Visualizing local bending of lattice planes by extending two-azimuth synchrotron X-ray diffraction datasets to asymmetric reflection

Abstract

Synchrotron X-ray rocking curve imaging (RCI) is modified to visualize local bending of lattice planes of a single crystal substrate (XR-V-LBLP). This method uses two-azimuth RCI datasets of asymmetric reflection or symmetric reflection. The analysis algorithm is described and a Python software code is provided in the Supplementary material. The two symmetrically equivalent $$11\bar 24$$ datasets obtained from a GaN (0001) 4-inch wafer are reanalyzed using this software. The normal vector, reciprocal-lattice vector, of the local lattice planes, which is approximately parallel to the sample surface, is formulated as the product of two rotation matrices. This vector is written in polar coordinates using the length and two declination angles, newly introduced in this article. The spatial and probability distributions of the declination angles are also presented. The proposed method enables visualization of the local shape or orientation of the lattice planes of the entire wafer. The limits of application of the method are examined for the samples studied. The sample is found to satisfy two conditions regarding the relative $$d$$-spacing difference and the curvature of the lattice planes at all 50 adjacent μm positions.

Keywords

• synchrotron x-ray characterization method
• x-ray diffraction topography
• rocking curve imaging
• local lattice-plane bending
• asymmetric reflection
• crystal perfection
• wafer