# InGaN Resonant-Cavity Light-Emitting Diodes with Porous and Dielectric Reflectors
## 3 Results
As for the matched RC-LED structure with 30 nm-thick Ta2O5 spacer layer, the two interference line patterns were observed apparently in the far-field PL spectra. The PL emission wavelength of the InGaN active layer was matched to the interference curve in the far-field PL spectra pattern as shown in Figure 3c. The intensity formula of the angle-resolved spectra was I(\(\lambda_{\alpha}\), \(\theta\)) = (2n\({}_{\mathrm{s}}\)T/m\({}_{\mathrm{c}}\))cos(\(\theta\)) = \(\lambda_{\alpha}\)cos(\(\theta\)), where ns is the refractive index of GaN (2.48), mc is the cavity mode number, and T represents the cavity thickness [26]. In Figure 3c, the simulated interference line patterns was matched to the peak emission wavelength of the InGaN active layer. The fitting thickness of the InGaN LED cavity structure was calculated as the value of 173 nm between the bottom porous DBR and the top dielectric DBR structure. The FP second order mode in the 1\(\lambda\) resonant cavity was matched to the PL emission wavelength of the InGaN active layer as shown in curve-a in Figure 3c. From the simulation results, the penetration depths were calculated as the value of 196 nm-thick for the bottom porous DBR and 138 nm-thick for the top dielectric DBR. The effective cavity length in curve-b consisted of the 148 nm-thick InGaN active layer, 30 nm-thick Ta2O5 spacer layer, the 196 nm-thick penetration depth of the porous DBR, and 138 nm-thick penetration depth of the dielectric DBR as shown in Figure 3c. The normalized PL intensity of the far-field radiation patterns of all LED structures were measured in Figure 3d. By forming the resonant-cavity structure, the divergent angle was drastically decreased from 114\({}^{\circ}\) for the ST-LED to 57\({}^{\circ}\) for the matched RC-LED structure. Figure 3: The photoluminescence (PL) emission spectra of (**a**) the ST-LED, (**b**) the non-matched RC-LED, and (**c**) the matched RC-LED were measured through the angle-resolved PL measurement. (**d**) Normalized far-field radiation patterns of all LED structures were measured. The peak emission intensity of the matched RC-LED structure was observed at normal direction (90\({}^{\circ}\)) that matched to the resonant cavity length between top dielectric and bottom porous DBR structures. In Figure 4, the optical pumping spectra of the InGaN resonant cavity structure were measured by using a Nd-YVO\({}_{4}\) 355 nm pulsed laser as laser excitation source. In Figure 4a, the PL peak intensities and the linewidth of the PL spectra were measured as a function of the laser excited power. By increasing the laser pumping power, the PL emission intensities had a non-linear increasing property. The threshold value of the laser pumping power (Pt) was measured as the value of 14.8 uW at room temperature. In the matched RC-LED structure, the linewidth of the PL spectra was reduced from 6.5 nm to 0.7 nm by increasing the laser pumping power. In Figure 4b, the PL emission spectra of the matched RC-LED structure were observed under 0.95 Pt, 1.02 Pt, and 1.05 Pt laser pumping power, respectively. The linewidth and dominated emission wavelength of the InGaN active layer were measured at 6.5 nm for the spontaneous emission peak (at 431.3 nm) and at 0.7 nm for the stimulated emission peak (at 431.8 nm). The lasing phenomenon of the matched InGaN resonant cavity structure was measured at 431.8 nm with a 0.7 nm linewidth at room temperature.