Embodiments provide an LED comprising a quantum well region operable to generate light and a substrate having an interface with the quantum well region, wherein light generated by the quantum well region traverses the interface to enter the substrate and exit the LED through an exit face of the substrate. The exit face may be opposite from and a distance from the interface, with some portion or all of this LED being shaped to optimize the light extraction efficiency of the device. The exit face can have at least 70% of a minimum area necessary to conserve brightness for a desired half-angle of light. Sidewalls of the LED may be positioned and shaped so that rays incident on a sidewall reflect to the exit face with an angle of incidence at the exit face at less than or equal to a critical angle at the exit face.