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Enhanced light extraction efficiency of GaN-based green micro-LED modulating by a thickness-tunable SiO2 passivation structure

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Abstract

Green micro-light emitting diodes (micro-LEDs) is one of the three primary color light sources as full-color display, which serves as a key research object in the field of micro-LED display. As the micro-LED size decreases, the surface-area-to-volume ratio of the device increases, leading to more serious damage on the sidewall by inductively coupled plasma (ICP) etching. The passivation process of SiO2 provides an effective method to reduce sidewall damage caused by ICP etching. In this work, green rectangular micro-LEDs with passivation layer thickness of 0∼600 nm was designed using the finite-difference time-domain (FDTD) simulation. In order to verify the simulation results, the micro-LED array was fabricated by parallel laser micro-lens array (MLA) lithography in high speed and large area. The effect of the SiO2 passivation layer thickness on the performance of the green micro-LED was analyzed, which shows that the passivation layer thickness-light extraction efficiency curve fluctuates periodically. For the sample with 90 nm thickness of SiO2 passivation layer, there exists a small leakage current and higher operating current density, and the maximum external quantum efficiency (EQE) is 2.8 times higher than micro-LED without SiO2 passivation layer.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

In the past few years, along with the fast development of miniaturization and integration of display devices, high-resolution displays have been the mainstream application of micro-LEDs of dimension smaller than 100 µm, which has drawn dramatically increasing interest and is deemed as the disruptive technology in the display industry [13]. Multinational corporations (MNCs) such as Apple and Samsung have been committed to research and development of micro-LED applications in smart watches and the vehicle display screen, where it is expected to extend further development in the areas of artificial reality (AR) and smart phones. The most direct approach for full-color display is to use three types of blue, green, and red pixels, which could be integrated to form an array, establishing a display effect with high resolution, high contrast and wide viewing angle [4].

Due to tunable wide bandgap, high thermal conductivity, high-temperature resistance, and radiation resistance, the III-nitride GaN semiconductors are considered as one of the most favorable materials for micro-LED devices, providing a good application prospect in the new generation of displays [58]. In addition, the micro-LED based on GaN has potential applications in visible light communication (VLC) [9,10], fluorescence sensing [11], and optoelectronic tweezing fields [12]. The GaN-based green micro-LED plays an essential role in full-color display arrays. However, the large lattice mismatch between InGaN and GaN materials results in a high dislocation density, reducing the minority carrier lifetime and shortening the minority carrier diffusion length. The grown GaN-based green LED still suffers from the low carrier recombination rate restrained by the quantum-confined Stark effect (QCSE), which can be attributed to the intrinsic spontaneous and piezoelectric polarization fields in GaN [13]. Besides, the indium content in green micro-LED should maintain a certain value and avoid excessive content, avoiding a large amount of stress and increased dislocation density [14]. On the other hand, the sidewall damage induced by the dry etching process becomes more and more inevitable as the decreased size of the green micro-LEDs. Obviously, along with the increasing surface-area-to-volume ratio, the sidewall damage contains more defects and impurities, introducing a large number of traps, which is extremely detrimental to the performance of micro-LED by increasing the non-radiative recombination attributed to Shockley-Read-Hall (SRH) effects at low current densities and Auger recombination at high current densities [15,16]. Thus, it is necessary to mitigate the sidewall damage effect to achieve high-efficiency GaN-based green micro-LEDs.

Recently, various passivation strategies were introduced in the GaN-based micro-LEDs to reduce the damage of the sidewall, which could control and stabilize the electrical properties of the semiconductor surface, as well as reduce the non-recombination rate [17]. Wong et al. revealed the sidewall passivation compact of blue micro-LEDs peaked at 430∼450 nm by comparing atomic-layer deposition (ALD) and plasma-enhanced chemical vapor deposition (PECVD) method for the same SiO2 passivation layer [18]. Afterward, Wong et al. used the ALD technology to deposit an Al2O3 passivation layer to improve the light output power of micro-LEDs [19]. Furthermore, Lee et al. combined the passivation advantages of ALD and PECVD by adopting the double passivation layer structure for blue micro-LEDs with a wavelength of 460∼480 nm [20]. These researches have improved the external quantum efficiency (EQE) performance of the visible micro-LEDs by coatings with sidewall passivation. Nevertheless, they mainly focus on the passivated materials and fabrication processes. There are few investigations on the influence of passivation layer thickness on light extraction efficiency (LEE) [21,22]. Thus, it is necessary to reveal the relationship between the passivation layer thickness and the light extraction efficiency of micro-LEDs for future applications.

In this work, the light extraction properties of green micro-LEDs were systematically investigated by tuning the SiO2 passivation layer thickness in the range of 0∼600 nm. We simulated the light propagating behaviors of the green micro-LED with the tunable passivation thickness, and designed the optimal thickness for efficient light extraction towards the top of the micro-LED. Experimentally, the green micro-LED arrays with different passivation layer thicknesses were fabricated based on parallel laser micro-lens array (MLA) lithography. The influence of passivation layer thickness on current density-voltage (J-V) characteristics, EQE, electroluminescence (EL), and light output power (LOP) of micro-LED devices is extensively explored. These results reveal the light extraction enhancement in a green micro-LED through the optimized passivation thickness, which provides a basis for achieving high-efficiency micro-LEDs beyond the green range by enhancing light extraction efficiency.

2. Theory and experimental details

2.1 Simulation

Finite-difference time-domain (FDTD) simulation was carried out to study light extraction behaviors versus the different passivation layer thicknesses of green micro-LEDs. The size of the mesa structure is designed as 50 µm × 50 µm, which includes a light emitting surface composed of a sapphire substrate, a 2500 nm GaN buffer layer, and a 1500 nm thick n-GaN, 130 nm thick multiple-quantum-wells (MQWs), 250 nm thick electron blocking layer (EBL), 200 nm thick p-GaN contact layer. The SiO2 passivation layer is controllable in the range of 0∼600 nm. The refractive index of GaN, SiO2, and air are 2.3, 1.5, and 1, respectively. Meanwhile, the light extraction efficiency with tunable passivation layer thickness of both SiO2 and Al2O3 was simulated for comparison, where it is found that both these two types of materials exhibited the similar behavior (as seen in Fig. S1). Besides, SiO2 is more popular due to its lower cost and easier fabrication process in large scale, which was selected as prior passivation material in the work. The source was placed in the middle of the interior of the model with the incident wavelength of 560 nm. The simulated domain adopts perfectly matched layer (PML) boundary conditions, fully absorbing the electromagnetic energy. To calculate the light extraction efficiency of green micro-LEDs, a dipole source was laid inside the quantum well to emit light, where a power monitor was placed at the bottom of its output light to obtain the extracted power of light. Due to the positive correlation between the light extraction efficiency and total light source power, the power monitor surrounding the dipole light source can also obtain the total power of the light source.

2.2 Epitaxy

The complete green LED structure was grown on a c-plane sapphire substrate by metal-organic vapor phase epitaxy (MOVPE) shown in Fig. 1(c). The precursors of In, Ga and N are trimethylindium (TMI), trimethylgallium (TMG), and ammonia (NH3), respectively. By controlling the flux and time of precursors TMI, TMG and NH3, the thickness of each layer can be precisely regulated. The whole epitaxial structure is composed of a 2500 nm undoped GaN buffer layer, a 1500 nm Si-doped n-GaN, 130 nm MQWs, 250-nm-thick AlGaN EBL and 200 nm Mg-doped p-GaN in sequence. The carrier concentration of p-GaN and n-GaN can reach 1017∼1018 cm-3.

 figure: Fig. 1.

Fig. 1. (a) Parallel laser MLA lithography machining system. (b) Schematic diagram of array alignment method. (c) The process flow chart for the micro-LED pixel.

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2.3 Lithography

The common lithography technologies include laser direct writing, digital DMD, electron beam, ion beam, and soft lithography [23]. However, the low throughput and defect generation restrict their wide applications. To overcome these issues, we utilized the parallel laser MLA lithography to fabricate large-area green micro-LED arrays [24]. Figure 1(a) shows the parallel laser MLA lithography machining system. The laser was excited at a wavelength of 405 nm with a maximum power of 500 mW, which was incident perpendicularly to the sample surface through MLA after passing through mirrors with a reflectivity of more than 98% and a 20x beam expanding mirror. Through the control of the shutter switch and the moving speed of the platform, the large-area array microstructure processing with flexible and controllable arbitrary patterns is realized, which is favorable for the fabrication of micro-LEDs. As shown in Fig. 1(b), a method of array alignment was proposed based on a parallel laser MLA lithography machining system. The array alignment method comprises three axes mobile stage with a positioning accuracy of less than ±1 µm, a charge-coupled device (CCD) with 1 µm resolution, and a display. The substrate with array structures on the stage moves the Z axis to the focal plane of the CCD detector, and the image will be received by the CCD detector. According to the array structures consistency, the ("cross mark") will coincide with the cross marks of the CCD detector, and then move the substrate to the exposure position to obtain the desired alignment result. Owing to the alignment error of both “cross mark” and array structures caused by the CCD pixel resolution at 1 µm as well as the repeated positioning accuracy error of the displacement platform at ±1 µm, the comprehensive alignment error always exists. In the actual operation process, the lateral error can be controlled within ∼5 µm to meet the alignment requirement of the device fabrication.

2.4 Device fabrication

Briefly, in order to achieve 50 µm × 50 µm mesa array structures, the mask with the positive photoresist AZ5214E (Resemi Corporation) and 100 nm SiO2 was performed for lithography, and the ICP etching method was used to achieve approximately 1330 nm to the n-GaN. Then, according to the deposition rate of 24.6 nm/min, the SiO2 passivation layers with different thicknesses were deposited by PECVD at 300 °C. The 15 µm circular patterns were designed for the fabrication of metal electrodes by secondary alignment lithography. The n- and p-metal contact consisting of 30/200/5 nm Ti/Al/Ti is fabricated by an electron-beam evaporation system. Finally, the manufactured green micro-LED arrays were annealed at 850 °C for 90 s under the nitrogen atmosphere to form ohmic contacts.

2.5 Characterization

The surface and sidewall morphologies of the fabricated micro-LED arrays were observed by a metallographic microscope (KX-4R) and a scanning electron microscopy (SEM, Gemini500) system, respectively. The J-V characteristics were measured by a semiconductor probe station composed of a source meter (Keithley 2410) and a probe station. The electroluminescence (EL) spectra of the micro-LEDs were collected under different operating voltages by a spectrometer (AvaSpace-HSC-TEC), where the fiber was fixed from the top of the device for signal collection. The EQE and LOP of micro-LED were evaluated by a LED photoelectric parameter tester (C1 + MT 200). The test system includes a power supply (Keithley 2636B) and marine optical spectrum card (measuring wavelength range 350∼1000 nm). A 2.5 µm probe was used to inject current, where the integrating sphere was placed on the top and the CCD was used for visual monitoring. The system schematic of the device EQE as well as LOP measurement is shown in Fig. S2 in Supplement 1. During CCD shooting, the overall luminous images captured by the same setting parameters could be collected in one step, and as-prepared samples will be located in the focal plane through manual adjustment, where the collection will be carried out after stabilizing for five seconds for the purpose of consistency. All the measurements were carried out at 300 K.

3. Results and discussion

In order to distinguish the thickness of different passivation layers, SiO2-n is nominated to represent the sample with the corresponding thickness. As shown in Fig. 2(a), a ray-tracing simulation by FDTD was conducted to investigate the light extraction efficiency of the designed green micro-LED structures. The device is without any sidewall passivation layers for the left part of the micro-LED structure. In contrast, the right part is covered with the deposited uniformly SiO2 layers on the p-GaN surface and sidewall. It can be clearly seen that more light is extracted toward the top of the green micro-LED when the passivation layer is adopted in the simulation model. This indicates the passivation layer is efficient for the light extraction of the emitted green light because of the decreased refractive index variation at the interfaces of SiO2/air. Furthermore, the varied refractive index can change the escaping light cone. Thus, it is essential to have a deep understanding of the relationship between SiO2 passivation thickness and light extraction efficiency.

 figure: Fig. 2.

Fig. 2. (a) The simulation model of micro-LEDs. (b) Relationship between the light extraction efficiency and passivation layer thickness. (c) The relationship between the outgoing light angle and the normalized transmissivity. (d) The far-field distribution patterns of micro-LED with different passivation layer thicknesses.

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Figure 2(b) shows the light extraction efficiency of the green micro-LED as the increasing thickness of the SiO2 passivation layer on the p-GaN and sidewall. The light extraction efficiency exhibits periodic oscillatory behavior when the passivated layer thickness increases. For structures SiO2-0, SiO2-90, SiO2-160, SiO2-330, SiO2-430, SiO2-530 nm, the LEE values achieve 8.6%, 12.2%, 9.2%, 9.9%, 11.5%, and 11.0%, respectively. Interestingly, the LEE has the maximum value for structure SiO2-90 nm. After achieving the peaked value, the LEE decreases with the increased SiO2 thickness. And then, the second peak appears as the varied passivation thickness. Due to the light interference cancellation induced by the introduced passivation, which can potentially change light path length and act as an efficient antireflection coating, the transmitted light outside the micro-LEDs could be significantly enhanced. The ideal thickness of the antireflection coating should satisfy the following formula [25]:

$$\begin{array}{{c}} {{d = }\frac{{{(2k\ +\ 1)\lambda }}}{{{4n}}}{(k = 0,1,2)}} \end{array}$$
where d represents the dielectric layer thickness, λ and n are the incident light wavelength and refractive index of the dielectric material, respectively. By substituting the incident wavelength of 560 nm and refractive index of 1.5, the minimum thickness of the antireflection layer was determined to be 93.3 nm. Thus, when k is 0, 1, 2, the passivation thicknesses are determined as 93.3 nm, 280 nm, and 466.6 nm, respectively. It is basically consistent with the simulation results of light extraction efficiency with tunable passivation thicknesses in Fig. 2(b). Furthermore, the far-field normalized transmissivity versus the outgoing light angle of different SiO2 thicknesses coated on the green micro-LED is shown in Fig. 2(c). It can be noted that the SiO2 passivation thickness significantly affects the optical transmissivity of the emitted light within the escaping cone around 23°. By introducing a certain thickness of SiO2 passivation layer on the surface and sidewall of micro-LED device, the interfacial reflection and refraction of green light emitted from quantum well could be significantly reduced, leading to more effectively captured photons transmitted from the device inside. Compared to the green micro-LED without any passivation coatings, the transmissivity intensity of the micro-LED with SiO2 layer is greatly enhanced. For the structure of SiO2-90 nm, the transmissivity of the green light is highest when the escaping cone ranges from 0° to 23°. Moreover, the far-field distributions of micro-LED with different passivation layer thicknesses are presented in Fig. 2(d). The far-field intensity of the passivation layer with 90 nm thickness maintains the maximum value for the outgoing angle of 0∼10°. In a broader range of angles from 0 to 20°, the distributed patterns of the 90 nm thick layer exhibit a uniform and intense light extraction intensity, which is favorable for the efficient light extraction of the micro-LEDs. The enhancement of extracted light distributions can be attributed to the enlarged escaping cone and the antireflection effect.

Based on the simulation results by FDTD, a series of green micro-LEDs with varying SiO2 passivation thicknesses were fabricated. As can be seen in Fig. 3(a), a large-area array of the mesa structure formed, and the size of the individual mesa was 50 µm × 50 µm by spacing at 50 µm. The unit of mesa structure in the array distributes uniformly, indicating the good consistency of the micro-LED fabrication in the experimental processing by MLA lithography. Figure 3(b) shows the cross-sectional morphologies of the mesa structure with the deposited SiO2 passivation layer. Obviously, the SiO2 passivation layer was uniformly deposited on the surface and the sidewall of the green micro-LED. From the inset, the sidewall angle of the mesa can be determined at approximately 23°. Meanwhile, one can notice that a V-shaped concave structure appears in the active region, which is beneficial for reducing current crowding and improving the crystal quality of green LEDs [26,27]. Moreover, Fig. 3(c) shows the optical morphologies of the micro-LED arrays, where both p and n-metal electrodes were in the shape of a circle at the diameter of 15 µm with the accurate position. The results show the advantages of MLA lithography in fabricating large-area and highly uniform micro-LED arrays with excellent reliability.

 figure: Fig. 3.

Fig. 3. (a) Mesa structure array of micro-LEDs. (b) Cross-sectional diagram and sidewall angle of SiO2 passivated samples. (c) Morphology of micro-LED arrays with electrodes.

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To probe the optoelectronic performances of the as-prepared samples with varying passivation thickness for the green micro-LEDs, the J-V characteristics ranging from -5 V to +20 V were first presented in Fig. 4(a). For the micro-LED without the SiO2 passivation layer deposited on the surface and sidewall, the leakage current density achieves 10−7 A/cm2 at a bias of -5 V. While the micro-LED was deposited with the passivation layer, the leakage current density significantly decreases. It can be observed that the device with SiO2-90 nm (the green curve) exhibits a minimum leakage current density as low as 8.85 × 10−11 A/cm2 at -5 V, indicating less leakage current loss by the deposition of SiO2 passivation layer. As the voltage gradually increases to forward voltage, the device for SiO2-90 nm exhibits the lowest threshold value at +2.0 V. However, the threshold voltage rises up to approximately +5.0 V for samples SiO2-0, SiO2-160, and SiO2-330 nm, and +7.0 V for SiO2-430 and SiO2-530 nm, respectively. This demonstrates the better current spreading and higher current density operating at a low voltage of the green micro-LEDs with the SiO2-90 nm passivation layer, undoubtedly leading to increased efficiency at a lower current [28].

 figure: Fig. 4.

Fig. 4. (a) J-V characteristics of micro-LEDs. (b) EQE of micro-LEDs with different SiO2 passivation layer thickness. (c) Light output power of corresponding samples under different current density. (d) Illumination intensity images of micro-LED for different passivation layer thickness under different current density.

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Figure 4(b) represents the normalized EQE of the green micro-LEDs with varying passivation layer thickness under increasing injected current densities. The EQE arises with the increasing current density and decreases sharply after achieving the peaked value under the higher current density for the sample without passivated SiO2 layer (the black curve). However, for all the samples with the passivation layer, the EQE rises up to a higher value and decreases to a relatively high level at the higher injected current density, tending to be stable at a current density of 40 A/cm2. It is noted that the EQE of SiO2-90 nm achieves the highest value among all samples. The enhancement of the maximum EQE value for SiO2-90 nm is 2.8 times higher than that of the SiO2-0 nm. Also, the sample with SiO2-90 nm shows the ability to suppress the efficiency droop ratio of the green micro-LEDs under the high current density. In addition, the EQE peak of the SiO2-160 nm was approximately 43.0% of SiO2-90 nm, which could be attributed to the thicker passivation layer and reduced antireflection effect. For the thicker deposition of 530 nm and 430 nm passivation layers, the EQE peaks appear at higher values than that of SiO2-160 nm, agreeing well with the calculated LEE varying with different thicknesses in Fig. 2(b). This also indicates the light interference cancellation and enhanced light transmissivity.

As the size decreases, the EQE of the micro-LED decreases, whereas the maximum current density that can be borne increases, leading to the improved heat dissipation at high injection current [29]. The LOP of the as-prepared micro-LEDs operates at 6 A/cm2, 10 A/cm2, and 20 A/cm2 with varied passivation layer thickness was analyzed, as illustrated in Fig. 4(c) and (d). One can see that the LOP is gradually improved by increasing the injected current density from 6 A/cm2 to 20 A/cm2. When the injected current density is 20 A/cm2, the LOP of SiO2-90, SiO2-160, SiO2-330, SiO2-430, and SiO2-530 nm achieves 6.74, 3.45, 4.04, 4.14 and 3.97 µW, respectively. However, the LOP of the green micro-LEDs with SiO2-0 nm is extremely low. Compared to the LOP of SiO2-0 nm at a current density of 6 A/cm2, the enhancement could be calculated as 11.23, 5.59, 5.59, 9.95, and 6.50 times for samples with SiO2-90, SiO2-160, SiO2-330, SiO2-430 and SiO2-530 nm, respectively. When the device is injected with a higher current density, the LOP enhancement dramatically increases. The optimized passivation thickness significant increases LOP, which is consistent with our simulation predictions.

Generally, micro-LED is required to operate at a relatively low current density when used for display applications. However, the device inevitably suffers from QCSE at a lower injection current density [30,31]. In order to study the influence of SiO2 passivation thickness on LOP for the future application of micro-LED display, we control the injection current density of the green micro-LED below 6 A/cm2, as observed in Fig. 5(a). A schematic visual diagram was depicted in Fig. 5(a) to explore the LOP for various passivation layer thicknesses in micro-LEDs at a low current density of 0∼6 A/cm2. When the thickness of the SiO2 passivation layer is constant, the LOP increases as the increased current density. On the other hand, the LOP varied with the passivation layer thickness in the condition that the injected current density is constant, which shows a high value at the thickness of 90 nm and 430 nm, and a low value at 0 nm and 160 nm. The micro-LED with SiO2-90 nm deposition was deduced to have better optoelectronic performances due to the efficient antireflection at the interfaces. Thus, the EL spectra of the green micro-LED with SiO2-90 nm passivation layer varying with the increasing voltages were carried out, as shown in Fig. 5(b). It is found that with a forward voltage increase from 10 V to 20 V, the emission wavelength shifts from 512 nm to 507 nm. Meanwhile, the full-width at half maximum (FWHM) was broadened from 18.46 nm to 19.25 nm. Due to the reduced QCSE effect by the increasing carrier injection shielding the influence of the polarization fields, the effective bandgap becomes wider, thereby causing the peaked wavelength blue-shifting [32]. In particular, at a bias voltage of 20 V, the surface and sidewall-passivated green micro-LED shows stability that can maintain functional performance at a high voltage and current density.

 figure: Fig. 5.

Fig. 5. (a) 3D line diagram of passivation thickness, current density, and light output power. (b) EL spectra for the micro-LED with different operating voltages.

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4. Conclusions

In this research, the FDTD simulations were performed to design the well-established simulation model of green micro-LEDs to study the influence of SiO2 passivation layer thickness in the range of 0∼600 nm on the light extraction efficiency. Using the parallel laser MLA lithography technique accompanied by the array alignment and nesting methods, a large number of green rectangular micro-LEDs in the dimension of 50 µm × 50 µm were efficiently fabricated at one-time within the range of 8 mm × 8 mm. The simulation predictions were verified by experimental results, which consistently shows that the light extraction efficiency of micro-LEDs can be improved by optimizing the thickness of the SiO2 passivation layer due to the light interference cancellation at the interface. For the structure of SiO2-90 nm, it has a lower leakage current and higher operating current density, where the maximum EQE could be 2.8 times higher than that of the structure SiO2-0 nm, effectively enhancing the luminous efficiency of the micro-LED.

Funding

National Key Research and Development Program of China (2021YFB3600102); National Natural Science Foundation of China (62135013, 62175203); Fujian Provincial Department of Science and Technology (2020H0006); Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province Applied Research Project (RD2020050301); Natural Science Foundation of Jiangxi Province of China (20212BAB202027).

Acknowledgment

We deeply appreciate the inspiring discussions from Prof. Rong Zhang and Prof. Minghui Hong in Xiamen University.

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.

Supplemental document

See Supplement 1 for supporting content.

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Supplementary Material (1)

NameDescription
Supplement 1       simulation and schematic diagram

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.

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Figures (5)

Fig. 1.
Fig. 1. (a) Parallel laser MLA lithography machining system. (b) Schematic diagram of array alignment method. (c) The process flow chart for the micro-LED pixel.
Fig. 2.
Fig. 2. (a) The simulation model of micro-LEDs. (b) Relationship between the light extraction efficiency and passivation layer thickness. (c) The relationship between the outgoing light angle and the normalized transmissivity. (d) The far-field distribution patterns of micro-LED with different passivation layer thicknesses.
Fig. 3.
Fig. 3. (a) Mesa structure array of micro-LEDs. (b) Cross-sectional diagram and sidewall angle of SiO2 passivated samples. (c) Morphology of micro-LED arrays with electrodes.
Fig. 4.
Fig. 4. (a) J-V characteristics of micro-LEDs. (b) EQE of micro-LEDs with different SiO2 passivation layer thickness. (c) Light output power of corresponding samples under different current density. (d) Illumination intensity images of micro-LED for different passivation layer thickness under different current density.
Fig. 5.
Fig. 5. (a) 3D line diagram of passivation thickness, current density, and light output power. (b) EL spectra for the micro-LED with different operating voltages.

Equations (1)

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d = ( 2 k   +   1 ) λ 4 n ( k = 0 , 1 , 2 )
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