Integrated diffraction gratings on the Bloch surface wave platform supporting bound states in the continuum

We propose and theoretically and numerically investigate integrated diffraction gratings for the Bloch surface wave (BSW) platform, which have subwavelength or near-subwavelength period. We demonstrate that, in the oblique incidence geometry of a transverse-electric polarized BSW and with a properly chosen band gap configuration of the photonic crystal supporting the surface waves, the proposed structures operate in the scattering-free regime, when the energy of the incident BSW is divided between the reflected and transmitted BSWs with the same polarization corresponding to the propagating diffraction orders of the grating, and not scattered away from the propagation surface. In this regime, the studied integrated gratings support high-Q resonances and bound states in the continuum not only in the subwavelength case when only the specular (zeroth) diffraction orders propagate, but also in the case when non-evanescent zeroth and −1st diffraction orders satisfy the so-called Littrow mounting condition. The proposed integrated gratings on the BSW platform can be used as efficient narrowband spatial or spectral filters operating in reflection, or as BSW beam splitters or deflectors operating in transmission. The obtained results may find application in two-dimensional photonic circuits for steering the BSW propagation.

Shape- and Element-Sensitive Reconstruction of Periodic Nanostructures with Grazing Incidence X-ray Fluorescence Analysis and Machine Learning

The characterization of nanostructured surfaces with sensitivity in the sub-nm range is of high importance for the development of current and next-generation integrated electronic circuits. Modern transistor architectures for, e.g., FinFETs are realized by lithographic fabrication of complex, well-ordered nanostructures. Recently, a novel characterization technique based on X-ray fluorescence measurements in grazing incidence geometry was proposed for such applications. This technique uses the X-ray standing wave field, arising from an interference between incident and the reflected radiation, as a nanoscale sensor for the dimensional and compositional parameters of the nanostructure. The element sensitivity of the X-ray fluorescence technique allows for a reconstruction of the spatial element distribution using a finite element method. Due to a high computational time, intelligent optimization methods employing machine learning algorithms are essential for timely provision of results. Here, a sampling of the probability distributions by Bayesian optimization is not only fast, but it also provides an initial estimate of the parameter uncertainties and sensitivities. The high sensitivity of the method requires a precise knowledge of the material parameters in the modeling of the dimensional shape provided that some physical properties of the material are known or determined beforehand. The unknown optical constants were extracted from an unstructured but otherwise identical layer system by means of soft X-ray reflectometry. The spatial distribution profiles of the different elements contained in the grating structure were compared to scanning electron and atomic force microscopy and the influence of carbon surface contamination on the modeling results were discussed. This novel approach enables the element sensitive and destruction-free characterization of nanostructures made of silicon nitride and silicon oxide with sub-nm resolution.

Sphere tangencies, line incidences and Lie’s line-sphere correspondence

Two spheres with centers p and q and signed radii r and s are said to be in contact if |p–q|2=(r–s)2. Using Lie’s line-sphere correspondence, we show that if F is a field in which –1 is not a square, then there is an isomorphism between the set of spheres in F3 and the set of lines in a suitably constructed Heisenberg group that is embedded in (F[i])3; under this isomorphism, contact between spheres translates to incidences between lines. In the past decade there has been significant progress in understanding the incidence geometry of lines in three space. The contact-incidence isomorphism allows us to translate statements about the incidence geometry of lines into statements about the contact geometry of spheres. This leads to new bounds for Erdős’ repeated distances problem in F3, and improved bounds for the number of point-sphere incidences in three dimensions. These new bounds are sharp for certain ranges of parameters.

Understanding near-surface polymer dynamics by a combination of grazing-incidence neutron scattering and virtual experiments

Neutron spin-echo spectroscopy is a unique experimental method for the investigation of polymer dynamics. The combination of neutron spin-echo spectroscopy with grazing-incidence geometry (GINSES) opens the possibility to probe the dynamics of soft-matter materials in the vicinity of the solid substrate in the time range up to 100 ns. However, the usage of the GINSES technique has some peculiarities and, due to the novelty of the method and complexity of the scattering geometry, difficulties in further data analysis occur. The current work discusses how virtual experiments within the distorted-wave Born approximation using the BornAgain software can improve GINSES data treatment and aid the understanding of polymer dynamics in the vicinity of the solid surface. With two examples, poly(N-isopropyl acrylamide) brushes and poly(ethylene glycol) microgels on Si surfaces, the simulation as well as the application of the simulation to the GINSES data analysis are presented. The approach allowed a deeper insight to be gained of the background effect and scattering contribution of different layers.

Small-angle X-ray scattering from GaN nanowires on Si(111): facet truncation rods, facet roughness and Porod's law

Small-angle X-ray scattering from GaN nanowires grown on Si(111) is measured in the grazing-incidence geometry and modelled by means of a Monte Carlo simulation that takes into account the orientational distribution of the faceted nanowires and the roughness of their side facets. It is found that the scattering intensity at large wavevectors does not follow Porod's law I(q) ∝ q −4. The intensity depends on the orientation of the side facets with respect to the incident X-ray beam. It is maximum when the scattering vector is directed along a facet normal, reminiscent of surface truncation rod scattering. At large wavevectors q, the scattering intensity is reduced by surface roughness. A root-mean-square roughness of 0.9 nm, which is the height of just 3–4 atomic steps per micrometre-long facet, already gives rise to a strong intensity reduction.

SnO2/TiO2 Thin Film n-n Heterostructures of Improved Sensitivity to NO2

Thin-film n-n nanoheterostructures of SnO2/TiO2, highly sensitive to NO2, were obtained in a two-step process: (i) magnetron sputtering, MS followed by (ii) Langmuir-Blodgett, L–B, technique. Thick (200 nm) SnO2 base layers were deposited by MS and subsequently overcoated with a thin and discontinuous TiO2 film by means of L–B. Rutile nanopowder spread over the ethanol/chloroform/water formed a suspension, which was used as a source in L–B method. The morphology, crystallographic and electronic properties of the prepared sensors were studied by scanning electron microscopy, SEM, X-ray diffraction, XRD in glancing incidence geometry, GID, X-ray photoemission spectroscopy, XPS, and uv-vis-nir spectrophotometry, respectively. It was found that amorphous SnO2 films responded to relatively low concentrations of NO2 of about 200 ppb. A change of more than two orders of magnitude in the electrical resistivity upon exposure to NO2 was further enhanced in SnO2/TiO2 n-n nanoheterostructures. The best sensor responses RNO2/R0 were obtained at the lowest operating temperatures of about 120 °C, which is typical for nanomaterials. Response (recovery) times to 400 ppb NO2 were determined as a function of the operating temperature and indicated a significant decrease from 62 (42) s at 123 °C to 12 (19) s at 385 °C A much smaller sensitivity to H2 was observed, which might be advantageous for selective detection of nitrogen oxides. The influence of humidity on the NO2 response was demonstrated to be significantly below 150 °C and systematically decreased upon increase in the operating temperature up to 400 °C.

Synchrotron X-Ray Topography Study on the Relationship between Local Basal Plane Bending and Basal Plane Dislocations in PVT-Grown 4H-SiC Substrate Wafers

Synchrotron monochromatic beam X-ray topography (SMBXT) in grazing incidence geometry shows black and white contrast for basal plane dislocations (BPDs) with Burgers vectors of opposite signs as demonstrated using ray tracing simulations. The inhomogeneous distribution of these dislocations is associated with the concave/convex shape of the basal plane. Therefore, the distribution of these two BPD types were examined for several 6-inch diameter 4H-SiC substrates and the net BPD density distribution was used for evaluating the nature and magnitude of basal plane bending in these wafers. Results show different bending behaviors along the two radial directions - [110] and [100] directions, indicating the existence of non-isotropic bending. Linear mapping of the peak shift of the 0008 reflection along the two directions was carried out using HRXRD to correlate with the results from the SMBXT measurements. Basal-plane-tilt angle calculated using the net BPD density derived from SMBXT shows a good correlation with those obtained from HRXRD measurements, which further confirmed that bending in basal plane is caused by the non-uniform distribution of BPDs. Regions of severe bending were found to be associated with both large tilt angles (95% black contrast BPDs to 5% white contrast BPDs) and abrupt changes in a and c lattice parameters i.e. local strain.