Luminescence enhancement by hydrogenation of Si:Er,O

Erbium (Er)- and oxygen (O)-doped Cz–Si was additionally doped with hydrogen, using plasma enhanced chemical vapour deposition. Photoluminescence (PL) spectra show a large enhancement especially for samples treated with solid phase epitaxy before hydrogenation and annealing at 900°C later. Secondary ion mass spectroscopy measurements give evidence for an enhanced diffusion of O and Er at this temperature towards the surface. Etching shows that the PL does not stem from the heavily doped surface layer but from a deeper region with lower Er concentration. This conclusion is supported by the appearance of the so-called “cubic” centre with low solubility. Comparing the PL yield of the hydrogenated samples to that of samples with similar Er volume concentration but without hydrogenation still gives a large enhancement. We thus conclude that hydrogen can enhance the solubility of the cubic centre in Si:Er,O.     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

A Stability Estimate for a Solution to a Three-Dimensional Inverse Problem for the Maxwell Equations

We consider the problem of determining dielectric permittivity and conductivity in the Maxwell equations. As additional information we prescribe the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindric domain. We establish a stability estimate for a solution to the inverse problem and a uniqueness theorem.     

Excitation of Waveguides with a Nonhomogeneous Filling

Radiation conditions are posed for an electromagnetic waveguide with a nonhomogeneous filling. The existence of a solution in a certain functional class is proved. A near-zone solution is obtained.     

On the Second Law of Thermodynamics and the Piston Problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio m/M is a very small parameter, where m is the mass of one particle of the gaz and M is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation in a previous work, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.     

Norm Series in High-Dimensional Local Fields

In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to high-dimensional local fields. Necessary and sufficient conditions for the existence of norm series are obtained. Bibliography: 12 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 60–83.     

Homogenization of Some Problems with Rapidly Oscillating Constraints

Homogenization theorems are proved for the problem of minimization of a quadratic integral functional on a set of admissible functions satisfying rapidly oscillating periodic constraints on the boundary of a perforated domain. At each point of the perforation surface, the trace of any admissible function belongs to a given segment of the real axis, and this segment periodically varies along the boundary. According to the structure of this field of segments on the boundary, we characterize the asymptotic behavior of the solutions (minimizers) as the period of the structure tends to zero.     

Une axiomatisation de la substitution

We investigate the notion of substitution in an abstract way, without defining it explicitly. We single out the essential features of the operation of performing a substitution in order to define a concept of substitutive structure, called logos. We then prove a completeness theorem making precise and justifying the intuition that formulas true for the usual substitution can be proved from the logos axioms only. To cite this article: M. Crabbé, C. R. Acad. Sci. Paris, Ser. I 338 (2004).