Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry

We present a white-light spectral interferometric technique for measuring the thickness of SiO₂ thin film on a silicon wafer. The technique utilizes a slightly dispersive Michelson interferometer with a cube beam splitter and a fibre-optic spectrometer to record channelled spectra in two configurations. In the first, a standard configuration with two identical metallic mirrors, the recorded channelled spectrum is fitted to the theoretical one to determine the effective thickness of the beam splitter made of BK7 optical glass. In the second configuration one of the mirrors is replaced by SiO₂ thin film on the silicon wafer and the recorded channelled spectrum is fitted to the theoretical one to determine the thin-film thickness. We consider multiple reflection within the thin-film structure, use the optical constants for all the materials involved in the set-up, and confirm very good agreement between theory and experiment. The technique is applied to four samples with various SiO₂ film thicknesses. PACS 07.60.Ly; 68.55.Jk; 78.20     

Catalytic enantioselective conjugate addition of dialkylzinc reagents to N-substituted-2,3-dehydro-4-piperidones

The first, highly enantioselective, copper/phosphoramidite-catalyzed conjugate addition of dialkylzinc reagents to N-substituted 2,3-dehydro-4-piperidones is described.     

Almost everywhere convergence of series in

We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence with , such that for every dynamical system and , converges almost everywhere. A similar result is obtained in the real variable context.

     

Doubly nonlocal Cahn–Hilliard equations

We consider a doubly nonlocal nonlinear parabolic equation which describes phase-segregation of a two-component material in a bounded domain. This model is a more general version than the recent nonlocal Cahn–Hilliard equation proposed by Giacomin and Lebowitz [26], such that it reduces to the latter under certain conditions. We establish well-posedness results along with regularity and long-time results in the case when the interaction between the two levels of nonlocality is strong-to-weak.     

Endpoint Bounds for the Quartile Operator

It is a result by Lacey and Thiele (Ann. of Math. (2) 146(3):693–724, 1997; ibid. 149(2):475–496, 1999) that the bilinear Hilbert transform maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2}}(\mathbb{R}) $ into $L^{p_{3}}(\mathbb{R})$ whenever (p ₁,p ₂,p ₃) is a Hölder tuple with p ₁,p ₂>1 and $p_{3}>\frac{2}{3}$ . We study the behavior of the quartile operator, which is the Walsh model for the bilinear Hilbert transform, when $p_{3}=\frac{2}{3}$ . We show that the quartile operator maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2}}(\mathbb{R}) $ into $L^{\frac{2}{3},\infty}(\mathbb{R})$ when p ₁,p ₂>1 and one component is restricted to subindicator functions. As a corollary, we derive that the quartile operator maps $L^{p_{1}}(\mathbb{R}) \times L^{p_{2},\frac{2}{3}}(\mathbb{R}) $ into $L^{\frac{2}{3},\infty}(\mathbb{R})$ . We also provide weak type estimates and boundedness on Orlicz-Lorentz spaces near p ₁=1,p ₂=2 which improve, in the Walsh case, the results of Bilyk and Grafakos (J. Geom. Anal. 16 (4):563–584, 2006) and Carro et al. (J. Math. Anal. Appl. 357(2):479–497, 2009). Our main tool is the multi-frequency Calderón-Zygmund decomposition from (Nazarov et al. in Math. Res. Lett. 17(3):529–545, 2010).     

Abrikosov-to-Josephson vortex lattice crossover in heavy fermion CeCoIn5

We present torque magnetization measurements on the quasi-2D heavy fermion superconductor CeCoIn₅ at temperatures down to 20 mK and magnetic fields up to 18?T. At orientations with the magnetic field perpendicular to the conducting planes, a prominent vortex lattice peak effect is present at around 0.5H _c2. The peak effect gradually disappears upon rotating the field into the plane parallel orientation. We interpret the absence of the peak effect for the plane parallel case as a transformation of the Abrikosov lattice into a Josephson vortex state, favored by the Pauli paramagnetic limit in CeCoIn₅ together with the unusually large condensation energy. Additionally, we do not observe flux avalanches as found in organic superconductors and suggest that the complete absence of vortex activity in the plane parallel field orientation is crucial for the formation of Fulde–Ferrell–Larkin–Ovchinnikov superconductivity in CeCoIn₅.