Patterned sapphire substrate, light emitting diode and fabrication method thereof

A patterned sapphire substrate having a first surface and a second surface opposite to each other, wherein:

• the first surface of the substrate is formed by arranging a plurality of interspaced patterns;
• the patterns have a plurality of side surfaces and at least one concave region sandwiched between adjacent side surfaces;
• a width of the concave region gradually decreases, and the concave region gradually becomes shallower, from a top to a bottom of the patterns;
• wherein:
• the patterns further comprise a top surface and a bottom surface, and the concave region is sandwiched between the adjacent side surfaces and the top surface of the patterns;
• the concave region is connected by two inclined surfaces;
• and
• a projection of the concave region on the bottom surface of the patterns appears as a triangle.