Determination of strain in epitaxial semiconductor structures by high-resolution X-ray diffraction

High-resolution X-ray diffraction is used to obtain the strain profile of a wide range of epitaxial semiconductor samples. The samples are divided into five categories: Strained layers on a substrate, (partly) relaxed layers on a substrate, strained-layer superlattice structures, multiple relaxed layers and relaxed superlattice structures and ionimplanted samples. For each category a measurement strategy and analysis method is given. Representative examples for each category are shown.     

Early-stage ordering in in-situ annealed Fe51Pt49 films

We evidenced an early-stage ordering (ESO) in Fe₅₁Pt₄₉ film before the appearance of superlattice diffraction (long-range-order, LRO) using 40-nm-thick films prepared by magnetron sputtering onto quartz substrate. The appearance of L1₀ phase for samples deposited at substrate temperatures (T_s) 400 °C and higher was verified by X-ray diffraction. Surface roughness of Fe₅₁Pt₄₉ films, obtained via X-ray specular reflectivity with computational fitting, increases from 3.8 to 11 Å as T_s is increased from 25 to 275 °C. As further increase of T_s to 375 °C, the roughness drops to 3.2 Å and then increases again to 38 Å with T_s up to 700 °C. Measurement on residual strain demonstrates that it is initially compressive at T_s<400 °C. Thereafter the strain transfers to a tensile one and increases in magnitude as increasing T_s up to 700 °C corresponding to LRO transformation. Local atomic rearrangement is observed for samples deposited at T_s>250 °C by using extended X-ray absorption fine structure. Coercivity of films increases from 10 to 460 Oe as T_s increase from 25 to 375 °C (ESO) and then from 460 to 10,700 Oe with T_s 375-700 °C (normal LRO). The worked out quantitative estimation of ESO engages with that of LRO before T_s 400 °C.     

Angular parameters in X-ray diffraction theory

In this article, we provide a detailed mathematical analysis of the Helmholtz equation, in the context of dynamical wide-angle X-ray scattering by deformed crystals. We show that the dynamical theory of diffraction may be written without introducing a sophisticated dispersion theory, by using the following simple condition for wavevectors: |K_h|=|K₀|=k. This choice gives simple way to describe the reciprocal space mapping phenomena in a dynamical approach and simulate the diffraction curves for strained crystals over many orders of reflection. Several theoretical approaches to obtaining the angular distribution of scattered intensity are discussed.     

Structural and Magnetic Properties of Codoped ZnO based Diluted Magnetic Semiconductors

Zn1-xCoxO （x = 0.01, 0.02, 0.05, 0.10 and 0.20） diluted magnetic semiconductors are prepared by the sol-gel method. The structural and magnetic properties of the samples are studied using x-ray diffraction （XRD）, extended x-ray absorption fine structure （EXAFS） and superconducting quantum interference device （SQUID）. The XRD patterns does not show any signal of precipitates that are different from wurtzite type ZnO when Co content is lower than x = 0.10. An EXAFS technique for the Co K-edge has been employed to probe the local structures around Co atoms doped in ZnO powders by fluorescence mode. The simulation results for the first shell EXAFS signals indicate that Zn sites can be substituted by Co atoms when Co content is lower than x = 0.05. The SQUID results show that the samples （x 〈 0.05） exhibit clear hysteresis loops at 300K, and magnetization versus temperature from 5 K to 350K at H = 100 Oe for the sample x = 0.02 shows that the samples have ferromagnetism above room temperature. A double-exchange mechanism is proposed to explain the ferromagnetic properties of the samples.     

A study of symmetrical LLL X-Ray polylithic interferometers on the basis of the Takagi equations

The Takagi approach to the dynamical theory of x-ray diffraction has been used to study LLL x-ray polylithic interferometers. A computational tool has been implemented to solve the Takagi equations with boundary conditions of the Cauchy type. The mean intensity, visibility and initial phase of the x-ray fringes generated by displacing the analyzer have been calculated for any wavefront, absorption of the incident radiation and for the most common geometric arrangements. Geometric aberrations of different kinds, introduced during interferometer preparation, are considered. The curve relevant to the calculated difference between the reflected and transmitted x-ray fringes as a function of analyzer rotation is in agreement with the experimental curve.     

Curved crystal analysis using a triple-crystal X-ray spectrometer

A Bragg crystal spectrometer using cylindrically curved crystals is designed to focus a divergent X-ray beam. The spectral resolution and precision of focus is determined by the quality of the concavely curved crystal. The analysis of the quality of the crystal was done using a triplecrystal X-ray spectrometer, comparing parallel and antiparallel X-ray scans of the third curved crystal, determining flaws resulting from the bend. Topics discussed include the derivation of the crystal's quality, conditions of alignment for the Bragg reflection, and X-ray beam width contributions to the FWHM. Organic and inorganic crystals with varying values of Bragg angles are used.     

EXAFS and XRD studies of an amorphous Co57Ti43 alloy produced by mechanical alloying

We have investigated the local atomic order of an amorphous Co₅₇Ti₄₃ alloy produced by mechanical alloying by means of x-ray diffraction and EXAFS analyses on Co and Ti K-edges. Average coordination numbers and average interatomic distances between first neighbors where found from EXAFS and compared with those determined using an additive hard sphere (AHS) model associated with an deconvolution, and also with data from bcc- Co₂Ti compound. EXAFS results obtained indicated a shortening in the Co-Ti and Ti-Ti average interatomic distances when compared to those found by using the AHS-RDF method and an increase in the Co-Co and Ti-Ti average interatomic distances and a shortening in the Co-Ti one when compared to the interatomic distances found in the bcc- Co₂Ti compound. In spite of these differences, average coordination numbers obtained from EXAFS and AHS-RDF are similar to each other and also to those found in bcc- Co₂Ti.     

Local electronic structure around Mn and Ga in Mn-doped GaN films showing room temperature ferromagnetism

Local electronic structures around Ga and Mn in Mn-doped GaN film with T_c of 940 K are investigated by K X-ray absorption near edge structure (XANES) analysis. It was found that the shape of the Ga XANES spectrum is remarkably similar to that of the un-doped GaN film indicating that the local electronic structure around Ga is not disturbed with Mn doping. As for the Mn XANES spectra, obvious pre-edge peaks were observed: the fine structures in the pre-edges correspond with calculated Mn 3d partial density of states which predict impurity band formation with the Fermi energy stays in the spin-up band. These findings imply that Mn 3d levels stay within the gap with the Fermi energy stays in the spin-up band.     

Adsorption model determination of N2O/Ag(1 1 0) by theoretical studies of near-edge X-ray absorption fine structure

The nitrogen 1s near-edge X-ray absorption fine structure (NEXAFS) spectra of the N₂O adsorbed on Ag(1 1 0) have been studied by the multiple-scattering cluster (MSC) and self-consistent field (SCF) DV-Xα methods. Two adsorption models, in which the N₂O molecule attached to the Ag substrate through the central nitrogen (N_C) atom and the terminal nitrogen (N_T) atom, respectively, have been checked up thoroughly. The MSC calculation and the R-factor analysis show that the N₂O molecule is attached to the Ag substrate through the terminal nitrogen atom with the adsorption height h = 3.4 ± 0.1 Å. In the overlayer the N₂O molecules arrange themselves into a tilted chain due to the interaction between the cations and the anions in the molecules. The physical cause of the resonances in the NEXAFS spectra mentioned above has been discussed by the DV-Xα method, which confirms the MSC calculations.     

Local structures of Mn in dilute magnetic semiconductor ZnMnO

The local structures of Mn atoms in (Zn, Mn)O have been investigated by extended x-ray absorption fine structure (EXAFS). For samples with lower Mn concentrations (<11%), EXAFS results show that the majority of Mn atoms are incorporated at Zn substitutional sites. Ferromagnetic behavior has been observed in those ZnMnO samples. It is the direct evidence to suppose that the ferromagnetism in (Zn, Mn)O is not due to Mn-related secondary phases but is intrinsic. When the Mn concentration is increased to 20% or higher, the EXAFS simulation shows the formation of MnO secondary phases and the films show a change from ferromagnetic (FM) to antiferromagnetic (AFM) state. We suggest that Mn-related secondary phases might be responsible for the transformation from FM to AFM state.     

Theoretical studies of the structure of C2H2 adsorbed on Si(0 0 1)

The carbon 1s near-edge X-ray absorption fine structure (NEXAFS) spectra of the acetylene (C₂H₂) at 1 ML coverage adsorbed on the Si(0 0 1)-(2 × 1) surface at room temperature have been investigated by multiple-scattering cluster (MSC). The MSC result shows that the correct adsorption model of C₂H₂/Si(0 0 1)-(2 × 1) is unique, i.e. the dimerized structure with two domains, (2 × 1) and (1 × 2).     

Residual surface stress measurements in YBa2Cu3Ox superconductors

XRD and residual surface stress (sin² ψ) measurements were carried out on YBa₂Cu₃O_x superconductors with varying oxygen stoichiometry (6.3 < x < 7.0). Slopes of the surface strain versus sin² ψ were plotted against oxygen content for certain reflections. Compressional surface stress has been found along the c-axis, while a tensile surface stress has been observed along the ab-plane. Both surface stresses were found to vary slightly with oxygen content. These findings qualitatively agree with a very small hydrostatic pressure effect on T_c for fully oxygenated YBa₂Cu₃O_x (x = 7) compared to oxygen deficient material at the surface.     

Extended X-ray absorption fine-structure (EXAFS) of a complex oxide structure: a full multiple scattering analysis of the Au L3-edge EXAFS of Au2O3

Crystalline Au₂O₃ was obtained by hydrothermal synthesis at 3000 atm and its extended X-ray absorption fine-structure (EXAFS) at the Au L₃-edge was measured at room temperature. A detailed full multiple scattering (MS) analysis using FEFF8 theory shows that only a small number of scattering paths contribute significantly to the EXAFS of Au₂O₃. Because of the complex unit cell (low local symmetry) of the Au₂O₃ structure, contributions of MS paths are almost negligible. The results indicate that FEFF8 theory provides a good reference for the analysis of Au-O phases.     

Microstructure of Epitaxial Er2O3 Thin Film on Oxidized Si (111) Substrate

Er₂O₃ thin films are grown on oxidized Si (111) substrates by molecular beam epitaxy. The sample grown under optimized condition is characterized in its microstructure, surface morphology and thickness using grazing incidence x-ray diffraction (GIXRD), atomic force morphology and x-ray reflectivity. GIXRD measurements reveal that the Er₂O₃ thin film is a mosaic of single-crystaldomains. The interplanar spacing d in-plane residual strain tensor ε_| and the strain relaxation degree ξ are calculated. The Poisson ratio μ obtained by conventional x-ray diffraction is in good agreement with that of the bulkEr₂O₃. In-plane strains in three sets of planes, i.e. (440), (404), and (044), are isotropic.     

Morphological and structural characterizations of CrSi2 nanometric films deposited by laser ablation

The structure and morphology of chromium disilicide (CrSi₂) nanometric films grown on 〈1 0 0〉 silicon substrates both at room temperature (RT) and at 740 K by pulsed laser ablation are reported. A pure CrSi₂ crystal target was ablated with a KrF excimer laser in vacuum (∼3 × 10⁻⁵ Pa). Morphological and structural properties of the deposited films were investigated using Rutherford backscattering spectrometry (RBS), grazing incidence X-ray diffraction (GID), X-ray reflectivity (XRR), scanning (SEM) and transmission electron microscopy (TEM). From RBS analysis, the films’ thickness resulted of ∼40 nm. This value is in agreement with the value obtained from XRR and TEM analysis (∼42 and ∼38 nm, respectively). The films’ composition, as inferred from Rutherford Universal Manipulation Program simulation of experimental spectra, is close to stoichiometric CrSi₂. GID analysis showed that the film deposited at 740 K is composed only by the CrSi₂ phase. The RT deposited sample is amorphous, while GID and TEM analyses evidenced that the film deposited at 740 K is poorly crystallised. The RT deposited film exhibited a metallic behaviour, while that one deposited at 740 K showed a semiconductor behaviour down to 227 K.     

Synthesis and structure of the monolayer hydrate K0.3CoO2·0.4H2O

The monolayer hydrate (MLH) K_0.3CoO₂·0.4H₂O was synthesized from K_0.6CoO₂ by extracting K⁺ cations using K₂S₂O₈ as an oxidant and the subsequent intercalation of water between the layers of edge-sharing CoO₆ octahedra. A hexagonal structure (space group P6₃/mmc) with lattice parameters a=2.8262(1) Å, c=13.8269(6) Å similar to the MLH Na_0.36CoO₂·0.7H₂O was established using high-resolution synchrotron X-ray powder diffraction data. The K/H₂O layer in the K-MLH is disordered, which is in contrast to the Na-MLH. At low temperatures metallic and paramagnetic behavior was found.     

Study of buried Si(1 1 1)-5 × 2-Au by surface X-ray diffraction

The structure of buried Si(1 1 1)-5 × 2-Au capped with amorphous Si was investigated using surface X-ray diffraction. It was found that the 5 × 2 structural periodicity is kept under the amorphous Si from the in-plane measurement. Furthermore, the intensity variation along the fractional-order rod indicates that Au atoms are located almost on the same plane.     

Disordered surface sheets in solid matter near bulk instabilities

In this article, I review surface-sensitive X-ray scattering experiments using evanescent X-ray scattering and asymptotic Bragg scattering techniques which have been carried out in order to investigate the thermodynamic behaviour of the surface and the subsurface layers when the bulk of the system approaches a phase transition. I discuss the surface structures of the binary alloys Fe₃Al and Cu₃Au close to the order-disorder transition, the surface of the molecular crystal NH₄Br near the critical temperature and ice single-crystal surfaces close the bulk melting point. The observed surface phenomena range from surface disorder and surface-induced new universal critical behaviour to surface melting and surface segregation. They all have in common that they are not bound to the outermost layers, but rather occur within a surface sheet whose thickness can grow to a mesoscopic or even macroscopic size.     

Age-induced phase transitions on mechanically alloyed amorphous GaSe

After aging it for four years at room temperature, a mechanically alloyed amorphous GaSe powder was transformed to a multi-phase crystalline alloy, where major phase is the trigonal Se one. The structural, thermal and optical properties of this aged amorphous GaSe were investigated through systematic X-ray diffraction, differential scanning calorimetry and Raman scattering measurements. The X-ray diffraction results on the aged GaSe powder suggest the presence of oxides, and X-ray absorption spectroscopy was employed to further investigate it.     

3D DuMond diagrams of multi-crystal Bragg-case synchrotron topography. I. Flat sample

The 3D representation of the DuMond diagram is used to explain the dimensional features of X-ray topographs obtained by multi-crystal configuration with a synchrotron beam. Symmetric Bragg-case reflections are considered for a flat double-crystal monochromator and a flat sample. Two ways of sample alignment are taken into account. They are referred to as σ–σ and σ–π geometries, where the diffraction plane of the sample is parallel and perpendicular, respectively, to the vertical diffraction plane of the monochromator (σ polarization). It is shown that the shape of the sample image is closely connected to the shape the diffraction domain common to monochromator and sample assumes in the 3D DuMond diagram. An experiment is reported for the less commonly used σ–π topography, showing how the lattice mismatch and its lateral homogeneity are determined in samples made by epilayer and substrate. Received: 31 July 2000 / Accepted: 25 January 2001 / Published online: 3 May 2001