I. Introduction
White light-emitting diodes (LEDs) have been developed and improved to the extent that they may replace traditional light sources, such as mercury lights and halogen lamps, in solid-state lighting (SSL) [1]. Usually, blue chip and yellow phosphor are combined to produce white-light LEDs for SSL [2]. To increase the adoption of LEDs, high-power white LEDs have been developed to enhance quantum or lumen efficiency [3]. Researches have shown that large electron-hole wavefunction overlap quantum wells and the surface plasmon approach increase internal quantum efficiency [4], [5]. Enhanced light extraction by internal reflection (ELiXIR) has been proposed to increase extraction efficiency. ELiXIR uses internal reflection to extract light from reflectors and enhance light extraction [6]. Luo et al. [7] used a hemisphere-shaped encapsulation to increase luminous efficiency and reduce the total internal reflection losses.