## 3 Results and Discussion  
The EL emission peak and the full-width half maximum (FWHM) versus injection current for the three LEDs with different LQWs are shown in Figure 2. It is obvious to see that both the emission wavelength and the FWHM increase with increasing LQW thickness. All the peaks of the three samples present an obvious blue-shift, which is caused by the carriers filling the localized states [23]. The large  
Figure 1: (**a**) Schematic epitaxial structure and (**b**) electroluminescent intensity mapping of the InGaN LED chip (1 mm\({}^{2}\)). blue-shift in the wavelength and wide FWHM for the InGaN LEDs with 5.2-nm LQW are mainly caused by a more inhomogeneous indium distribution as well as a larger piezoelectric field within the active region. The EQE can be calculated by EQE = (\(P_{\text{output}}\)/_lvv_)/(\(I\)/_q_), where \(P_{\text{output}}\), _hv_ and \(I\) are the output power, photonic energy and the injection current, respectively. The measured absolute and normalized EQE of the three LEDs are plotted in Figure 3a,b. It is clear that the LED with a wider LQW thickness presents a small efficiency droop, a larger onset-droop current and a relatively low peak EQE. Importantly, the LED with an LQW thickness of 5.2 nm shows a negligible efficiency droop, in which the EQE reduces from a peak value of 38.8% to 36.4% at 100 A/cm\({}^{2}\). Meanwhile, the onset-droop current density is raised from 3 A/cm\({}^{2}\) to 40 A/cm\({}^{2}\) as the LQW thickness increases from 3.0 nm to 5.2 nm. The droop ratio is defined as (Max_IQE-IQE)/Max_IQE, where the Max_IQE presents the peak IQE. From Figure 3b, we can see that the efficiency droop ratio is significantly alleviated from 30% to 7% at 100 A/cm\({}^{2}\) as the LQW thickness increases from 3.0 nm to 5.2 nm. The peak efficiency decreases from 69.6% to 38.8% as the LQW thickness increases from 3.0 to 5.2 nm, which can be explained by the larger quantum confinement stark effect (QCSE) [17; 18] and the subsequent reduction of the electron-hole wavefunction overlap. These results suggest that there is a balance to achieve both high efficiency and efficiency droop for the \(c\)-plane InGaN LEDs by tuning the LQW thickness, which is one of the easiest and controllable parameters during MOCVD epitaxial growth. It is worth pointing out that the efficiency of LEDs with a wide LQW thickness of 5.2 nm is estimated to surpass the efficiency of the conventional highly efficient LEDs with 3.0-nm thick LQW at a current density of 200 A/cm\({}^{2}\) (2A). Therefore, the \(c\)-plane polar LEDs with a wide LQW show benefits in efficiency by operating at a high current density due to the ultra-low efficiency droop, which is very easy to be adopted in mass production. We do believe that the peak EQE for the LEDs with a wide LQW can be further improved by optimizing the LQW crystal quality such as adopting a lower InGaN QW growth rate or using the AlGaN insertion layer to reduce the Shockley-Read-Hall (SRH) nonradiative recombination. Figure 2: (**a**) The electroluminescent (EL) emission peak and (**b**) full-width half maximum (FWHM) versus injection current for the LEDs with different last quantum wells (LQWs) of 3.0 nm, 4.5 nm and 5.2 nm. A modified ABC model with the consideration of the shrink of InGaN QW is employed in our previous study to investigate the carrier recombination dynamics in InGaN MQWs. IQE can be calculated by [24; 25], where \(I\) is the current injected into the active region, \(V_{\text{active}}\) is the physical volume of the active region, and \(q\) is the elementary charge. Due to the localized carriers in the potential minima of In-rich InGaN clusters [26; 27; 28], it is reported that the effective active region volume (\(V_{\text{effective}}\)) is smaller than the \(V_{\text{active}}\). [PERSON] et al. showed that the effective QW thickness of InGaN blue LEDs would be reduced to only \(\sim\)1.0 nm with a \(V_{\text{active}}\) of 2.5-3.0 nm [16; 29].