A light-emitting diode structure includes an AuSn or AuIn-containing bonding layer over a substrate, a metal layer disposed over the bonding layer, a p-type doped gallium nitride (p-GaN) layer disposed over the metal layer, a n-type doped gallium nitride (n-GaN) layer approximate the p-GaN layer, a multiple quantum well structure disposed between the n-GaN and p-GaN layers, and a conductive contact disposed on the n-GaN layer. The n-GaN layer includes a rough surface with randomly distributed dips. The nano-sized dips have diameters distributed between about 100 nm and about 600 nm, have a dip density ranging from about 107 grains/cm2 to about 109 grains/cm2, and are spaced from each other with an average spacing S, average diameter D, and a ratio S/D that ranges between about 1.1 and about 1.5. The conductive contact is disposed on some of the nano-sized dips of the rough surface.