Schematic diagram of the InGaN LED structures with stepped-MQW and the compositionally graded-MQW. 

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... InGaN-based light-emitting diodes (LEDs) being the key driver for solid-state lighting technology, the device performance at high injection current density is limited by efficiency droop. A number of possible mechanisms had been suggested to account for the droop, summarized as fol- lows: Auger recombination [1], carrier delocalization [2], and current injection efficiency quenching [3]. The severe band bending in c-plane InGaN/GaN multiple quantum well (MQW) arising from the built-in spontaneous and piezoelectric polarization fields [4] – [6] was also accounted for the ma- jor root cause of the issue. As the severe band banding leads to the reduced oscillator strength, which is inversely proportional to the spatial electron-hole separation, non-uniform distribution of carriers in MQW, and electron leakage, especially at the QW closest to p-GaN [7] – [9]. In typical LED structures, the electron blocking layer (EBL) has been incorporated between the active region and p-GaN to increase overall carrier concentration by reflecting electrons back into the active region. The downside of the EBL scheme is the reduction of the hole injection efficiency, due to severe band bending and valance band (VB) offset at AlGaN/GaN inter- face which can promote electron leakage [10] – [12]. Solutions suggested to partly mitigate the side-effects of EBL are: graded-EBL [13], lattice-matched InAlN-EBL [14], [15], superlattice-EBL [16], [17] and, graded-superlattice-EBL [8], [18]. EBL-less designs based on insertion of un- doped-GaN-layer in between active-region and p-GaN layer [19], GaN – AlGaN – GaN as last barrier [20], AlGaN-step-like-barriers [21], thin-AlGaN-barriers [22], specially-designed p-InGaN barrier [23], and two-step Mg-doped p-GaN [24] were also proposed to improve carrier confine- ment. Although the carrier concentration improves in these theoretical and experimental studies, the issues of non-uniform carrier distribution remain, which may again lead to efficiency droop of MQW. Thus, active region design that promotes uniform carriers distribution for reducing electron leakage, and improving hole injection become important. One of the possible ways to increase the output power and alleviate efficiency droop, is to improve the wavefunction overlap in the InGaN QWs by using QWs with non-conventional shapes [25] – [31], semi-polar [32], [33] or non-polar [34], [35] QWs as active material in LED structures. InGaN/GaN graded MQW LED with EBL based on linear grading realized using MOCVD showed $ 2.5 times larger quantum efficiency rollover threshold as compared to the conventional stepped-MQW-LED [29]. This improvement has been attributed to the reduced polarization field, and reduced band bending in the graded-MQW based active region. In this study, we design graded-MQW active region to achieve uniform carrier distribution with high radiative recombination in the active region, without resorting to AlGaN-based EBL or QW- barrier large bandgap insertion layers. In agreement with the obtained simulation results, extended quantum efficiency rollover threshold was obtained for graded-MQW-LED as compared to the conventional stepped-MQW-LED. To investigate the effect of grading profile on carrier distribution and recombination rate considering growth implementation, we have studied various graded schemes, i.e., the linear, parabolic and Fermi-function profiles in the simulation. A graded-MQW-LED was grown on c-plane sapphire template substrate using plasma assisted molecular beam epitaxy (PAMBE), and the efficiency droop was compared with a stepped- MQW-LED. Micro-LEDs with circular mesa diameter (D) of 80 m were fabricated. Fig. 1 shows the designed layer structures for the stepped- and graded-MQW LEDs on sap- phire-based GaN template substrate. The LED structures consist of 650 nm thick n-GaN layer, followed by five pairs of QWs and a 100 nm p-GaN cap layer. The active regions of the simulated stepped-MQW-LED consist of five pairs of In 0 : 2 Ga 0 : 8 N (3 nm)/GaN (12 nm), while that of graded-MQW consists of GaN ð 12 nm Þ = In 0 ! 0 : 2 Ga 1 ! 0 : 8 N ð 1 : 75 nm Þ = In 0 : 2 Ga 0 : 8 N ð 0 : 5 nm Þ = In 0 : 2 ! 0 Ga 0 : 8 ! 1 N (1.75 nm)/GaN (12 nm) QWs, respectively. Simulations were performed considering energy band alignment, comparison of carrier densities in MQW, spatial wavefunction overlap, electric field, and recombination rates using the NEXTNANO software [36]. The active region of simulated LED structure was assigned an unintentional background electron carrier concentration of 1 Â 10 16 cm À 3 to prevent doping induced non-radiative recombination, and im- purity scattering. The conduction-to-valance-band offsets ratio, Á E c = Á E v , was taken as 70 : 30 for the material system [37]. Band parameters for ternary alloy InGaN were calculated based on Vegard's law [38]. The electron and hole, effective masses, and the elastic, piezoelectric and deformation potentials for the ternary compound were extrapolated linearly [39]. The Arora model was used to obtain doping dependent mobilities for the intrinsic InGaN ...