A textured substrate is disclosed which is amenable to deposition thereon of epitaxial single crystal films of materials such as diamond, cubic boron nitride, boron phosphide, beta-silicon carbide, and gallium nitride. The textured substrate comprises a base having a generally planar main top surface from which upwardly extends a regular array of posts, the base being formed of single crystal material which is crystallographically compatible with epitaxial single crystal materials to be deposited thereon. The single crystal epitaxial layers are formed on top surfaces of the posts which preferably have a quardrilateral cross-section, e.g., a square cross-section whose sides are from about 0.5 to about 20 micrometers in length, to accommodate the formation of substantially defect-free, single crystal epitaxial layers thereon. The single crystal epitaxial layer may be selectively doped to provide for p-type and p.sup.+ doped regions thereof, to accommodate fabrication of semiconductor devices such as field effect transistors.