In this work, theoretical investigation of the influence of Auger recombination coefficient and built-in polarization field on the internal quantum efficiency (IQE) in terms of lateral-vertical single quantum well (SQW) as well as multiquantum well (MQW) GaN-based blue light-emitting diodes are presented. The degradation effect of the built-in polarization field on the IQE of vertical light-emitting diodes is used to strengthening the Auger recombination coefficient in comparison to lateral light-emitting diodes. This result has been found consistent in both single-as well as multi-quantum well structures. In addition, when Auger recombination coefficient has been included in the analysis, vertical multiquantum well structure shows more degradation in the IQE in comparison to the lateral structures. The effect has been dominant in vertical MQW case.

With the recent advancement in technology, III-Nitride materials have gained tremendous attention due to their exceptional light emission characteristics ranging from ultraviolet region to blue & green region of electromagnetic spectrum.1,2 For instance, GaN-based blue and green light-emitting diodes (LEDs) have been employed in traffic lamps and color displays. GaN-based LEDs show improved efficiency at low injection current density but at higher injection current density the device efficiency is reduced significantly. The efficiency decreases as the value of injected current increases beyond few milliamperes.3–7 This phenomenon is known as “efficiency droop” and it is observed over a wide range of the visible spectrum.1,8 Some of the proposed explanations of the efficiency droop are Auger recombination,9 carrier delocalization,1,8 carrier leakage10 and nonradiative recombination.11,12

III-Nitride materials are known to have strong polarization induced electric fields due to their wurtzite crystal geometry as well as strain between the epilayers due to lattice mismatch. This results in quantum-confined stark effect (QCSE) causing spatial separation of the electron-hole wavefunctions within the quantum well thus reducing the radiative recombination probability13–17 and results in efficiency droop. Many growth mechanisms have been utilized in order to minimize the efficiency droop such as reducing strain between layers, minimizing the spatial separation of wavefunctions using polarization- and lattice-matched layers in heterostructures18–26 and by exploiting non- or semi-polar substrates27–30 

Efficiency droop at low and high current densities can be explained by using recombination rate equation.31 At low current densities, SRH recombination is the dominant mechanism but at higher current densities Auger recombination becomes dominant. Also as the injection current increases the current spreading length decreases which in turn reinforces efficiency droop.32 In addition, the current crowding effect in LEDs also influences efficiency droop phenomena.32,33

In this paper, we have performed numerical simulations in order to find out the influence of the roles of internal polarization effect as well as the role of Auger recombination on the efficiency droop of internal quantum efficiency (IQE) of GaN-based vertical SQW and MQW as well as lateral SQW and MQW LED structures. In literature, the influence of the two key parameters on the IQE has not been discussed, according to our knowledge, on the basis of two different device structures.

In this work, four GaN-based blue LEDs are simulated. First is a lateral single quantum well (LSQW), the second one is a lateral multiquantum well (LMQW) structure, the third one is vertical single quantum well (VSQW) and the fourth one is vertical multiquantum well (VMQW) structure. The active region is made up of InGaN quantum well layer 2.5 nm thick with 15% Indium composition, i.e. In0.15GaN. The quantum well is sandwiched between two GaN barriers having thickness of 10 nm each. Above active region, there is p-doped AlGaN electron blocking layer (EBL) having thickness of 20 nm and a p-doping of 5×1017 cm-3. Above EBL there is a p-GaN layer having thickness of 150 nm with p-doping of 1×1018 cm-3. Below QW active layer there is an n-type GaN layer of thickness 2000 nm and having n-doping 5×1018 cm-3. SRH recombination lifetime, both for electrons and holes, is 25 ns. The n- and p-electrodes in vertical structures are 300 um each whereas n- and p-electrodes in lateral structure are 100 um and 300 μm respectively. The mesa size in lateral structure is 100 μm x 100 μm. All the four structures have similar doping conditions. In MQW structures, 5 QWs have been employed. The VSQW and VMQW as well as LSQW and LMQW structures are shown in Figure 1(a), (b), (c) and (d) respectively.

FIG. 1.

Diagrammatic illustration of the GaN-based vertical (a) SQW and (b) MQW along with lateral (c) SQW and (d) MQW LED device structures.

FIG. 1.

Diagrammatic illustration of the GaN-based vertical (a) SQW and (b) MQW along with lateral (c) SQW and (d) MQW LED device structures.

Close modal

Spontaneous recombination or radiative recombination in light-emitting diodes can be calculated either by using Van Roosbroeck-Shockley model or by Einstein model.34 Here it is calculated by taking direct integration of the spectrum of spontaneous emission along with the function of Lorentzian line. The polarization effect is estimated by applying theoretical model of Fiorentini et al.35 

First simulations were performed by setting C coefficient equal to zero in all structures and varying the internal polarization, shown by symbol P, between 0 and 0.5, where P = 0 signifies that the internal polarization has been neglected. Initially when P = 0, it can be seen in Figure 2 that the value of IQE reached unity at a very low current density and later saturated with increasing current density. This behavior is consistent with the fact that when P = 0, the IQE is supposed to be droop-free,36 provided that other droop-mechanisms are neglected. If we look at Figure 2(a), LSQW sharply reached unity in comparison to VSQW at low current density. This sharp increase could be explained by increasing radiative recombination in comparison to the nonradiative SRH recombination.37,38 Figure 2(b) depicts the MQW case of the vertical and lateral structures in consideration. In the Figure 1, the IQE of VMQW and LMQW are identical over the entire range of the current density unlike Figure 2(a), where the LSQW structure quickly reached saturation at low current density in comparison to the VSQW.

FIG. 2.

IQE as a function of current density for GaN-based lateral and vertical (a) SQW and (b) MQW blue LED structures at P =0 and 0.5 with C=0 respectively.

FIG. 2.

IQE as a function of current density for GaN-based lateral and vertical (a) SQW and (b) MQW blue LED structures at P =0 and 0.5 with C=0 respectively.

Close modal

In contrast, when P is set to 0.5, which is a commonly used value to consider the effect of polarization in blue LEDs in the literature,39,40 the expected droop in the IQE is observed with increasing current density. When P = 0.5, the efficiency droop of VSQW as well as VMQW is observed to be greater than LSQW and LMQW respectively. The overall droop of LMQW and VMQW structures is also improved in comparison to LSQW and VSQW structures respectively, which is a typical improvement of MQW structures over SQW structures.41 

Next simulations were performed by setting Auger recombination coefficient C = 2×10-30 cm6/sec, which is one of the highest reported in the literature,42 for all the structures with P = 0 and P = 0.5 as shown in Figure 3.

FIG. 3.

IQE as a function of current density for GaN-based lateral and vertical (a) SQW and (b) MQW blue LEDs structures at C = 2×10-30 cm6/sec with P=0 respectively.

FIG. 3.

IQE as a function of current density for GaN-based lateral and vertical (a) SQW and (b) MQW blue LEDs structures at C = 2×10-30 cm6/sec with P=0 respectively.

Close modal

When P = 0 and Auger coefficient C is fixed, the efficiency droop of the IQE curve is governed by the nonradiative recombination mechanisms at higher current densities. For P > 0, the overall decrease in the IQE is the combined result of the two phenomena, i.e. polarization-assisted electron leakage current and the nonradiative recombination at higher carrier density.36 In Figure 3(a), it can be observed that the IQE sharply declines at low current density after attaining its maximum. This is true for all the four cases in the figure. At P = 0.5, LSQW saturates slightly earlier than VMQW which means that combined effect of the polarization-charge density and Auger recombination has quickly dominated the radiative recombination in the given current density range. From Figure 3(b), it can be seen that Auger recombination has a stronger effect on the VMQW device in both the cases, i.e. P = 0 and P = 0.5, in comparison to LMQW. This is true both for the SQW structures and MQW structures. The IQE of MQW LEDs is much better than SQW LEDs in comparison once again as was observed in Figure 2. It is known that Auger recombination could be minimized by increasing the active volume with the number of QW layers. Increase in the number of QWs distributes the carrier density in the active region of the device thus decreasing the dominating effect of Auger recombination.43 We believe that because of the comparatively smaller mesa size in our lateral structures, the performance of the lateral structures have shown overall better performance in comparison to the vertical structures.44 In addition, the increased area of contact of n-electrode in vertical devices is also responsible for their higher contact resistance, thus increased limitation to the injection current in the device in comparison to the lateral devices.45 

The influence of polarization in SQW and MQW lateral and vertical LEDs, by neglecting Auger recombination coefficient C, has been found to have a stronger effect on the vertical structures in comparison to the lateral structures. In addition, when Auger recombination is considered, this too has a stronger influence on the degradation of the IQE of vertical multiquantum well than the lateral multiquantum well. In our analysis, IQE of lateral structures of both the SQW and MQW structures are observed to be better, in general in comparison of the vertical counterparts. The combined effect of both the internal polarization as well Auger recombination has an overall high degradation effect understandably. In addition, the MQW structures have shown some degree of improvement, in contrast to SQW structures, in the overall IQE characteristics despite the presence of the two droop-causing mechanisms, i.e. polarization charge density and Auger recombination.

The authors would like to thank team Crosslight® in providing the requisite support. In addition, the authors would like to thank Higher Education Commission of Pakistan and Ghulam Ishaq Khan Institute for providing the required facilities to conduct the research work.

This work was financially supported by the Machine Learning Research Group; Prince Sultan University Riyadh; Saudi Arabia [RG-CCIS-2017-06-02]; The authors are grateful for this support.

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