# Performance of Nanostructures within InGaN-Based Multiquantum-Well Light-Emitting Devices
## 3 Results and Discussion  
Figure 1 schematically represents the structures of the samples investigated in this study. The MQB structure shown in Figure 1b is engineered to align a forbidden energy miniband of the MQB superlattice with the conduction band minimum to enhance conduction band discontinuity [18; 19; 20]. For the MQB structure, the electron wave function of the _j_th layer can be calculated by solving a one-dimensional Schrodinger equation, and is expressed as  
\[\varphi_{j}(\mathrm{x})=A_{j}exp\left(ik_{j}x\right)+B_{j}exp\left(-ik_{j}x \right).\]  
\(k_{j}\) denotes the wave number in the _j_th layer and  
\[k_{j}=\sqrt{2m_{j}^{*}\left(E-V_{j}\right)}/\hbar,\]  
where \(m_{j}^{*}\) is the electron effective mass in the _j_th layer, \(E\) is the energy of an electron, and \(V_{j}\) is the potential height of the _j_th layer. By matching the wave functions and their first derivatives divided by the effective mass at each interface, we obtain  
\[\varphi_{j-1}\left(x_{j-1}\right)=\varphi_{j}(x_{j-1}),\]  
\[\frac{1}{m_{j-1}^{*}}\frac{d\varphi_{j-1}}{dx}=\frac{1}{m_{j}^{*}}\frac{d \varphi_{j}}{dx}\]  
Considering the coupling between the incident wave functions and the outgoing wave functions through the MQBs, the reflectivity probability \(R\) against incident electron energy is defined as \[R=|B_{1}/A_{1}|^{2},\]  
which can be obtained by the transfer matrix method [21; 22]. According to the method, the layer structure which includes an In\({}_{0.15}\)Ga\({}_{0.85}\)N well layer and a five-period In\({}_{0.02}\)Ga\({}_{0.98}\)N/GaN barrier layer is calculated. In the simulation, the conduction discontinuity for InGaN-GaN is assumed to be approximately 62% of the band gap difference \(\Delta Eg\). Following the linear Vegard's law, the bandgap and the electron effective mass that we used in the simulation were 3.03 eV and 0.1865 \(m_{0}\), respectively, for In\({}_{0.15}\)Ga\({}_{0.85}\)N; 3.43 eV and 0.1982 \(m_{0}\) respectively, for In\({}_{0.02}\)Ga\({}_{0.98}\)N, where \(m_{0}\) is the free electron mass. Due to the interference effect, the MQB structures characteristically exhibit regions of high reflectivity for electrons with energy above the bulk potential barrier. The simulated result shown in Figure 1b illustrates that a band of nonallowed electron states is created above the classical barrier height by 1.08 times relative to the conventional GaN barrier. Because the MQB nanostructure increases the band discontinuity, it is expected to prevent the electrons from overflowing as operated at high temperatures and high driving currents. Observing the EL spectra of the samples measured at 300 K and 350 K and at injection current of 20 mA and 100 mA shown in Figure 2, the higher EL spectra intensity for the sample with MQBs provides evidence of the improvement of carrier confinement and inhibited carrier leakage in the active layer. Moreover, the emission peak energies for sample with MQBs are larger than those of sample with conventional GaN barriers. Considering the lesser indium composition in the well layer and the indium content in the barrier layer for the MQB sample, the smaller polarization charges and the reduced internal field in the well layer can be achieved [23]. The reduced polarization field leads to an increased electron-hole wave function overlap, which also enhances the EL peak intensity and results in larger EL peak energies for the MQB sample. Figure 1: Potential energy profiles of the samples with (**a**) conventional-barrier structure and (**b**) with multiquantum-barrier structure, where \(U\) and \(\Delta U\) are the classical and enhanced barrier height, respectively. Figure 2: Electroluminescence spectra of the samples with conventional barrier layers and with multiquantum barriers at temperature 300 K and 350 K and at injection current of (**a**) 20 mA, and (**b**) 100 mA. The evolution of EL spectra for the sample with conventional GaN barriers over a temperature range from 20 to 380 K is shown in Figure 3a.