Seeds are implanted in a regular pattern upon an undersubstrate. A GaN 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.