Open Access
Add to BibSonomy
Abstract
The role of a superlattice distributed Bragg reflector (SL DBR) as the p-type electron blocking layer (EBL) in a GaN micro-light-emitting diode (micro-LED) is numerically investigated to improve wall-plug efficiency (WPE). The DBR consists of AlGaN/GaN superlattice (high refractive index layer) and GaN (low refractive index layer). It is observed that the reflectivity of the p-region and light extraction efficiency (LEE) increase with the number of DBR pairs. The AlGaN/GaN superlattice EBL is well known to reduce the polarization effect and to promote hole injection. Thus, the superlattice DBR structure shows a balanced carrier injection and results in a higher internal quantum efficiency (IQE). In addition, due to the high refractive-index layer replaced by the superlattice, the conductive DBR results in a lower operation voltage. As a result, WPE is improved by 22.9% compared to the identical device with the incorporation of a conventional p-type EBL.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
InGaN/GaN micro-LEDs (size ≤ 100 μm) provide high brightness, wide color gamut and long lifetime, and thus, are considered a promising candidate for next generation displays [1,2]. In particular, the low power storage of augmented reality (AR), virtual reality (VR), and smartwatches make micro-LED the most attractive lighting source. These days, energy efficiency reducing electricity demand in electrical products is one of the key factors to fight against climate change. Thus, to build up an eco-friendly society, artificial light sources with low energy cost have replaced incandescent lamps and fluorescent lamps. The U.S. Department of Energy has provided a report to point out the significance of energy-saving light sources, reducing greatly energy consumption [3]. Therefore, energy-efficient InGaN/GaN micro-LED is essential for widespread lighting and display applications. In the micro-LED community, external quantum efficiency (EQE), describing the ratio between the emitted photons and the injected carriers, is considered as the most important parameter [4]. The EQE is related to IQE and is given by $EQE = IQE \times LEE$, where LEE is the light extraction efficiency [5]. However, EQE does not count on the operation voltage and, thus, cannot indicate the power consumption accurately. Instead, the WPE can provide a better power efficiency criterion [5], which is expressed by [6]:
Achieving high WPE on micro-LED requires improvements on IQE, LEE, and the low-operating forward voltage (${V_F}$). In InGaN micro-LEDs, IQE can be improved by addressing electron overflow and insufficient hole injection issues. Although the p-type AlGaN EBL blocks the electron overflow, it also prevents the hole injection due to the wide bandgap and polarization effect [9,10]. Besides, it is reported that low hole injection is directly related to the drop of IQE and high ${V_F}$ [5,11]. To solve these issues, the p-type AlGaN/GaN superlattice (SL) has been used as an EBL. By releasing the stress and changing the polarization effect, SL EBL increases the effective electron barrier height and decreases the effective hole barrier height. Therefore, the electron overflow is reduced while keeping a high hole injection [12–15]. As a result, ${V_F}$ is decreased as the hole injection is promoted.
Low LEE in micro-LED is the main issue to reach high WPE. Due to the high refractive indices of GaN and sapphire, it causes a small light output angle [16]. Thus, a large part of the light is lost by total internal reflection. The LEE of InGaN micro-LED is less than 20% and is independent of size [17]. The package can greatly improve the LEE of conventional LED (size ≥ 1 mm) by adding a dome structure to guide the light out, which improves LEE up to 70% [18,19]. However, as the device size and pitch decrease, it is hard for high PPI micro-LED array to be packaged. To increase the LEE of micro-LED, distributed Bragg reflector (DBR) has been incorporated into the device structure [20–22]. Since the active layers in LED emit light over 360 degrees and only one side emission is utilized, the energy loss is severe. The optimized DBR for InGaN LED, usually composed of SiO2/TiO2, has high reflectivity and acts as a mirror to reflect the light downward or upward, and thus greatly increases LEE [20–22]. However, for the flip-chip device, which is suitable for high PPI display, the DBR design will induce high complexity on mask design and a high requirement on fabrication accuracy [20].
In this work, we propose the SL DBR structure as a p-type EBL to improve the WPE for bottom-emitting (light emission at angles between 180° and 360°) blue GaN micro-LED devices. SL DBR could have the SL EBL’s function due to the similar structure. We expect that SL DBR has the potential to enhance the light outcoupling as well as to promote IQE and reduce ${V_F}$. Thus, optical and electrical characteristics of InGaN/GaN micro-LED with three different p-type EBLs of AlGaN/SL/SL DBR are systematically studied, which include the reflectivity and LEE enhancement with different DBR pairs, and etc. In addition, the electrical performance including band diagrams, carrier concentration, IQE and IV profile are analyzed to clearly reveal the function of SL DBR.
Our results exhibit that the SL DBR devices show a higher reflectivity and LEE than traditional design and SL EBL device. In particular, in the SL DBR devices, the reflectivity and the LEE enhance as the number of DBR pairs increase. It is found that the SL DBR devices have similar electrical characteristics to SL EBL device, i.e., enhanced IQE and reduced ${V_F}$. The main electrical parameters such as electron and hole concentration, IQE, ${V_F}$ shows the negligible variation by the increased number of DBR pair.
2. Device architectures
Figure 1 shows the schematic structure for typical GaN-based blue micro-LED grown on the sapphire substrate along the c-axis served as the Ref device in the study. The device structure consists of a 4-μm undoped GaN layer (u-GaN) on sapphire substrate, followed by a 4-μm n-type doped GaN layer (n-GaN) with a Si doping concentration of 5×1018cm-3 [23,24]. The MQWs layers consist of six pairs of In0.15Ga0.85N(2.2nm)/GaN(11nm) quantum well/barrier, which emit blue light with the peak wavelength of ∼450nm. In Ref micro-LED, the p-region is composed of a 20nm p-type Al0.2Ga0.8N EBL layer and a 50nm p-GaN, with the Mg doping concentration of 1×1019cm-3. The device size is set to be 30×30μm2. To enhance light outcoupling, an SL DBR structure is replaced as the p-region instead of EBL. The traditional materials composing DBR, such as SiO2 and TiO2, are insulated or wide-bandgap semiconductors, which block the carrier's transportation. Thus, AlGaN and GaN are chosen for allowing carrier transportation. Further, SL structure is applied to replace the traditional uniform high refractive index layer of DBR. The SL structure reported by Yu et al. [12] showed a good carrier transportation and, thus, his SL structure was adapted in our study. Here, the low refractive index material is the GaN layer (44nm), and the high refractive index material is Al0.15Ga0.85N(2nm)/GaN(4nm) SL layer (8 pairs, 48nm in total). The thickness and pairs of the Al0.15Ga0.85N layer and GaN layer of SL is designed to reflect blue light (∼450nm). We expect that the GaN and SL layers can provide a good carrier transport characteristic as well as reflectivity. Since more DBR pairs can give higher reflectivity, the number of DBR (NDBR) pairs is varied from 2 to 6, ensuring the carrier transport. Here we designed SD A (NDBR = 2), SD B (NDBR = 4), and SD C (NDBR = 6), as seen in Fig. 1. The p-region has a uniform Mg doping concentration of 1×1019cm-3. Finally, to compare the performance of our SL DBR device and the reported SL EBL device [12], we simulate the structure with the EBL replaced by SL (labelled as SE in Fig. 1). The p-region components are shown in Table 1.
Fig. 1. Schematic diagram of micro-LEDs in the study. The electrodes are labelled as black. SD A, SD B, and SD C correspond to the 2, 4, and 6 pairs of DBRs in SL DBR devices. SE has the SL as EBL.
Table 1. P-region components for Ref, SE, and SD A/B/C. SL components are shown.
The numerical simulation is done by APSYS, the advanced physics models including K·P theory based multiple quantum well model for InGaN material systems. To take tunneling effect into consideration, the tunneling model is induced for all SL layers. All micro-LEDs have the same parameters except the p-region. The Auger recombination coefficients of AlGaN, GaN, InGaN are set to be 2.3×10−30cm6s-1, 1×10−30cm6s-1, 2×10−30cm6s-1 respectively, which were obtained by PL measurement [25,26]. The energy band offset ratio between the conduction band and valance band is 0.7/0.3. The trap states were measured by deep-level transient spectroscopy [27,28]. For the electron trap, the location is set at 0.24eV below the conduction band, the capture cross-section is 3.4×10−17cm2, and the concentration is 1×1013cm-3 [27]. For the hole trap, the location is set at 0.46eV above the valance band, the capture cross-section is 2.1×10−15cm2, and the concentration is 1.6×1015cm-3 [28]. Other band parameters can be found in Vurgaftman's work [29].
3. Results and discussions
In the Ref device, the role of EBL is to block only electron leakage. In SE device, SL EBL is designed to have dual function of blocking the electron leakage and enhancing hole injection. Compared to them, the SL DBR devices of SD A/B/C are expected not only to enhance the light outcoupling, but also to have the dual function of SL EBL.
The reflectivities in the upward direction of the p-region for all devices are calculated to estimate the enhancement of light outcoupling. The refractive indices of Al0.15Ga0.85N (2.34), Al0.2Ga0.8N (2.31) and GaN (2.47) are used [30,31]. The calculated reflectivity vs. wavelength is displayed Fig. 2(a). EBL layer (solid green line) and SL EBL layer (solid black line) have reflectivity of about 0.17 in the wavelength region of the EL peak (dotted black line). The reflectivities of the SL DBRs (solid blue/magenta/red lines) are clearly higher than those of Ref and SL EBL at the emission wavelengths. Further, the reflectivity increases, and the width of the stop band decreases as the number of DBR pairs increases, as expected. The SL DBR in SD C device has about twice higher reflectivity compared to the EBL layer. Figures 2(b) shows the output power of the micro-LED as a function of current density. Thus, it is natural to expect higher LEE for SL DBR devices. The angular light distribution is shown in the polar plot. The radius is proportional to light intensity. The calculated LEE of SD C is 11.5% higher than that of Ref and 11.3% higher than that of SL EBL. Thus, the enhancement of light outcoupling is attributed to the DBR structure reflecting light into the downward direction, leading to the reduction of emission light loss from the active layer. For SD A/B/C, the LEE increases as the number of DBR increases. Also notice that the EQE of SD A/B/C are clearly higher than that of both Ref and SE. We find that at the normal working current density of 5A/cm2, the output power of SD C is 18.5% higher than that of Ref and 11.7% higher than that of SL EBL. The enhancement of output power of SD C is quite similar to the LEE enhancement, compared to SE. Thus, it leads us to conclude that SL DBR layer in SD C could have the similar improvement of the hole injection by the SL EBL layer, leading to a close IQE of SL EBL layer, accompanying the improvement of LEE.
Fig. 2. (a) Reflectivity as a function of wavelength for Ref, SE, and SD A/B/C. The black dotted line: The EL spectrum of SD A at 5A/cm2. (b) Left: EQE as a function of current density for Ref, SE, and SD A/B/C devices. Right: Output power as a function of current density for Ref, SE, SD A/B/C devices. The angular light distribution is shown in polar plot.
The improvement of the hole injection in SD A/B/C could be explained by considering the polarization effect. The polarization effect in the last barrier layer and p-region is compared for Ref and SD A. The total polarization intensity consists of spontaneous polarization and piezoelectric polarization. For GaN, InGaN, and AlGaN, the spontaneous polarizations are opposite to the c-axis, but the piezoelectric polarizations are different. The compressive strain-induced piezoelectric polarization of InGaN is along the c-axis, which canceled spontaneous polarization [32]. Thus, the sheet charge at the GaN (barrier)/InGaN (well) interface is dominant by GaN’s polarization-induced positive charge. On the other hand, AlGaN has stronger spontaneous polarization [33] and tensile induced piezoelectric polarization, opposite to the c-axis. The net polarization intensity of AlGaN is higher than that of GaN [34]. Therefore, the AlGaN layer (EBL) causes the positive sheet charge at the GaN (barrier)/AlGaN (EBL) interface. The positive sheet charge [32] at the interface induces to make the conduction and valence bands of the last barrier bend down to the p-side as seen in Fig. 3(a). Thus, the conduction band (valence band) of AlGaN barrier layer is close to (far away) the quasi-Fermi level for electrons (holes), as seen in Fig. 3(a). However, since the SL can effectively reduce the stress caused by lattice mismatch between GaN and AlGaN [35], the SL's polarization strength is decreased. The negative interface charge is more determined by GaN. Thus, the band of the last barrier for SL EBL bends upward to the p side, as shown in Figs. 3(b). The same effect happens in SD A/B/C as seen in Fig. (c - e), too. The solid red lines in Fig. 3 represent the calculated conduction and valence bands, respectively. The green dotted lines represent the quasi-Fermi levels. As the results, for SE, SD A/B/C, the conduction bands of AlGaN are far away from the quasi-Fermi levels for electrons, and the valance bands of AlGaN are close to the quasi-Fermi levels for holes. For Ref device, the calculated energy levels of the conduction and the valance bands in the last barrier (labeled as pink) move down 50meV.
Fig. 3. Energy band diagrams of (a) Ref, (b) SE, (c) SD A, (d) SD B, and (e) SD C devices at 100A/cm2. The MQWs, EBL, and SL are marked. Only a single SL is shown. Red line: band diagram. Green dotted line: Quasi-Fermi levels. The quantum wells are labeled as blue (the last quantum well is labeled as grey), the last barrier is labeled as pink, the EBL is labeled as green, and the SL is labeled as yellow.
On the other hand, for SD A, the conduction and valance bands of the last barrier move up 110meV. Thus, the different polarization at the interface induces different effective barrier heights between the barrier layer of MQW and p-side. For SE and SD A/B/C devices, the effective electron barrier heights increase, and the effective hole barrier heights decrease, compared with Ref device.
For the ref device, the effective electron barrier height between the active and EBL layers is 387meV. Although the Al0.15Ga0.85N of SE and SD A/B/C have a smaller bandgap, the band difference on the last barrier makes SE and SD A/B/C have a higher effective electron barrier height and a lower effective hole barrier height than those of the Ref device. The effective electron barrier heights of SE and SD A/B/C are calculated as 485meV, 490meV, 502meV, and 512meV, respectively. On the other hand, the effective hole barrier height of the Ref device is 372meV. SE and SD A/B/C have much lower effective hole barrier heights of 282meV, 282meV, 283meV, and 285meV, respectively. As we expected earlier, the SL DBR structures have the close effective electron and hole barrier heights to those of SL EBL. Thus, it can be expected that the devices with the SL DBR have the similar blocking of electron leakage but a much better hole injection than Ref, i.e., the similar behaviors of SL EBL.
Our expectation can be confirmed by comparing the carrier concentration profiles of the last quantum well (close to p-side). Since the typical working current density for micro-LED is under 10A/cm2, the carrier concentration profiles are calculated at 5A/cm2 and the results are displayed in Figs. 4(a). Notice that the hole concentrations (dotted lines) of SE (black line), SD A (blue line), SD B (magenta line), and SD C (red line) are about 40% higher than that of the Ref device. It confirms our expectation, which is that the reduced effective hole barrier height promotes hole injection. Further, SE and SD A/B/C have the close hole concentration. Since the SL DBR layer have a larger thickness of about 100nm per pair, the hole injection may be slightly reduced. However, a balanced carrier injection is observed. For the Ref device, the electron concentration is nearly two times of hole concentration, which is unbalanced. On the other hand, SE and SD A/B/C show that the difference between the electron concentration and hole concentration is less than 20%. The balanced carrier injection enhances radiative recombination. For radiative electron-hole recombination, the bimolecular rate equation from the van Roosbroeck–Shockley model is [36]:
where ${R_{Rad}}$ is the radiative recombination rate, ${F_{cv}}$ is the electron-hole wave-function overlap, B is the bimolecular recombination coefficient, $n$ and $p$ are the electron concentration and hole concentration, respectively. For a specific current density, balanced carrier injection achieves the max radiative recombination rate. In addition, the reduced polarization effect of quantum well promotes the higher carrier wave function overlap, which increases the recombination probability. Therefore, SL EBL and SD A/B/C have a higher radiative recombination rate than that of the Ref device. For example, the radiative recombination rate of the SD A device is 8% higher than that of the Ref device. In addition, the Auger recombination rate can be expressed by [36]: where ${R_{Auger}}$ is the auger recombination rate, ${C_p}$ and ${C_n}$ are the Auger coefficients. Balanced carrier injection results in a lower auger recombination rate, too. From ABC model [37], the higher radiative recombination rate and a lower Auger recombination rate occur a higher peak IQE and peak shift, as shown in Figs. 4(b). It shows clearly that SL EBL and SD A/B/C have the close IQE, as expected.Fig. 4. (a) The hole concentrations (dashed line) and electron concentrations (solid line) of the last quantum well (close to p-side) at 5A/cm2 of Ref, SE, SD A/B/C. The locations of data are shifted 3nm for each structure for clear comparison. The last quantum well regions are labeled as grey. (b), IQE as a function of current density of Ref, SE, SD A/B/C.
The SL structure also reduces the ${V_F}$. The J-V characteristics are shown in Fig. 5. The micro-LEDs with superlattice DBR have higher current densities than that of Ref device at the same forward voltages. In other words, when operated at the same current density, the proposed structures have a lower ${V_F}$, leading to reduce power consumption. The dynamic resistance in Fig. 5, which is the differential of current density to voltage, exhibits the similar trend of ${V_F}$ in Fig. 5. The lower dynamic resistance indicates a lower increment of ${V_F}$ and thus the smaller drop of WPE. For typical operating current density range (< 10A/cm2), the dynamic resistances of SD A/B/C devices are lower than that of Ref device. Thus, the proposed structures have slow-growing ${V_F}$ and lower drop of WPE.
Fig. 5. Left: Current density as a function of applied forward voltage for Ref, SE, SD A/B/C. Right: Dynamic resistance as a function of applied forward voltage for Ref, SE, SD A/B/C.
Finally, Fig. 6 shows the WPE as a function of current density. Here the only the bottom emission is considered for calculating WPE. It exhibits clearly that the SL DBR layers increase the WPE of InGaN micro-LEDs. In particular, WPE of SD C device is 22.9% higher than that of Ref device at 5A/cm2.
Our results have important implications for the development of micro-LED displays with chip sizes of less than 10 nm. The WPE is related to IQE, LEE, and ${V_F}$, according to Eq. (1). To achieve a high WPE of micro-LEDs, all three parameters, LEE, IQE, and ${V_F}$ are required to be optimized. However, the latest research indicated that IQE droop is related to the intrinsic surface state [38]. Thus, it is hard to enhance IQE by passivation for smaller micro-LED (5um for VR display). In this case, LEE and ${V_F}$ optimization could be the easier way to enhance WPE. DBR layer increases the LEE as shown in Fig. 2 and the SL layer improves the hole injection. Eventually, the IQE is enhanced, and ${V_F}$ is reduced. Notice that the rough surface or pattern substrate surface to reach high LEE [39] is not considered in our model. Hence, the LEE of all devices are close to empirical value $\textrm{1/4}{n^2}$. The WPE difference between SE and SL DBR structures are mainly attributed to the LEE enhancement. The optimized DRR structure like increased number of pairs or the DBRs with large reflective index difference of the stack structure [40] could give to higher LEE enhancement. On the other hand, the micro-LED displays need the collimated light to reduce crosstalk. Thus, the approach using patterned structures or rough surface on micro-LED improving the LEE could not be a good way to perform. In addition, due to the high chip density and small p contact area, it is hard for VR to design a top DBR structure for flip-chip micro-LED. Thus, SL DBR is the efficient way to enhance light outcoupling.
4. Conclusion
Our studies showed that the p-type SL DBR enhances the LEE, proportional to the number of DBR pairs, compared to p-type EBL and SL EBL. It still shows the similar electrical characteristics of p-type SL EBL. It means that a AlGaN/GaN SL DBR facilitates hole injection by reducing the hole barrier height and achieved a balanced carrier injection. Thus, the balanced carrier injection promoted radiative recombination while auger recombination is suppressed, leading to a higher IQE. In addition, the increment of carrier injection is reflected in the reduction of ${V_F}$. These overall improvement leads to a 22.9% improvement of WPE.
Funding
High-level University Fund (G02236005); Science and Technology Planning Project of Shenzhen Municipality (KQTD20170810110313773).
Acknowledgments
We thank Crosslight Software, Inc. China for their technical support and Dr. Zihui Zhang of Hebei University of Technology for his insightful discussion.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. Y. Huang, G. Tan, F. Gou, M.-C. Li, S.-L. Lee, and S.-T. Wu, “Prospects and challenges of mini-LED and micro-LED displays,” J. Soc. Inf. Disp. 27(7), 387–401 (2019). [CrossRef]
2. T. Wu, C.-W. Sher, Y. Lin, C.-F. Lee, S. Liang, Y. Lu, S.-W. Huang Chen, W. Guo, H.-C. Kuo, and Z. Chen, “Mini-LED and Micro-LED: Promising Candidates for the Next Generation Display Technology,” Appl. Sci. 8(9), 1557 (2018). [CrossRef]
3. I. Navigant Consulting, M. Yamada, J. Penning, S. Schober, K. Lee, and C. Elliott, “Energy Savings Forecast of Solid-State Lighting in General Illumination Applications,” U. S. D. o. Energy, ed. (2019).
4. M. S. Wong, D. Hwang, A. I. Alhassan, C. Lee, R. Ley, S. Nakamura, and S. P. DenBaars, “High efficiency of III-nitride micro-light-emitting diodes by sidewall passivation using atomic layer deposition,” Opt. Express 26(16), 21324–21331 (2018). [CrossRef]
5. J. Piprek, “Efficiency Models for GaN-Based Light-Emitting Diodes: Status and Challenges,” Materials (Basel) 13(22), 5174 (2020). [CrossRef]
6. J.-I. Shim and D.-S. Shin, “Measuring the internal quantum efficiency of light-emitting diodes: towards accurate and reliable room-temperature characterization,” Nanophotonics 7(10), 1601–1615 (2018). [CrossRef]
7. L. Y. Kuritzky, C. Weisbuch, and J. S. Speck, “Prospects for 100% wall-plug efficient III-nitride LEDs,” Opt. Express 26(13), 16600–16608 (2018). [CrossRef]
8. K. Bulashevich, S. Konoplev, and S. Karpov, “Effect of Die Shape and Size on Performance of III-Nitride Micro-LEDs: A Modeling Study,” Photonics 5(4), 41 (2018). [CrossRef]
9. C. H. Wang, C. C. Ke, C. Y. Lee, S. P. Chang, W. T. Chang, J. C. Li, Z. Y. Li, H. C. Yang, H. C. Kuo, T. C. Lu, and S. C. Wang, “Hole injection and efficiency droop improvement in InGaN/GaN light-emitting diodes by band-engineered electron blocking layer,” Appl. Phys. Lett. 97, 261103 (2010). [CrossRef]
10. Z.-H. Zhang, S.-W. Huang Chen, Y. Zhang, L. Li, S.-W. Wang, K. Tian, C. Chu, M. Fang, H.-C. Kuo, and W. Bi, “Hole Transport Manipulation To Improve the Hole Injection for Deep Ultraviolet Light-Emitting Diodes,” ACS Photonics 4(7), 1846–1850 (2017). [CrossRef]
11. D. S. Meyaard, G.-B. Lin, Q. Shan, J. Cho, E. Fred Schubert, H. Shim, M.-H. Kim, and C. Sone, “Asymmetry of carrier transport leading to efficiency droop in GaInN based light-emitting diodes,” Appl. Phys. Lett. 99, 251115 (2011). [CrossRef]
12. C. T. Yu, W. C. Lai, C. H. Yen, and S. J. Chang, “Effects of InGaN layer thickness of AlGaN/InGaN superlattice electron blocking layer on the overall efficiency and efficiency droops of GaN-based light emitting diodes,” Opt. Express 22(S3), A663–670 (2014). [CrossRef]
13. A. J. Tzou, D. W. Lin, C. R. Yu, Z. Y. Li, Y. K. Liao, B. C. Lin, J. K. Huang, C. C. Lin, T. S. Kao, H. C. Kuo, and C. Y. Chang, “High-performance InGaN-based green light-emitting diodes with quaternary InAlGaN/GaN superlattice electron blocking layer,” Opt. Express 24(11), 11387–11395 (2016). [CrossRef]
14. B. Janjua, T. K. Ng, A. Y. Alyamani, M. M. El-Desouki, and B. S. Ooi, “Enhancing Carrier Injection Using Graded Superlattice Electron Blocking Layer for UVB Light-Emitting Diodes,” IEEE Photonics J. 6, 1–12 (2014). [CrossRef]
15. Y. Yan Zhang and Y. An Yin, “Performance enhancement of blue light-emitting diodes with a special designed AlGaN/GaN superlattice electron-blocking layer,” Appl. Phys. Lett. 99(22), 221103 (2011). [CrossRef]
16. F. Gou, E. L. Hsiang, G. Tan, P. T. Chou, Y. L. Li, Y. F. Lan, and S. T. Wu, “Angular color shift of micro-LED displays,” Opt. Express 27(12), A746–A757 (2019). [CrossRef]
17. F. Olivier, A. Daami, C. Licitra, and F. Templier, “Shockley-Read-Hall and Auger non-radiative recombination in GaN based LEDs: A size effect study,” Appl. Phys. Lett. 111(2), 022104 (2017). [CrossRef]
18. B. P. Yonkee, E. C. Young, S. P. DenBaars, S. Nakamura, and J. S. Speck, “Silver free III-nitride flip chip light-emitting-diode with wall plug efficiency over 70% utilizing a GaN tunnel junction,” Appl. Phys. Lett. 109(19), 191104 (2016). [CrossRef]
19. L. Y. Kuritzky, A. C. Espenlaub, B. P. Yonkee, C. D. Pynn, S. P. DenBaars, S. Nakamura, C. Weisbuch, and J. S. Speck, “High wall-plug efficiency blue III-nitride LEDs designed for low current density operation,” Opt. Express 25(24), 30696–30707 (2017). [CrossRef]
20. S. J. C. C. H. Chen, Y. K. Su, G. C. Chi, J. K. Sheu, and J. F. Chen, “High-Efficiency InGaN–GaN MQW Green Light-Emitting Diodes With CART and DBR Structures,” IEEE J. Sel. Top. Quantum Electron. 8, 284 (2002). [CrossRef]
21. S. Zhou, C. Zheng, J. Lv, Y. Gao, R. Wang, and S. Liu, “GaN-based flip-chip LEDs with highly reflective ITO/DBR p-type and via hole-based n-type contacts for enhanced current spreading and light extraction,” Opt. Laser Technol. 92, 95–100 (2017). [CrossRef]
22. S. Zhou, H. Xu, M. Liu, X. Liu, J. Zhao, N. Li, and S. Liu, “Effect of Dielectric Distributed Bragg Reflector on Electrical and Optical Properties of GaN-Based Flip-Chip Light-Emitting Diodes,” Micromachines (Basel) 9(12), 650 (2018). [CrossRef]
23. J. Kou, C. C. Shen, H. Shao, J. Che, X. Hou, C. Chu, K. Tian, Y. Zhang, Z. H. Zhang, and H. C. Kuo, “Impact of the surface recombination on InGaN/GaN-based blue micro-light emitting diodes,” Opt. Express 27(12), A643–A653 (2019). [CrossRef]
24. Z.-H. Zhang, Y. Ji, W. Liu, S. Tiam Tan, Z. Kyaw, Z. Ju, X. Zhang, N. Hasanov, S. Lu, Y. Zhang, B. Zhu, X. Wei Sun, and H. Volkan Demir, “On the origin of the electron blocking effect by an n-type AlGaN electron blocking layer,” Appl. Phys. Lett. 104, 233505 (2014). [CrossRef]
25. Y. C. Shen, G. O. Mueller, S. Watanabe, N. F. Gardner, A. Munkholm, and M. R. Krames, “Auger recombination in InGaN measured by photoluminescence,” Appl. Phys. Lett. 91, 141101 (2007). [CrossRef]
26. F. Nippert, M. Tollabi Mazraehno, M. J. Davies, M. P. Hoffmann, H.-J. Lugauer, T. Kure, M. Kneissl, A. Hoffmann, and M. R. Wagner, “Auger recombination in AlGaN quantum wells for UV light-emitting diodes,” Appl. Phys. Lett. 113(7), 071107 (2018). [CrossRef]
27. L. Rigutti, A. Castaldini, and A. Cavallini, “Anomalous deep-level transients related to quantum well piezoelectric fields in InyGa1−yN/GaN-heterostructure light-emitting diodes,” Phys. Rev. B 77(4), 045312 (2008). [CrossRef]
28. N. Tetsuo, T. Yutaka, K. Tatsuya, T. Kazuyoshi, and K. Tetsu, “The trap states in lightly Mg-doped GaN grown by MOVPE on a freestanding GaN substrate,” J. Appl. Phys. 123, 161405 (2018). [CrossRef]
29. I. Vurgaftman and J. R. Meyer, “Band parameters for nitrogen-containing semiconductors,” J. Appl. Phys. 94(6), 3675–3696 (2003). [CrossRef]
30. J. F. Muth, J. D. Brown, M. A. L. Johnson, Z. Yu, R. M. Kolbas, J. W. Cook, and J. F. Schetzina, “Absorption Coefficient and Refractive Index of GaN, AlN and AlGaN Alloys,” MRS Internet J. Nitride Semicond. Res. 4(S1), 502–507 (1999). [CrossRef]
31. S. Adachi, Optical constants of crystalline and amorphous semiconductors: numerical data and graphical information (Springer Science & Business Media, 2013).
32. A. Ashok, D. Vasileska, S. M. Goodnick, and O. L. Hartin, “Importance of the Gate-Dependent Polarization Charge on the Operation of GaN HEMTs,” IEEE T. Electron Dev. 56(5), 998–1006 (2009). [CrossRef]
33. B. Fabio and F. Vincenzo, “Spontaneous polarization and piezoelectric constants of III-V nitrides,” Phys. Rev. B 56, R10024 (1997). [CrossRef]
34. F. Bernardini, V. Fiorentini, and D. Vanderbilt, “Accurate calculation of polarization-related quantities in semiconductors,” Phys. Rev. B 63(19), 193201 (2001). [CrossRef]
35. S. S. Y. T. K. Kim, J. K. Son, Y. G. Hong, and G. M. Yang, “Growth of a GaN Epilayer on a Si (111) Substrate by Using an AlN/GaN Superlattice and Application to a GaN Microcavity Structure with Dielectric-Distributed Bragg Reflector,” J. Korean Phys. Soc. 50(3), 801–805 (2007). [CrossRef]
36. E. F. Schubert, T. Gessmann, and J. K. Kim, “Light emitting diodes,” Kirk-Othmer Encyclopedia of Chemical Technology (2000).
37. G. Verzellesi, D. Saguatti, M. Meneghini, F. Bertazzi, M. Goano, G. Meneghesso, and E. Zanoni, “Efficiency droop in InGaN/GaN blue light-emitting diodes: Physical mechanisms and remedies,” J. Appl. Phys. 114, 071101 (2013). [CrossRef]
38. F. Jiang, B.-R. Hyun, Y. Zhang, and Z. Liu, “Role of Intrinsic Surface States in Efficiency Attenuation of GaN-Based Micro-Light-Emitting-Diodes,” Phys. Status Solidi Rapid Res. Lett. 15, 2000487 (2020). [CrossRef]
39. Z.-T. Li, K. Cao, J.-S. Li, Y. Tang, L. Xu, X.-R. Ding, and B.-H. Yu, “Investigation of Light-Extraction Mechanisms of Multiscale Patterned Arrays With Rough Morphology for GaN-Based Thin-Film LEDs,” IEEE Access 7, 73890–73898 (2019). [CrossRef]
40. G. Y. Shiu, K. T. Chen, F. H. Fan, K. P. Huang, W. J. Hsu, J. J. Dai, C. F. Lai, and C. F. Lin, “InGaN Light-Emitting Diodes with an Embedded Nanoporous GaN Distributed Bragg Reflectors,” Sci. Rep. 6(1), 29138 (2016). [CrossRef]
