## 3 Results
### Effects of TiO\({}_{2}\) NS Monolayer on the Device Performance of LED  
Following experimental methods, we fabricated TiO\({}_{2}\) NS arrays/LED chips. Figure S1a,b shows optical microscope images of a blue LED chip with Am- and An-TiO\({}_{2}\) NSs. The images clearly show that the TiO\({}_{2}\) NS monolayer was successfully formed and transferred on the fabricated LEDs chip via the icing transfer method. The magnified SEM images of Am- (Figure S1c,d) and An-TiO\({}_{2}\) (Figure S1e,f) NS arrays formed on p-GaN show the well-aligned sphere arrays of Am- and An-TiO\({}_{2}\) without surface damage. Figure 4: (**a**) Absorbance spectra and (**b**) transmittance of TiO\({}_{2}\) monolayers using An- (dot-line) and Am-TiO\({}_{2}\) (black-line) nanosphere monolayers. The effects on the light extraction efficiency (LEE) of Am-TiO\({}_{2}\) and An-TiO\({}_{2}\) monolayers being transferred onto LED chips were investigated by optical and electrical performance measurements. The electroluminescence (EL) spectra for LED chips with Am- and An-TiO\({}_{2}\) monolayers were measured at the fixed injection current of 20 mA, as shown in Figure 5a. The effect on EL intensity of LED chips with Am-TiO\({}_{2}\) NS array is the strongest among the three samples. The integrated EL intensity of the samples covered with An-TiO\({}_{2}\) NS and Am-TiO\({}_{2}\) NS arrays exhibited enhancements of 1.3 and 7.9 times, respectively, over that of the reference LED chips at 443 nm emission wavelength. Optical microscopy images of emitted light obtained from LED chips with Am- and An-TiO\({}_{2}\) monolayer arrays are shown in the inset of Figure 5a. LED chip with Am-TiO\({}_{2}\) monolayer arrays showed the brightest emission intensity and uniform emission area at a low current injection of 0.5 mA. These indicate that Am-TiO\({}_{2}\) NS monolayers can dramatically improve the light extraction of LED chips. In addition, to evaluate the LEE of the LED chips, light output powers (LOPs) -current-voltage (L-I-V) were measured at the injection current ranging from 0 to 100 mA, as shown in Figure 5b. The LOPs of the Am-TiO\({}_{2}\) NSs array /LEDs chip were higher by factors of 2.8 and 3.1 times compared to the An-TiO\({}_{2}\) monolayer=coated LED chip and reference LED chip, respectively, at 100 mA. This large enhancement in the LOP of LED chips with Am-TiO\({}_{2}\) NS arrays can be attributed to the efficient propagation of light from the GaN layer to the TiO\({}_{2}\) NS and superior mitigation of back reflection of light at the interface of TiO\({}_{2}\) NSs and air [32; 33]. Figure 5: (**a**) EL spectra of LED chips with An- and Am-TiO\({}_{2}\) NS arrays with an injection current of 20 mA. Emission images of LED chips are shown in inset. (**b**) L-I-V curves and (**c**) external quantum efficiency (EQE) of LED chips with different TiO\({}_{2}\) NS arrays as a function of injected current (at I = 0–100 mA). The external quantum efficiency (EQE) of the LED chips with and without a TiO\({}_{2}\) NS array at the injection current range of 0-100 mA were measured, as shown in Figure 5c. Although there are efficiency drops in data as current levels increase, LED chips with Am-TiO\({}_{2}\) NS arrays still showed higher EQE than other LED chips. EQE is expressed as EQE = IQE \(\times\) LEE, where IQE is the internal quantum efficiency and LEE is the light extraction efficiency. The values of IQE of all blue LED chips are assumed to be the same since they have the same epitaxial structure. Therefore, the improvement of the EQE of the LED chips with the Am-TiO\({}_{2}\) NS arrays results from the increased LEE of the LED chips at I = 100 mA. The measured EQE from the samples covered with An- and Am-TiO\({}_{2}\) NS arrays exhibited enhancements of 1.1 and 3.1 times more than a bare LED chip, respectively, at 100 mA. The EQEs of LEDs with Am-TiO\({}_{2}\) NS arrays exhibit a stable boost of 3 times over LEDs with An-TiO\({}_{2}\) NS arrays over the entire range of injection currents applied in this experiment.