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Effects of the polarization field distribution in the quantum well layer of InGaN light-emitting diodes (LEDs) on their photoelectric properties are numerically studied. Specifically, the polarization and built-in electricfield distributions, energy band diagrams, carrier concentrations, radiative recombination rate, carrier current density, electroluminescence (EL) spectra, and internal quantum efficiency (IQE) are investigated. The simulation results suggest that the triangular polarization field distribution contributes to uniform carrier distribution in the quantum wells, which inhibits electron current leakage and enhances radiative recombination. In addition, the effects of the polarization field on InGaN multiple quantum wells (MQWs) are effectively suppressed by implementation of triangular MQWs, which leads to minimization of the resulting efficiency droop. LEDs incorporated with triangular MQWs with gallium face-oriented inclination band profiles exhibit a 128% improvement in EL intensity at 20 mA and a 9% reduction in droop at 100 mA in comparison to the conventional square-MQW LEDs.
© 2014 Optical Society of America
1. Introduction
InGaN light-emitting diodes (LEDs) are currently of great interest for applications in lighting, displays, sensing, biotechnology, medical instrumentation, and other fields [1–6]. However, the development of InGaN LEDs for the realization of high-power, high-brightness applications is plagued by the problem of reduction in emission efficiency at high injection current densities (efficiency droop). The reason for the occurrence of efficiency droop remains a topic of active research [7]. Various research groups have identified the reasons as being Auger recombination processes [8], overflow electron current [9], inefficient carrier injection [10], and transport mechanisms [11]. It has also been reported [12, 13] that the proposed nonradiative Auger recombination process is unlikely to be the cause of efficiency droop since the Auger recombination coefficients are too low to account for the efficiency losses. The effects of overflow electron current on droop were investigated using polarization-matched AlInGaN multiple quantum wells (MQWs) [14], AlxGa1-xN,and lattice-matched InAlN electron-blocking layers (EBLs) [15] and by adopting nonpolar and semipolar growth directions [16]. The polarization field in these structures can be eliminated in the active region to restrain the electron current leakage and to enhance the uniformity of hole distribution throughout the active region. While these approaches have been shown to improve the efficiency, the use of MQWs and EBLs degrades the carrier injection and transport mechanisms. In addition, the growth of quaternary AlxGa1-x-yInyN limits the maximum incorporation of indium content into the alloy [17], and the growth of nonpolar or semipolar GaN-based MQWs remains hindered by the existence of a high threading dislocation density and basal stacking faults along the c-direction [18].
Recently, several research groups have proposed that efficiency droop can be suppressed by designing the polarization field distribution in MQWs and EBLs [19, 20]. For example, the graded composition of quantum barriers or the EBL can enable the enhancement of hole injection and suppression of electron overflow [11]. Moreover, the nonsquare shape of QWs has been experimentally and theoretically demonstrated to suppress efficiency droop [21]. The experiment confirmed that the triangular MQW LEDs showed a higher intensity and a narrower linewidth of EL, a lower operation voltage, and a stronger light-output power [22, 23]. The calculations have shown that the triangular MQW LEDs exhibited high IQE and low efficiency droop because of the lower Auger recombination rate, improved carrier distribution, and reduced influence of polarization fields compared to square MQW LEDs [24–26].
In the present study, we designed three different InGaN LED structures with triangular MQWs and compared their polarization field distributions with those of conventional LEDs with square MQWs. Furthermore, we performed a numerical simulation to analyze and compare the photoelectric properties of the designed triangular-MQW LEDs with those of the conventional LEDs in order to determine the correlation between polarization distribution and the photoelectric properties of InGaN LEDs.
2. Calculation model and parameters
In this study, we numerically investigate the optical and electrical properties of the conventional InGaN LED with square MQWs and a newly designed InGaN LED with triangular MQWs by using six-by-six K·P method. Figure 1 shows schematic diagrams of the four LED designs. The 3-μm-thick n-GaN layer (n-doping = 6 × 1018 cm−3) is used as the template of the LEDs. The active region consists of a 5-period In0.18Ga0.82N (3.6 nm)/GaN (12 nm) MQW. On top of the active region is a 20-nm-thick p-Al0.15Ga0.85N EBL (p-doping = 5 × 1017cm−3) and a 0.2-μm-thick p-GaN caplayer (p-doping = 1.2 × 1018 cm−3). The band offset ratio, ∆Ec/∆Ev = 0.7/0.3, serves as a default parameter in the simulation. The electron and hole mobilities are assumed to be 100 and 10 cm2V−1s−1, respectively, and the operating temperature is assumed to be 300 K. Other material parameters of the semiconductors and a detailed description of the simulation model are reported elsewhere [27, 28].
Fig. 1 (a) Schematic diagram of LED structures and (b) distribution of indium composition in SS-MQW, ST-MQW, GOAT-MQW, and NOAT-MQW.
The conventional InGaN LED with symmetric square MQWs (hereafter SS-MQW) was used as a reference. As shown in Fig. 1(a), the thickness of one QW was 3.6 nm, with a uniform indium composition of approximately 0.18. In this study, we designed three different InGaN LED structures with triangular MQWs, as described next. The thickness of one QW was set as 3.6 nm, and the graded indium composition ranged from 0 to 0.18. The InGaN LED with symmetric triangular MQWs (hereafter ST-MQW) has a symmetric distribution of the indium composition in the QWs. As shown in Fig. 1(b), the thicknesses of both the graded sides and of the uniform side of the QW were all set as 1.2 nm. Figures 1(c) and 1(d) show the distribution of the indium composition in the InGaN LED with asymmetric triangular MQWs (hereafter AT-MQW) in the QWs. The thicknesses of the steep graded side, uniform side, and inclined graded side of the QW were set as 0.6, 1.2, and 1.8 nm, respectively. In Fig. 1(c), the asymmetric QW is seen to incline toward the gallium face orientation, which is hereafter referred to as the gallium face-oriented inclination AT-MQW (GOAT-MQW in short). By contrast, in Fig. 1(d), it is seen that the asymmetric QW inclined toward the nitrogen face orientation, hereafter referred to as the nitrogen face-oriented inclination AT-MQWs (NOAT-MQW in short).
3. Results and discussion
Figure 2 shows a plot of the calculated polarization field and built-in electricfield for all four MQW structures at 20 mA.The polarizations of the SS-MQW and ST-MQW show rectangular and isosceles-triangle-shaped distributions, respectively, because polarization charges at the GaN/InGaN interface are distributed symmetrically on both sides of the quantum barrier. For the GOAT-MQW and NOAT-MQW, the asymmetrical graded indium composition in the QW leads to an asymmetric distribution of the triangular polarization and built-in electricfield and is bent toward the gallium face and the nitrogen face respectively, as shown in Figs. 2(a) and 2(b). The graded-indium-composition QWs can weaken the piezoelectric polarization and reduce the polarization charge at the GaN/InGaN interface in comparison to what can be achieved by the uniform-indium-composition QWs.
Fig. 2 Distribution of polarization field (a) and built-in electricfield (b) for SS-MQW, ST-MQW, GOAT-MQW, andNOAT-MQW at 20 mA.
Figure 3 shows the simulated energy band diagram and enlarged drawing of the QW near the EBL of the four different MQW structures at 20 mA. For the SS-MQW, the energy band in the QW is strongly bent toward the gallium face. This band bending causes the conduction band edge of the barriers to be higher than that of the EBL, as shown in Fig. 3(a). Thus, insufficient electron blocking efficiency and result an severe electron current leakage can be expected in this structure. Owing to the quantum confined stark effect (QCSE), the electron and hole wave functions separate partially, which results in poor overlap between them, as well as a reduction of the radiative recombination rate and the internal quantum efficiency (IQE). The ST-MQW structure has a symmetric triangular QW that is attributed to the symmetric distribution of the polarization field. Further, for the GOAT-MQW structure, the slopes of the triangular QWs are oriented in the opposite direction of the polarization field. The bending of the energy band seems to be compensated by applying the NOAT-MQW structure. Moreover, the electron and hole wave functions of the triangular QWs in this structure are closely integrated, which enhances the overlap integration that is facilitated by these QWs, as shown in Figs. 3(b).
Fig. 3 Energy band diagram(a) and enlarged drawing(b) of QW near EBL of SS-MQW, ST-MQW, GOAT-MQW and NOAT-MQW at 20 mA.
Figure 4(a) shows the calculated distribution of carrier concentrations in the last two QWs for the four different MQW structure designs. The electron and hole concentrations reflect the wave function distribution in the QW. Separated spatial distributions of the electron and hole envelope functions can be easily observed in the SS-MQWs because of the internal polarization fields produced by QCSE. Contrarily, in the ST-MQWs, GOAT-MQWs, and NOAT-MQWs, the carrier concentration is observed to be slightly higher, and the overlap between the electron and hole concentrations is better in the last two QWs, as shown in Fig. 4(a). It is noteworthy that the carrier injection can be improved by implementing triangular QWs. Figure 4(b) shows the calculated distributions of the radiative recombination rates for the four MQW structure designs. For the SS-MQW, the radiative recombination rate clearly occurred in the final QW nearest to the p-side, because of the nonuniform carrier distribution resulting from the poor hole transport in the MQWs and the high electron mobility that resulted in the accumulation of carriers in the final QW nearest of the p-side. However, the triangular QWs exhibit a higher radiative recombination rate distribution in the last two QWs. The radiative recombination rate increases by 187%, 193%, and 175% in the ST-MQWs, GOAT-MQWs, and NOAT-MQWs, respectively [Fig. 4(b)]. In the case of the NOAT-MQW as well, the carrier distribution is nonuniform. As shown in Fig. 3, the electrons in the QWs tend to move rapidly toward the p-side because of the nitrogen face-oriented inclination for NOAT-MQW (Fig. 3), which results in lower radiative recombination rates. Among all four MQW structure designs, the GOAT-MQW exhibits the most uniform distribution of the radiative recombination rate. The graded barrier band profile of the GOAT-MQW enhances the carrier distribution. The distribution of the radiative recombination rate of the ST-MQW lies between those of the NOAT-MQW and GOAT-MQW. Therefore, it is concluded that the GOAT-MQW structure can achieve the highest radiative recombination rate among the four MQW structures.
Fig. 4 Distribution of carrier concentrations (a) and radiative recombination rates(b) of SS-MQW, ST-MQW, GOAT-MQW, and NOAT-MQW structures at 20 mA.
A uniform hole distribution is beneficial for suppression of carrier leakage. With the aim of comparing leakage currents of the four MQW structures, the distribution of elctron and hole current densities are plotted at a current of 20 mA, as shown in Fig. 5.It can be seen that the hole leakage current is nearly 0 owing to transport impediment [Fig. 5(a)]. For the SS-MQW, the hole current is distributed only in the last QW. The other three MQW structures, with triangular QWs, show more uniform distributions of the hole current. However, the electron leakage currents of all four MQW structures are significant[Fig. 5(b)]. For the SS-MQW, the electron current leakage is as high as 46.2%. However, the presence of the triangular QW suppresses the electron current leakage and enhances hole injection, and therefore, the carrier distribution is more uniform. The electron leakage currents are 4.3%, 4.2%, and 4.0% for the ST-MQW, GOAT-MQW, and NOAT-MQW, respectively. The electrons that have escaped from the MQWs participate in nonradiative recombination, resulting in an efficiency droop of the MQWs.
Fig. 5 Distribution of hole current densities(a) and electron current densities(b) for SS-MQW, ST-MQW, GOAT-MQW, andNOAT MQW at 20 mA. Inset: Enlarged drawing of current densities near the EBL of the triangular QWs structures.
Figure 6 shows the optical properties, i.e., the electroluminescence (EL) spectra and IQE, of the four MQW structure designs. The spectral intensity of the ST-MQW, NOAT-MQW, and GOAT-MQWare higher by 105%, 120%, and 128% than that of the SS-MQW [Fig. 6(a)]. The higher radiative recombination rate in the triangular MQW structures prominently enhances the luminescence of the LEDs. Moreover, the EL spectrum of the GOAT-MQW structure is blue-shifted by 28 nm relative to that of the SS-MQW structure because of an increase in the effective energy band gap [Fig. 3(b)]. From the IQE curves in Fig. 6(b), we can see the occurrence of an obvious efficiency droop of 32% at 100 mA in the SS-MQW structure. However, there is an obvious reduction in the efficiency droop when MQWs with a triangular polarization fieldare used. For example, the GOAT-MQW has a slight efficiency droop of 23% at 100 mA, as shown in Fig. 6(b). Therefore, implementation of triangular QWs leads to effective suppression of effects of the polarization field on the InGaN MQWs and subsequent minimization of the resulting efficiency droop.
Fig. 6 Electroluminescence (EL) spectra at 20 mA(a) and IQE as a function of current density (b) for SS-MQW, ST-MQW, GOAT-MQW, andNOAT-MQW.
4. Conclusions
In conclusion, the performance of InGaN LEDs is markedly improved when the square QWs of conventional InGaN LEDs are replaced with triangular QWs, owing to the appropriately modified polarization field distribution, low electron current leakage, high carrier injection efficiency, high radiative recombination rate, and small efficiency droop. The simulation results indicate that the use of triangular QW structures enhances the performance of InGaN LEDs, particularly in terms of their high-current-injection operation.
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (Grant No.51002102), Shanxi Province science and technology innovation team project(Grant No.2012041011) Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant No.KJ131308) and Natural Science Foundation of Shanxi Province (Grant No. 2014021019-1).
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