphere. The decomposed Ni formed a solid solution with Cu. The Cu diffusion occurred above 400 °C for Ni-B layer and above 600 °C for Ni-P layer, respectively. Because the decomposition temperature of Ni-P layer is about 200 °C higher than that of Ni-B layer, the Ni-P layer is a more effective barrier for Cu than the Ni-B layer.     

Large Discrepancy In Homogenous Quasi-Arithmetic Progressions

We prove that the class of homogeneous quasi-arithmetic progressions has unbounded discrepancy. That is, we show that given any 2-coloring of the natural numbers and any positive integer D, one can find a real number α≥1 and a set of natural numbers of the form {0, [α], [2α], [3α], . . . , [kα]} so that one color appears at least D times more than the other color. This was already proved by Beck in 1983, but the proof given here is somewhat simpler and gives a better bound on the discrepancy.     

An Enumerative Geometry for Magic and Magilatin Labellings

A magic labelling of a set system is a labelling of its points by distinct positive integers so that every set of the system has the same sum, the magic sum. Examples are magic squares (the sets are the rows, columns, and diagonals) and semimagic squares (the same, but without the diagonals). A magilatin labelling is like a magic labelling but the values need be distinct only within each set. We show that the number of n × n magic or magilatin labellings is a quasipolynomial function of the magic sum, and also of an upper bound on the entries in the square. Our results differ from previous ones because we require that the entries in the square all be different from each other, and because we derive our results not by ad hoc reasoning but from a general theory of counting lattice points in rational inside-out polytopes. We also generalize from set systems to rational linear forms. Dedicated to the memory of Claudia Zaslavsky, 1917–2006 Received August 10, 2005     

Effects of in situ thermal annealing on the structural, optical, and electrical properties in Hg0.7Cd0.3Te epilayers grown on CdTe buffer layers

Scanning electron microscopy (SEM), Fourier transform infrared (FTIR) transmission, and Hall effect measurements were performed to investigate the structural, optical, and electrical properties of as-grown and in situ-annealed Hg_0.7Cd_0.3Te epilayers grown on CdTe buffer layers by using molecular beam epitaxy. After the Hg_0.7Cd_0.3Te epilayers had been annealed in a Hg-cell flux atmosphere, the SEM images showed that the surface morphologies of the Hg_0.7Cd_0.3Te thin films were mirror-like with no indication of pinholes or defects, and the FTIR spectra showed that the transmission intensities had increased in comparison to that of the as-grown Hg_0.7Cd_0.3Te epilayer. Hall-effect measurements showed that n-Hg_0.7Cd_0.3Te epilayers were converted to p-Hg_0.7Cd_0.3Te epilayers. These results indicate that the surface, optical, and electrical properties of the Hg_1 − xCd_xTe epilayers are improved by annealing and that as-grown n-Hg_1 − xCd_xTe epilayers can be converted to p-Hg_1 − xCd_xTe epilayers by in situ annealing.     

Optimality problem for infinite dimensional bilinear systems

For any finite dimensional control system with arbitrary cost, Pontryagin's Maximum Principle (PMP) [N. Bensalem, Localisation des courbes anormales et problème d'accessibilité sur un groupe de Lie hilbertien nilpotent de degré 2, Thèse de doctorat, Université de Savoie, 1998. [6]] gives necessary conditions for optimality of trajectories. In the infinite dimensional case, it is well known that these conditions are no more true in general. The purpose of this paper is to establish an “approached” version of PMP for infinite dimensional bilinear systems, with fixed final time and without constraints on the final state. Moreover, if the set of control is contained in a closed bounded convex subset with operators defining its dynamics are compact, or if it is contained in a finite dimensional space, we get an “exact” version of PMP. We also give two applications of these results. The first one deals with sub-Riemannian geometry on nilpotent Hilbertian Lie groups for which we can define a sub-Riemannian distance. The second one deals with heat equation for which we analyse the necessary conditions to give the optimal controls.     

Euler configurations and quasi-polynomial systems

Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to r ^b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.     

Positive solutions and eigenvalue regions of two-delay singular systems with a twin parameter

The paper is concerned with a two-delay singular differential system with a twin parameter. Applying fixed-point index theory, we show the relationship between the asymptotic behaviors of nonlinearities (at zero and infinity) and the open regions (eigenvalue regions) of parameters, which are correlated with delays, such that the system has zero, one and two positive solution(s).     

Mackey Topologies and Mixed Topologies in Riesz Spaces

The possibility of characterizing the Mackey topology of a dual pair of vector spaces as a generalized inductive limit (or mixed) topology is investigated. Positive answers are given for a wide range of dual pairs of Riesz spaces (vector lattices) and non-commutative Banach function spaces (or symmetric operator spaces).     

Correlations of Active Galactic Nuclei with Microquasars

Correlations of active galactic nuclei (AGNs) with microquasars are discussed based on the coexistence of the Blandford-Znajek (BZ) and magnetic coupling (MC) processes (CEBZMC) in black hole (BH) accretion disk.The proportions of several quantities of BH systems for both AGNs and microquasars are derived by combining the observational data with CEBZMC. It is shown that the square of the magnetic field at the BH horizon is inversely proportional to the BH mass, while the accretion rate of the disk is proportional to the BH mass. In addition, the very steep emissivity indexes from the recent XMM-Newton observations of the nearby bright Seyfert 1 galaxy MCG-6-30-15 and the microquasars XTE J1650-500 are well fitted by considering the MC effects on the disk radiation. These results suggest strongly the correlations of A GNs with microquasars.