## 4 Results and Discussion  
Energy band diagram is shown in Figure 2. The R-LED and W-LED energy band diagrams are shown. The shaded areas are highlighting the quantum well region. The energyband in both the cases is strongly tilted towards the p-side because of the built-in electromechanical field direction. The W-shape well can utilize the carrier localization within the well to improve the carrier confinement and consequent radiative recombination. Strong band-bending in W-LED is observed because of the increased electrostatic field, owing to the indium fluctuation i.e., 34%-28%-34%, which also hinders carrier transport in the W-LED apart from the indium localization [28; 29; 31; 45; 47; 48]. The influence of the electrostatic field and carrier transport in our proposed device is presented in detail in the following discussion. The inclined triangular wells in the reference structure are known to reduce theelectron-hole wavefunction overlap, therefore reducing the overall device performance [9; 32; 47]. This overlap is further reduced in green LEDs due to increased built-in electrostatic field arising from the increased indium composition and lattice mismatch [32]. The wells are also inclined in the W-LED but the W-shaped indium composition in the well improves the electron-hole wavefunction overlap, due to its peculiar composition fluctuations, leading to the improved device performance. Figure 3 shows the estimation of carrier concentrations in the quantum wells of the two devices. The electron concentrations in Figure 3a are quite identical in the two devices, which means that the W-LED has no significant influence on the electron current transport in the quantum wells. The electron concentration peaks towards the p-side of the well. In contrast, the hole concentration in W-LED in Figure 3b shows significant enhancement in comparison to W-LED, specifically in the quantum well towards p-side, which means that significant radiative recombination is expected because of the improved confinement of the holes in the active region. The hole concentration peaks towards the n-side of the quantum well, which also suggests that radiative recombination is expected to occur towards the p-side of the quantum well. The hole concentration tends to decrease in each quantum well from p-side to n-side in the reference structure, which is consistent with the reported results [47]. Since strong localization of holes is known to occur due to the fluctuations in indium composition [28; 29; 31; 32], this results in most of the holes being confined in the last QW of the proposed W-LED in comparison to the first QW, where negligible holes exist, in addition to the effect of increased band-bending coming from the comparatively higher electrostatic field in W-LED. Figure 3: Comparison of carrier concentrations: (**a**) Electrons and (**b**) Holes in the two devices in semilogarithmic scale. Figure 2: Comparison of band energy: (**a**) Conduction band energy; and, (**b**) Valence band energy. Figure 4a shows the estimation of the radiative recombination rates in the two devices. It can be observed that the radiative recombination rate in W-LED is more than twice than that of R-LED. This is due to the significant accumulation of holes in the well towards the p-side, as discussed in Figure 3. Since the holes are concentrated more towards the n-side in each QW, the radiative recombination in each quantum well is also concentrated towards the n-side because of the better electron-hole wavefunction overlap towards the n-side of the well. Because of the reduction of hole concentration from p-side towards the n-side of the device, owing to the reduced hole transport, the radiative recombination is asymmetrically reduced in the quantum wells of both devices [49]. Figure 4b,c show that W-LED has reduced Shockley-Read-Hall and Auger recombination rates in comparison to R-LED.