Anderson localization and Lifshits tails for random surface potentials

We consider Schrödinger operators on L²(R^d) with a random potential concentrated near the surface R^d₁×{0}⊂R^d. We prove that the integrated density of states of such operators exhibits Lifshits tails near the bottom of the spectrum. From this and the multiscale analysis by Boutet de Monvel and Stollmann [Arch. Math. 80 (2003) 87-97] we infer Anderson localization (pure point spectrum and dynamical localization) for low energies. Our proof of Lifshits tails relies on spectral properties of Schrödinger operators with partially periodic potentials. In particular, we show that the lowest energy band of such operators is parabolic.     

A model for phosphorus segregation at the silicon-silicon dioxide interface

A new model for phosphorus segregation at the Si-SiO₂ interface is derived and verified by experimental data. The model considers for the first time, a third phase, the interface layer itself, in addition to the Si and SiO₂ phases, and the dynamics of the three-phase system is described in terms of rate equations. In particular, the phosphorus compound formation in the interface layer (phosphorus pile-up), which renders the dopant electrically inactive to a large extent, is described as a competition of the dopant in silicon and in silicon dioxide in filling and depleting a constant density of interface traps. Our model allows an unambiguous correlation of the dopant concentration on both sides of the interface with the integral dose of the interface phosphorus pile-up. Experimental data for different phosphorus concentrations, different temperatures, and different oxidation ambients, including inert anneals, are fitted by a single curve.     

Synthesis and Properties of a selenium-bridged bisquinolone

The preparation of the selenium-bridged bisquinolone 5 has been investigated. Compound 5 was methylated giving the N-methyl derivative 6 . Compound 5 and phosphorus oxychloride yielded 4-chloroquinoline 8 which was converted to novel selenium heterocycles 7, 11 and 12 and the 4-phenoxy product 9 .     

Continuous bordering of matrices and continuous matrix decompositions

Summary. Let be the set of all real -matrices of rank . We prove that for there are no continuous vector fields such that the bordered matrix is regular for all . This result has some relevance for the numerical analysis of steady state bifurcation. As a by-product we show that there is no nonvanishing continuous vector field with for all , where is the set of all matrices of rank deficiency one. This implies that there is no singular value decomposition of depending continuously on in any matrix set which contains . As another application we prove that in general there is no global analytic singular value decomposition for analytic matrix valued functions of more than one real variable. Received October 6, 1993 / Revised version received July 18, 1994     

Resonance phenomena in a semi-infinite string with a periodic end

We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t^½, respectively, occur if either ω² is an eigenvalue of A or (i) ω² is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x > a (‘standing wave’).