Numerical simulation of Bragg-case section topographic images ofdislocations in silicon

Abstract

Synchrotron white beam with a wavefront limited by a 5 µm slit was used for obtaining the Bragg-case section patterns in siliconsubstrates and epitaxial layers. The section images contained variousinterference fringes, such as the Uragami fringes and fringes caused bycrystal curvature. The system of fringes connected with individual defectswas also observed.The experimental images were compared with simulated theoretical imagesobtained by numerical integration of the Takagi-Taupin equations. Areasonably good correspondence was obtained for dislocations inclined tothe surface and misfit dislocations. The elements of the image wereanalysed using the visualization of |Dh|2 and |Do|2 intensities inthe plane of diffraction, where an additional amount of transmitted waveintensity indicated the decomposition of wavefields or the reflection ofthe redirected waves from the surfaces. Comparative studies of simulatedprecipitation images and modification of dislocation images caused bycurvature and by the diffusion of an epitaxial junction were alsoperformed.