Differential Models, Numerical Simulations and Applications

This Special Issue includes 12 high-quality articles containing original research findings in the fields of differential and integro-differential models, numerical methods and efficient algorithms for parameter estimation in inverse problems, with applications to biology, biomedicine, land degradation, traffic flows problems, and manufacturing systems

Structural defects in MOVPE grown CdTe/GaAs

This work presents a study of the character and distribution of structural defects in (00l)CdTe buffer layers grown on GaAs substrates by metal organic vapour phase epitaxy (MOVPE). These are of importance as hybrid substrates for the growth of Cd(_x)Hg(1-x)Te (CMT), a prominent infrared detector material. The 14.5% mismatch between CdTe and GaAs leads to a high-density of dislocations at the CdTe/GaAs interface, and threading through the layer. The presence of linear and planar defects is detrimental to the performance of CMT devices and it is desirable to reduce the density of dislocations to below l0(^5)cm(^-2). Results of high resolution X-ray diffraction (HRXRD) studies on a series of MOVPE grown CdTe/GaAs epilayers of different thickness and on a single thick layer which was repeatedly etched and remeasured are reported. Threading dislocation density was estimated from HRXRD full width at half maximum (FWHM) using a relationship proposed by Gay, Hirsch and Kelly and was found to decrease rapidly in the initial stages of layer growth. An optimum buffer layer thickness of 8µm is proposed for the subsequent growth of CMT. Rocking curves were recorded from a single thick CdTe/GaAs epilayer for wavelengths in the range 0.69-1.95A at the Daresbury SRS, and this data is extrapolated to infinite absorption to obtain an estimate of the rocking curve width representative of the surface of a thick layer. A number of models which attempt to describe the reduction in threading dislocation density with increasing thickness are reviewed and a new model based on the coalescence of like dislocations is developed. The models are compared to published data for layers with misfit in the range 0.23-14.6%. The models previously developed by Tachikawa and Yamaguchi and by Durose and Tatsuoka are shown to be the more appropriate for describing the dislocation density distribution in highly mismatched layers. Results of the transmission electron microscopy of CdTe/GaAs epilayers, both in plan view and cross-section, showing the character of dislocations threading through thick CdTe buffer layers are presented. Many dipoles composed of 30º type dislocations with Burgers vectors parallel to the interface were observed and found to adopt an orientation whereby the component dislocations had no effect on misfit strain. In cross-section, 30º type dislocations with Burgers vectors inclined to the interface were found to be numerous, 60º and screw type threading dislocations were also observed, but the cross-section projection axis made analysis of these types difficult. The screw and edge components of 30º , 60º and screw type threading dislocations are compared and it is found that the Burgers vector component causing layer tilt is of magnitude (a(_o)/2) for each type. Annealing of CdTe/GaAs epilayers under di-methyl cadmium flow was found to have no deleterious effect on layer morphology but did not result in a narrower X-ray rocking curve. Based upon HRXRD FWHM, 8µm thick CdTe buffer layers grown by MOVPE are estimated to have a dislocation density of about 3xl0(^8)cm(^-2). Even after many of the threading dislocations have been bent over at the CdTe/CMT interface, their density in MOVPE grown CMT/CdTe/GaAs is still greatly in excess of the l0(^5)cm(^-2) desired. The issues discussed and conclusions drawn in this thesis represent a thorough study of the continuing progress towards high quality MOVPE growth of CMT

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described