Structural defects in SiC and Ge microcrystals

M. Podhorský, M. Meduňa

Department of Condensed Matter Physics, Masaryk University, Brno, Czech Republic

martinpodhorskyj@gmail.com

Reciprocal space mapping (RSM) is a method of X-Ray analysis which can provide us with useful structural information about studied samples, such as mismatch, strain, relaxation and defects of epitaxial grown layers on a substrate [1].

The studied samples consisted of large array of Ge and SiC microcrystals grown by Low-energy plasma-enhanced chemical vapor deposition (LEPECVD) technique [2]. This method enables fast, low-temperature epitaxial growth of crystals onto micrometer-scale tall pillars etched into Si(001). The method was developed at ETH Zürich, where the samples were also prepared in the group from H. von Känel [3]. It enables to grow relatively thick layers with different lattice parameters of high structural quality [3, 4]. The samples were subjected to X-Ray study in order to obtain structural information. 

In our experiment we used Rigaku SmartLab diffractometer, which uses X-Ray source with characteristic wavelength of 0.154 nm and a hybrid multi-dimensional pixel detector HyPix-3000. The data acquisition by the detector can be done in 0D, 1D and 2D regime. For our analysis we opted for the linear regime. We placed the sample on a goniometric table and put a series of linear slits and monochromators between the source, sample and the detector. First we measured QxQz reciprocal space maps (RSMs) around symmetric and asymmetric diffractions of the samples at two different azimuths (0° and 90°), particularly (004) and (224) for Ge and (004) and (113) for SiC, from which we obtained the lattice parameter, strain and relaxation of the array of microcrystals.

The next part of our measurement was aimed to obtain RSMs of the samples in the plane parallel to sample surface (QxQy). This is impossible to do with standard laboratory set-up, which enables us to measure only the QxQz plane of the reciprocal space. One way of obtaining the QxQy RSM for certain Qz is to measure multiple QxQz RSMs at different azimuthal rotations and transforming them using Radon transform [5]. Radon transform is a mathematical method used to construct 3D intensity images from 2D slices, commonly used in computer tomography [6].

We measured RSM of one diffraction maximum, particularly (004) and (002) for Ge and SiC respectively, at different azimuths ranging from 0° up to 180° with a 2° step. The QxQz RSMs measured at different azimuthal angles were transformed into a series of sinograms, from which it was possible to obtain series of QxQy RSMs for the measured range of Qz positions.  Examples of reconstructed QxQy RSMs are shown in Figure 1.

The obtained QxQy RSMs for different Qz form set of slices through the reciprocal space which can generally built a 3D RSM. The distribution of scattered intensity in 3D reciprocal space can then provide another view on analysis of structural defects such as local lattice strain, misfit dislocations or stacking faults present in the studied samples.

Figure 1. QxQy RSMs for a) Ge and b) SiC samples. In a) the maximum was cut out in order to showcase the satellite maxima. The maxima originate from crystal lattice bending and they copy a four-fold symmetry of microcrystal geometry. The satellite maxima in b) correspond to cuts through streaks {111} originating from defects (stacking faults) in the SiC microcrystal layer [7].

1. U. Pietsch, V. Holý, T. Baumbach, High-Resolution X-Ray Scattering, Springer New York, NY, 2004.

2. C. Rosenblad, H.R. Deller, T. Graf, E. Müller, H. von Känel, Journal of Crystal Growth 188, (1998), 125.

3. C.V. Falub, H. von Känel, F. Isa, R. Bergamaschini, A. Marzegalli, D. Chrastina, G. Isella, E. Müller, P. Niedermann, L. Miglio, Science, 335, (2012), 1330.

4. H. von Känel, L. Miglio, D. Crippa, T. Kreiliger, M. Mauceri, M. Puglisi, F. Mancarella, R. Anzalone, N. Piluso, F. La Via, Materials Science Forum 821–823, (2015), 193.

5. M. Meduňa, F. Isa, F. Brennan, H. von Känel, J. Appl. Cryst. 55, (2022) in print.

6. P. Suetens, Fundamentals of Medical Imaging, Cambridge University Press, 2009.

7.  M. Meduňa, T. Kreiliger, M. Mauceri, M. Puglisi, F. Mancarella, F. La Via, D. Crippa, L. Miglio, H. von Känel, Journal of Crystal Growth 507, (2019), 70.

We acknowledge Claudiu V. Falub and Hans von Känel for providing the SiC and SiGe microcrystal samples.