Highly [1 1 1]-oriented rhombohedral hetero-structure epitaxy of cubic SiGe semiconductor on trigonal c-plane sapphire was achieved and characterized with two new advanced X-ray diffraction methods to control the formation of primary-twin crystals. The formation of twin crystals on (1 1 1) plane was controlled with growth parameters such that the volume percentage of primary-twin crystal was reduced from 40% to 0.3% compared to the majority single crystal. The control of stacking faults can yield single-crystalline semiconductors without defects or improved thermoelectric materials with twinned crystals for phonon scattering while maintaining electrical integrity. In this study, about 94% of all epitaxial layers were fabricated in a single-crystalline phase. We propose the temperature-dependent alignment model of energetically favored majority single-crystalline SiGe layer on c-plane sapphire. This study shows that nearly single-crystalline cubic semiconductors can be grown in the [1 1 1] orientation on the basal (0 0 0 1) planes of selected trigonal crystal substrates. (C) 2008 Elsevier B.V. All rights reserved.