## 3 Results and Discussion
To elucidate the light outcoupling effects of metal layer, three-dimensional finite-difference time-domain (FDTD) simulations were studied, and the results were compared with the experimental results, as shown in Figure 4. The LED structures with the Ag NW/NP TCE were used in the FDTD simulation. To understand the effects of the geometric configuration on QW-SP coupling in the LEDs, a numerical calculation was performed based on a genetic algorithm by setting a periodic boundary condition. In this investigation, pulse emission sources with TE and TM polarization were used by propagating light to the slab representing the LED. As shown in Figure 4, light propagates along the interface between GaN and Ag NW, and the PL is significantly enhanced by LSP-QW coupling when the thickness of the p-GaN layer is 45 nm. In addition, many photons with TE and TM polarization are radiated by the leakage mode at the NW-NP junction, as shown in Figure 4a,c,e.g. These results indicated that the enhanced PL intensity afforded by the Ag NW/NP TCE can be attributed to an enhancement in the leakage and scattering rate by Ag NPs in LSP-QW coupling. However, when the distance between the Ag NWs and NPs is large, the light extraction is not significantly improved, as shown in Figure 4b,d,f,g. From FDTD simulation, in Ag-NW-based TCE, NP can act as a light scattering point to improve the extraction of photons. So, to improve the light extraction, it is desirable to increase the of density of NPs. Figure 5a,b show the time-resolved PL spectra of the LEDs without TCEs and with Ag NW and Ag NW/NP TCEs for p-GaN thicknesses of 120 and 45 nm at the temperature of room temperature (300 K), respectively. As expected, the penetration of SP-QW coupling was observed only in the samples with a 45 nm thick p-GaN layer, and there was no change in decay time in the LEDs with a 120 nm thick p-GaN layer. However, the decay time decreased significantly in the LEDs with Ag NW TCEs and Ag NW/NP TCEs when the p-GaN thickness was 45 nm. In Figure 5, all decay curves were fitted with an exponential decay model. In the LED with a 45 nm thick p-GaN layer, the calculated decay times were 10, 1, and 0.5 ns for LEDs without a TCE, with the Ag NW TCE, and with the Ag NW/NP TCE, respectively. The Purcell effect is defined as the ratio of the classical radiated power to the dipole of the cavity to the dipole emission power of the bulk material, thus predicting the rate of spontaneous emission of an LED [28]. The Purcell factor is be calculated numerically using a commercial grade finite-difference time-domain (FDTD) simulation with suggested method by [PERSON] et. al. The Purcell factor of LED with Ag NW/NP TCE was calculated to 37 at 465 nm. This value is reasonable in QW-SP-coupled LEDs to improve the spontaneous emission [29]. Therefore, the spontaneous rate of LED with Ag NW/NP-based TCEs can be increased by strong coupling between the QWs and TCE. The current-voltage (I-V) characteristics and the optical output power of a blue LED without TCEs, with Ag NW, and with Ag NW/NP TCEs were studied. We found that the electrical properties of LEDs is improved by adopting Ag NP in both LED with 45 nm and 120 nm thick p-GaN, as shown in Figure 6a. This result can be attributed to the improvement of the Ohmic behavior with atomic inter-diffusion during the thermal  
Figure 4: FDTD simulation of Ag NW/NP TCEs using sapcing between the Ag NW and Ag NP of 20 nm with (**a**) 45 nm and (**c**) 120 nm-thick p-GaN for TE mode and (**e**) 45 nm and (**g**) 120 nm-thick p-GaN for TM mode. That of of Ag NW/NP TCEs using sapcing between the Ag NW and Ag NP of 100 nm with (**b**) 45 nm and (**d**) 120 nm-thick p-GaN for TE mode and (**f**) 45 nm and (**h**) 120 nm-thick p-GaN for TM mode. Figure 5: Time-resolved PL spectra of blue LEDs without TCE and with and without Ag NPs with (**a**) 120 nm thick and (**b**) 45 nm thick p-GaN layer. annealing process to form NP [30]. As shown in Figure 6b, the output power of LEDs with 120 nm thick p-GaN are decreased with Ag NW or Ag NW/NP TCE.