Ullrich Pietsch

High-resolution x-ray scattering from thin films and multilayers

Part 1 Experimental realization: basic elements of an equipment resolution elements diffractometers and reflectometers. Part 2 The theory of X-ray diffraction and its realization by the experiment: kinematical X-ray scattering from ideal crystals kinematical X-ray diffraction from deformed thin layers kinematical X-ray diffraction from randomly disturbed layers dynamical X-ray diffraction in perfect layers dynamical X-ray diffraction in slightly deformed layers optical reflection of X-rays from ideal layers optical reflection of X-rays from layers with rough interfaces dynamical X-ray diffraction in strongly asymmetric cases grazing incidence diffraction (GID). Appendices: elements of the formal theory of scattering structure factors, dispersion corrections and extinction length.

High-Resolution X-Ray Scattering

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Depth‐resolved measurement of lattice relaxation in Ga1−xInxAs/GaAs strained layer superlattices by means of grazing‐incidence x‐ray diffraction

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Linear viscoelastic analysis of formation and relaxation of azobenzene polymer gratings.

The state of relaxation in two different superlattices (SLs) of a system with large lattice mismatch, Ga0.8In0.2As/GaAs grown on GaAs [001] by molecular beam epitaxy, has been investigated by surface‐sensitive grazing‐incidence diffraction (GID). The SL is squeezed between the substrate and a thick GaAs top layer. The thickness of individual GaInAs layers ta (active layer) is the same in both samples, while the GaAs barrier thickness tb is different. We have studied the influence of the thickness ratio tb/ta on the state of relaxation for different distances from the sample surface. We find that for thick barriers the whole SL remains coherently strained and for the thinner barrier thickness the SL is partially relaxed against the the GaAs top layer. The GID technique was applied for the first time to obtain depth resolution of the lateral lattice parameter in a SL. It is demonstrated to be especially well suited for SL systems with a small difference of the average electron density between the sublayers....

The energy-dispersive reflectometer/diffractometer at BESSY-I

Surface relief gratings on azobenzene containing polymer films were prepared under irradiation by actinic light. Finite element modeling of the inscription process was carried out using linear viscoelastic analysis. It was assumed that under illumination the polymer film undergoes considerable plastification, which reduces its original Youngs modulus by at least three orders of magnitude. Force densities of about 10(11) N/m3 were necessary to reproduce the growth of the surface relief grating. It was shown that at large deformations the force of surface tension becomes comparable to the inscription force and therefore plays an essential role in the retardation of the inscription process. In addition to surface profiling the gradual development of an accompanying density grating was predicted for the regime of continuous exposure. Surface grating development under pulselike exposure cannot be explained in the frame of an incompressible fluid model. However, it was easily reproduced using the viscoelastic model with finite compressibility.

Critical points in a crystal and procrystal

We describe the set-up of an energy-dispersive reflectometer installed at the 6 T wavelength shifter (WLS) of the storage ring BESSY-I. It can be used for reflectometry and in-plane diffraction studies of thin films under ambient conditions. Due to the exponential decay of the incident spectrum, the whole useful energy range between keV is not available simultaneously. Absorbing the highly-intensive low-energy part of the spectrum, the specular reflectivity can be recorded up to using maximum angles of incidence and exit of . Up to the intensity is high enough to detect small angle Bragg peaks of a fatty acid salt multilayer separated by , (d is the multilayer period) in about 15 s with sufficient counting statistics. After normalization by the incident spectrum the energy-dispersive reflectivity spectrum provides information similar to that from an angular-dispersive experiment, but in a much shorter time. Besides the specular reflectivity, our set-up provides the possibility of simultaneous measurement of the in-plane momentum transfer (grazing incidence diffraction). For in-plane lattice parameter measurements a second detector is attached on a circle perpendicular to the plane of incidence. As in the angular-dispersive set-up, it enables investigation of the in-plane arrangement of a fatty acid salt multilayer in about 15 s. Keeping the in-plane Bragg angle fixed, the respective in-plane Bragg peaks appear for different energies and can be selected by changing .

Individual GaAs nanorods imaged by coherent X‐ray diffraction

The critical points in the model electron density distributions of LiF, NaF, NaCl, and MgO crystals, constructed from accurate X-ray diffraction data, are determined. For LiF and MgO they are compared with those obtained from a Hartree–Fock electron density calculation. Both experiment and theory show the same type of critical points on the bond lines. The topological features in areas between structural units, where the electron density is low and near-uniform, turn out to be model dependent and cannot be established well with the data available. Topological analysis of procrystals (hypothetical systems consisting of spherical atoms or ions placed on the same sites as atoms in real crystal) show that (3, −1) critical points, usually connected with bonding interaction, are observed on interatomic lines in these nonbonded systems as well.

Application of a pnCCD in X-ray diffraction: a three-dimensional X-ray detector

Using scanning X-ray diffraction microscopy with a spot size of 220 x 600 nm, it was possible to inspect individual GaAs nanorods grown seed-free through circular openings in a SiN(x) mask in a periodic array with 3 microm spacing on GaAs[111]B. The focused X-ray beam allows the determination of the strain state of individual rods and, in combination with coherent diffraction imaging, it was also possible to characterize morphological details. Rods grown either in the centre or at the edge of the array show significant differences in shape, size and strain state.

X-ray investigations of the molecular mobility within polymer surface gratings

The first application of a pnCCD detector for X-ray scattering experiments using white synchrotron radiation at BESSY II is presented. A Cd arachidate multilayer was investigated in reflection geometry within the energy range 7 keV < E < 35 keV. At fixed angle of incidence the two-dimensional diffraction pattern containing several multilayer Bragg peaks and respective diffuse-resonant Bragg sheets were observed. Since every pixel of the detector is able to determine the energy of every incoming photon with a resolution DeltaE/E approximately 10(-2), a three-dimensional dataset is finally obtained. In order to achieve this energy resolution the detector was operated in the so-called single-photon-counting mode. A full dataset was evaluated taking into account all photons recorded within 10(5) detector frames at a readout rate of 200 Hz. By representing the data in reciprocal-space coordinates, it becomes obvious that this experiment with the pnCCD detector provides the same information as that obtained by combining a large number of monochromatic scattering experiments using conventional area detectors.

Investigations of semiconductor superlattices by depth‐sensitive x‐ray methods

The physical origin of surface relief patterning on amorphous polymer films containing azobenzene-side chains induced by holographic exposure with visible light of about 450 nm is not yet fully understood. To understand the nature of the induced material transport is of special interest to describe the dynamic processes occurring in thin films below the glass transition temperature TG. Thus, we investigated films made from the polar (poly {4′-[2-(methacryloxy) ethyl]-ethyl}amino-4-nitroazobenzene, TG=129 °C) and less polar {poly[4-(2-methacryloxy)-ethyl] azobenzene, TG=80 °C} azobenzene side-chain homopolymers and performed temperature-resolved coherent x-ray and visible (VIS) light scattering measurements of the thermally induced erasure of the surface gratings. The simultaneous use of x-ray synchrotron light (λ=0.14 nm) and VIS laser light (λ=633 nm) allows the detection of the material flow on different lengths scales. We did not find remarkable differences in the thermal behavior of polar and nonpolar...