## 3 Experimental Results  
As a structure to be placed away from PSS within the outer surface of LEDs, the GaN nano-pillars and the air-void surrounding the nano-pillars filled with SiO\({}_{2}\) NPs were fabricated as described above (Figure 1). To confirm the formation of nano-pillars and air-voids after regrowth, the cross-sectional images were obtained using FE-SEM. Figure 2a,b shows that the air-voids surrounding the nano-pillars were filled with the SiO\({}_{2}\) NPs. With this configuration, GaN overgrowth begins on the upper part of each nano-pillar. The overgrowth expands laterally crossing the air-void and merges with adjacent laterally overgrown regions starting from neighboring nano-pillars. Figure 2c,d shows that GaN layer is formed on the top of the air-void and nano-pillars. This picture means that while the upper space of the air-void of Figure 2a,b was covered with GaN overgrowth, SiO\({}_{2}\) NPs contributed to keep the shape and size of the air-void. As a result, the density of threading dislocations was diminished as shown in Appendix B. SiO\({}_{2}\) NP LED shows 4 times lower TD density than that of the reference, which is a considerable improvement of the crystalline quality. Figure 3 shows the performances of SiO\({}_{2}\) NP LED compared to the reference LED. When 20 mA current is injected into the SiO\({}_{2}\) NP LED and the reference LED, forward voltage is 2.84 V and 2.97 V, respectively (Figure 3a). The decrease of the forward voltage is considered as the result of the series resistance decrease caused by the TD decrease. This decrease in TD density comes in addition to the decrease of TD density produced by growth on the PSS which presents both in the reference and modified LED structures. From this perspective, the nano-pillar layer overcomes disadvantages of dislocation density control in PSS, resulting in better performance of the forward voltage. In relation to LEE, Figure 3b shows that the light output of the SiO\({}_{2}\) NP LED is 13.5% higher than that of the reference LED. Figure 2: (**a**) Tilted field emission scanning electron microscopy (FE-SEM) image of the SiO\({}_{2}\) nano-particles (NPs) among nano-pillars. (**b**) Zoomed-in image to show the NPs clearly in air-void. (**c**) FE-SEM image of cross-section of the regrown GaN layer with air-voids and nano-pillars. (**d**) Close-up image of cross-section of revealed SiO\({}_{2}\) NPs filling the air-voids on the left. Table 1 shows that the IQE of the SiO\({}_{2}\) NP LED measured at 100 mA was 4.5% higher than that of the reference LED. The ABC model is well known to explain the rate of total recombination in LEDs. A, B, and C stands for Shockley-Read, radiative, and Auger recombination coefficient, respectively. The IQE was calculated with the ABC model under assumptions that the A and B coefficients were a function of current I, and C was much smaller than 10\({}^{-30}\) (cm\({}^{6}\cdot\)s\({}^{-1}\)) [23]. In the ABC model, the A coefficient is related to non-radiative recombination which describes the efficiency decrease due to non-radiative recombination on localized states. These defect levels can be due to localized states on dislocations and also to deep traps associated with point defects. However, in case of InGaN/GaN MQW LED, IQE increase was not proportional to TD decrease and localized. In composition fluctuation also affected the efficiency [24]. In addition, it has been observed that the density of deep Shockley-Hall-Read traps in modified structures was measurably lower than in reference structures [25]. Experiments with electron irradiation indicate that the increase in concentration of some of the detected deep traps correlated with the decrease of the EQE of irradiated LEDs [26]. Table 2 shows LEE calculated based on the light output data measured with integrating sphere system and the IQE of Table 1. The LEE increase is obtained with calculation using LEE = EQE/ IQE.