Triple-crystal X-ray Diffractometry Research Articles

Dynamical theory of X-ray diffraction by crystals with different surface relief profiles.

A dynamical theory is developed of X-ray diffraction on a crystal with surface relief for the case of high-resolution triple-crystal X-ray diffractometry. Crystals with trapezoidal, sinusoidal and parabolic bar profile models are investigated in detail. Numerical simulations of the X-ray diffraction problem for concrete experimental conditions are performed. A simple new method to resolve the crystal relief reconstruction problem is proposed.

Simulation of Reciprocal Space Maps with the Use of Spectral Angular Diagrams in the Triple Crystal X-Ray Diffraction Scheme

An approach to the simulation of reciprocal space maps corresponding to the maps obtained experimentally by the triple crystal X-ray diffractometry (TXD) is proposed. A specific feature of the approach is the use of spectral angular distribution diagrams of X-ray radiation, which allows one to visualize the two-dimensional pattern of the spectral angular “composition” of an X-ray beam after its interaction with each element of the scheme and thus to take into account the contribution of the hardware function of the experimental setup. The algorithms developed allow calculations for a wide class of radiation sources (from an X‑ray tube with any material of the anode to a synchrotron radiation source) and X-ray optical elements (slits, X-ray mirrors of monochromators, and analyzers). The results of simulation are compared with the experimental data for dispersive diffraction geometry, which confirms the adequacy of the proposed approach and its applicability to the simulation of a diffraction pattern corresponding to a real experiment in the triple crystal scheme.

Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

Dynamical Theory of Triple-Crystal X-ray Diffractometry and Characterization of Microdefects and Strains in Imperfect Single Crystals

Formation of unusual nonferroic domains in TeO2 single crystals under external electric field

The formation of unusual slowly relaxing domains under an external dc electric field has been revealed in paratellurite (TeO2) crystals. These domains differ from those arising in ferroics (ferromagnets, ferroelectrics, ferroelastics, etc.). The effect is characterized by the existence of a threshold field strength (at which domains begin to be formed) and long equilibrium settling times (up to a few hours, depending on the electric field strength). A crystal returns to the initial single-domain state also after a few hours after the field is switched off. High-resolution triple-crystal X-ray diffractometry has revealed that domains retaining the paraelastic tetragonal phase rotate with respect to each other in space without changing their lattice parameter. The domain sizes are 2–4 mm, depending on the field strength. Currently, the exact mechanisms of domain formation are unclear. Possible reasons for the formation of these defects and an analogy of the observed effects with the behavior of liquid crystals under electric field are discussed.

Phase diffraction gratings based on a Si(400) crystal

The X-ray optical properties of diffraction gratings fabricated on the basis of a Si(400) crystal with a period of D = 1 μm are studied by triple-crystal X-ray diffractometry. The diffraction gratings are manufactured both by silicon profiling during the process of plasma chemical etching and by forming a phase-shift grating on the surface of a Si crystal. The principal difference in the diffraction properties of these gratings is demonstrated. The presence of an Au phase-shift grating is shown to lead to the formation of a two-dimensional diffraction pattern, whereas Si profiling leads to the formation of only a one-dimensional diffraction pattern.

Anomalous X-ray transmission through sapphire crystals

The triple-crystal X-ray diffractometry of anomalous X-Ray transmission is used to investigate sapphire single crystals grown in protective gaseous media with the help of the horizontal directional-crystallization method. The dependences between the integral intensities of anomalously transmitted and Bragg-Laue reflected X-ray beams (Ti and Ri, respectively) and the thickness of the samples under study, which enable us to determine regions of thin- and thick-crystal approximation, have been obtained at 2.52 ≤ μt ≤ 18.9. The integral coefficient μi of interference absorption and the integral characteristic yi are calculated in the dynamic thick-crystal approximation. It is demonstrated that dislocations are distributed mainly within the small-angle boundaries of a grown sapphire crystal. It is ascertained that the parameter μi is highly sensitive to the dislocation density and the pattern of the dislocation distribution in a crystal.

Double- and triple-crystal X-ray diffractometry of microdefects in silicon

Double- and triple-crystal X-ray diffractometry of microdefects in silicon

Formation of porous nanostructured lead telluride films by an anodic electrochemical etching method

Comprehensive research of the structural, optical and electrical properties of a PbTe/CaF2/Si(1 1 1) epitaxial system after anodic electrochemical treatment in a Norr solution electrolyte with a low current density of 6 mA cm−2 was carried out. It is shown that the anodizing results in the increase of the band gap and resistivity and in the decrease of the refractive index of lead telluride. Using secondary ion mass spectrometry, a specific change of the C, K, H element distribution in depth of PbTe films after electrochemical treatment was detected. It is demonstrated that the set of presented experimental results can be explained from the standpoint of the formation of a mesoporous structure of lead telluride with a porosity value of about 50%. The effective radius of PbTe nanoparticles is equal to 13 nm. Triple-crystal x-ray diffractometry results analysis showed that the pores have spherical voids with an average dimension of 40 nm.

X-ray study of structural features of GaSb(Si) single crystals grown using a set of diffraction methods under various heat and mass transfer conditions

Structural features of GaSb(Si) single crystals grown under various heat and mass transfer conditions were studied by x-ray topography and by double- and triple-crystal diffractometry. It was shown that a decrease in the convective flow intensity during crystal growth by the vertical Bridgman method with axisymmetric upper heat supply in comparison with the Czochralski method eliminates growth striations (caused by microsegregation) and improves the uniformity of electrical parameters of materials. According to triple-crystal x-ray diffractometry data, the increased density of structural defects observed in some crystal regions causes significant lattice distortions, which makes an additional contribution to crystal inhomogeneity. Some specific features in x-ray topography images of growth striations, caused by a high silicon concentration and a dopant state deviation from an ideal substitutional solid solution, were revealed.

X-ray diffraction investigation into the specific features of the growth kinetics of oxygen-containing precipitates in Czochralski-grown silicon crystals

The formation and growth of defects (precipitates and dislocation loops) during isothermal decomposition of a supersaturated oxygen-containing solid solution in Czochralski-grown silicon crystals are investigated using triple-crystal x-ray diffractometry. It is established that oxygen-containing precipitates grow through diffusion and that the formation of dislocation loops is associated with both the coagulation of embedded silicon atoms and the generation of dislocation loops by stresses induced in the vicinity of the oxygen-containing precipitates.

Characterization of porous InP(001) layers by triple-crystal X-ray diffractometry

The structure of porous layers fabricated on the surface of an InP(001) semiconductor wafer by electrochemical oxidation has been studied by triple-crystal X-ray diffractometry. It is shown that, depending on the probe potential (current density), column-shaped pores of two types with different orientations with respect to the substrate are formed. It is established that, at a probe potential of ∼6 V, pores are extended along the current lines (CLO pores) and directed normally to the sample surface. With a decrease in the potential to ∼3 V, the longitudinal axes of pores are oriented at an angle of ζ = 52° ± 2° to the sample surface (CO pores). The average diameter and length of pores are determined (∼80 and 300–900 nm, respectively) and the porosity of the samples is evaluated (P ∼ 40–60%). The obtained data on the pore parameters are in satisfactory agreement with the scanning electron microscopy data.

Acoustic Pulse Echoes Probed with Time-Resolved X-Ray Triple-Crystal Diffractometry

Acoustic pulse echoes generated by femtosecond laser irradiation were detected using time-resolved x-ray triple-crystal diffractometry. The determined time-dependent longitudinal strain component for pulse echoes in silicon and gallium arsenide plates showed that the polarity of the strain pulse was dependent on the optically induced initial stress, and that the bipolar pulse waveform was gradually deformed and broadened in the course of propagation. The three-dimensional wave front distortion of pulse echoes was shown simply as the pulse duration broadening, which was consistent with a boundary roughness for an unpolished plate.

Determination of the dynamic deformation tensor by time-resolved triple-crystal diffractometry

Triple-crystal X-ray diffractometry has been combined with time-resolved measurement techniques. A simple time-resolved technique was employed by using a digital storage oscilloscope and a fast X-ray detector. The time dependence of the deformation tensor was determined for a gallium arsenide wafer after a flash of a 130 fs laser pulse. The laser pulse produced instantaneous expansion resulting in a localized convex surface. Time-resolved measurements showed that a flexural standing wave, explained well by the classical elasticity theory for thin plates, appeared in the relaxation process.

X-ray Diffraction Study of the Effect of Neutron Irradiation on the Defect Formation in Silicon Crystals Grown by the Czochralski Method and Annealed at High Temperatures

The effect of x-ray scattering by neutron-irradiated and reference (unirradiated) silicon crystals grown by the Czochralski method and annealed at temperatures of 850–1050°C on the defect formation is comparatively investigated using triple-crystal x-ray diffractometry. The sizes and concentrations of clusters composed of point defects and dislocation loops formed during decomposition of an oxygen-containing solid solution and subsequent clusterization of the point defects are calculated.

X-ray diffraction determination of the interface structure of CdSe/BeTe superlattices

Structural study of CdSe/BeTe superlattices (SLs) grown by molecular beam epitaxy on GaAs substrate was performed by using double and triple crystal x-ray diffractometry. The period of the studied structures was about 5 nm, while the thickness of thin CdSe insertions varied from 0.4 to 1.5 monolayer. It is shown that new Be–Se bonds arise at the BeTe–CdSe interfaces in addition to the Be–Se bonds expected at the CdSe–BeTe interfaces. From the analysis of the diffraction curves of 002-reflection the complex composition of interfaces and thin insertions has been determined and contribution of all types of bonds in each SL period calculated. The diffraction curves of 004-reflection were used for the specification of the fine structure of the interfaces.

X-ray diffractometric study of the influence of a buffer layer on the microstructure of molecular-beam epitaxial InN layers of different thicknesses

Thin layers of InN are grown by molecular beam epitaxy on (0001) sapphire substrates. The influence of thin (15 nm) InN buffer layers and their temperature treatment on the structural quality of the grown layers is investigated by double-crystal and triple-crystal x-ray diffractometry. It is revealed that the preliminary high-temperature (900°C) annealing of the buffer layer leads to a notable improvement in the quality of the layers grown on this buffer. The densities of vertical screw and vertical edge dislocations decrease (to 1.9×108 cm−2 and 1.3×1011 cm−2, respectively) with an increase in the distance from the interface (by ∼1 µm).

Morphological and structural characteristics of homoepitaxial 4H-SiC thin films by chemical vapor deposition using bis-trimethylsilylmethane precursor

High quality 4H-SiC monocrystalline films were homoepitaxially grown on 8.0° off-oriented (0001) 4H-SiC at a low temperature (1643 K) by metal-organic chemical vapor deposition (MOCVD). The correlation between the structural properties of the films and the growth parameters, in particular, the substrate temperature, and the flow rate of source material BTMSM, was investigated to elucidate the possible benefits of a single precursor on low-temperature thin film growth. The films were examined by optical microscopy, scanning electron microscopy (SEM), triple crystal X-ray diffractometry (TCD), and photoluminescence. Reciprocal space mapping results of the (0004) Bragg spot showed that the full width at half maximum (FWHM) of the rocking curve of the epilayer grown at 1643 K was 9.3 arcsec, which is extremely low as compared with the lowest value reported (13 arcsec). The high film quality was confirmed by low-temperature photoluminescence. The homoepitaxial growth condition for high quality monocrystalline 4H-SiC was also suggested in terms of the growth temperature and supersaturation of the source material.

Effect of Duration of Thermal Diffusion of Boron on Silicon Structure Studied by Triple-Crystal X-ray Diffractometry

Effect of Duration of Thermal Diffusion of Boron on Silicon Structure Studied by Triple-Crystal X-ray Diffractometry

Study of surface and interface roughnesses in porous silicon by high-resolution X-ray methods

The methods of triple-crystal X-ray diffractometry and the total external X-ray reflection are used to study porous silicon films on a p-type single crystal Si(111) substrate. For the first time, an increase of the pseudopeak intensity was experimentally observed for thick porous films. The following film characteristics are determined: thickness (1.8 μm), strain (3.8 × 10−3), porosity (70%), pore size (∼5 nm), roughness height of the surface (∼3 nm) and the film—substrate interface (∼7 nm), and correlation length (∼7–10 nm). It is shown that the main contribution to the pseudopeak intensity for thin films on single crystal substrates comes from angular broadening of the incident beam formed by the exit slit of a monochromator of a finite width. It is shown that the method is very sensitive to density inhomogeneity in subsurface crystal layers.

Anisotropy of fields of stress in Si monocrystals with ordered dislocation structure

An attempt is made with X-ray triple crystal diffractometry to detect anisotropy of X-ray scattering by a structure consisting of a number of parallel dislocations, introduced into silicon by specially controlled sample deformation. Diffuse component scattering increased if the plane of scattering was perpendicular to the direction of dislocations ( ϕ=90°). The magnitude of this effect increases with increasing density of the introduced dislocations and depends on the direction of their Burgers vectors. The respective changes of the equal-intensity contours of X-ray scattering near reciprocal lattice points for the 111 reflection are investigated. The magnitudes of coherent and diffuse components of integral reflectivity were obtained experimentally. This yields quantitative information on the diffraction characteristics of structural perfection of the material. The dependencies of these characteristics are given, as well as of half-widths of a principal peak of a diffraction curve, on the angle of sample orientation relative to the X-ray beam ϕ and ϑ B. A comparison of appropriate data with those obtained for dislocation-free crystals of non-crucible zone melting silicon is carried out. The results obtained are discussed within the framework of existing theories of X-ray scattering and dislocation complexes.