Embodiments of an LED disclosed has an emitter layer shaped to a controlled depth or height relative to a substrate of the LED to maximize the light output of the LED and to achieve a desired intensity distribution. In some embodiments, the exit face of the LED may be selected to conserve radiance. In some embodiments, shaping the entire LED, including the substrate and sidewalls, or shaping the substrate alone can extract 100% or approximately 100% of the light generated at the emitter layers from the emitter layers. In some embodiments, the total efficiency is at least 90% or above. In some embodiments, the emitter layer can be shaped by etching, mechanical shaping, or a combination of various shaping methods. In some embodiments, only a portion of the emitter layer is shaped to form the tiny emitters. The unshaped portion forms a continuous electrical connection for the LED.