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X-ray diffraction in thin layers containing small randomly placed defects is described by means of the kinematical diffraction theory and optical coherence formalism. The method enables us to calculate both the diffracted intensity and its angular distribution, so that it can be used for simulating double crystal and triple crystal x-ray diffractometry experiments. The theory has been applied to experimental data obtained from diffractometry measurements of an epitaxial ZnTe layer with mosaic structure after several steps of chemical thinning. A good agreement of the theory with experiments has been achieved. I. INTFlODUCTlONX-ray diffractometry is a powerful tool for characterizing the structure of thin monocrystalline layers. It is frequently used for determining the lattice parameters of the layer and the layer thickness. The crystalline quality of the layer has been characterized mainly by measuring the width of the rocking curve (FWHM) by means of x-ray double crystal diffractometry (DC).iw3 From the FWHM the dislocation density can be determined.4 This approach, however, has been developed for polycrystalline samples and in the case of single crystals it can only be used for a rough estimate.Triple crystal diffractometry (TC) is frequently used for investigating the x-ray diffuse scattering. It has been demonstrated'-* that contour maps of diffuse scattering measured near the reciprocal lattice point (RELP) are related with the defect structure of the sample.Structural defects in heteroepitaxial layers are caused mainly by threading dislocations and their climb.' They are generated by a coalescence process of seed islands occurring during a three-dimensional layer growth at the substrate surface. The crystallographic structure of relaxed heteroepitaxial layers can be modeled by the conception of mosaic structure. The mosaic block size corresponds with the mean distance between threading dislocations.The aim of this paper is to present a theoretical approach enabling us to calculate both the DC reflection curves and the TC contour maps of thin layers with randomly distributed small defects. We demonstrate that analyzing the entire form of a DC reflection curve we can get more information about the defects than using only FWHM. The general theory is used for calculating the DC "'Permanent address: Instituto de Pesquisas Espaciais, CP 515, 12201-S.J.Campos, SP, Brazil.reflection curves and TC contour maps of thin epitaxial layers with mosaic structure and the results are compared with DC and TC measurements of a ZnTe epitaxial layer grown on a GaAs substrate. II. X-RAY DIFFRACTION IN DISTORTED CRYSTALSWe restrict ourselves to the kinematical diffraction theory. This simplification can be performed if the total crystal thickness 7' is much smaller than the x-ray extinction length. In the case of diffraction on a thin distorted layer lying on a thick (or semi-infinite) substrate this approach is applicable if we do not consider the diffraction in the substrate, i.e., the substrate must not diffract if the layer...

Intensities of X-ray diffraction and X-ray diffuse scattering are calculated on the basis of the kinematical approximation of the statistical dynamical diffraction theory for crystals with randomly distributed small defects. Various approaches are derived for defect parameter determination (the density, size, and strength of defects) and some of them are compared with previously published X-ray methods. The theoretical results obtained for two various defect models are proved by double and triple crystal diffractometry measurements.Aufgrund der kinematischen Niiherung fur die statistische dynamische Beugungstheorie der Rontgenstrahlen in Kristallen mit statistisch verteilten Mikrodefekten werden die Beugungsintensitgt und die diffuse Streuung der Rontgenstrahlen berechnet. Verschiedene Methoden fur die Bestimmung der Defektparameter (Defektdichte, DefektgroRe und Kraft des Deformationsfeldes), die aus der Theorie folgen, werden mit publizierten Methoden verglichen. Die theoretischen Ergebnisse werden mit diffraktometrischen Messungen verglichen.

Abstract. X-ray diffraction in thin layers and layered systems is described using the optical coherence approach and the semi-kinematical diffraction theory. Two defect models in thin layers eve considered-the mosaic structure model and the model of interface roughness. For both defect models the reflection curves of a thin layer and a superlattice have been calculated and compared with double-crystal x-ray diffractometry results on superlattices and epitaxial layers. The distribution of the diffusely scattered intensity near a reciprocal lattice point has been calculated theoretically for both models and it has been proved experimentally by double-and triple-crys!al diffractometry of epitaxial layers with mosaic structure. It has been demonstrated that the theory yields a tool for estimating the predominant defect type in a layered structure.

The structural defects in a (GaAs)J(AIAs), superlattice are studied experimentally and theoretically as well. Three models for the defects are proposed, which follow from the SL growth kinetics. Direct expressions for the reflectivities are derived from the semikinematical approximation of X-ray diffraction, assuming that the statistical parameters characterizing the defect models are distributed normally. On the basis of a numerical fit of the theoretical and experimental double crystal X-ray rocking curves the mean lattice parameter and the mean chemical composition as well as their statistical dispersions are found for a [(GaAs),/(A1As),],,, superlattice. The X-ray diffraction curves enable one to find the most probable model for the actual structural defects in the real superlattice.Die Strukturdefekte in einem (GaAs)J(AIAs),-Supergitter werden theoretisch und experimentell untersucht. Drei verschiedene Defektmodelle werden angenommen, die aus der Wachstumskinetik der Supergitter folgen. Aufgrund der semikinematischen Beschreibung der Rontgenbeugung in Supergittern werden die gebeugten Intensitaten unter der Voraussetzung berechnet, daD die Strukturdefekte im Kristall statistisch verteilt sind. Aus dem Vergleich der theoretischen und experimentellen Rokkingkurven werden die Parameter der Supergitter (die Gitterkonstante und die chemische Zusammensetzung) und ihre statistische Dispersionen bestimmt. Die Analyse der gemessenen Rockingkurven ermoglicht, das wahrscheinlichste Defektmodell in den realen Supergittern zu finden.

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Nitrogen doping during crystal growth is used to create nitrogen–vacancy(–oxygen) complexes. These complexes enhance the nucleation of silicon oxide precipitates. The precipitates and other volume defects in silicon wafers serve as gettering centres for metal impurities during the device processing. We have studied nitrogen-doped silicon wafers (001) from the origin, middle and end of the ingot, annealed at low (750°C) and high (1050°C) temperatures, using triple-axis high-resolution x-ray diffraction. The reciprocal space intensity distributions from clusters, stacking faults and dislocation loops were modelled using the Krivoglaz theory and a continuum model of the defect deformation field. Good agreement of the theory with the experimental data was achieved for the model of dislocation loops. The symmetry of measured reciprocal space maps determines the type of dislocation loops and from extracted linear scans in the ⟨111⟩ direction we can obtain the radius and concentration of the loops. These parameters were combined with the results from selective etching and infrared absorption spectroscopy. Concentration of interstitial oxygen, shape, stoichiometry and volume fraction of precipitates were obtained from absorption spectra taken at room and liquid nitrogen temperature.

We report on the technology and basic electrical properties of ten-fold stacked Nb/Si/Nb Josephson junction (J J PACS numbers: 68.65.+g, 7/~.50.+r,