X-ray nanodiffraction at individual SiGe/Si(001) dot molecules and its numerical description based on kinematical scattering theory

Abstract

Individual self-assembled SiGe/Si(001) dot molecules were investigated by scanning x-ray nanodiffraction with a beam size of 250 nm in diameter (full width at half maximum). The samples contain dot molecules with either one, two, three, or four dots. Different azimuthal configurations were measured and compared with simulated diffraction patterns. We have combined finite element calculations, kinematic scattering simulations, and experimental measurements to obtain information about lateral positional correlation as well as strain and germanium content within individual dot molecules.

Scanning X-ray nanodiffraction: from the experimental approach towards spatially resolved scattering simulations

“…Falling lines in the left picture and rising lines in the right picture of Figure 4c give the orientation of the two SiGe islands that are illuminated, and the RSM with honeycomb-like patterns in the center image of Figure 4c is typically obtained from three- or fourfold DMs. However, in case of scanning directly over a fourfold DM also, the left and right RSM in Figure 4c would show honeycomb-like patterns like previously measured at the ESRF [4]. …”

“…In this case, around the Si(004) reflection, a honeycomb-like pattern of three islands becomes visible, but at the SiGe(004) reflection, a pattern with diagonal lines appears since the third SiGe island itself was not illuminated directly. In a nanodiffraction experiment, we measured the diffusely scattered intensities at one individual SiGe DM that also reveal similar patterns of substrate and structure reflection: In Figure 6, a RSM near the SiGe(004) reflection is shown where a honeycomb-like pattern becomes visible, which is reminiscent of the pattern at the Si(004) substrate reflection investigated in reference [4]. The measurements at the Si(004) reflection have been actually performed at the same SiGe DM like the RSM presented in Figure 6 (beamline ID13/ESRF, 250-nm X-ray spot focused by Kirkpatrick-Baez mirrors at 12.4 keV).…”

“…Like in the previous experiment, the images of the weighting factors (Figure 4a) and weighted displacement field (Figure 4b) show the spot positions for the simulation. The corresponding simulated diffraction patterns depicted in (Figure 4c) originate from positional correlation function of the SiGe dots within a DM [4]. From the direction of the lines in Figure 4c (left and right column), it can be derived which part of a DM has been illuminated, and one can distinguish between different kinds of DM consisting of one, two, or four SiGe islands including their azimuthal orientation.…”

“…The captured images represent reciprocal space maps (RSMs) showing 2D slices through the three-dimensional (3D) reciprocal space (see also Figure 1b). The speckle pattern and diffuse surrounding of Bragg reflections in RSMs can then reveal positional ordering of objects, shape of structures, or strain field within the investigated material [4,8,9]. …”

Perfect crystals grown from imperfect interfaces

“…Traditionally, destructive techniques based on transmission electron microscopy (TEM) have been the methods of choice to analyse their crystal perfection, composition and strain123. With the advent of nanofocused X-ray beams45678910 and advanced X-ray diffraction (XRD) imaging techniques111213141516 available at third-generation synchrotrons it has become possible to address individual crystals down to the nanoscale non-destructively. The role of strain induced by lattice misfit in determining the properties of epitaxial heterostructures and nanostructures can hardly be overemphasized.…”