## 4 Simulation and Discussion  
To understand the experimental results, an Advanced Physical Model of Semiconductor Devices (APSYS) simulation program was used to simulate the electron current distributions and the band structures. In order to get the change rule and avoid the complication of simulation, 3 QWs, 5 QWs, 10 QWs and 15 QWs, and a 1 nm Al\({}_{0.92}\)Ga\({}_{0.08}\)N EBL were chosen. Tables 2 and 3 list the electron and hole concentrations and the thicknesses for different layers used in the simulation, respectively. Figure 4 shows the electron current distribution under an injection current of 120 mA. It can be seen that the electron current overflowing to p-type layers decreased as the QW number increased. More and more carriers were exhausted in the active region as the QW number increased, which was believed to result in the decrease of the parasitic peak intensity as shown in Figure 2 and the increase of output power as shown in Figure 3. The localized state due to the fluctuation of the In composition is generally referred to be the dominant emission mechanism in InGaN QWs. Nevertheless, the radiative recombination from QWs was the dominant emission mechanism in AlGaN QWs. The increase in QW number will result in the increase of radiative recombination centers for both cases. However, the total thickness of the epilayer increased as the QW number increased, which would lead to the strain relaxation. It was well known that the localized states (due to the fluctuation of In composition in InGaN QWs) mainly resulted from the strain state. Therefore, the relaxation of strain influenced the optical properties of InGaN QWs. However, in AlGaN QWs, the strain state only has influence on the polarization field and the relaxation of the strain (mainly the tensile strain) can decrease the field, which contributes to the improvement of emission from AlGaN QWs. Therefore, in this work, as the QW number increased to 40, the EL intensity still continued to increase. However, for the same QW number, the LED with a 1 nm Al\({}_{0.92}\)Ga\({}_{0.08}\)N EBL showed a far lower electron current overflow than those without EBL. To understand the phenomenon, the band structures for both LEDs were simulated. Figure 5a,b shows the band structures of LEDs with and without a 1 nm Al\({}_{0.92}\)Ga\({}_{0.08}\)N EBL under an injection current of 120 mA, respectively. The barrier height for electron overflow in the LED without EBL was 0.255 eV. The insertion of the EBL resulted in a higher barrier height of 0.302 eV, which decreased the electron current overflowing to the p-type layers. It was believed that the use of AlN as an EBL would increase the barrier height further. The band structures \begin{table}
\begin{tabular}{c c} \hline \hline
**Layers** & **Electron Concentration(cm\({}^{-3}\))** & **Hole Concentration (cm\({}^{-3}\))** \\ \hline p-GaN & \(5\times 10^{18}\) \\ p-Al\({}_{0.3}\)Ga\({}_{0.7}\)N & \(5\times 10^{17}\) \\ p-Al\({}_{0.6}\)Ga\({}_{0.4}\)N & \(5\times 10^{17}\) \\ n-Al\({}_{0.6}\)Ga\({}_{0.4}\)N & \(5\times 10^{18}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The electron and hole concentrations used in the simulation. Figure 3: The pulse current dependent relative output power for LEDs A, B, C and D.  
of LEDs with 3 QWs, 10 QWs and 15 QWs are shown in Figure 6a-c, respectively. It can be seen that the barrier heights for electron overflow under the same injection for different numbers of QWs were almost the same, which indicated that the decrease of electron overflow with increasing QW number was just due to the increase in volume of the active region. Figure 4: The electron current distribution under an injection current of 120 mA for LEDs with 3 QWs, 5 QWs, 10 QWs and 15 QWs and the 5 QW LED with a 1 nm Al\({}_{0.92}\)Ga\({}_{0.08}\)N EBL. The labels at the top of the graph refer to the different layers in the LED with 5 QWs and a 1 nm Al\({}_{0.92}\)Ga\({}_{0.08}\)N EBL.