Hetero-epitaxial semiconductor materials comprising cubic crystalline semiconductor alloys grown on the basal plane of trigonal and hexagonal substrates, in which misfit dislocations are reduced by approximate lattice matching of the cubic crystal structure to underlying trigonal or hexagonal substrate structure, enabling the development of alloyed semiconductor layers of greater thickness, resulting in a new class of semiconductor materials and corresponding devices, including improved hetero-bipolar and high-electron mobility transistors, and high-mobility thermoelectric devices.