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.