An electrode structure is disclosed for enhancing the brightness and/or efficiency of an LED. The electrode structure can have a metal electrode and an optically transmissive thick dielectric material formed intermediate the electrode and a light emitting semiconductor material. The electrode and the thick dielectric cooperate to reflect light from the semiconductor material back into the semiconductor so as to enhance the likelihood of the light ultimately being transmitted from the semiconductor material. Such LED can have enhanced utility and can be suitable for uses such as general illumination. The semiconductor material can have a cutout formed therein and a portion of the electrode can be formed outside of the cutout and a portion of the electrode can be formed inside of the cutout. The portion of the electrode outside the cutout can be electrically isolated from the semiconductor material by the dielectric material.