Effect of As doping on the photoluminescence of nanocrystalline Ge embedded in SiO2 matrix

Samples of nanocrystalline ⁷⁴Ge embedded in amorphous SiO₂ film were prepared by ⁷⁴Ge ion implantation and subsequent primary thermal annealing. These samples were irradiated by neutron flux in a nuclear reactor then the second annealing followed. Irradiation with thermal neutrons leads to doping of nanocrystalline ⁷⁴Ge with As impurities due to nuclear transmutation of isotope ⁷⁴Ge into ⁷⁵As. Transmission electron microscope, X-ray fluorescence, X-ray photoelectron spectroscopy, laser Raman scattering and photoluminescence of the obtained samples were measured. It was observed that with the increase in As-donors concentration, photoluminescence intensity first increased but then significantly decreased. An explanatory model of this non-monotonic behavior was discussed.     

On the observation closest to the origin

Out of n i.i.d. random vectors in $\text{R}$^d let X¹_n be the one closest to the origin. We show that X¹_n has a nondegenerate limit distribution if and only if the common probability distribution satisfies a condition of multidimensional regular variation. The result is then applied to a problem of density estimation.     

Small and Large Time Scale Analysis of a Network Traffic Model

Empirical studies of the internet and WAN traffic data have observed multifractal behavior at time scales below a few hundred milliseconds. There have been some attempts to model this phenomenon, but there is no model to connect the small time scale behavior with behavior observed at large time scales of bigger than a few hundred milliseconds. There have been separate analyses of models for high speed data transmissions, which show that appropriate approximations to large time scale behavior of cumulative traffic are either fractional Brownian motion or stable Lévy motion, depending on the input rates assumed. This paper tries to bridge this gap and develops and analyzes a model offering an explanation of both the small and large time scale behavior of a network traffic model based on the infinite source Poisson model. Previous studies of this model have usually assumed that transmission rates are constant and deterministic. We consider a nonconstant, multifractal, random transmission rate at the user level which results in cumulative traffic exhibiting multifractal behavior on small time scales and self-similar behavior on large time scales.     

Characterizations and Examples of Hidden Regular Variation

Random vectors on the positive orthant whose distributions possess hidden regular variation are a subclass of those whose distributions are multivariate regularly varying. The concept is an elaboration of the coefficient of tail dependence of Ledford and Tawn (1996, 1997). We provide characterizations and examples of such distribution in terms of mixture models and product models.Sidney Resnicks research was partially supported by NSF grant DMS-0303493 and NSA grant MSPF-02G-183 at Cornell University.This revised version was published online in March 2005 with corrections to the cover date.     

Influence of rapid thermal annealing on the specific features of defect generation in silicon wafers during the formation of effective internal getters

The specific features of the defect generation in silicon wafers subjected to a rapid thermal annealing during the formation of an internal getter have been investigated using optical microscopy and transmission electron microscopy. It has been established that rapid thermal annealing leads to a significant intensification of the decomposition of a supersaturated solid solution of oxygen in silicon, especially in the central region of the wafer. This intensification is responsible for the appearance of characteristic differences in sizes, densities, and morphological features of the microdefects generated in the samples subjected to a rapid thermal annealing as compared to the samples after a conventional heat treatment. The results obtained have demonstrated that the use of rapid thermal annealing has undoubted advantages in the formation of effective internal getters in silicon wafers.     

Transition kernels and the conditional extreme value model

Classical multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction and this assumption requires that each marginal distribution be individually attracted to a univariate extreme value distribution. The Heffernan and Tawn (J R Stat Soc Ser B (Stat Methodol) 66(3):497–546, 2004) alternative extremal model for multivariate data does not require all the components belong to an extremal domain of attraction but assumes instead the existence of an asymptotic approximation to the conditional distribution of the random vector given one of the components is extreme. Combined with the knowledge that the conditioning component belongs to a univariate domain of attraction, this leads to an approximation of the probability of certain risk regions. The original focus on conditional distributions has technical drawbacks but is a natural assumption in many contexts. The technical drawbacks are overcome by relying on convergence of measures and the theory of extended regular variation Heffernan and Resnick (Ann Appl Probab 17(2):537–71, 2007); Das and Resnick (Extremes 14(1):29–61, 2000a); Das et al. (Adv Appl Probab 45(1):139–163, 2013). We compare the two approaches and describe in what way relying on variational limit properties of conditional distributions restricts the class of limit approximations.     

Modeling multiple risks: hidden domain of attraction

A sub-model of multivariate regular variation called hidden regular variation facilitates more accurate estimation of joint tail probabilities in the presence of asymptotic independence. A related concept called hidden domain of attraction can sometimes offer similar estimation assistance in circumstances where hidden regular variation is absent. Examples and discussion illustrate strengths and limitations of this concept. We outline estimation techniques where applicable.