Beryllium diffusion across GaAs/(Al,Ga)As heterojunctions and GaAs/AlAs superlattices during MBE growth

Beryllium diffusion during MBE growth of (Al, Ga)As layers, (Al, Ga)As/GaAs heterojunctions and GaAs/AlAs superlattices has been studied by electrochemical C-V and secondary ion mass spectrometry (SIMS) concentration profiling, in conjunction with transmission electron microscopy. Diffusion times were comparatively short since they were limited to part of the growth sequence, so non-equilibrium effects had a significant influence. The results are consistent with an interstitial-substitutional mechanism in which lattice site incorporation becomes more difficult with increasing band gap enthalpy. Incorporation involves a kick-out reaction which leads to the observed disordering of the superlattices.     

Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace

Summary The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies, by Pitman- Yor, and the authors, of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points.The following principle governs the passage from results in the plane to results in space:Let B be a three-dimensional Brownian motion, and P ₁, ..., P _k, k planes which intersect two by two. Then, the convergences in distribution concerning the planar Brownian motions B ⁱ (1ik), defined respectively as the orthogonal projections of B on P _i (1ik), take place jointly, and the corresponding limit variables are independent.     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

Asymptotic expansions for dynamic programming recursions with general nonnegative matrices

This paper is concerned with the study of the asymptotic behavior of dynamic programming recursions of the form $$x(n + 1) = \mathop {\max }\limits_{P \in \mathcal{K}} Px(n), n = 0,1,2,...,$$ where ? denotes a set of matrices, generated by all possible interchanges of corresponding rows, taken from a fixed finite set of nonnegative square matrices. These recursions arise in a number of well-known and frequently studied problems, e.g. in the theory of controlled Markov chains, Leontief substitution systems, controlled branching processes, etc. Results concerning the asymptotic behavior ofx(n), forn→∞, are established in terms of the maximal spectral radius, the maximal index, and a set of generalized eigenvectors. A key role in the analysis is played by a geometric convergence result for value iteration in undiscounted multichain Markov decision processes. A new proof of this result is also presented.     

Two-photon absorption and energy band structure of orthorhombic Hg2Cl2 crystals

Dependence of two-photon absorption (TPA) rate on the state of polarization of a laser beam is investigated in the low-temperature orthorhombic modification of Hg₂Cl₂ crystals. Theoretical calculations of the dependence of TPA rate on the direction of polarization vector of the beam are performed for centrosymmetric points, Y, Z, T, R andS of the Brillouin zone. The domain structure of real crystals is taken into consideration and it is shown that periodicity of the polarization dependence may indicate whether TPA is due to transitions either at, Y, Z, T orR, S points. The polarization dependence of TPA cannot, however, distinguish between points inside these two groups. Comparison of theory with a low-temperature (T 8·5 K) experimental curve of polarization dependence is discussed. It is shown that the experiment can be explained in main features by a model of noninteracting oriented linear dipoles. Further, on the basis of TPA measurements, a simple energy band structure of Hg₂Cl₂ is proposed regarding Hg₂Cl₂ crystal as a linear chain of molecules.The authors express thanks to Dr. . Barta for supplying the Hg₂Cl₂ crystals, Dr. Z. Bryknar for critical comments and Dr. B. Velický for stimulating discussion. We thank also Dr. V. Kohlová for assistance during measurement.