Dynamical scattering in coherent hard x-ray nanobeam Bragg diffraction

Abstract

Unique intensity features arising from dynamical diffraction arise in coherent x-ray nanobeam diffraction patterns of crystals having thicknesses larger than the x-ray extinction depth or exhibiting combinations of nanoscale and mesoscale features. We demonstrate that dynamical scattering effects can be accurately predicted using an optical model combined with the Darwin theory of dynamical x-ray diffraction. The model includes the highly divergent coherent x-ray nanobeams produced by Fresnel zone plate focusing optics and accounts for primary extinction, multiple scattering, and absorption. The simulation accurately reproduces the dynamical scattering features of experimental diffraction patterns acquired from a GaAs/AlGaAs epitaxial heterostructure on a GaAs (001) substrate.

Electrode-induced lattice distortions in GaAs multi-quantum-dot arrays

“…The dynamical diffraction theory accurately predicts diffraction from crystals with thicknesses larger than the x-ray extinction depth and accounts for effects such as multiple scattering, primary extinction, refraction, and absorption. 20,35 The x-ray intensity distribution in the nanobeam diffraction patterns was predicted by computing the incident x-ray wavefield at the focal spot using an optical simulation method, computing the diffracted wavefield using the Darwin dynamical theory of x-ray diffraction, and propagating the diffracted wavefield to the detector. 20,36 In other nanobeam diffraction studies the wavefront at the x-ray focal spot is often retrieved using ptychographic algorithms.…”

“…20,35 The x-ray intensity distribution in the nanobeam diffraction patterns was predicted by computing the incident x-ray wavefield at the focal spot using an optical simulation method, computing the diffracted wavefield using the Darwin dynamical theory of x-ray diffraction, and propagating the diffracted wavefield to the detector. 20,36 In other nanobeam diffraction studies the wavefront at the x-ray focal spot is often retrieved using ptychographic algorithms. 37 It is not possible at present, however, to use ptychography to retrieve the focused beam amplitude and phase from diffraction patterns that include dynamical effects.…”

“…Nanobeam diffraction experiments yield complex distributions of scattered intensity that must be interpreted carefully in order to identify the intensity features appearing in each diffraction pattern unambiguously. 20,21 First, a measurement of the tilt near an isolated 275 nm-wide electrode allowed the value of the residual stress to be determined. The tilt and strain were then predicted at arbitrary locations within the device and for arbitrary electrode widths using a mechanical simulation incorporating this value of the residual stress.…”

“…2(a)with a spacing of 0.13. The angles at which the signals appear, their relative intensities, and their angular widths are not reproduced by the kinematical theory of x-ray diffraction but can be accurately modeled using dynamical diffraction 20.…”

Simulation and modeling of diffraction pattern of crystallography: a fractal approach

“…Raleigh-Sommerfold model was applied to distinct optics media for evaluation of propagation of near-field diffractive pattern by optical system and calculations were compared to the intensity distributions (Gillen and Guha 2004). In the context of diffraction pattern (Pateras et al 2018), dynamical diffraction effects of GaAs/AlGaAs hetero structure crystals were evaluated to solve the key scientific problems of magnetic materials.…”