Dynamical X-ray Diffraction Research Articles

A sensitive method to detect strain in silicon crystals using X-ray dynamical diffraction

A very sensitive method to detect long-range strain in otherwise perfect crystalline materials is presented. In this method, a specimen is set vertically in a diffraction apparatus under the symmetrical Laue condition, in which the scattering vector is horizontal. The specimen is then rotated along the scattering vector, with the Bragg condition being kept satisfied. Experiments were carried out using Si crystals of 714 µm thickness with X-rays of 0.4 Å wavelength. The Si crystals were strained by scratching the surface with a glass-cutter. A characteristic behaviour of the integrated intensities was observed. When the specimens were rotated in the opposite direction, the integrated intensities were different and sharply enhanced integrated intensities of the higher order reflections were observed when the specimens were rotated from their initial vertical positions. The observed results can be explained using the dynamical theory of X-ray diffraction for distorted crystals, with the assumption that the specimens were bent along an axis lying on the specimen surface. This method of rotating the crystal along the scattering vector is a very sensitive method to detect minute strains induced by device fabrication processes. The detection limit for the presented specimen is estimated to be equivalent to a uniform bending with a radius of curvature of 7000 m.

A universal computation method for two-beam dynamical X-ray diffraction.

A general-purpose method that includes nearly all possible two-beam diffraction mechanisms is presented for calculating diffracted and specularly reflected X-ray intensities from single crystals. Based on this method, it is demonstrated that a small universal computational routine can be developed to accurately treat two-beam diffraction for any scattering geometry.

Interdiffusion in Coherent Si0.90Ge0.10/Si0.95Ge0.05 Superlattices

ABSTRACTWe present the use of x-ray scattering from Si1-XGeX/Si1-YGeY superlattices as a tool for measuring the concentration dependence of interdiffusivity in Si/SiGe epitaxial thin films. Although x-ray scattering from compositionally modulated films is an ultra-high-sensitivity technique for measuring interdiffusion in a variety of systems, the concentration dependence of Si/SiGe interdiffusion complicates its interpretation. We show that these complications can be avoided using Si1-XGeX/Si1-YGeY superlattices with a small compositional modulation. This strategy is assessed using numerical simulations of both interdiffusion and dynamical x-ray diffraction. We demonstrate its effectiveness by measuring the activation enthalpy and exponential prefactor for interdiffusion in compressively strained Si0.925Ge0.075. The results are 4.38 ± 0.05 eV and 36 ± 9 cm2/s respectively.

The generalized pendulum analogy of the X-ray dynamical diffraction by one-dimensional regularly deformed crystals.

The pendulum analogy has been generalized in a form suitable for the case of an off-Bragg position. It is shown that, by introducing a time variation of the pendula masses, this analogy can be supplied to simulate the X-ray dynamical diffraction by a one-dimensional regularly deformed crystal. The correspondence between the adiabatic invariants of the new mechanical system and the invariants of the Eikonal approximation of the X-ray dynamical theory is established

Resonant x-ray intensity enhancement in a two-layer crystalline heterostructure

By using numerical simulation, we have found a resonant x-ray intensity enhancement taking place under high-angle x-ray dynamical diffraction in a two-layer crystalline heterostructure. This enhancement is shown to be associated with the excitation of guided modes inside the structure.

Determination of the parameters of a rough surface from the dynamical X-ray diffraction data

A new method is proposed for determining the roughness parameters from X-ray diffraction data. The method is based on a controllable displacement of reflecting planes under an external tangential pressure. It is shown that the displacement of atomic planes near the rough surface upon sample compression increases in proportion to the applied stress and strongly depends on the roughness parameters. Rough surfaces with determinate periodic and random reliefs are considered together with the corresponding features of X-ray rocking curves.

On the Theory of X-Ray Diffraction and X-Ray Standing Waves in the Multilayered Crystal Systems

The theory for the Bragg dynamical X-ray diffraction and the yield of the secondary radiation scattered via incoherent channels under conditions of X-ray diffraction (X-ray standing wave technique) is developed for the crystal systems composed from many layers. The formulae are derived in a form suitable for a computer simulation of the experimental angular or energy spectra as well as for a determination of unknown parameters via fitting. The Bragg case (reflection) and the Laue case (transmission) are considered within the same approach. The universal computer program is created and its operation is demonstrated on two examples. It is shown that the model of the multilayered crystal system may be a useful tool for analyzing a lot of problems where the one-dimensional crystal-lattice distortions of different kinds influence the rocking curve and the curve of the secondary radiation yield. In the first example the In0.5Ga0.5P epitaxial film on the GaAs substrate is considered. The experimental angular spectra of the X-ray reflectivity and the yield of the In Lα and P Kα fluorescence in the Bragg case are described by fitting the parameters of the structure. In the second example the Laue case of X-ray diffraction in a sample having a monotonously increasing (decreasing) shift of the Bragg angle with increasing depth is analyzed. The phenomenon of the complete switching of the X-ray beam from the incident direction to the direction of reflection is calculated and discussed.

Determination of strain state and composition of highly mismatched group-III nitride heterostructures by x-ray diffraction

We present an accurate model for the dynamical x-ray diffraction analysis ofhighly mismatched materials systems. Our approach features an exact incidenceparameter as well as an exact calculation of the changes of Bragg angle andlattice plane inclination due to strain. We show that the commonly usedapproximations for these parameters are, in general, unable to describediffraction profiles of different reflections consistently, and utterly fail fora strain on the order of 1% or more. The model as presented explicitlyconsiders crystals with zincblende and wurtzite structure of arbitrary orientation and theresulting distortions. The validity of our model is demonstrated by various experimental examples, including closely lattice-matched GaAs/AlAs structures on GaAs(001) and GaAs(113),as well as highly mismatched GaN layers, (Al, Ga)N/GaN and GaN/(In, Ga)N heterostructures on 6H-SiC(0001) and γ-LiAlO2(100).

Динамическая дифракция рентгеновских лучей в сверхрешётках

Динамическая дифракция рентгеновских лучей в сверхрешётках

Influence of ultrasonic vibrations on thermal diffuse scattering in X-ray dynamical diffraction conditions

A theory of thermal diffuse scattering (TDS) in a crystal disturbed by high frequency ultrasonic vibrations is considered. In this case additional X-ray reflexes (satellites) are formed which can be used for obtaining information about vibrational excitations in a crystal. By varying the incident angle one can excite all the satellites one after another and detect the variation in the TDS yield. The possibilities of the experimental observation of these phenomena will also be discussed.

STUDIES OF THE IMPURITY EFFECTS ON CRYSTALLINE QUALITY BY HIGH-RESOLUTION X-RAY DIFFRACTION

Sr(NO3)2 single crystals with different impurities doped were grown from aqueous solutions. The distribution of impurities in Sr(NO3)2 crystals were investigated by electron probe micoranalysis. Results show that the distribution of impurities illustrates a compositional zoning behaviour. The Ba2+ has a higher concentration in the {100} growth sectors than in the {111} sectors. On the contrary, Pb2+ has a higher concentration in {111} growth sectors than in {100} sectors. The crystalline perfection of the pure and Ba2+ or Pb2+ doped Sr(NO3)2 crystals was studied by high-resolution X-ray rocking curve technique. The high-resolution X-ray rocking curve of the ideal Sr(NO3)2 crystal was theoretically calculated based on the dynamical X-ray diffraction theory. High-resolution X-ray diffraction results show that the crystalline quality in the growth sectors of the pure Sr(NO3)2 crystal is fairly high, since its experimental rocking curve is very close to the theoretical calculation. However, in the areas of the sector boundary the full width at half maximum of the rocking curve gets broader due to the lattice stress in the boundary area. The doping of impurities will deteriorate the quality of the crystal and induce an inhomogeneity behaviour of the crystalline quality. As for the Ba2+ doped Sr(NO3)2 crystal, the crystalline quality in {111} growth sectors is higher than that in {100} sectors. On the contrary, the crystalline quality in {100} growth sectors is higher than that in {111} sectors for Pb2+ doped Sr(NO3)2 crystal. This coincides well with the composition distributions of the dopants.

Quantitative X-ray standing-wave phase analysis by means of photoelectrons

Quantitative information on a subsurface layer structure is obtained through the determination of the photoelectron escape depth by using the photoelectrons emitted by an X-ray standing wavefield in the range of dynamical X-ray diffraction from high-quality crystals. A simple method to determine the mean escape depthLof low-energy-loss photoelectrons is proposed, based on the analysis of the phase of the X-ray standing wavefield in a specially designed epitaxic structure grown by molecular-beam epitaxy. The valueL= 24 nm is obtained for GaSb crystals with CuKα1radiation as a probe. As an example of the complimentary application of the technique, an Sb-based single-quantum-well structure was analysed by using both high-resolution X-ray diffraction and the X-ray standing-wave method.

Non-projectiveness of X-ray Pendellösung-fringed diffraction images

It has been experimentally found that X-ray moiré fringes are not exactly given as a projected figure from the specimen crystal as predicted by the standard theory of X-ray dynamical diffraction, but show a kind of spatial oscillation along the beam path out of the crystal. This paper reports that a similar spatial oscillation has been found for Pendellösung fringes in a similar experiment recording plane-wave X-ray topographs of a silicon wedge crystal onto a set of multi-stacked films. The oscillation of the Pendellösung fringes was easily found among the simultaneous topographs on the multi-stacked films by examining the fringe profiles, and was also found in topographic images by somewhat careful inspection. It is noteworthy that a simple reciprocal correspondence was observed between the amplitude of fringe oscillation and the fringe contrast. This finding of non-projectiveness, i.e. the fringe oscillation noted above, in Pendellösung fringes as well as in moiré fringes suggests that the non-projectiveness occurs as a very basic property of X-ray interference fringes produced by crystal diffraction.

Evolving shock-wave profiles measured in a silicon crystal by picosecond time-resolved x-ray diffraction

Picosecond time-resolved x-ray diffraction is used to probe single-crystal silicon under pulsed-laser irradiation (300 ps pulse at 1.4 J/cm2) at an interval of 60 ps. The observed rocking curves show shock compression of the silicon lattice by the laser irradiation. Uniaxial strain profiles perpendicular to the Si(111) plane are estimated using dynamical x-ray diffraction theory. The temporal and spatial evolution of the profiles indicates a propagating shock wave with the velocity of 9.4 km/s inside the silicon crystal. The observed maximum compression is 1.05%, which corresponds to a pressure of 2.18 GPa.

X-ray dynamical diffraction: the concept of locally plane wave

X-ray dynamical diffraction: the concept of locally plane wave

X-ray double-crystal characterization of the strain relaxation in GaAs/GaN xAs 1− x/GaAs(0 0 1) sandwiched structures

An X-ray diffraction method, estimating the strain relaxation in an ultrathin layer, has been discussed by using kinematic and dynamical X-ray diffraction (XRD) theory. The characteristic parameter ΔΩ , used as the criterion of the strain relaxation in ultrathin layers, is deduced theoretically. It reveals that ΔΩ should be independent of the layer thickness in a coherently strained layer. By this method, we characterized our ultrathin GaN x As 1− x samples with N contents up to 5%. XRD measurements show that our GaN x As 1− x layers are coherently strained on GaAs even for such a large amount of N. Furthermore, a series of GaN x As 1− x samples with same N contents but different layer thicknesses were also characterized. It was found that the critical thickness ( L c ) of GaNAs in the GaAs/GaNAs/GaAs structures determined by XRD measurement was 10 times smaller than the theoretical predictions based on the Matthews and Blakeslee model. This result was also confirmed by in situ observation of reflection high-energy electron diffraction (RHEED) and photoluminescence (PL) measurements. RHEED observation showed that the growth mode of GaNAs layer changed from 2D- to 3D-mode as the layer thickness exceeded L c . PL measurements showed that the optical properties of GaNAs layers deteriorated rapidly as the layer thickness exceeded L c .

X-ray dynamical diffraction: the concept of a locally plane wave

The long distance between the source and the experiment and the small source size, now available at third-generation synchrotron sources, leads to new optical characteristics for X-ray diffraction. It is shown that, under certain conditions, the intensity received by a point located on the exit surface of a crystal is described by the diffraction of a locally plane wave. Each point along the surface is influenced by a plane wave with a varying departure from Bragg angle. In such a case, it is possible to visualize the rocking curve of the crystal as a function of the position along the exit surface. This represents a topographic method to obtain the reflectivity curve of the crystal instead of the usual goniometric method. Applications will be described in a forthcoming paper.

High-resolution x-ray diffraction, x-ray standing-wave, and transmission electron microscopy study of Sb-based single-quantum-well structures

Ga 0.6 Al 0.4 Sb/GaSb single-quantum-well structures grown by molecular-beam epitaxy on GaSb substrates with different well thicknesses, have been studied by high-resolution x-ray diffraction and x-ray standing-wave methods. By fitting the diffraction curves, thickness, composition, and the static Debye–Waller factor were obtained for each layer of the structures. The analysis of the angular dependence of the yield of photoelectrons emitted by the x-ray standing-wave field in the range of the dynamical x-ray diffraction was used for selecting the most appropriate set of layer parameters among those which gave virtually identical fittings of the diffraction curves. Relatively broadened GaAlSb/GaSb interfaces were found in all of the samples. This result was confirmed by high-resolution transmission electron microscopy investigation of one of the samples. The effect of the surface degradation due to the chemical reaction with the atmosphere of the free surface of the upper Ga0.6Al0.4Sb layer was considered.

Dynamical X-ray diffraction analysis of Solid Phase Epitaxy growth of Si1-yCy heterostructures

AbstractThe strain and damage produced on Si substrates by high-dose ion implantation of Si and C is investigated after thermal treatments by double and triple crystal X-ray diffraction, high ressolution transmission electron microscopy (HRTEM) and Secondary Ion Mass Spectrometry (SIMS). Si implantation (180 keV, 5×1015 Si at cm−2) at liquid nitrogen temperature forms a buried amorphous layer. Annealing at temperatures close to 650°C results in epitaxial films with significant defect recovery. X-ray rocking curves show the existence of interference fringes on the left hand side of the 004 Si peak indicating the presence of tensile strained Si layers due to the generation of Si interstitials during the implantation process. C implantation, at 60 keV, 7×1015 cm−2 and 450°C, in the preamorphized Si wafers results in the growth of Si1-yCy epitaxial films with a low amount of substitutional carbon (y≍ 0.1%). Rapid thermal annealing at 750°C results in highly defective epitaxial films with a maximum carbon content close to 0.4%.The high density of defects is responsible for the partial strain relaxation observed in those layers. The amount of substitutional Si also decreases drastically with increasing temperature. Profile fitting of rocking curves using dynamical X-ray theory is used to estimate the C concentration and the strain and disorder profiles of the heterostructures.

X-Ray diffraction analysis of bandgap-engineered distributed bragg reflectors

Compositionally graded interfaces between constitutive layers of the distributed Bragg reflectors (DBRs) in vertical cavity surface emitting lasers (VCSELs) greatly reduce operating voltages. In this paper, we demonstrate the use of high-resolution x-ray diffraction (HRXRD) in the characterization of a bandgap-engineered DBR. The final structure of the DBR is determined by comparing the Bragg peak intensities and locations in the x-ray rocking curve measurements with those of dynamical x-ray diffraction simulations. The aluminum concentration of the graded interface region is determined as a function of distance to within 2%. The width of the interface is accurate to within 1.5 nm. Such sensitivity demonstrates the utility of the non-invasive x-ray technique in characterizing not only the DBR, but also the entire VCSEL structure.