Growth conditions are developed, based on a temperature-dependent alignment model, to enable formation of cubic group IV, group II-V and group II-VI crystals in the [111] orientation on the basal (0001) plane of trigonal crystal substrates, controlled such that the volume percentage of primary twin crystal is reduced from about 40% to about 0.3%, compared to the majority single crystal. The control of stacking faults in this and other embodiments can yield single crystalline semiconductors based on these materials that are substantially without defects, or improved thermoelectric materials with twinned crystals for phonon scattering while maintaining electrical integrity. These methods can selectively yield a cubic-on-trigonal epitaxial semiconductor material in which the cubic layer is substantially either directly aligned, or 60 degrees-rotated from, the underlying trigonal material.