Asymmetric Diffractions Research Articles

Engineered asymmetric diffractions of diagonal-line odd-symmetric phase gratings

A two-dimensional multi-element phase grating has been designed in terms of the offset refractive index to exhibit the spatially odd symmetry (antisymmetry) along one transparent diagonal line with an even number of rectangular elements while leaving other elements in a unit cell opaque. This grating can be engineered to attain a few intriguing phenomena of asymmetric diffraction, including the elimination of equally spaced oblique diffraction lines, the elimination of alternately crossed oblique diffraction lines, and the selection of equally spaced oblique diffraction lines. These phenomena of engineered asymmetric diffraction are well explained via destructive interference between transmitted field amplitudes from paired, dual-paired, and successive elements along the transparent diagonal line.

Terahertz cascaded metasurfaces for both spin-symmetric and asymmetric beam diffractions with active power distribution

Ultra-compact and tunable devices for terahertz (THz) beam manipulation are highly desired in wireless communication and radar scanning. Although the appearance of the Pancharatnam-Berry (PB) metasurface has provided strategies for THz beam scanning, active output power distribution is still difficult to achieve, and the flexibility of beam manipulation is limited by a single metasurface. In this work, we demonstrated an all-dielectric cascaded metasurface consisting of a spin-decoupled metasurface and a PB metasurface. The conjugated characteristic of the PB phase for two photonic spin states is broken with highly efficient high-order diffractions of wave vector superposition through the cascaded metasurfaces, and both spin-symmetric and spin-asymmetric transmissions are obtained by designing the differences in metasurface bandwidth. Moreover, the output power between the deflection beams can be actively tuned by changing the incident polarization state, achieving power modulation ratios of 99.3% and 95.1% for the two conjugated spin beams, respectively. Therefore, this work realizes controllable wave division multiplexing and power distribution and opens new avenues for the design of ultra-compact multifunctional devices.

Visualization of local strain in 4H-SiC trench metal-oxide-semiconductor field-effect transistor using synchrotron nanobeam X-ray diffraction

We investigated the local strain in a silicon carbide (4H-SiC) (0001) trench metal-oxide semiconductor field-effect transistor (MOSFET) using synchrotron nanobeam X-ray diffraction (nano-XRD) at the SPring-8 BL13XU beamline. Using X-rays incident on the 4H-SiC trench cross section, diffraction measurements were performed on the and planes. Intensity maps of the and diffractions yielded images reflecting the trench structure. The spatial resolution of the 4H-SiC intensity map in the [0001] direction was higher than that for the diffraction because the angle of incidence was close to perpendicular to the sample. From two-dimensional reciprocal space maps of the symmetric and asymmetric diffractions, the tilt and the - and (0004)-plane strain components were individually separated and visualized. A tensile strain of approximately 0.1% was found in the region between the trenches. These results indicate the effectiveness of nano-XRD for strain visualization in trench MOSFETs and similar electronic devices.

A structural analysis of ultrathin barrier (In)AlN/GaN heterostructures for GaN‐based high‐frequency power electronics

Metal–organic chemical vapor deposition (MOCVD) is one of the best growth methods for GaN‐based materials as well‐known. GaN‐based materials with very quality are grown the MOCVD, so we used this growth technique to grow InAlN/GaN and AlN/GaN heterostructures in this study. The structural and surface properties of ultrathin barrier AlN/GaN and InAlN/GaN heterostructures are studied by X‐ray diffraction (XRD) and atomic force microscopy (AFM) measurements. Screw, edge, and total dislocation densities for the grown samples have been calculated by using XRD results. The lowest dislocation density is found to be 1.69 × 108 cm−2 for Sample B with a lattice‐matched In0.17Al0.83N barrier. The crystal quality of the studied samples is determined using (002) symmetric and (102) asymmetric diffractions of the GaN material. In terms of the surface roughness, although reference sample has a lower value as 0.27 nm of root mean square values (RMS), Sample A with 4‐nm AlN barrier layer exhibits the highest rough surface as 1.52 nm of RMS. The structural quality of the studied samples is significantly affected by the barrier layer thickness. The obtained structural properties of the samples are very important for potential applications like high‐electron mobility transistors (HEMTs).

Heteroepitaxial AlN growth on c-plane sapphire substrates by ammonia-free high temperature metalorganic chemical vapor deposition

AlN films were hetero-epitaxially grown on c-plane sapphire substrates by ammonia-free high temperature metalorganic chemical vapor deposition (AFHT-MOCVD). The dependence of the AlN growth rate on the flow rate of source gases (H2, N2 and trimethylaluminum (TMA)) and the growth temperature were systematically investigated. The maximum AlN growth rate up to ∼4.0 μm/hour was obtained at the present growth conditions. Based on the experimental results, the possible mechanisms in the AFHT-MOCVD growth concerning the gas reactions are qualitatively discussed. The as-grown AlN epilayers were characterized by high-resolution X-ray diffraction (HRXRD), scanning electron microscope (SEM) and scanning transmission electron microscope (STEM). The narrow full width at half maximum (FWHM) values of symmetric (0002) and asymmetric (10–12) AlN diffractions are obtained ((0002): 211 arcsec, (10–12): 325 arcsec from a ∼3 μm thick AlN epilayer), showing the potential of the growth technique for the high quality AlN growth.

Non-conventional scans in high-resolution X-ray diffraction analysis of epitaxial systems

High resolution X-ray diffraction is commonly used for the analysis of single crystalline epitaxial layers exhibiting high degree of crystal perfection. The method enables to resolve fine variations of the measured intensities and therefore is very efficient in the investigation of the structural parameters of single or multilayered epitaxial systems. In this article the method combining the standard HR technique with grazing incidence set-up is outlined. It is shown that in non-coplanar geometry the intensity distribution within the section of reciprocal space perpendicular to the sample surface, standardly scanned in coplanar geometry, can be measured at constant angle of incidence α. For asymmetric diffractions that are not accessible in coplanar geometry the value of α can be decreased to extremely low values close to zero making the method depth-sensitive. The effect of non-coplanar geometry on the angular resolution is analyzed and the possible application of φ scans in asymmetric non-coplanar geometry is discussed. The proposed scans are illustrated by measurements on selected GaN based epitaxial layers and they can be applied also to other types of epitaxial systems with medium crystal quality.

Observation of Threading Dislocations in Ammonothermal Gallium Nitride Single Crystal Using Synchrotron X-ray Topography

Synchrotron monochromatic-beam x-ray topography observation has been performed on high-quality ammonothermal gallium nitride single crystal to evaluate threading dislocations (TD) in a nondestructive manner. Asymmetric diffractions with six equivalent g-vectors of 11–26, in addition to a symmetric diffraction with g = 0008, were applied to determine the Burgers vectors (b) of dislocations. It was found that pure edge-type TDs with \( {\varvec b} = \left\langle {11 - 20} \right\rangle /3 \) did not exist in the sample. A dominant proportion of TDs were of mixed type with \( {\varvec b} = \left\langle {11 - 20} \right\rangle /3 + \left\langle {0001} \right\rangle \), i.e., so-called c + a dislocations. Pure 1c screw dislocations with \( {\varvec b} = \left\langle {0001} \right\rangle \) and TDs with c-component larger than 1c were also observed.

Towards high-flux X-ray beam compressing channel-cut monochromators

The issue of a high-flux X-ray beam compressing channel-cut monochromator for applications in X-ray metrology is addressed. A Ge(111) compressor with compression ratio 20.3 was designed on the principle of a combination of symmetric and highly asymmetric diffractions. A pilot application of the single-point diamond technology (SPDT) to finish active surfaces of X-ray optics was tested, providing 50% flux enhancement as compared to a Ge(220) counterpart prepared by traditional surface treatment. This is much more than the theoretical 22% forecast and shows the potential of SPDT for preparation of high-flux X-ray compressors with a high compression ratio, where highly asymmetric diffraction with a very low exit angle is inevitable. The implications for efficient collection of X-rays from microfocus X-ray sources are discussed. A comparison of Ge compressors with Ge parallel channel-cut monochromators combined with a 50 µm slit shows the several times higher flux of the former, making them applicable in X-ray diffraction experiments at medium resolution. Furthermore, the Ge(111) compressor was tested as a collimator in high-resolution grazing-incidence small-angle X-ray scattering (GISAXS) measurements of surface gratings, providing experimental resolution close to 400 nm. This is ∼100 nm smaller than that achieved with the Ge(220) compressor but still approximately twice that of commercial SAXS/GISAXS laboratory setups.

Asymmetric diffraction based on a passive parity-time grating

Optical structures with balanced loss and gain provide an efficient platform to study the features of light propagation under non-Hermitian parity-time symmetry. Here, we report a feasible design of one-dimensional parity-time symmetric diffraction grating, where the real and imaginary parts of refractive index are separately modulated. Due to the spontaneous breaking of parity-time symmetry at the exceptional point, asymmetric diffractions are observed between a pair of oblique incident light. This asymmetric phenomenon, determined by the modulation direction of the introduced parity-time symmetry, is also polarization-dependent. The coupled-mode theory is implemented to theoretically analyze the polarization dependent asymmetric diffraction, showing consistence with numerical simulations. Our findings may provide a feasible way for manipulating light and instructively inspire the development of diffraction optics.

Growth of Low-Dislocation-Density AlN under Ga Irradiation

A simple growth technique for the reduction of threading dislocation density of AlN under Ga irradiation during initial growth stage is proposed. In X-ray rocking curve measurements, linewidth of (0002) and (1102) diffraction for 500-nm-thick AlN were 100 and 260 arcsec, respectively. The threading-dislocation density of the AlN was estimated to be ∼8×108 cm-2 from the symmetric and asymmetric diffractions. The AlGaN/AlN multi-quantum well structure was grown on the high-quality AlN layer. By cathodoluminescence mapping measurements, intense deep-UV emission at 246 nm was observed from the area of more than 90%. The low dislocation density AlN is an ideal template for deep-UV optical devices.

Monolithic two-dimensional beam compressor for hard x-ray beams

Using asymmetric diffraction in grazing incidence or in grazing emergence it is possible to expand or compress an x-ray beam in one dimension. Combining two asymmetric diffractions with non-coplanar planes of diffraction it is possible to obtain two-dimensional beam expansion or compression. This paper reports on a monolithic two-dimensional x-ray beam compressor consisting of two non-coplanar asymmetrically inclined {311} diffractors prepared in one silicon crystal block and tested at Optics beamline BM05 at ESRF, Grenoble. The design of the x-ray beam compressor, the results of beam tracing image simulation, the experimental arrangement used for testing and the properties of the x-ray microbeams formed are presented. For the beam energy of 9.5 keV 10- and 13-times beam compression in two directions was observed. Using a metal grid in the incident beam more than 400 microbeams smaller than 10 µm and separated by less than 5 µm were obtained in the outgoing beam. A gain of up to 100 times in intensity per unit area was obtained in comparison with the x-ray beam magnifier geometry, demonstrating a real two-dimensional beam compression.

Effect of the ratio of TMIn flow to group Ⅲ flow on the properties of InGaN/GaN multiple quantum wells

Triple-axis x-ray diffraction (TXRD) and photoluminescence (PL) spectra are used to assess the influence of the ratio of TMIn flow to group Ⅲ flow on structural defects, such as dislocations and interface roughness, and optical properties of multiple quantum wells(MQWs). In this paper the mean densities of edge and screw dislocations in InGaN/GaN MQWs are obtained by ωscan of every satellite peak of (0002) symmetric and (1012) asymmetric diffractions. At the same time, the interface roughness is measured by the radio of the full width at half maximum of satellite peaks to the peak orders. The experimental results showed that the density of dislocation, especially of edge dislocation, and interface roughness increase with the increase of the ratio, which leads to the decrease of PL properties. It also can be concluded that the edge dislocation acts as nonradiative recombination centers in InGaN/GaN MQWs. Also noticed is that the variation of the ratio has more influence on edge dislocation than on screw dislocation.

Structural and optical properties of thick freestanding GaN templates

Structural and optical properties of thick (larger than 160 μm) freestanding hydride vapor phase epitaxy GaN templates have been investigated. AFM measurements showed that flat and smooth surface could be fabricated. High-resolution X-ray diffraction studies carried out with different spectrometer slit for the symmetric and asymmetric diffractions show that the linewidth increases with increasing slits width, indicating that a considerable degree of tilting and twisting of the individual grains are still present in these thick samples. Raman scattering measurements performed in a few samples indicate good crystalline quality and reduced strain. Very sharp and intense exciton related lines (FWHM less than 1 meV) have been observed in the low temperature photoluminescence spectra. Variable-temperature photoluminescence experiments were performed on both the growth surface and interface to identify the nature of the recombination processes observed in the luminescence spectra. FTIR absorption measurements show the presence of at least two donors with binding energy of 30.5 and 33.6 meV.

Quantitative determination of the spatial coherence from the visibility of equal-thickness fringes.

Spatial coherence of the undulator radiation in the horizontal direction is measured by a wedge-shaped crystal interferometer. The Borrmann effect, the effect of the angular divergence of the incidence and the wavefront matching of the collimating asymmetric diffractions with the interferometer are discussed to estimate the coherence factor. The spatial coherence length of 145 microm is experimentally determined, which is enhanced by the collimators about 100 times more than expected from the source size.

X-ray phase-contrast imaging with submicron resolution by using extremely asymmetric Bragg diffractions

We have obtained x-ray phase-contrast images with high spatial resolution by using extremely asymmetric Si 111 Bragg diffractions near the critical angle of the total reflection. The x-ray image could be magnified to 294 times in both vertical and horizontal directions. By using this x-ray microscopy system, we have observed clear phase-contrast images of a 0.7-μm-wide gold-line pattern.

Analysis and observation of finite beam Bragg diffraction by a thick planar phase grating

A numerical-impulse-response technique for studying the propagation and diffraction of finite-width beams in planar phase gratings is described. It can account for both symmetric and asymmetric diffractions. The grating-length-to-beam-width ratio is shown to govern the extent of beam-profile distortion and selectivity sidelobe suppression. Trade-offs between diffraction efficiency and beam profile have also been demonstrated. Theoretical results have been verified by experimental observations in a planar waveguide geometry of diffracted beams that change from a single diffraction peak to multiple peaks as the grating-length-to-beam-width ratio increases.

Dynamical theory of X-ray diffraction for the study of crystal surfaces

The Darwin dynamical theory is extended to the asymmetric diffractions of the Bragg and Laue cases in a form suited for treating the crystal with a different structure on its surface by using the characteristic matrix method. For ideal crystals, the exact analytical solutions valid for any incidence condition are obtained as a function of the general expression of the deviation parameter within the two-beam approximation. It is shown that the exact expressions are reduced to the expressions given by the conventional theories using the appropriate approximations in the cases of CTR (crystal truncation rod) scattering, specular reflectivity and Bragg reflection including the condition of a Bragg angle of 90°. Next the Darwin theory is extended to the coplanar three-beam case to study the effect of other beams on CTR scattering. It is shown that the reflectivity of CTR scattering obtained by the two-beam approximation holds good except when the other beam satisfies the Bragg condition, and the modulation in the reflectivity on such conditions is sensitive enough to get information of the surface structure.

Deep seismic profile of the Amazonian Craton (northern Brazil)

Deep seismic profiling of the Amazonian craton (northern Brazil) reveals previously unknown deep structural features buried beneath a thin, relatively flat Phanerozoic sedimentary cover (Amazon basin). The seismic signature of the Precambrian crust is characterized by a transparent shallow basement down to 8–9 km followed by a highly reflective middle and lower crust. Middle and lower crustal events are dominated by abundant dipping, asymmetric arcuate reflections and diffractions, the shallowest of which occur beneath a structural arch (Jutaí arch). Although wide angle refraction data are unavailable, a decrease in the number of coherent reflections at about 15 s two‐way travel time (45 km) and small drops in amplitude and increases in average frequency are interpreted to mark the Moho. The deep Amazonian seismic line is located near the westernmost boundary of the Amazonian craton, imaging the Rondonian province, one of the youngest geochronological provinces of the craton (middle Proterozoic). To the south, the Rondonian basement crops out, revealing schists, gneisses, granulites, and important volumes of anorogenic granites. The prominent, laterally extensive arcuate reflections observed within the middle and lower crust may be related to this anorogenic magmatic activity, perhaps corresponding to layered intrusive complexes. On the other hand, intrusion of mantle derived material during an early Paleozoic rifting, as well as the Mesozoic episodes of mafic intrusion may also have contributed to this seismic signature. Similar seismic signatures found in eastern Australia and on COCORP profiles of the central U.S. craton suggest that such cratonic terranes may have undergone similar tectonic evolution. In the upper crust, probable fault plane reflections associated with ENE‐WSW reverse faults of Jurassic‐Early Cretaceous age may sole into the top of the reflective zone, suggesting that the lower limit of the transparent upper crust may represent a rheological boundary.

Geometrical principles of the monolithic X-ray magnifier

The principles of the monolithic X-ray magnifier based on two successive asymmetric non-coplanar diffractions from the same crystal are analyzed from the geometrical point of view. The conditions of the distortion-free two-dimensional pattern magnification are formulated by means of matrix formalism. The general solution of the problem of determination of the crystal surface planes satisfying the conditions of distortion-free magnification is derived in the closed form. The calculation is performed on the basis of the kinematical theory of diffraction. It is shown that the number of solutions is infinite for any given pair of diffraction vectors and magnification. General properties of the solution are illustrated by some examples. The effect of the refraction of X-rays on the pattern distortion is estimated. The results suggest that the refractive index correction has a negligible influence on the distortion of the magnified pattern. The results presented enable us to prepare monolithic X-ray magnifiers or demagnifiers that can be used in various fields of X-ray optics, especially in X-ray topography and X-ray lithography.

Basic equations for multiple successive diffraction and angle distortion minimization in X-ray magnifiers

In the paper, conditions for three-dimensional coplanar and non-coplanar successive multiple X-ray diffraction and the basic imaging equations for multiple X-ray diffraction modelling by a computer are given. As an example, one crystal X-ray magnifier with two non-coplanar asymmetric diffractions has been studied more deeply with the aim to minimize the angle distortion in the magnified image. Experimental results obtained with such an optimized magnifier are presented.