arXiv subjects

Michael Krumrey

Publications and source records attributed to Michael Krumrey.

13 recordsLinked to original sources

arXiv2022

Small-Angle X-ray Scattering: Characterization of cubic Au nanoparticles using Debye's scattering formula

We propose a versatile software package in the form of a Python extension, named CDEF (Computing Debye's scattering formula for Extraordinary Formfactors), to approximately calculate scattering profiles of arbitrarily shaped nanoparticles for small-angle X-ray scattering (SAXS). CDEF generates a quasi-randomly distributed point cloud in the desired particle shape and then applies the open source software DEBYER for efficient evaluation of Debye's scattering formula to calculate the SAXS pattern. If self-correlation of the scattering signal is not omitted, the quasi-random distribution provides faster convergence compared to a true random distribution of the scatterers, especially at higher momentum transfer. The usage of the software is demonstrated for the evaluation of scattering data of Au nanocubes with rounded edges, which were measured at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II in Berlin. Our implementation is fast enough to run on a single desktop computer and perform model fits within minutes. The accuracy of the method was analyzed by comparison with analytically known form factors and verified with another implementation, the SPONGE, based on a similiar principle with fewer approximations. Additionally, the SPONGE coupled to McSAS3 allows us to further retrieve information on the uncertainty of the size distribution using a Monte-Carlo uncertainty estimation algorithm.

cond-mat.mes-hall↗

arXiv2020

Extracting Dimensional Parameters of Gratings Produced with Self-Aligned Multiple Patterning Using GISAXS

Background: To ensure consistent and high-quality semiconductor production at future logic nodes, additional metrology tools are needed. For this purpose, grazing-incidence small-angle X-ray scattering (GISAXS) is being considered because measurements are fast with a proven capability to reconstruct average grating line profiles with high accuracy. Aim: GISAXS measurements of grating line shapes should be extended to samples with pitches smaller than 50 nm and their defects. The method's performance should be evaluated. Approach: A series of gratings with 32 nm pitch and deliberately introduced pitchwalk is measured using GISAXS. The grating line profiles with associated uncertainties are reconstructed using a Maxwell solver and Markov-Chain Monte Carlo (MCMC) sampling combined with a simulation library approach. Results: The line shape and the pitchwalk are generally in agreement with previously published transmission small-angle X-ray scattering (SAXS) results; however the line height and line width show deviations of (1.0 +/- 0.2) nm and (2.0 +/- 0.7) nm, respectively. The complex data evaluation leads to relatively high pitchwalk uncertainties between 0.5 nm and 2 nm. Conclusions: GISAXS shows great potential as a metrology tool for small-pitch line gratings with complex line profiles. Faster simulation methods would enable more accurate results.

physics.app-ph↗

arXiv2019

Influence of the electrode nano/microstructure on the electrochemical properties of graphite in aluminum batteries

Herein we report on a detailed investigation of the irreversible capacity in the first cycle of pyrolytic graphite electrodes in aluminum batteries employing 1-ethyl-3-methylimidazolium chloride:aluminum trichloride (EMIMCl:AlCl3) as electrolyte. The reaction mechanism, involving the intercalation of AlCl4 in graphite, has been fully characterized by correlating the micro/nanostructural modification to the electrochemical performance. To achieve this aim a combination of X-ray diffraction (XRD), small angle X-ray scattering (SAXS) and computed tomography (CT) has been used. The reported results evidence that the irreversibility is caused by a very large decrease in the porosity, which consequently leads to microstructural changes resulting in the trapping of ions in the graphite. A powerful characterization methodology is established, which can also be applied more generally to carbon-based energy-related materials. Introduction

cond-mat.mtrl-sci↗

arXiv2019

Distortion analysis of crystalline and locally quasicrystalline 2D photonic structures with GISAXS

In this study, grazing incidence small-angle X-ray scattering (GISAXS) is used to collect statistical information on dimensional parameters in an area of 20 mm x 15 mm on photonic structures produced by nanoimprint lithography. The photonic structures are composed of crystalline and locally quasicrystalline two-dimensional patterns with structure sizes between about 100 nm and 10 $μ$m to enable broadband visible light absorption for use in solar energy harvesting. These first GISAXS measurements on locally quasicrystalline samples demonstrate that GISAXS is capable of showing the locally quasicrystalline nature of the samples while at the same time revealing the long-range periodicity introduced due to the lattice design. We describe the scattering qualitatively in the framework of the distorted wave Born approximation using a hierarchical model mirroring the sample design, which consists of a rectangular and locally quasicrystalline supercell which is repeated periodically to fill the whole surface. The nanoimprinted samples are compared to a sample manufactured using electron beam lithography and the distortions of the periodic and locally quasiperiodic samples are quantified statistically. Due to the high sensitivity of GISAXS to deviations from the perfect lattice, the misalignment of the crystallographic axes was measured with a resolution of 0.015°, showing distortions up to +/- 0.15° in the investigated samples.

cond-mat.mes-hall↗

arXiv2017

Reconstructing Detailed Line Profiles of Lamellar Gratings from GISAXS Patterns with a Maxwell Solver

Laterally periodic nanostructures were investigated with grazing incidence small angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerically solving Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, due to the discrepancy between incident wavelength and finite-element size. This drawback vanishes for GISAXS due to the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop dimensional metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art e-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows a detailed reconstruction of the grating line shape also for thick, non-homogeneous substrates. The reconstructed geometrical line shape models are statistically validated by applying a Markov chain Monte Carlo (MCMC) sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nm uncertainty.

physics.comp-ph↗

arXiv2017

Grazing Incidence Small Angle X-Ray Scattering (GISAXS) on Small Targets Using Large Beams

GISAXS is often used as a versatile tool for the contactless and destruction-free investigation of nanostructured surfaces. However, due to the shallow incidence angles, the footprint of the X-ray beam is significantly elongated, limiting GISAXS to samples with typical target lengths of several millimetres. For many potential applications, the production of large target areas is impractical, and the targets are surrounded by structured areas. Because the beam footprint is larger than the targets, the surrounding structures contribute parasitic scattering, burying the target signal. In this paper, GISAXS measurements of isolated as well as surrounded grating targets in Si substrates with line lengths from $50\,{\rmμm}$ down to $4\,{\rmμm}$ are presented. For the isolated grating targets, the changes in the scattering patterns due to the reduced target length are explained. For the surrounded grating targets, the scattering signal of a $15\,{\rmμm}\,\times\,15\,{\rmμm}$ target grating structure is separated from the scattering signal of $100\,{\rmμm}\,\times\,100\,{\rmμm}$ nanostructured surroundings by producing the target with a different orientation with respect to the predominant direction of the surrounding structures. The described technique allows to apply GISAXS, e.g. for characterization of metrology fields in the semiconductor industry, where up to now it has been considered impossible to use this method due to the large beam footprint.

cond-mat.mes-hall↗

arXiv2016

Correlated Diffuse X-ray Scattering from Periodically Nano-Structured Surfaces

Laterally periodic nanostructures were investigated with grazing incidence small angle X-ray scattering. To support an improved reconstruction of nanostructured surface geometries, we investigated the origin of the contributions to the diffuse scattering pattern which is correlated to the surface roughness. Resonant diffuse scattering leads to a palm-like structure of intensity sheets. Dynamic scattering generates the so-called Yoneda band caused by a resonant scatter enhancement at the critical angle of total reflection and higher-order Yoneda bands originating from a subsequent diffraction of the Yoneda enhanced scattering at the grating. Our explanations are supported by modelling using a solver for the time-harmonic Maxwell's equations based on the finite-element method.

cond-mat.mes-hall↗

arXiv2014

Nanoparticle characterization by continuous contrast variation in SAXS with a solvent density gradient

Many low-density nanoparticles show a radial inner structure. This work proposes a novel approach to contrast variation with SAXS based on the constitution of a solvent density gradient in a glass capillary in order to resolve this internal morphology. Scattering curves of a polymeric core-shell colloid were recorded at different suspending medium contrasts at the four-crystal monochromator beamline of PTB at the synchrotron radiation facility BESSY II. The mean size and size distribution of the particles as well as an insight into the colloid electron density composition were determined using the position of the isoscattering points in the Fourier region of the scattering curves and by examining the Guinier region in detail. These results were corroborated with a model fit to the experimental data, which provided complementary information about the inner electron density distribution of the suspended nanoparticles.

cond-mat.soft↗

arXiv2014

Traceable GISAXS measurements for pitch determination of a 25 nm self-assembled polymer grating

The feature sizes of only a few nanometers in modern nanotechnology and next-generation microelectronics continually increase the demand for suitable nanometrology tools. Grazing incidence small-angle X-ray scattering (GISAXS) is a versatile technique to measure lateral and vertical sizes in the nm-range, but the traceability of the obtained parameters, which is a prerequisite for any metrological measurement, has not been demonstrated so far. In this work, the first traceable GISAXS measurements, demonstrated with a self-assembled block copolymer grating structure with a nominal pitch of 25 nm, are reported. The different uncertainty contributions to the obtained pitch value of 24.83(9) nm are discussed individually. The main uncertainty contribution results from the sample-detector distance and the pixel size measurement, whereas the intrinsic asymmetry of the scattering features is of minor relevance for the investigated grating structure. The uncertainty analysis provides a basis for the evaluation of the uncertainty of GISAXS data in a more general context, for example in numerical data modeling.

cond-mat.mtrl-sci↗

arXiv2014

Characterization of an in-vacuum PILATUS 1M detector

A dedicated in-vacuum X-ray detector based on the hybrid pixel PILATUS 1M detector has been installed at the four-crystal monochromator beamline of PTB at the electron storage ring BESSY II in Berlin. Due to its windowless operation, the detector can be used in the entire photon energy range of the beamline from 10 keV down to 1.75 keV for small-angle X-ray scattering (SAXS) experiments and anomalous SAXS (ASAXS) at absorption edges of light elements. The radiometric and geometric properties of the detector like quantum efficiency, pixel pitch and module alignment have been determined with low uncertainties. The first grazing incidence SAXS (GISAXS) results demonstrate the superior resolution in momentum transfer achievable at low photon energies.

physics.ins-det↗

arXiv2013

A diffraction effect in X-ray area detectors

When an X-ray area detector based on a single crystalline material, for instance, a state of the art hybrid pixel detector, is illuminated from a point source by monochromatic radiation, a pattern of lines appears which overlays the detected image. These lines can be easily found by scattering experiments with smooth patterns, such as small-angle X-ray scattering. The origin of this effect is the Bragg reflection in the sensor layer of the detector. Experimental images are presented over a photon energy range from 3.4 keV to 10 keV, together with a theoretical analysis. The intensity of this pattern is up to 20%, which can disturb the evaluation of scattering and diffraction experiments. The patterns can be exploited to check the alignment of the detector surface with the direct beam, and the alignment of individual detector modules with each other in the case of modular detectors, as well as for the energy calibration of the radiation.

physics.ins-det↗

arXiv2008

Ground-based calibration and characterization of the Fermi Gamma-Ray Burst Monitor Detectors

One of the scientific objectives of NASA's Fermi Gamma-ray Space Telescope is the study of Gamma-Ray Bursts (GRBs). The Fermi Gamma-Ray Burst Monitor (GBM) was designed to detect and localize bursts for the Fermi mission. By means of an array of 12 NaI(Tl) (8 keV to 1 MeV) and two BGO (0.2 to 40 MeV) scintillation detectors, GBM extends the energy range (20 MeV to > 300 GeV) of Fermi's main instrument, the Large Area Telescope, into the traditional range of current GRB databases. The physical detector response of the GBM instrument to GRBs is determined with the help of Monte Carlo simulations, which are supported and verified by on-ground individual detector calibration measurements. We present the principal instrument properties, which have been determined as a function of energy and angle, including the channel-energy relation, the energy resolution, the effective area and the spatial homogeneity.

astro-ph↗

arXiv2007

Calibration of the GLAST Burst Monitor detectors

The GLAST Burst Monitor (GBM) will augment the capabilities of GLAST for the detection of cosmic gamma-ray bursts by extending the energy range (20 MeV to > 300 GeV) of the Large Area Telescope (LAT) towards lower energies by 2 BGO-detectors (150 keV to 30 MeV) and 12 NaI(Tl) detectors (10 keV to 1 MeV). The physical detector response of the GBM instrument for GRBs is determined with the help of Monte Carlo simulations, which are supported and verified by on-ground calibration measurements, performed extensively with the individual detectors at the MPE in 2005. All flight and spare detectors were irradiated with calibrated radioactive sources in the laboratory (from 14 keV to 4.43 MeV). The energy/channel-relations, the dependences of energy resolution and effective areas on the energy and the angular responses were measured. Due to the low number of emission lines of radioactive sources below 100 keV, calibration measurements in the energy range from 10 keV to 60 keV were performed with the X-ray radiometry working group of the Physikalisch-Technische Bundesanstalt (PTB) at the BESSY synchrotron radiation facility, Berlin.

astro-ph↗