Light emitting diodes include a diode region having first and second opposing faces that include therein an n-type layer and a p-type layer, an anode contact that ohmically contacts the p-type layer and extends on the first face, and a cathode contact that ohmically contacts the n-type layer and also extends on the first face. The anode and cathode contacts extend on the first face to collectively cover substantially all of the first face. A small gap may be provided between the contacts.