In-doped gallium oxide micro- and nanostructures: morphology, structure, and luminescence properties

The influence of indium doping on morphology, structural, and luminescence properties of gallium oxide micro- and nanostructures is reported. Indium-doped gallium oxide micro- and nanostructures have been grown by thermal oxidation of metallic gallium in the presence of indium oxide. The dominant morphologies are beltlike structures, which in many cases are twisted leading to springlike structures, showing that In diffusion in Ga2O3 influences the microstructure shapes. High-resolution transmission electron microscopy has revealed the presence of twins in the belts, and energy-dispersive X-ray spectroscopy in the scanning electron microscopy (SEM) has detected a segregation of indium impurities at the edges of planar structures. These results suggest that indium plays a major role in the observed morphologies and support the assumption of a layer by layer model as growth mechanism. An additional assessment of indium influence on the defect structure has been performed by cathodoluminescence in the SEM, X-ray photoelectron microscopy, and spatially resolved Raman spectroscopy

Analytic Expansions of (max,+) Lyapunov Exponents

We give an explicit analytic series expansion of the #max; +##Lyapunov exponent ##p# of a sequence of independent and identically distributed random matrices in this algebra, generated via a Bernoulli scheme depending on a small parameter p. Akey assumption is that one of the matrices has a unique eigenvector. This allows us to use a representation of this exponent as the mean value of a certain random variable, and then a discrete analogue of the so-called light-tra#c perturbation formulas to derive the expansion. We show that it is analytic under a simple condition on p. This also provides a closed form expression for all derivatives of ##p# at p = 0 and approximations of ##p# of any order, together with an error estimate for #nite order Taylor approximations. Several extensions of this are discussed, including expansions of multinomial schemes depending on small parameters #p 1 ;:::;p m # and expansions for exponents associated with iterates of a class of random operators which includes the class of so called topical operators. Several examples pertaining to computer and communication sciences are investigated: timed event graphs, resource sharing models and heaps models

EUROCONTROL Experimental Centre

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