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Several of the patented methods included in this suite of technologies enable super-hetero-epitaxy of rhombohedral/cubic compound semiconductors on specially oriented trigonal (e.g. sapphire) or hexagonal (e.g. quartz) crystal wafer substrates. This includes alignment of the growth crystal lattice with the underlying substrate lattice to minimize misfit strain-induced dislocation defects in the growing crystal. Thus thicker, defect-free crystal layers can be made. Rhombohedral/Cubic crystal twin defects which is 60 degree rotated on [111] orientation in a rhombohedral/cubic SiGe layer structure can be reduced to well less than 1% by volume, essentially providing a defect-free semiconductor material. Alternately, engineered lattice structures with a high degree of twinning can provide SiGe with improved thermoelectric properties due to the phonon scattering that inhibits thermal conduction without compromising electrical conductivity. Additional patented technologies in this suite provide for physical vapor deposition (PVD) growth methods utilizing molten sputtering targets and thermal control of heated substrates, including electron beam heating, in order to give the atoms in the sputtered vapor or on the substrate surface the energy needed for the desired crystal growth. The remaining patented technologies enable x-ray diffraction methods for detecting and mapping crystal twin defects across the entire as-grown semiconductor layer. These defects are critical to the performance of any semiconductor device manufactured from such compound semiconductor materials.