Abstract: Seeds are implanted in a regular pattern upon an undersubstrate. An AlxInyGa1?x?yN (0?x?1, 0?y?1, 0<x+y?1) mixture crystal is grown on the seed implanted undersubstrate by a facet growth method. The facet growth makes facet pits above the seeds. The facets assemble dislocations to the pit bottoms from neighboring regions and make closed defect accumulating regions (H) under the facet bottoms. The closed defect accumulating regions (H) arrest dislocations permanently. Release of dislocations, radial planar defect assemblies and linear defect assemblies are forbidden. The surrounding accompanying low dislocation single crystal regions (Z) and extra low dislocation single crystal regions (Y) are low dislocation density single crystals.

Abstract: A liquid encapsulation Czockralski method for growing a single crystal of a semiconductor compound which comprises: melting a semiconductor compound in the presence of a B.sub.2 O.sub.3 liquid encapsulant to form a two phase liquid; dipping a semiconductor seed crystal into the compound melt covered with the B.sub.2 O.sub.3 encapsulant; growing the crystal from the compound melt by pulling up and rotating the seed crystal; and, cooling the crystal in a cooling zone above a crucible. The cooling zone is maintained at a substantially uniform temperature distribution with a small temperature gradient by using primarily an independently controlled crystal cooling zone heater H3. In addition, an independently controlled melt heater H1 and an independently controlled crystal growing heater H2 are employed. Also, a crystal cooling zone heat shield 11 can be provided to aid in slowly cooling the grown crystal in the substantially uniform temperature distribution.