Light-emitting device having a patterned substrate and the method thereof

A light-emitting device, comprising:

• a sapphire substrate comprising a flat surface, a lower surface, and a plurality of depressions between the flat surface and the lower surface;
• a semiconductor buffer layer filled the plurality of depressions and formed on the flat surface;
• and
• a light-emitting stack comprising III-V semiconductor, overlaying the semiconductor buffer layer, comprising a first conductivity type semiconductor layer, an active layer, and a second conductivity type semiconductor layer,
• wherein in a plan view of the light-emitting device, one of the plurality of depressions comprises an opening top portion having a first top-view shape and a bottom portion having a second top-view shape,
• wherein in a cross-sectional view of the light-emitting device, the one of the plurality of depressions comprises a sidewall portion connecting the opening top portion and the bottom portion, and
• wherein in a cross-sectional view of the light-emitting device, the sidewall portion near the opening top portion or the bottom portion is a curve.