Reciprocal Space Mapping Technique Research Articles

Combining x-ray real and reciprocal space mapping techniques to explore the epitaxial growth of semiconductors

In the present work, the importance of determining the strain states of semiconductor compounds with high accuracy is demonstrated. For the matter in question, new software titled LAPAs, the acronym for LAttice PArameters is presented. The lattice parameters as well as the chemical composition of Al1−x In x N and Ge1−x Sn x compounds grown on top of GaN- and Ge- buffered c-Al2O3 and (001) oriented Si substrates, respectively, are calculated via the real space Bond’s method. The uncertainties in the lattice parameters and composition are derived, compared and discussed with the ones found via x-ray diffraction reciprocal space mapping. Broad peaks lead to increased centroid uncertainty and are found to constitute up to 99% of the total uncertainty in the lattice parameters. Refraction correction is included in the calculations and found to have an impact of 0.001 Å in the lattice parameters of both hexagonal and cubic crystallographic systems and below 0.01% in the quantification of the InN and Sn contents. Although the relaxation degrees of the nitride and tin compounds agree perfectly between the real and reciprocal-spaces methods, the uncertainty in the latter is found to be ten times higher. The impact of the findings may be substantial for the development of applications and devices as the intervals found for the lattice match the condition of Al1−x In x N grown on GaN templates vary between ∼1.8% (0.1675–0.1859) and 0.04% (0.1708–0.1712) if derived via the real- and reciprocal spaces methods.

Processing macromolecular diffuse scattering data.

Diffuse scattering is a powerful technique to study disorder and dynamics of macromolecules at atomic resolution. Although diffuse scattering is always present in diffraction images from macromolecular crystals, the signal is weak compared with Bragg peaks and background, making it a challenge to visualize and measure accurately. Recently, this challenge has been addressed using the reciprocal space mapping technique, which leverages ideal properties of modern X-ray detectors to reconstruct the complete three-dimensional volume of continuous diffraction from diffraction images of a crystal (or crystals) in many different orientations. This chapter will review recent progress in reciprocal space mapping with a particular focus on the strategy implemented in the mdx-lib and mdx2 software packages. The chapter concludes with an introductory data processing tutorial using Python packages DIALS, NeXpy, and mdx2.

Microstructure study of YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7-<i>δ</i></sub> thin film with synchrotron-based three-dimensional reciprocal space mapping

High-temperature superconducting films can be used for fabricating the cutting-edge high-temperature superconducting microwave devices because of their low microwave surface resistances. However, the microwave surface resistances of high-temperature superconducting materials are particularly sensitive to microstructure due to their special two-dimensional superconducting mechanisms and extremely short superconducting coherence lengths. To investigate the correlations between microstructure and microwave surface resistance of high-temperature superconducting materials, YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7-<i>δ</i></sub> (YBCO) films with different thickness are grown on (00l)-oriented MgO single-crystal substrates by using the pulsed laser deposition (PLD) technique. Electrical measurements reveal that their superconducting transition temperatures and room temperature resistances do not show significant difference. However, their microwave surface resistances in superconducting state display a significant difference. The characterizations of the microstructures of YBCO films by synchrotron radiation three-dimensional reciprocal space mapping(3D-RSM) technique show that the number of the grains with CuO<sub>2</sub> face parallel to the surface (c crystals), and the consistency of grain orientation are the main causes for the difference in microwave surface resistance.

Confronting Vegard’s rule in Ge1−x Sn x epilayers: from fundamentals to the effect of defects

Comprehensive and systematic study challenging the application of Vegard’s rule to germanium tin solid solutions grown on germanium buffer layers and 100 silicon substrates is presented. The binary’s lattice parameters, composition and respective uncertainties are determined through x-ray diffraction via reciprocal space mapping technique employing newly developed software. The tin content is confirmed by Rutherford backscattering spectrometry and energy dispersive x-ray spectroscopy. The statistical agreement between the tin contents derived by the different structural characterization techniques suggests the binary to follow generically the Vegard’s rule in the range of low Sn molar fractions (<5%). Phase separation, Sn segregation, point defects, post-growing oxygen impurities, and deteriorated surface morphology are found to be relevant within the ∼200 nm germanium tin films. Although, complex mechanisms triggering composition/strain heterogeneities are found in the analysed Ge1−x Sn x compounds, the deviation from the perfect crystals is suggested to be not enough to distort the in- and out-of-plane lattice parameters away from its empirical linear combination.

Recent advances in small angle x-ray scattering for superlattice study

Small-angle x-ray scattering is used for the structure determination of superlattice for its superior resolution, nondestructive nature, and high penetration power of x rays. With the advent of high brilliance x-ray sources and innovative computing algorithms, there have been notable advances in small angle x-ray scattering analysis of superlattices. High brilliance x-ray beams have made data analyses less model-dependent. Additionally, novel data acquisition systems are faster and more competitive than ever before, enabling a more accurate mapping of the superlattices' reciprocal space. Fast and high-throughput computing systems and algorithms also make possible advanced analysis methods, including iterative phasing algorithms, non-parameterized fitting of scattering data with molecular dynamics simulations, and the use of machine learning algorithms. As a result, solving nanoscale structures with high resolutions has become an attainable task. In this review, we highlight new developments in the field and introduce their applications for the analysis of nanoscale ordered structures, including nanoparticle supercrystals, nanoscale lithography patterns, and supramolecular self-assemblies. Particularly, we highlight the reciprocal space mapping techniques and the use of iterative phase retrieval algorithms. We also cover coherent-beam-based small angle x-ray scattering techniques such as ptychography and ptycho-tomography in view of the traditional small angle x-ray scattering perspective.

Determination of poisson’s ratio using growth temperature variations of InGaN/GaN MQW

In this study, InGaN/GaN/Al2O3 multi-quantum well (MQW) structure is investigated in 300–450 °C growth temperature range with steps of 50 °C. By the help of lattice constants at four different growth temperatures strain values are gained. Plot of strain in a- versus strain in c- is used to determine Poisson’s ratio for GaN in the structure. Poisson’s ratio is determined as 0.36. Reciprocal space mapping (RSM) technique of X-ray diffraction (XRD) method is used to gain peak positions of the sample instead of w–θ scans because it gives more accurate results. Shifts in peak positions by variations of growth temperatures are shown. Lattice parameter equations are used with τ modification angles which minimise the errors caused from tilt of c- in hexagonal unit cell. This work is original because Poisson’s ratio of GaN is determined using a natural method, variations in growth temperatures. It is also emphasised that RSM is a more sensitive method of XRD for determining structural properties of nitrite-based semiconductors.

Observing relaxation in device quality InGaN templates by TEM techniques

Device quality InGaN templates are synthesized using the semibulk (SB) approach. The approach maintains the film's 2D growth and avoids the formation of indium-metal inclusions. The strain relaxation processes of the grown InxGa1−xN templates are accompanied by variations in the indium content (x) and lattice parameters (a and c) across the InGaN template's thickness as the residual strain is continuously decreasing. This strain and lattice parameters' variation creates difficulties in applying standard x-ray Diffraction (XRD) and Reciprocal Space mapping (RSM) techniques to estimate the residual strain and the degree of the elastic strain relaxation. We used high-resolution High-angle annular dark-field scanning transmission electron microscopy and Energy-dispersive x-ray spectroscopy (EDS) to monitor the variations of the indium content, lattice parameters, and strain relaxation across the growing InxGa1−xN templates. We show that strain relaxation takes place by V-pit defect formation. Some of these V-pits are refilled by the GaN interlayers in the InxGa1−xN SB templates, while others propagate to the template surface. We present an alternative approach combining photoluminescence (PL) and EDS for estimating the degree of strain relaxation in these InxGa1−xN templates. The values obtained for the degree of relaxation estimated from TEM studies and PL measurements are within reasonable agreement in this study. Device quality InxGa1−xN templates with x ∼ 0.08, with a degree of relaxation higher than 70%, are achieved.

Experimental and Theoretical Study of the Triple-Crystal High-Resolution X-Ray Diffraction Scheme in Reciprocal Space Mapping Technique

The triple-crystal high-resolution X-ray diffraction scheme has been experimentally and theoretically investigated using reciprocal space mapping. The procedure for calculating the spectral angular instrumental functions of diffractometer to take into account the influence of mirror, monochromator, analyzer, and slits on the intensity distribution near reciprocal lattice point is described. Good coincidence of calculated and experimental cross sections of reciprocal space maps (RSMs) is shown by an example of a perfect Si(110) single crystal.

Time-resolved X-ray reciprocal space mapping of a crystal in an external electric field

A reciprocal space mapping technique with the use of triple-crystal time-resolved X-ray diffractometry has been developed and implemented using a laboratory X-ray source for the first time. This technique allows studying fast processes that occur in a sample under external influences that cause reversible deformations of its crystal lattice. It also allows distinguishing these processes in time and distinguishing different types of crystal deformations caused by these actions. The essence of the technique is to measure time dependences of the intensity for each point of the reciprocal space in the vicinity of the diffraction maximum in three-axis diffraction geometry by subjecting the sample to repeated and structurally identical action of a strong electric field, with the subsequent construction of the time evolution of the two-dimensional reciprocal space map. The time resolution is achieved with the use of a high-speed multichannel intensity analyzer synchronized with a high-voltage source. The results of measuring the reciprocal space maps with a laboratory radiation source with a time resolution of up to 10 ms are demonstrated for a piezoelectric crystal of lanthanum gallium silicate subjected to an external electric field with the field strength 3.08 kV mm−1, which is close to the sample breakdown value.

Impact of an InxGa1–xAs Capping Layer in Impeding Indium Desorption from Vertically Coupled InAs/GaAs Quantum Dot Interfaces

This study describes the effect of a thin GaAs spacer of 4.5 nm thickness in a bilayer-coupled InAs quantum dot (QD) heterostructure. Here, we report the first demonstration of InAs/GaAs QDs capped by self-assembled InxGa1–xAs layers. Self-assembled InxGa1–xAs layers were introduced into each intermediate layer across the interface of InAs QDs and the GaAs layer in a vertical-coupled bilayer QD (VCBQD) heterostructure to prevent indium desorption from the QDs. A change in the indium content in the seed-layer InAs QDs changes the self-assembly position and modifies the InxGa1–xAs layer thickness. A theoretical approach was presented to study the formation of self-assembled InxGa1–xAs layers at each strain-free layer. We showed that the strain energy at the second intermediate (εzz2) layer is greater than that at the first intermediate (εzz1) layer; εzz2 depends on the vertical strain channel length. The impact of the InxGa1–xAs layer thickness on the strain energy was studied using high-resolution transmission electron microscopy; a shorter strain channel length was found to facilitate the formation of a more relaxed and larger-sized self-assembled InxGa1–xAs layer in the active layer. This InxGa1–xAs layer formed at the intermediate layer acts as a capping layer or a protective shield for the indium adatoms, preventing their desorption from the InAs QDs. Furthermore, we studied the thermal stability of the self-assembled InxGa1–xAs layer by annealing the VCBQD samples at 700 and 800 °C. This aspect has been investigated for the first time ever in a study of the coupling efficiency between the InAs QDs and InxGa1–xAs capping layer. A high-resolution in-plane (2θχ/ϕ) reciprocal space mapping (RSM) technique provided the connection between the in-plane reciprocal lattice point of the InAs QDs and InxGa1–xAs layers and revealed the strain and coupling between them. InAs QDs fully covered with the self-assembled InxGa1–xAs layer enhanced the photoluminescence intensity by 77% and had an activation energy of 467 meV.

Microstructural analysis of an epitaxial AlN thick film/trench-patterned template by three-dimensional reciprocal lattice space mapping technique

Three-dimensional (3D) lattice plane microstructures were investigated at local regions in an epitaxial AlN thick film grown on a trench-patterned AlN/sapphire template. A 3D reciprocal lattice space mapping technique combined with cross-sectional X-ray microdiffraction using an appropriate Bragg reflection quantitatively revealed the inhomogeneity of the lattice structures in the AlN film without loss of spatial resolution. The results showed a strong correlation of the lattice plane tilt/twist and variations with respect to the void configuration, the patterning structure of the template, and the dislocation morphologies confirmed by transmission electron microscopy.

Comprehensive studies of interfacial strain and oxygen vacancy on metal–insulator transition of VO2 film

As a typical strong correlation material, vanadium dioxide (VO2) has attracted wide interest due to its particular metal–insulator transition (MIT) property. However, the relatively high critical temperature (Tc) of ~68 °C seriously hinders its practical applications. Thus modulating the phase transition process and decreasing the Tc close to room temperature have been hot topics for VO2 study. In the current work, we conducted a multi-approach strategy to control the phase transition of VO2 films, including the interfacial tensile/compressive strain and oxygen vacancies. A synchrotron radiation reciprocal space mapping technique was used to directly record the interfacial strain evolution and variations of lattice parameters. The effects of interfacial strain and oxygen vacancies in the MIT process were systematically investigated based on band structure and d-orbital electron occupation. It was suggested that the MIT behavior can be modulated through the combined effects of the interfacial strain and oxygen vacancies, achieving the distinct phase transition close to room temperature. The current findings not only provide better understanding for strain engineering and oxygen vacancies controlling phase transition behavior, but also supply a combined way to control the phase transition of VO2 film, which is essential for VO2 film based device applications in the future.

Epitaxial integration of a nanoscale BiFeO3 phase boundary with silicon.

The successful integration of the strain-driven nanoscale phase boundary of BiFeO3 onto a silicon substrate is demonstrated with extraordinary ferroelectricity and ferromagnetism. The detailed strain history is delineated through a reciprocal space mapping technique. We have found that a distorted monoclinic phase forms prior to a tetragonal-like phase, a phenomenon which may correlates with the thermal strain induced during the growth process.

Enhanced UV detection by non-polar epitaxial GaN films

Nonpolar a-GaN (11-20) epilayers were grown on r-plane (1-102) sapphire substrates using plasma assisted molecular beam epitaxy. High resolution x-ray diffractometer confirmed the orientation of the grown film. Effect of the Ga/N ratio on the morphology and strain of a-GaN epilayers was compared and the best condition was obtained for the nitrogen flow of 1 sccm. Atomic force microscopy was used to analyze the surface morphology while the strain in the film was quantitatively measured using Raman spectroscopy and qualitatively analyzed by reciprocal space mapping technique. UV photo response of a-GaN film was measured after fabricating a metal-semiconductor-metal structure over the film with gold metal. The external quantum efficiency of the photodetectors fabricated in the (0002) polar and (11-20) nonpolar growth directions were compared in terms of responsivity and nonpolar GaN showed the best sensitivity at the cost of comparatively slow response time.

Measurement of periodicity and strain in arrays of single crystal silicon and pseudomorphic Si1−xGex/Si fin structures using x-ray reciprocal space maps

Characterization of the periodicity and strain state of an array of lithographically patterned silicon and silicon-germanium alloy on silicon fins using reciprocal space mapping of Bragg diffraction peaks is presented. Various patterned structures with different pitch values of 90 nm, 65 nm, and 42 nm have been studied and data for the 42 nm pitch sample is discussed in this paper. Diffraction from fin arrays is treated kinematically analogous to periodic surface grating structures. Diffraction from the symmetric 004 planes is used to calculate pitch and analyze the pitch walking pattern which appears as harmonic peaks on either side of the fin peaks. Pitch walking refers to the presence of two periodicities in the array due to the lithographic process. Longitudinal scans are evaluated at the fin peak positions to probe into the shape of the fin structure. Nonrectangular fin shapes resulted in peak splitting of the longitudinal scans of higher order fin peaks indicating a finite sidewall slope. Asymmetric 224 planes were analyzed to study the quality and strain-relaxation of the fin structures both parallel and perpendicular to the fin length using reciprocal space mapping techniques.

Investigating crystal microstructure of niobium materials by an x-ray diffraction reciprocal space mapping technique

An x-ray diffraction reciprocal spacing mapping (RSM) technique was applied to investigate crystal quality of Nb films and bulk materials, relevant to superconducting radio frequency applications. The RSM study used different x-ray penetration depths to study material processes after two different surface treatments: mechanical polishing or energetic condensation (a plasma process). The study revealed the material's microstructure evolution for the two different processes. The RSM plots revealed crystal quality of the materials at different thickness. The novel, differential-depth RSM technique presented in this study substantiated the following facts: (1) For a heteroepitaxial Nb film $\mathrm{Nb}(100)/\mathrm{MgO}(100)$, a film thickening process, via a cathodic arc-discharge Nb ion deposition (energetic condensation), created a near-perfect single crystal Nb on the surface top layer. (2) For a fine mechanically polished single-crystal bulk Nb material, the microstructure on the top surface layer is more disordered than that at a greater depth.

Misfit dislocation anisotropies in the InGaAs/GaAs(001) interface measured using X-ray topography and reciprocal space mapping

The anisotropies of misfit dislocations (MDs) formed at an InGaAs/GaAs(001) interface grown by molecular beam epitaxy were investigated using X-ray topography and X-ray reciprocal space mapping techniques. The MDs bunched in small regions to form MD bunches. The number of MDs running along the direction (α-MDs) included in one MD bunch was larger than that along the [110] direction (β-MDs). In addition, the bunched α-MDs were aligned more periodically than the other MDs.

Effects of in Content on Anisotropies in Strain Relaxation Processes of InGaAs/GaAs (001) Measured by Real-Time Three-Dimensional Reciprocal Space Mapping

The effects of In incorporation on anisotropies in the strain relaxation mechanisms of InGaAs on GaAs systems are investigated using a three-dimensional reciprocal space mapping (3D-RSM) technique. Relaxation processes are classified as belonging to one of the following four phases: no relaxation, gradual relaxation, rapid relaxation, and relaxation saturation. Anisotropies appear in the gradual relaxation phase and almost disappear in the rapid relaxation phase. These anisotropies are enhanced by In content. When In content is low, both α- and β-misfit dislocations (MDs) are observed at the same thickness; the density of α-MDs increases more rapidly than that of β-MDs. When In content is high, only α-MDs appear in the gradual relaxation phase. These results suggest that In atoms prevent nucleation and/or gliding of β-MDs.

High‐resolution reciprocal space mapping of distributed Bragg reflectors and virtual substrates

AbstractEpitaxially grown silicon germanium alloy layers, prepared as virtual substrates for modulation‐doped field effect transistors, and InxGa1−xAs and GaPxAs1−x graded layers on GaAs substrates prepared as distributed Bragg reflectors (DBRs), have been investigated by the reciprocal space mapping (RSM) technique. These structures possess a strong concentration gradient and crystallographic lattice relaxation across the layer, which makes the data analysis challenging. Using kinematic diffraction theory for RSM analysis gives a rather simple way to evaluate the concentration, tilt and relaxation gradients, and the layer thicknesses, as well as the dependence of these values on the azimuthal direction of the diffraction plane. The density of 60° misfit dislocations for partially relaxed layers is also estimated. Characteristics of wide aperture Bragg reflectors based on these structures are calculated.

Epitaxial Structure of (001)- and (111)-Oriented Perovskite Ferrate Films Grown by Pulsed-Laser Deposition.

We report epitaxial growth and structures of SrFeO2.5 (SFO) films on SrTiO3 (STO) (001) and (111) substrates by pulsed-laser deposition. Reflection high-energy electron diffraction intensity oscillations were observed during the initial growth on both substrates, reflecting a layer-by-layer growth mode of the formula unit cell. It was found that the films were stabilized with a monoclinic structure that was derived from the original orthorhombic structure of bulk Brownmillerite. Using an X-ray reciprocal space mapping technique, in-plane domain structures and the orientation relationship were investigated. In addition, the impact of laser spot area on the epitaxial structures was studied. For the films grown on the (001) STO, the orientation relationship was robust against the change of the laser spot area: SFO(001)//STO(001) and SFO(100)//STO(100) for the out-of-plane and the in-plane, respectively, with the [001] axis tilted toward the 4-fold a- and b-axes by ∼1.4°, whereas nearly (111)-oriented films were obtained on the (111) STO, exhibiting a complicated manner of tilting that depended on laser spot area. The observed variation in tilting configurations can be understood in terms of possible atomic arrangements at the SFO/STO interface. These results present a guide to control the heteroepitaxial growth and structure of (111)-oriented noncubic perovskites.