Abstract

A strategically constructed substrate, patterned sapphire with silica array (PSSA), was developed to boost the efficiency of patterned sapphire substrate (PSS) in GaN-based light-emitting diodes (LEDs) application. The light output power of a flip-chip LED on PSSA improved by 16.5% at 120 mA than that of device grown on PSS. The XRD and STEM measurements revealed that the GaN epilayer grown on PSSA had better crystalline quality compared to the epilayer grown on PSS, which was the result of decreased misfit at coalescence boundary in the PSSA case. Moreover, the light extraction efficiency of the flip-chip LED on PSSA was significantly enhanced, benefiting from the small refractive-index contrast between the patterned silica array and air. This small refractive-index contrast also contributed to a more convergent emission pattern for the flip-chip LED on PSSA, as demonstrated by the far-field radiation pattern measurements. The discovery that PSSA could excel at defect suppression and light extraction revealed a new substrate platform for III-nitride optoelectronic devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

GaN-based visible light emitting diodes (LEDs) have attracted tremendous attention for their use in the fields of high-resolution display, visible light communication, automotive front lighting, and general lighting, owing to their high luminous efficiency, long operation lifetime, and low energy consumption [18]. In order to achieve excellent device performance, high quality GaN films are required. Owing to the limited size and high cost of bulk GaN substrate, the commercial GaN-based LEDs are generally grown on c-plane sapphire substrate. However, the lattice mismatch and difference in thermal expansion coefficients between GaN and sapphire induce high density of threading dislocations (TDs) (108–1010 cm2) [9]. The TDs propagating through the GaN buffer layer to the InGaN/GaN multiple quantum wells (MQWs) act as nonradiative recombination centers for injected carriers, resulting in a huge reduction of internal quantum efficiency (IQE). Therefore, it is important to find out effective methods to reduce the threading dislocation density (TDD) in GaN film, so as to effectively improve the performance of GaN-based LEDs. Various growth techniques have been proposed to reduce the TDD, such as epitaxial lateral overgrowth, pendeoepitaxy, and in situ SiNx nanomask [1012]. On the other hand, the majority of generated photons in the active region are trapped inside LEDs due to the large refractive index difference between GaN and air, leading to a low light extraction efficiency (LEE). A myriad of approaches, such as photonic crystal [13], surface roughness [14], air cavities [15], and patterned sapphire substrate (PSS) [16], have been developed to improve LEE of GaN-based LEDs.

The flip-chip LEDs, which are inverted compared to top-emitting LEDs, can overcome the thermal issues and non-uniform current spreading [17]. In this configuration, rays emit mainly from the transparent substrates. Most of GaN-based flip-chip LEDs, which occupy a major portion of the current LED market, have adopted few micron-pitch PSS. PSS serves as 2D dielectric gratings for improved light extraction as well as growth templates for pristine GaN crystallinity [1822]. However, breakthroughs in light extraction are limited in flip-chip LEDs because the large refractive index contrast at GaN-sapphire and sapphire-air interfaces is predetermined. In addition, further decrease in TDD of GaN film grown on PSS remains a worldwide challenge due to the misoriented growth of GaN on the patterned sidewall, which is a major limitation for further improvement in IQE. Therefore, it is important to explore novel substrate strategies for the III-N heterostructures, which is capable to suppress the misoriented growth of GaN on the patterned sidewall and meanwhile decrease the refractive index contrast at GaN-substrate or substrate-air interfaces. In our previous study [23], we were devoted to reducing TDD by the suppression of misoriented AlGaN growth on sidewalls of patterned substrates using PSSA technology. Meanwhile, the positive influence of PSSA on light extraction for lateral structure LEDs were mentioned as a parasitical advantage. However, the LEE improvement mechanism for lateral structure and flip-chip LEDs is entirely different. Hence, the effect of PSSA on the optical and electrical properties of GaN-based flip-chip visible LEDs is still needed for further exploration.

In this work, we presented that cone-shaped patterned sapphire with silica array (PSSA) could act as an outstanding substrate for highly efficient flip-chip visible LEDs. Since no GaN islands formed on the silica array cone sidewall regions, the LED grown on PSSA effectively decreased the misfit existing in the coalescence boundary of GaN grown on the sidewall regions and c-plane region of the substrate. Additionally, in our previous study, AlGaN/cone-shaped silica interface reflects more rays into the top escape route to improve the LEE owing to the larger refractive index contrast, as compared to the AlGaN/PSS interface. In the flip-chip LED on PSSA, the smaller refractive index contrast between silica array and air led to that more rays refract from silica array to air, resulting in a higher LEE, as compared to that between sapphire array and air. Owing to the existence of refractive index contrast between silica array and sapphire, the use of PSSA rendered the flip-chip LEDs a more convergent emission pattern. Owing to the improvement of crystal quality and LEE, the external quantum efficiency (EQE) of the flip-chip LED on PSSA was better than the devices grown on PSS. This suggests that PSSA is a promising substrate that has the potential to be exploited in the III-nitride LEDs.

2. Experiment

Two types of substrate including PSS and PSSA for the growth of GaN-based blue LEDs were prepared. The detailed fabrication processes for the PSS were illustrated in the previous work [24]. The sizes of periodic sapphire cones were 2.8 µm diameter, 3 µm center-to-center spacing, and 2 µm height. The PSSA were prepared by a thermal reflow photoresist technique in combination with the inductively coupled plasma (ICP) etching process. Figure 1 shows the schematic illustration of the manufacturing process of the PSSA substrate.

 

Fig. 1. Schematic illustration of fabrication process for PSSA substrate.

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A 15 nm-thick AlN nucleation layer was deposited on PSS and PSSA at 650 °C by feeding 120 sccm N2, 30 sccm Ar, and 1 sccm O2 in sputtering system (NMC iTops A330). The InGaN/GaN LED structure was grown on the two types of substrate with sputtered AlN nucleation layer via metal organic chemical vapor deposition (MOCVD) (AIXTRON Crius II_L). Figure 2(a) shows schematic representation of the GaN-based flip-chip LED structure grown on PSSA with 15 nm-thick sputtered AlN NL. The LED structure consists of a 3.0 µm-thick undoped GaN buffer layer, a 2.5 µm-thick Si-doped n-GaN layer (Si doping = 1.5 × 1019 cm−3), a 260 nm-thick lightly Si-doped n-GaN layer (Si doping = 5 × 1017 cm−3), three pairs of In0.02Ga0.98N (1.5 nm)/GaN (30 nm) interlayers (IL), six pairs of In0.05Ga0.95N (1.5 nm)/GaN (9 nm) superlattices (SL), nine-period In0.16Ga0.84N (3 nm)/GaN (12 nm) multiple quantum well (MQW) active layer with emission wavelength of λ = 445 nm, a 15 nm-thick low temperature p-GaN layer, a 25 nm-thick p-Al0.2Ga0.8N electron blocking layer (Mg doping = 1 × 1020 cm−3), a 80 nm-thick Mg-doped p-GaN layer (Mg doping = 6 × 1019 cm−3). The detailed fabrication processes for the flip-chip LED with a dimension of 380 µm × 760 µm were presented in the previous work [25]. The schematic illustration of the flip-chip LED is demonstrated in Fig. 1(a).

 

Fig. 2. (a) Schematic illustration of the GaN-based flip-chip LED structure grown on PSSA. (b) Cross-sectional STEM image of the GaN-based LED epitaxial structure grown on PSSA. (c) Simulated energy band diagram of GaN-based LED. (d) In-situ reflectance and temperature transients during the epitaxial growth of GaN-based LED on PSSA.

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GaN epilayers grown on PSS and PSSA were analyzed in detail by scanning transmission electron microscopy (STEM), X-ray diffraction (XRD), and Raman spectroscopy. Figure 2(b) shows the cross-sectional STEM image of GaN epitaxial layers grown on PSSA. Figure 2(c) illustrates the simulated band diagram of GaN-based LED. The band diagram was simulated using SimuLED software, which is a widely used engineering tool for LED design and optimization [26]. The use of In0.02Ga0.98N/GaN IL and In0.05Ga0.95N/GaN SL reduced the effective barrier heights for both electrons in conduction band and holes in valence band, leading to an increased effective electron capture rate. Figure 2(d) shows in-situ reflectance and temperature transients during the epitaxial growth of GaN-based LEDs on PSSA.

3. Results and discussion

To probe the structural properties of the samples grown on different substrates, we performed cross-sectional STEM and XRD studies. Figures 3(a) and 3(b) show the STEM images of LED grown on PSS and PSSA. At the initial stage of epitaxial growth, TDs generated at the GaN/sapphire interface and bent to sapphire cone-patterns. Therefore, the ICP process in Fig. 1 (Step 6) was adopted for the PSSA to provide thin pedestals of sapphire at the base of the SiO2 cones. Similar to the growth of AlGaN on PSSA [23], the coalescence boundary of misfit GaN is effectively decreased since PSSA is capable of eliminating the nucleation of GaN islands on the SiO2 cone sidewall regions. The decrease of the coalescence boundary leads to less misfit strain, resulting in lower TDD.

 

Fig. 3. (a) Cross-sectional STEM images of GaN grown on PSS. (b) Cross-sectional STEM images of GaN grown on PSSA. (c) XRD rocking curves of GaN films grown on PSS and PSSA.

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We also explored the role of different substrates on the TDD through extensive structural analysis. Figure 3(c) shows the XRD ω-rocking curve for (002) and (102) planes of GaN films grown on PSS and PSSA. The full width at half maximum (FWHM) of ω-rocking curves for (002) and (102) planes decrease from 230 arcsec and 205 arcsec to 111 arcsec and 141 arcsec, respectively. Consistent with STEM results, the decrease of XRD FWHM reveals that the GaN film grown on PSSA has lower TDD than the GaN film grown on PSS. The TDD can be roughly estimated using the empirical formula [27]:

$$N = \frac{{{\beta ^2}}}{{4.35 \times {{|\boldsymbol{b} |}^2}}},$$
where β is the FWHM of XRD rocking curve, b is the Burgers vector of corresponding dislocations. According to Eq. (1), The total TDDs in GaN films grown on PSS and PSSA are calculated to be 3.3 × 108 cm−2 and 1.3 × 108 cm−2, respectively.

When growing GaN-based LEDs on hetero-substrates, large mismatch between GaN and sapphire results in residual in-plane compressive stress in LEDs. The residual stress will induce a piezoelectric field, which has a great influence on optical characteristics of LEDs [28]. Generally, the quantum-confined Stark effect (QCSE) is caused by spontaneous and piezoelectric polarization fields. The relaxation of stress can relieve the QCSE [29,30]. Therefore, we further investigated the influence of the substrate on the strain state of the LED. Figure 4(a) shows the simulated energy band diagram of InGaN/GaN MQW for different strain relaxation. With the increase of strain relaxation, the energy band of MQW becomes less inclined due to the decrease of piezoelectric field. To evaluate the stress state of GaN films grown on different substrates, samples are characterized using Raman spectroscopy. The frequency shift of high-energy Raman E2 mode is usually adopted to identify the magnitude of stress in III-nitride compounds. The Raman frequency will shift to the higher frequency side of the stress-free position (blue shifts) due to the existence of residual in-plane compressive stress [31]. As shown in Fig. 4(b), Raman peaks of E2 (high) mode in GaN films grown on PSS and PSSA are 569.20 cm−1 and 568.84 cm−1, respectively. The residual stress in the GaN films can be calculated using the linear approximation to the frequency shift biaxial stress relationship:

$$\sigma = \frac{{\Delta \omega }}{\kappa },$$
where Δω is the relative E2 (high) Raman peak shift, k is the Raman stress coefficient (4.2 cm−1/GPa) for the E2 (high) mode of GaN, and σ is the residual stress. According to Eq. (2), the residual in-plane compressive stress for these samples are 0.61, and 0.52 GPa, respectively, indicating that the incorporation of the PSSA reduces the compressive stress in the GaN film, due to the decrease of coalescence boundary of misfit GaN as mentioned above. Figures 4(c) and 4(d) show the room-temperature electroluminescence (EL) spectra of LEDs on PSS and PSSA at various injection current levels, respectively. With an injection current of 60 mA, the peak emission wavelengths of EL spectra of LEDs grown on PSS and PSSA are 452 and 445 nm, respectively. The blue-shift of peak emission wavelength reveals that the relaxation of in-plane compressive stress in the LED grown on PSSA weakens the piezoelectric field and hence alleviates the QCSE.

 

Fig. 4. (a) Simulated energy band diagram of the InGaN/GaN MQW structure for different relaxation cases without applied bias voltage. (b) Raman scattering spectra of GaN films grown on PSS and PSSA at room temperature. EL spectra of (c) LED grown on PSS and (d) LED grown on PSSA at various injection currents.

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To explore the effects of the substrates on the optical and electrical performance, we measured the light output power (LOP)-current-voltage (L-I-V) curves of flip-chip LEDs. Figure 5(a) shows representative current-voltage (I-V) curves of flip-chip LEDs on PSS and PSSA. Coincident I-V curves indicate that the substrates have no effect on electrical performance of devices. With an injection current of 120 mA, the LOP-current (L-I) curves of flip-chip LEDs on PSS and PSSA shown in Fig. 5(b) are 193.8 and 225.7 mW, respectively. The LOP of flip-chip LEDs on PSSA exhibits a 16.5% increment, compared to that of flip-chip LEDs on PSS. The EQE measurements highlight the advantage of switching from PSS to PSSA, as presented in Fig. 5(c). The peak EQEs of flip-chip LEDs on PSS and PSSA are 67.8% and 77.7%, respectively. The introduction of PSSA substrate not only improves the crystalline quality, but also increases the overall LEE, as discussed later in this work.

 

Fig. 5. (a) I-V and (b) L-I characteristics of LEDs grown on PSS and PSSA. (c) EQEs of LEDs grown on PSS and PSSA versus current curves.

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4. Mechanism of light extraction enhancement in PSSA

To further reveal the mechanism of light extraction enhancement in PSSA, the Light Tools software, based on Monte Carlo ray tracing method, was applied to delineate the optical characteristics of flip-chip LEDs on different substrates. The Monte Carlo ray-tracing method has been widely adopted to simulate the behavior of numerous rays randomly emitted from the active region using the laws of geometrical optics. Here, the simulation results with only geometrical optics considered are acceptable since the pattern size is much larger than the wavelength of light [32]. Figures 6(a)–6(c) sketch the cross-sectional ray-tracing of flip-chip LEDs on flat sapphire substrate (FSS), PSS and PSSA. The pattern of substrate has been simulated but it is invisible in the figure due to the small size. As illustrated in Figs. 6(a)–6(c), the flip-chip LED on PSSA demonstrated a significantly enhanced top emission and a reduced sidewall emission compared with the flip-chip LEDs on FSS and PSS. As a result, the flip-chip LED on PSSA exhibited the most collimated light emission, as presented in Figs. 6(d)–6(f). A highly directional emission pattern with a small far-field emission angle is important for high-resolution display application.

 

Fig. 6. Cross-sectional ray-tracing of flip-chip LEDs on (a) FSS, (b) PSS and (c) PSSA. Top-view far-field radiation patterns of flip-chip LEDs on (d) FSS, (e) PSS and (f) PSSA.

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We schematically illustrated the possible optical paths at different interfaces to reveal the mechanism of improving LEE for the flip-chip LEDs on PSSA. Figure 7(a) shows transmittance of light at different incident angles for the flip-chip LEDs on FSS, PSS and PSSA. Figure 7(b) shows schematic illustration of light with different incident angles for the flip-chip LEDs on FSS, PSS and PSSA. Since the critical angle of total internal reflection (TIR) at the sapphire-air interface is 34°, optical rays with an incident angle less than 34° can directly propagate from sapphire into air. The incident angle of light at the GaN-substrate interface can be calculated using Snell’s law:

$${n_i}\sin {\theta _i} = {n_t}\sin {\theta _t},$$
where ni and nt are the refractive indices for the GaN and the sapphire, respectively; θi and θt are the incident angle and refracting angle, respectively. In terms of Eq. (3), optical rays incident between 0° and 24° in the flip-chip LED on FSS can directly emit into air without any reflection at each interface. Similarly, optical rays incident between 10° and 40° in the flip-chip LED on PSS and optical rays incident between 20° and 48° in the flip-chip LED on PSSA can directly emit into air without any reflection at each interface. The effect of the optical rays incident beyond these scope on improving LEE is inessential, since most of these optical rays are internally absorbed through multiple TIR, resulting in a relatively low transmittance as shown in Fig. 7(a). For the flip-chip LED on PSS, the refraction angle of optical rays at GaN-sapphire interface is in the range of 0° - 34°, while the refraction angle of light at silica-sapphire interface for the flip-chip LED on PSSA is in the range of 0° - 24°. In other words, the flip-chip LED on PSSA exhibits a higher collimated light emission in comparison to the flip-chip LED on PSS.

 

Fig. 7. (a) Simulated transmittance and (b) schematic illustration of light with different incident angles for the flip-chip LEDs on FSS, PSS and PSSA.

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Figure 8(a) shows the simulated and experimentally measured far-field radiation patterns of the flip-chip LEDs on PSS and PSSA. The simulation results agree well with the experiments. Compared to the flip-chip LED on PSS, the flip-chip LED on PSSA exhibits an 11.5% enhancement in LEE and a significantly higher top emission intensity. The analysis of top emission for the flip-chip LEDs on FSS, PSS and PSSA is shown in Fig. 8(b). Since the critical angle of TIR at the GaN-sapphire interface is 46° and the vertex angle of cone is 68°, optical rays at incident angles ranging from 10° to 90° are refracted from the GaN into the sapphire cones in the case of the flip-chip LED on PSS. Similarly, since the critical angle of TIR at the GaN-SiO2 interface is 36°, optical rays at incident angles ranging from 20° to 90° are refracted from the GaN into the SiO2 cones in the case of flip-chip LEDs on PSSA. Because the size of the cone is much larger than the distance between the cones, the probability of light refracting into the substrate can be expressed as the probability of light refracting from the sidewall of the cone to the substrate. Based on the range of incident angles of the optical rays refracted to cones, 89% light can emit from GaN into sapphire in the flip-chip LED on PSS, while 78% light can emit from GaN into SiO2 in the flip-chip LED on PSSA. The escape probability of light at the flat interface of different materials depends on the probability of rays emitting into the escape cone. The probability is calculated by:

$$p = \frac{1}{{4{n^2}}}.$$
From Eq. (4), the escape probability of rays in PSS from sapphire to air is 8%. For the top emission of LEDs grown on PSSA in Fig. 8(c), we can come to the following equations according to the Snell’s law:
$${n_{Si{O_2}}}\sin {\theta _1} = {n_{Sapphire}}\sin {\theta _2},$$
$${n_{Sapphire}}\sin {\theta _2} = {n_{Air}}\sin {\theta _3}.$$
Based on Eqs. (5) and (6), we can obtain:
$${n_{Si{O_2}}}\sin {\theta _1} = {n_{Air}}\sin {\theta _3}.$$
As demonstrated in Eq. (7), the angle of rays in PSSA that escape from top the surface is only determined by SiO2 and air. Furthermore, there is no TIR at SiO2-sapphire interface, since the refractive index of SiO2 is smaller than that of sapphire. Overall, Eq. (4) is also suitable for the rays in SiO2 array. Consequently, the probability of rays in PSSA that refract from SiO2 array to sapphire substrate and then escape into air is 12%. For flip-chip LEDs, the DBR will reflect the downward rays to the top surface. As a result, the LEEs at top surfaces are calculated to be 14% (89%×8%×2) and 18% (78%×12%×2) for the flip-chip LEDs on PSS and PSSA, respectively. These LEEs are the escape probability of rays which can directly emit to air without any reflection at each interface. The above discussion suggests that the PSSA decreases the number of rays refracted into SiO2 cones due to the larger refractive index contrast at the GaN-SiO2 interface in comparison with that at the GaN-sapphire interface. However, the refractive index contrast between SiO2 and air is smaller than that between sapphire and air. Therefore, rays in the SiO2 cones have a larger probability of escaping into air.

 

Fig. 8. (a) Simulated and experimentally measured far-field radiation patterns of flip-chip LEDs on PSS and PSSA. (b) Analysis of top emission for the flip-chip LEDs on FSS, PSS and PSSA. (c) Top emitting route of rays in SiO2 array.

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We further investigate the effect of the diameter (D), height (H) and period (P) of the silica array on LEE of flip-chip LEDs. Figure 9(a) shows the LEE of flip-chip LEDs grown on PSSA with different fill factors (D/P). With the increase of fill factor, the LEE first increases and then decreases. Undoubtedly, the silica array will enhance the extraction probability of rays whose incident angles are larger than the critical angle of TIR at the GaN-sapphire interface, owing to the scattering of rays. Meanwhile, the silica array will reduce the extraction probability of rays whose incident angles are less than the critical angle of TIR at the GaN-sapphire interface. Therefore, in order to achieve a higher LEE, it is better to choose a fill factor ranging from 0.7 to 0.9. Figure 9(b) shows the LEE of the flip-chip LED grown on PSSA with different slanted angles (α = arctan (2H/D)). A change in slanted angles of silica array can substantially impact the top LEE, while it has negligible effect on sidewall LEE.

 

Fig. 9. (a) LEE of LED grown on PSSA with different fill factors (D/P). (b) LEE of LED grown on PSSA with different slanted angles (α = arctan (2H/D)). D, P and H are the diameter, period and height of the silica array, respectively.

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5. Conclusions

In summary, we have developed a new PSSA substrate to improve efficiency of GaN-based flip-chip visible LEDs. We demonstrate that the proposed PSSA design represents a highly robust substrate platform, which is capable to eliminate the nucleation of GaN islands on the SiO2 cone sidewall regions, thus reducing TDD in GaN-based LEDs. We note that the GaN film grown on PSSA exhibits better crystalline quality than the GaN film grown on PSS. We further show that the flip-chip LED on PSSA exhibits a more collimated emission pattern and higher top emission intensity than the flip-chip LED on PSS due to the smaller refractive index contrast between the cone array and air. Owing to the improved crystalline quality and enhanced LEE, the LOP of the flip-chip LED on PSSA provides a 16.5% improvement over the flip-chip LED on PSS under 120 mA injection current. This work demonstrates a significant step forward in the development of high-performance LEDs for high-resolution display.

Funding

National Natural Science Foundation of China (51675386, 51775387, 52075394); Natural Science Foundation of Hubei Province (2018CFA091).

Disclosures

The authors declare no conflicts of interest.

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22. S.-M. Jeong, S. Kissinger, D.-W. Kim, S. Jae Lee, J.-S. Kim, H.-K. Ahn, and C.-R. Lee, “Characteristic enhancement of the blue LED chip by the growth and fabrication on patterned sapphire (0001) substrate,” J. Cryst. Growth 312(2), 258–262 (2010). [CrossRef]  

23. H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020). [CrossRef]  

24. S. Zhou, S. Yuan, H. Ding, and S. Liu, “Improved light output power of LEDs with embedded air voids structure and SiO2 current blocking layer,” Appl. Surf. Sci. 305, 252–258 (2014). [CrossRef]  

25. S. Zhou, X. Liu, H. Yan, Z. Chen, Y. Liu, and S. Liu, “Highly efficient GaN-based high-power flip-chip light-emitting diodes,” Opt. Express 27(12), A669–A692 (2019). [CrossRef]  

26. S. Y. Karpov, “Modeling of III-nitride light-emitting diodes: progress, problems, and perspectives,” Proc. SPIE 7939, 79391C (2011). [CrossRef]  

27. R. Chierchia, T. BWttcher, H. Heinke, S. Einfeldt, S. Figge, and D. Hommel, “Microstructure of heteroepitaxial GaN revealed by x-ray diffraction,” J. Appl. Phys. 93(11), 8918–8925 (2003). [CrossRef]  

28. T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020). [CrossRef]  

29. S. F. Chichibu, A. C. Abare, M. P. Mack, M. S. Minsky, T. Deguchi, D. Cohen, P. Kozodoy, S. B. Fleischer, S. Keller, and J. S. Speck, “Optical properties of InGaN quantum wells,” Mater. Sci. Eng., B 59(1-3), 298–306 (1999). [CrossRef]  

30. K. A. Bulashevich, S. Y. Karpov, and R. A. Suris, “Analytical model for the quantum-confined Stark effect including electric field screening by non-equilibrium carriers,” Phys. Status Solidi B 243(7), 1625–1629 (2006). [CrossRef]  

31. B. Park, R. S. Kumar, M. Moon, M. Kim, T. Kang, W. Yang, and S. Kim, “Comparison of stress states in GaN films grown on different substrates: Langasite, sapphire and silicon,” J. Cryst. Growth 425, 149–153 (2015). [CrossRef]  

32. L. X. Li, P. G. Stegmann, S. Rosenkranz, W. Schäfer, and C. Tropea, “Simulation of light scattering from a colloidal droplet using a polarized Monte Carlo method: application to the time-shift technique,” Opt. Express 27(25), 36388–36404 (2019). [CrossRef]  

References

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  1. N. Padmasali and S. G. Kini, “A lifetime performance analysis of LED luminaires under real-operation profiles,” IEEE Trans. Electron Devices 67(1), 146–153 (2020).
    [Crossref]
  2. J. Bai, Y. F. Cai, P. Feng, P. Fletcher, X. M. Zhao, C. Q. Zhu, and T. Wang, “A direct epitaxial approach to achieving ultrasmall and ultrabright InGaN micro light-emitting diodes (µLEDs),” ACS Photonics 7(2), 411–415 (2020).
    [Crossref]
  3. K. R. Son, T. H. Lee, B. R. Lee, H. S. Im, and T. G. Kim, “Nitride-based microlight-emitting diodes using AlN thin-film electrodes with nanoscale indium/tin conducting filaments,” Small 14(49), 1801032 (2018).
    [Crossref]
  4. K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
    [Crossref]
  5. G. Yuan, K. L. Xiong, C. Zhang, Y. F. Li, and J. Han, “Optical engineering of modal gain in an III-nitride laser with nanoporous GaN,” ACS Photonics 3(9), 1604–1610 (2016).
    [Crossref]
  6. Y. Lin, J. E. Huang, Y. Gao, Y. L. Gao, C. Yang, Z. H. Li, S. D. Lei, and Z. Chen, “Determining phosphor temperature in light-emitting diode based on divisional normalized emission power,” IEEE Electron. Device Lett. 40(10), 1650–1653 (2019).
    [Crossref]
  7. J. S. Park, Y. H. Sung, J. Y. Na, D. Kang, S. K. Kim, H. Lee, and T. Y. Seong, “Use of a patterned current blocking layer to enhance the light output power of InGaN-based light-emitting diodes,” Opt. Express 25(15), 17556–17561 (2017).
    [Crossref]
  8. L. J. Tan, K. Wang, Z. J. Xie, M. Zhong, L. S. Lu, H. Wang, and R. H. Yao, “Improving the –3 dB bandwidth of micro-size LEDs through p-electrode patterns for visible light communication,” Appl. Opt. 59(23), 7004–7011 (2020).
    [Crossref]
  9. B. Sun, G. Haunschild, C. Polanco, J. Ju, L. Lindsay, G. Koblmüller, and Y. K. Koh, “Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films,” Nat. Mater. 18(2), 136–140 (2019).
    [Crossref]
  10. Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
    [Crossref]
  11. K. Chung, H. Yoo, J. K. Hyun, H. Oh, Y. Tchoe, K. Lee, H. Baek, M. Kim, and G.-C. Yi, “Flexible GaN light-emitting diodes using GaN microdisks epitaxial laterally overgrown on graphene dots,” Adv. Mater. 28(35), 7688–7694 (2016).
    [Crossref]
  12. J. Jeong, J. Jang, J. Hwang, C. Jung, J. Kim, K. Lee, H. Lim, and O. Nam, “Improved performance of semi-polar (11-22) GaN-based light-emitting diodes grown on SiNx interlayer,” J. Cryst. Growth 370, 114–119 (2013).
    [Crossref]
  13. J. J. Wierer Jr, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
    [Crossref]
  14. T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84(6), 855–857 (2004).
    [Crossref]
  15. Y. J. Moon, D. Moon, J. Jang, J. Y. Na, J. H. Song, M. K. Seo, S. Kim, D. Bae, E. H. Park, Y. Park, S. K. Kim, and E. Yoon, “Microstructured air cavities as high-index contrast substrates with strong diffraction for light-emitting diodes,” Nano Lett. 16(5), 3301–3308 (2016).
    [Crossref]
  16. S. Zhou, H. Hu, X. Liu, M. Liu, X. Ding, C. Gui, S. Liu, and L. J. Guo, “Comparative study of GaN-based ultraviolet LEDs grown on different-sized patterned sapphire substrates with sputtered AlN nucleation layer,” Jpn. J. Appl. Phys. 56(11), 111001 (2017).
    [Crossref]
  17. M. Liu, S. Zhou, X. Liu, Y. Gao, and X. Ding, “Comparative experimental and simulation studies of high-power AlGaN-based 353 nm ultraviolet flip-chip and top-emitting LEDs,” Jpn. J. Appl. Phys. 57(3), 031001 (2018).
    [Crossref]
  18. S. Zhou, H. Xu, H. Hu, C. Gui, and S. Liu, “High quality GaN buffer layer by isoelectronic doping and its application to 365 nm InGaN/AlGaN ultraviolet light-emitting diodes,” Appl. Surf. Sci. 471(31), 231–238 (2019).
    [Crossref]
  19. H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
    [Crossref]
  20. S. Nakamura and M. R. Krames, “History of gallium–nitride-based light-emitting diodes for illumination,” Proc. IEEE 101(10), 2211–2220 (2013).
    [Crossref]
  21. 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 9(12), 650 (2018).
    [Crossref]
  22. S.-M. Jeong, S. Kissinger, D.-W. Kim, S. Jae Lee, J.-S. Kim, H.-K. Ahn, and C.-R. Lee, “Characteristic enhancement of the blue LED chip by the growth and fabrication on patterned sapphire (0001) substrate,” J. Cryst. Growth 312(2), 258–262 (2010).
    [Crossref]
  23. H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020).
    [Crossref]
  24. S. Zhou, S. Yuan, H. Ding, and S. Liu, “Improved light output power of LEDs with embedded air voids structure and SiO2 current blocking layer,” Appl. Surf. Sci. 305, 252–258 (2014).
    [Crossref]
  25. S. Zhou, X. Liu, H. Yan, Z. Chen, Y. Liu, and S. Liu, “Highly efficient GaN-based high-power flip-chip light-emitting diodes,” Opt. Express 27(12), A669–A692 (2019).
    [Crossref]
  26. S. Y. Karpov, “Modeling of III-nitride light-emitting diodes: progress, problems, and perspectives,” Proc. SPIE 7939, 79391C (2011).
    [Crossref]
  27. R. Chierchia, T. BWttcher, H. Heinke, S. Einfeldt, S. Figge, and D. Hommel, “Microstructure of heteroepitaxial GaN revealed by x-ray diffraction,” J. Appl. Phys. 93(11), 8918–8925 (2003).
    [Crossref]
  28. T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020).
    [Crossref]
  29. S. F. Chichibu, A. C. Abare, M. P. Mack, M. S. Minsky, T. Deguchi, D. Cohen, P. Kozodoy, S. B. Fleischer, S. Keller, and J. S. Speck, “Optical properties of InGaN quantum wells,” Mater. Sci. Eng., B 59(1-3), 298–306 (1999).
    [Crossref]
  30. K. A. Bulashevich, S. Y. Karpov, and R. A. Suris, “Analytical model for the quantum-confined Stark effect including electric field screening by non-equilibrium carriers,” Phys. Status Solidi B 243(7), 1625–1629 (2006).
    [Crossref]
  31. B. Park, R. S. Kumar, M. Moon, M. Kim, T. Kang, W. Yang, and S. Kim, “Comparison of stress states in GaN films grown on different substrates: Langasite, sapphire and silicon,” J. Cryst. Growth 425, 149–153 (2015).
    [Crossref]
  32. L. X. Li, P. G. Stegmann, S. Rosenkranz, W. Schäfer, and C. Tropea, “Simulation of light scattering from a colloidal droplet using a polarized Monte Carlo method: application to the time-shift technique,” Opt. Express 27(25), 36388–36404 (2019).
    [Crossref]

2020 (6)

N. Padmasali and S. G. Kini, “A lifetime performance analysis of LED luminaires under real-operation profiles,” IEEE Trans. Electron Devices 67(1), 146–153 (2020).
[Crossref]

J. Bai, Y. F. Cai, P. Feng, P. Fletcher, X. M. Zhao, C. Q. Zhu, and T. Wang, “A direct epitaxial approach to achieving ultrasmall and ultrabright InGaN micro light-emitting diodes (µLEDs),” ACS Photonics 7(2), 411–415 (2020).
[Crossref]

L. J. Tan, K. Wang, Z. J. Xie, M. Zhong, L. S. Lu, H. Wang, and R. H. Yao, “Improving the –3 dB bandwidth of micro-size LEDs through p-electrode patterns for visible light communication,” Appl. Opt. 59(23), 7004–7011 (2020).
[Crossref]

Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
[Crossref]

H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020).
[Crossref]

T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020).
[Crossref]

2019 (5)

S. Zhou, X. Liu, H. Yan, Z. Chen, Y. Liu, and S. Liu, “Highly efficient GaN-based high-power flip-chip light-emitting diodes,” Opt. Express 27(12), A669–A692 (2019).
[Crossref]

L. X. Li, P. G. Stegmann, S. Rosenkranz, W. Schäfer, and C. Tropea, “Simulation of light scattering from a colloidal droplet using a polarized Monte Carlo method: application to the time-shift technique,” Opt. Express 27(25), 36388–36404 (2019).
[Crossref]

S. Zhou, H. Xu, H. Hu, C. Gui, and S. Liu, “High quality GaN buffer layer by isoelectronic doping and its application to 365 nm InGaN/AlGaN ultraviolet light-emitting diodes,” Appl. Surf. Sci. 471(31), 231–238 (2019).
[Crossref]

B. Sun, G. Haunschild, C. Polanco, J. Ju, L. Lindsay, G. Koblmüller, and Y. K. Koh, “Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films,” Nat. Mater. 18(2), 136–140 (2019).
[Crossref]

Y. Lin, J. E. Huang, Y. Gao, Y. L. Gao, C. Yang, Z. H. Li, S. D. Lei, and Z. Chen, “Determining phosphor temperature in light-emitting diode based on divisional normalized emission power,” IEEE Electron. Device Lett. 40(10), 1650–1653 (2019).
[Crossref]

2018 (4)

K. R. Son, T. H. Lee, B. R. Lee, H. S. Im, and T. G. Kim, “Nitride-based microlight-emitting diodes using AlN thin-film electrodes with nanoscale indium/tin conducting filaments,” Small 14(49), 1801032 (2018).
[Crossref]

K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
[Crossref]

M. Liu, S. Zhou, X. Liu, Y. Gao, and X. Ding, “Comparative experimental and simulation studies of high-power AlGaN-based 353 nm ultraviolet flip-chip and top-emitting LEDs,” Jpn. J. Appl. Phys. 57(3), 031001 (2018).
[Crossref]

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 9(12), 650 (2018).
[Crossref]

2017 (3)

J. S. Park, Y. H. Sung, J. Y. Na, D. Kang, S. K. Kim, H. Lee, and T. Y. Seong, “Use of a patterned current blocking layer to enhance the light output power of InGaN-based light-emitting diodes,” Opt. Express 25(15), 17556–17561 (2017).
[Crossref]

H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
[Crossref]

S. Zhou, H. Hu, X. Liu, M. Liu, X. Ding, C. Gui, S. Liu, and L. J. Guo, “Comparative study of GaN-based ultraviolet LEDs grown on different-sized patterned sapphire substrates with sputtered AlN nucleation layer,” Jpn. J. Appl. Phys. 56(11), 111001 (2017).
[Crossref]

2016 (3)

Y. J. Moon, D. Moon, J. Jang, J. Y. Na, J. H. Song, M. K. Seo, S. Kim, D. Bae, E. H. Park, Y. Park, S. K. Kim, and E. Yoon, “Microstructured air cavities as high-index contrast substrates with strong diffraction for light-emitting diodes,” Nano Lett. 16(5), 3301–3308 (2016).
[Crossref]

K. Chung, H. Yoo, J. K. Hyun, H. Oh, Y. Tchoe, K. Lee, H. Baek, M. Kim, and G.-C. Yi, “Flexible GaN light-emitting diodes using GaN microdisks epitaxial laterally overgrown on graphene dots,” Adv. Mater. 28(35), 7688–7694 (2016).
[Crossref]

G. Yuan, K. L. Xiong, C. Zhang, Y. F. Li, and J. Han, “Optical engineering of modal gain in an III-nitride laser with nanoporous GaN,” ACS Photonics 3(9), 1604–1610 (2016).
[Crossref]

2015 (1)

B. Park, R. S. Kumar, M. Moon, M. Kim, T. Kang, W. Yang, and S. Kim, “Comparison of stress states in GaN films grown on different substrates: Langasite, sapphire and silicon,” J. Cryst. Growth 425, 149–153 (2015).
[Crossref]

2014 (1)

S. Zhou, S. Yuan, H. Ding, and S. Liu, “Improved light output power of LEDs with embedded air voids structure and SiO2 current blocking layer,” Appl. Surf. Sci. 305, 252–258 (2014).
[Crossref]

2013 (2)

J. Jeong, J. Jang, J. Hwang, C. Jung, J. Kim, K. Lee, H. Lim, and O. Nam, “Improved performance of semi-polar (11-22) GaN-based light-emitting diodes grown on SiNx interlayer,” J. Cryst. Growth 370, 114–119 (2013).
[Crossref]

S. Nakamura and M. R. Krames, “History of gallium–nitride-based light-emitting diodes for illumination,” Proc. IEEE 101(10), 2211–2220 (2013).
[Crossref]

2011 (1)

S. Y. Karpov, “Modeling of III-nitride light-emitting diodes: progress, problems, and perspectives,” Proc. SPIE 7939, 79391C (2011).
[Crossref]

2010 (1)

S.-M. Jeong, S. Kissinger, D.-W. Kim, S. Jae Lee, J.-S. Kim, H.-K. Ahn, and C.-R. Lee, “Characteristic enhancement of the blue LED chip by the growth and fabrication on patterned sapphire (0001) substrate,” J. Cryst. Growth 312(2), 258–262 (2010).
[Crossref]

2009 (1)

J. J. Wierer Jr, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
[Crossref]

2006 (1)

K. A. Bulashevich, S. Y. Karpov, and R. A. Suris, “Analytical model for the quantum-confined Stark effect including electric field screening by non-equilibrium carriers,” Phys. Status Solidi B 243(7), 1625–1629 (2006).
[Crossref]

2004 (1)

T. Fujii, Y. Gao, R. Sharma, E. L. Hu, S. P. DenBaars, and S. Nakamura, “Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening,” Appl. Phys. Lett. 84(6), 855–857 (2004).
[Crossref]

2003 (1)

R. Chierchia, T. BWttcher, H. Heinke, S. Einfeldt, S. Figge, and D. Hommel, “Microstructure of heteroepitaxial GaN revealed by x-ray diffraction,” J. Appl. Phys. 93(11), 8918–8925 (2003).
[Crossref]

1999 (1)

S. F. Chichibu, A. C. Abare, M. P. Mack, M. S. Minsky, T. Deguchi, D. Cohen, P. Kozodoy, S. B. Fleischer, S. Keller, and J. S. Speck, “Optical properties of InGaN quantum wells,” Mater. Sci. Eng., B 59(1-3), 298–306 (1999).
[Crossref]

Abare, A. C.

S. F. Chichibu, A. C. Abare, M. P. Mack, M. S. Minsky, T. Deguchi, D. Cohen, P. Kozodoy, S. B. Fleischer, S. Keller, and J. S. Speck, “Optical properties of InGaN quantum wells,” Mater. Sci. Eng., B 59(1-3), 298–306 (1999).
[Crossref]

Ahn, H.-K.

S.-M. Jeong, S. Kissinger, D.-W. Kim, S. Jae Lee, J.-S. Kim, H.-K. Ahn, and C.-R. Lee, “Characteristic enhancement of the blue LED chip by the growth and fabrication on patterned sapphire (0001) substrate,” J. Cryst. Growth 312(2), 258–262 (2010).
[Crossref]

Bae, D.

Y. J. Moon, D. Moon, J. Jang, J. Y. Na, J. H. Song, M. K. Seo, S. Kim, D. Bae, E. H. Park, Y. Park, S. K. Kim, and E. Yoon, “Microstructured air cavities as high-index contrast substrates with strong diffraction for light-emitting diodes,” Nano Lett. 16(5), 3301–3308 (2016).
[Crossref]

Baek, H.

K. Chung, H. Yoo, J. K. Hyun, H. Oh, Y. Tchoe, K. Lee, H. Baek, M. Kim, and G.-C. Yi, “Flexible GaN light-emitting diodes using GaN microdisks epitaxial laterally overgrown on graphene dots,” Adv. Mater. 28(35), 7688–7694 (2016).
[Crossref]

Bai, J.

J. Bai, Y. F. Cai, P. Feng, P. Fletcher, X. M. Zhao, C. Q. Zhu, and T. Wang, “A direct epitaxial approach to achieving ultrasmall and ultrabright InGaN micro light-emitting diodes (µLEDs),” ACS Photonics 7(2), 411–415 (2020).
[Crossref]

Bulashevich, K. A.

K. A. Bulashevich, S. Y. Karpov, and R. A. Suris, “Analytical model for the quantum-confined Stark effect including electric field screening by non-equilibrium carriers,” Phys. Status Solidi B 243(7), 1625–1629 (2006).
[Crossref]

BWttcher, T.

R. Chierchia, T. BWttcher, H. Heinke, S. Einfeldt, S. Figge, and D. Hommel, “Microstructure of heteroepitaxial GaN revealed by x-ray diffraction,” J. Appl. Phys. 93(11), 8918–8925 (2003).
[Crossref]

Cai, Y. F.

J. Bai, Y. F. Cai, P. Feng, P. Fletcher, X. M. Zhao, C. Q. Zhu, and T. Wang, “A direct epitaxial approach to achieving ultrasmall and ultrabright InGaN micro light-emitting diodes (µLEDs),” ACS Photonics 7(2), 411–415 (2020).
[Crossref]

Cha, Y. J.

K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
[Crossref]

Chang, C. Y.

H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
[Crossref]

Chang, Y. M.

H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
[Crossref]

Chen, C.

H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020).
[Crossref]

Chen, W. L.

H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
[Crossref]

Chen, Z.

Y. Lin, J. E. Huang, Y. Gao, Y. L. Gao, C. Yang, Z. H. Li, S. D. Lei, and Z. Chen, “Determining phosphor temperature in light-emitting diode based on divisional normalized emission power,” IEEE Electron. Device Lett. 40(10), 1650–1653 (2019).
[Crossref]

S. Zhou, X. Liu, H. Yan, Z. Chen, Y. Liu, and S. Liu, “Highly efficient GaN-based high-power flip-chip light-emitting diodes,” Opt. Express 27(12), A669–A692 (2019).
[Crossref]

Cheng, H. Y.

H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
[Crossref]

Chichibu, S. F.

S. F. Chichibu, A. C. Abare, M. P. Mack, M. S. Minsky, T. Deguchi, D. Cohen, P. Kozodoy, S. B. Fleischer, S. Keller, and J. S. Speck, “Optical properties of InGaN quantum wells,” Mater. Sci. Eng., B 59(1-3), 298–306 (1999).
[Crossref]

Chierchia, R.

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K. Chung, H. Yoo, J. K. Hyun, H. Oh, Y. Tchoe, K. Lee, H. Baek, M. Kim, and G.-C. Yi, “Flexible GaN light-emitting diodes using GaN microdisks epitaxial laterally overgrown on graphene dots,” Adv. Mater. 28(35), 7688–7694 (2016).
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B. Park, R. S. Kumar, M. Moon, M. Kim, T. Kang, W. Yang, and S. Kim, “Comparison of stress states in GaN films grown on different substrates: Langasite, sapphire and silicon,” J. Cryst. Growth 425, 149–153 (2015).
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K. R. Son, T. H. Lee, B. R. Lee, H. S. Im, and T. G. Kim, “Nitride-based microlight-emitting diodes using AlN thin-film electrodes with nanoscale indium/tin conducting filaments,” Small 14(49), 1801032 (2018).
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K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
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B. Sun, G. Haunschild, C. Polanco, J. Ju, L. Lindsay, G. Koblmüller, and Y. K. Koh, “Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films,” Nat. Mater. 18(2), 136–140 (2019).
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B. Sun, G. Haunschild, C. Polanco, J. Ju, L. Lindsay, G. Koblmüller, and Y. K. Koh, “Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films,” Nat. Mater. 18(2), 136–140 (2019).
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K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
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K. R. Son, T. H. Lee, B. R. Lee, H. S. Im, and T. G. Kim, “Nitride-based microlight-emitting diodes using AlN thin-film electrodes with nanoscale indium/tin conducting filaments,” Small 14(49), 1801032 (2018).
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S.-M. Jeong, S. Kissinger, D.-W. Kim, S. Jae Lee, J.-S. Kim, H.-K. Ahn, and C.-R. Lee, “Characteristic enhancement of the blue LED chip by the growth and fabrication on patterned sapphire (0001) substrate,” J. Cryst. Growth 312(2), 258–262 (2010).
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Lee, H.

Lee, K.

K. Chung, H. Yoo, J. K. Hyun, H. Oh, Y. Tchoe, K. Lee, H. Baek, M. Kim, and G.-C. Yi, “Flexible GaN light-emitting diodes using GaN microdisks epitaxial laterally overgrown on graphene dots,” Adv. Mater. 28(35), 7688–7694 (2016).
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K. R. Son, T. H. Lee, B. R. Lee, H. S. Im, and T. G. Kim, “Nitride-based microlight-emitting diodes using AlN thin-film electrodes with nanoscale indium/tin conducting filaments,” Small 14(49), 1801032 (2018).
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H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
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H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
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Y. Lin, J. E. Huang, Y. Gao, Y. L. Gao, C. Yang, Z. H. Li, S. D. Lei, and Z. Chen, “Determining phosphor temperature in light-emitting diode based on divisional normalized emission power,” IEEE Electron. Device Lett. 40(10), 1650–1653 (2019).
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J. Jeong, J. Jang, J. Hwang, C. Jung, J. Kim, K. Lee, H. Lim, and O. Nam, “Improved performance of semi-polar (11-22) GaN-based light-emitting diodes grown on SiNx interlayer,” J. Cryst. Growth 370, 114–119 (2013).
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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 9(12), 650 (2018).
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S. Zhou, H. Hu, X. Liu, M. Liu, X. Ding, C. Gui, S. Liu, and L. J. Guo, “Comparative study of GaN-based ultraviolet LEDs grown on different-sized patterned sapphire substrates with sputtered AlN nucleation layer,” Jpn. J. Appl. Phys. 56(11), 111001 (2017).
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T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020).
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S. Zhou, X. Liu, H. Yan, Z. Chen, Y. Liu, and S. Liu, “Highly efficient GaN-based high-power flip-chip light-emitting diodes,” Opt. Express 27(12), A669–A692 (2019).
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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 9(12), 650 (2018).
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M. Liu, S. Zhou, X. Liu, Y. Gao, and X. Ding, “Comparative experimental and simulation studies of high-power AlGaN-based 353 nm ultraviolet flip-chip and top-emitting LEDs,” Jpn. J. Appl. Phys. 57(3), 031001 (2018).
[Crossref]

S. Zhou, H. Hu, X. Liu, M. Liu, X. Ding, C. Gui, S. Liu, and L. J. Guo, “Comparative study of GaN-based ultraviolet LEDs grown on different-sized patterned sapphire substrates with sputtered AlN nucleation layer,” Jpn. J. Appl. Phys. 56(11), 111001 (2017).
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T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020).
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B. Park, R. S. Kumar, M. Moon, M. Kim, T. Kang, W. Yang, and S. Kim, “Comparison of stress states in GaN films grown on different substrates: Langasite, sapphire and silicon,” J. Cryst. Growth 425, 149–153 (2015).
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Y. J. Moon, D. Moon, J. Jang, J. Y. Na, J. H. Song, M. K. Seo, S. Kim, D. Bae, E. H. Park, Y. Park, S. K. Kim, and E. Yoon, “Microstructured air cavities as high-index contrast substrates with strong diffraction for light-emitting diodes,” Nano Lett. 16(5), 3301–3308 (2016).
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K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
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Y. J. Moon, D. Moon, J. Jang, J. Y. Na, J. H. Song, M. K. Seo, S. Kim, D. Bae, E. H. Park, Y. Park, S. K. Kim, and E. Yoon, “Microstructured air cavities as high-index contrast substrates with strong diffraction for light-emitting diodes,” Nano Lett. 16(5), 3301–3308 (2016).
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Park, Y.

Y. J. Moon, D. Moon, J. Jang, J. Y. Na, J. H. Song, M. K. Seo, S. Kim, D. Bae, E. H. Park, Y. Park, S. K. Kim, and E. Yoon, “Microstructured air cavities as high-index contrast substrates with strong diffraction for light-emitting diodes,” Nano Lett. 16(5), 3301–3308 (2016).
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T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020).
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K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
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S. F. Chichibu, A. C. Abare, M. P. Mack, M. S. Minsky, T. Deguchi, D. Cohen, P. Kozodoy, S. B. Fleischer, S. Keller, and J. S. Speck, “Optical properties of InGaN quantum wells,” Mater. Sci. Eng., B 59(1-3), 298–306 (1999).
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Sun, B.

B. Sun, G. Haunschild, C. Polanco, J. Ju, L. Lindsay, G. Koblmüller, and Y. K. Koh, “Dislocation-induced thermal transport anisotropy in single-crystal group-III nitride films,” Nat. Mater. 18(2), 136–140 (2019).
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H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020).
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K. Chung, H. Yoo, J. K. Hyun, H. Oh, Y. Tchoe, K. Lee, H. Baek, M. Kim, and G.-C. Yi, “Flexible GaN light-emitting diodes using GaN microdisks epitaxial laterally overgrown on graphene dots,” Adv. Mater. 28(35), 7688–7694 (2016).
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H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020).
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J. Bai, Y. F. Cai, P. Feng, P. Fletcher, X. M. Zhao, C. Q. Zhu, and T. Wang, “A direct epitaxial approach to achieving ultrasmall and ultrabright InGaN micro light-emitting diodes (µLEDs),” ACS Photonics 7(2), 411–415 (2020).
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Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
[Crossref]

T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020).
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J. J. Wierer Jr, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
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H. Li, H. Y. Cheng, W. L. Chen, Y. H. Huang, C. K. Li, C. Y. Chang, Y. R. Wu, T. C. Lu, and Y. M. Chang, “Three dimensional characterization of GaN-based light emitting diode grown on patterned sapphire substrate by confocal Raman and photoluminescence spectromicroscopy,” Sci. Rep. 7(1), 45519 (2017).
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S. Zhou, H. Xu, H. Hu, C. Gui, and S. Liu, “High quality GaN buffer layer by isoelectronic doping and its application to 365 nm InGaN/AlGaN ultraviolet light-emitting diodes,” Appl. Surf. Sci. 471(31), 231–238 (2019).
[Crossref]

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 9(12), 650 (2018).
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Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
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B. Park, R. S. Kumar, M. Moon, M. Kim, T. Kang, W. Yang, and S. Kim, “Comparison of stress states in GaN films grown on different substrates: Langasite, sapphire and silicon,” J. Cryst. Growth 425, 149–153 (2015).
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K. Chung, H. Yoo, J. K. Hyun, H. Oh, Y. Tchoe, K. Lee, H. Baek, M. Kim, and G.-C. Yi, “Flexible GaN light-emitting diodes using GaN microdisks epitaxial laterally overgrown on graphene dots,” Adv. Mater. 28(35), 7688–7694 (2016).
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Y. J. Moon, D. Moon, J. Jang, J. Y. Na, J. H. Song, M. K. Seo, S. Kim, D. Bae, E. H. Park, Y. Park, S. K. Kim, and E. Yoon, “Microstructured air cavities as high-index contrast substrates with strong diffraction for light-emitting diodes,” Nano Lett. 16(5), 3301–3308 (2016).
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K. J. Son, T. K. Kim, Y. J. Cha, S. K. Oh, S. J. You, J. H. Ryou, and J. S. Kwak, “Impact of plasma electron flux on plasma damage-free sputtering of ultrathin tin-doped indium oxide contact layer on p-GaN for InGaN/GaN light-emitting diodes,” Adv. Sci. 5(2), 1700637 (2018).
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G. Yuan, K. L. Xiong, C. Zhang, Y. F. Li, and J. Han, “Optical engineering of modal gain in an III-nitride laser with nanoporous GaN,” ACS Photonics 3(9), 1604–1610 (2016).
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S. Zhou, S. Yuan, H. Ding, and S. Liu, “Improved light output power of LEDs with embedded air voids structure and SiO2 current blocking layer,” Appl. Surf. Sci. 305, 252–258 (2014).
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Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
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Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
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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 9(12), 650 (2018).
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J. Bai, Y. F. Cai, P. Feng, P. Fletcher, X. M. Zhao, C. Q. Zhu, and T. Wang, “A direct epitaxial approach to achieving ultrasmall and ultrabright InGaN micro light-emitting diodes (µLEDs),” ACS Photonics 7(2), 411–415 (2020).
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Zhao, Y.

Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
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Zhao, Z.

T. Liu, D. Li, H. Hu, X. Huang, Z. Zhao, W. Sha, C. Jiang, C. Du, M. Liu, X. Pu, B. Ma, W. Hu, and Z. Wang, “Piezo-phototronic effect in InGaN/GaN semi-floating micro-disk LED arrays,” Nano Energy 67, 104218 (2020).
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H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020).
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M. Liu, S. Zhou, X. Liu, Y. Gao, and X. Ding, “Comparative experimental and simulation studies of high-power AlGaN-based 353 nm ultraviolet flip-chip and top-emitting LEDs,” Jpn. J. Appl. Phys. 57(3), 031001 (2018).
[Crossref]

S. Zhou, H. Hu, X. Liu, M. Liu, X. Ding, C. Gui, S. Liu, and L. J. Guo, “Comparative study of GaN-based ultraviolet LEDs grown on different-sized patterned sapphire substrates with sputtered AlN nucleation layer,” Jpn. J. Appl. Phys. 56(11), 111001 (2017).
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Appl. Opt. (1)

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Appl. Surf. Sci. (3)

S. Zhou, H. Xu, H. Hu, C. Gui, and S. Liu, “High quality GaN buffer layer by isoelectronic doping and its application to 365 nm InGaN/AlGaN ultraviolet light-emitting diodes,” Appl. Surf. Sci. 471(31), 231–238 (2019).
[Crossref]

Y. Zhao, S. R. Xu, J. C. Zhang, C. F. Zhang, P. X. Li, Z. Y. Lin, Y. C. Zhang, H. Zhou, Z. Wang, R. S. Peng, X. M. Fan, J. J. Du, and Y. Hao, “Optical properties evolution of GaN film grown via lateral epitaxial overgrowth,” Appl. Surf. Sci. 513(30), 145816 (2020).
[Crossref]

S. Zhou, S. Yuan, H. Ding, and S. Liu, “Improved light output power of LEDs with embedded air voids structure and SiO2 current blocking layer,” Appl. Surf. Sci. 305, 252–258 (2014).
[Crossref]

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S. Zhou, H. Hu, X. Liu, M. Liu, X. Ding, C. Gui, S. Liu, and L. J. Guo, “Comparative study of GaN-based ultraviolet LEDs grown on different-sized patterned sapphire substrates with sputtered AlN nucleation layer,” Jpn. J. Appl. Phys. 56(11), 111001 (2017).
[Crossref]

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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 9(12), 650 (2018).
[Crossref]

Nano Energy (2)

H. Hu, B. Tang, H. Wan, H. Sun, S. Zhou, J. Dai, C. Chen, S. Liu, and L. J. Guo, “Boosted ultraviolet electroluminescence of InGaN/AlGaN quantum structures grown on high-index contrast patterned sapphire with silica array,” Nano Energy 69, 104427 (2020).
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[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. Schematic illustration of fabrication process for PSSA substrate.
Fig. 2.
Fig. 2. (a) Schematic illustration of the GaN-based flip-chip LED structure grown on PSSA. (b) Cross-sectional STEM image of the GaN-based LED epitaxial structure grown on PSSA. (c) Simulated energy band diagram of GaN-based LED. (d) In-situ reflectance and temperature transients during the epitaxial growth of GaN-based LED on PSSA.
Fig. 3.
Fig. 3. (a) Cross-sectional STEM images of GaN grown on PSS. (b) Cross-sectional STEM images of GaN grown on PSSA. (c) XRD rocking curves of GaN films grown on PSS and PSSA.
Fig. 4.
Fig. 4. (a) Simulated energy band diagram of the InGaN/GaN MQW structure for different relaxation cases without applied bias voltage. (b) Raman scattering spectra of GaN films grown on PSS and PSSA at room temperature. EL spectra of (c) LED grown on PSS and (d) LED grown on PSSA at various injection currents.
Fig. 5.
Fig. 5. (a) I-V and (b) L-I characteristics of LEDs grown on PSS and PSSA. (c) EQEs of LEDs grown on PSS and PSSA versus current curves.
Fig. 6.
Fig. 6. Cross-sectional ray-tracing of flip-chip LEDs on (a) FSS, (b) PSS and (c) PSSA. Top-view far-field radiation patterns of flip-chip LEDs on (d) FSS, (e) PSS and (f) PSSA.
Fig. 7.
Fig. 7. (a) Simulated transmittance and (b) schematic illustration of light with different incident angles for the flip-chip LEDs on FSS, PSS and PSSA.
Fig. 8.
Fig. 8. (a) Simulated and experimentally measured far-field radiation patterns of flip-chip LEDs on PSS and PSSA. (b) Analysis of top emission for the flip-chip LEDs on FSS, PSS and PSSA. (c) Top emitting route of rays in SiO2 array.
Fig. 9.
Fig. 9. (a) LEE of LED grown on PSSA with different fill factors (D/P). (b) LEE of LED grown on PSSA with different slanted angles (α = arctan (2H/D)). D, P and H are the diameter, period and height of the silica array, respectively.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

N = β 2 4.35 × | b | 2 ,
σ = Δ ω κ ,
n i sin θ i = n t sin θ t ,
p = 1 4 n 2 .
n S i O 2 sin θ 1 = n S a p p h i r e sin θ 2 ,
n S a p p h i r e sin θ 2 = n A i r sin θ 3 .
n S i O 2 sin θ 1 = n A i r sin θ 3 .

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