Sapphire substrate having triangular projections with outer perimeter formed of continuous curve

A sapphire substrate having a principal surface for growing a nitride semiconductor to form a nitride semiconductor light emitting device comprises a plurality of projections on the principal surface. Each of the projections has a bottom that has a substantially polygonal shape. Each side of the bottom of the projections has a depression in its center. Vertexes of the bottoms of the respective projections extend in a direction that is within a range of ±10 degrees of a direction that is rotated clockwise by 30 degrees from a crystal axis "a" of the sapphire substrate.