Directional high-efficiency nanowire LEDs with reduced angular color shift for AR and VR displays
1 Introduction
High resolution density, wide field of view (FoV), lightweight and compact formfactor, and low power consumption are demanding requirements for augmented reality (AR) and virtual reality (VR) displays1. Compared to active-matrix liquid crystal displays (LCDs) and organic light-emitting diode (OLED) displays, microLED (μLED) is attracting more ·attention due to its high peak brightness, excellent dark state, high resolution density, small formfactor, and long lifetime2-5. Recently, JBD (Jade Bird Display) announced a 0.22-inch full-color μLED panel with 5K pixels per inch (PPI) by monolithic integration, and the red, green, and blue (R, G, B) sub-pixel pitch is only 2.5 μm. At 2022 Touch Taiwan, PlayNitride also exhibited a 0.49-inch full-color µLED demo with 2.5-µm subpixel size by quantum-dot color conversion and sub-pixel rendering. However, to match with human visual acuity which is 60 pixels per degree (PPD), a PPI of 6.7K is required for a 0.3-inch display panel to offer 40° FoV for AR applications6. To reduce the pixel size further, the increased sidewall defects would dramatically decrease the internal quantum efficiency (IQE), which in turn increases the power consumption7-10. In addition, producing efficient GaN based green and red μLEDs remains a technical challenge11.
Nanowire LEDs show great potential for achieving high resolution density and high external quantum efficiency (EQE) at the same time12-14. In 2018, Aledia reported a nanowire LED12 whose EQE is independent of pitch size when the pitch size is reduced from 1000 μm to 5 μm. For nanowire LEDs with submicron diameter, the IQE can still achieve 58.5%15 and the vertical structure functions as a waveguide to effectively couple the light out16. Additionally, the out-of-plane design can effectively enhance dopant incorporation17, 18, increase heat dissipation19, reduce dislocation density20, 21, and support multi-color monolithic integration22-24. Among different nanowire structures, InGaN/GaN dot-in-wire hexagonal LED is attractive due to its diameter-dependent emission wavelength and excellent electrical performance25. Remarkably, the emission wavelength of the InGaN/GaN nanowire LED depends on its diameter due to the shorter lateral diffusion length of Indium adatom than GaN adatom26. In comparison with small diameter nanowires, the large diameter LED exhibits a reduced Indium adatom incorporation and, therefore, a smaller percentage of Indium existing in its active region, which in turn leads to a shorter emission wavelength. Thus, a full-color display can be achieved by solely changing the nanowire’s diameter. However, these sub-wavelength nanowires exhibit different angular radiation patterns in the far-field, leading to a noticeable angular color shift27. Additionally, the size-dependent waveguide modes are excited in each nanowire so that each one has a different outcoupling efficiency to the environment28. For AR/VR applications, a directional light engine is preferred due to the small etendue of human eye pupil29, 30 whose accepting cone is typically within ±20°. Therefore, the geometry of the nanowire should be optimized to achieve matched radiation patterns for the three primary colors, high light extraction efficiency (LEE), and narrow angular luminance distribution simultaneously.
In this paper, we optimize the InGaN/GaN nanowire LED geometry by 3D dipole cloud through a commercial wave optics simulation software Finite-Difference Time-Domain (FDTD, Ansys inc.). Firstly, we match the InP nanowire’s angular distribution results from 2D dipole cloud simulation with measurement and compare it with traditional central dipole simulation method to validate the accuracy of the model. Secondly, we calculate and analyze the radiation pattern, color gamut, angular color shift, and LEE of full-color InGaN/GaN nanowire LEDs by 3D dipole cloud. Finally, we optimize the nanowire LED by geometrical engineering. After optimization, the angular color shift within the ±20° viewing cone is consistently lower than the human eye’s just-noticeable difference, and the angular full width at half maximum (FWHM) of [blue, green, red] nanowire LEDs is reduced from [48°, 47°, 35°] to [37°, 33°, 24°], while the effective LEE of RGB nanowire LEDs is increased by 7.8%, 36.2%, and 7.4%, respectively.
2 Results and discussion
2.1 Angular distribution matching of InP nanowire LED
Fig. 1. (a ) 3D-FDTD InP nanowire LED simulation schematic. (b ) Simulated far-field radiation patterns of InP nanowire LED. The experimental data (black curve) included for comparison are from ref.31.
2.2 Full-color InGaN/GaN simulation model
Our multicolor single InGaN/GaN dot-in-nanowire LED model is built based on Ra’s experimental results25. As indicated in
Fig. 2. (a ) Schematic of FDTD simulation model in x-z plane. (b ) Top view of blue hexagonal nanowire LED. (c ) Measured EL spectra of single nanowire LEDs with different diameters from ref.25.
In x-y plane, due to the hexagonal structure, dipoles are divided into two directions: short axis and long axis, which are defined by inscribed circle and circumscribed circle, respectively. During each simulation, the long axis dipoles are matched with x-axis initially. Then, the short axis dipoles are matched to x-axis by simply rotating the structure by 30°. Here, we denote this axis dependence to be L and S. Each adjacent dipole is separated by 50 nm. For an example of blue nanowire LED shown in
2D Angular distribution and LEE calculation
From FDTD 2D power monitor, the far field distribution A as a function of (θ, φ) is calculated for each wavelength λ, polarization state p (I or O), simulation axis a (L or S), and dipole position (x, z). Firstly, the wavelength and polarization dependencies can be eliminated by considering the spectral average of the source38:
where θ is the polar angle, φ is the azimuthal angle, and S(λ) is the emission spectrum. The simulation axis dependence can be eliminated by separating A1 into long-axis dipoles and short-axis dipoles. In addition, the position independent angular distribution is calculated by integrating the active area in x-y plane and then summing the results together from each active layer. The position-averaged angular distribution for long axis (A2L) and short axis (A2S) can be calculated as:
where RL and RS represent the radius of long-axis dipoles and short-axis dipoles, respectively. Note that in
where k describes the in-plane rotation.
The LEE of an LED is defined by the ratio of the emitting power and dipole power. For each dipole, the LEE can be calculated as:
where PE is the total power received by the large emission box monitor and PD is the total power calculated by the small dipole box monitor as shown in
The position-averaged angular distributions for long- and short-axis dipole responses are:
Here, the short-axis dipole response is normalized by the inscribed circle area because each LEE is calculated separately. The total LEE is the summation of both axis dipole responses:
where BL=
For AR applications, we define the effective LEE to be the light received within ±20° in the far-field because only the extracted light within this accepting cone can be received by the imaging system. Therefore, the wavelength and polarization state independent effective LEE in
where r is the ±20° spectral coefficient which is calculated as:
The calculation of the rest part is identical to the total LEE as shown in
2D Angular distribution and angular color shift
Fig. 3. (a –c ) Normalized 2D angular distribution for (a) blue, (b) green, and (c) red LEDs. (d ) Normalized 1D angular distribution when azimuthal angle φ=0°.
Fig. 4. (a ) Simulated color triangle of the GaN/InGaN nanowire LED display and CIE coordinates of 18 reference colors at 0° viewing angle. (b ) Simulated color shift of 18 reference colors from 0° to 20° viewing angle. Inset: Simulated average color shift from 0° to 30° viewing angle.
2.5 LEE and near-field distribution maps
According to
2.6 Optimization
For such nanowire LEDs, the angular distribution and LEE are highly dependent on three factors: 1) n-GaN/p-GaN thickness, 2) p-GaN capping layer thickness, and 3) nanowire diameter. The n-GaN/p-GaN thickness determines the interference between the dipole in MQW and the reflection from the substrate, air, and Ti mask; the p-GaN capping thickness decides the outcoupling efficiency, and the diameter controls possible waveguide modes in the nanowire. Since the emission wavelength is highly dependent on the diameter, we focus on optimizing the first two factors. Considering the real application that all electrodes are fabricated at the same height, the main bodies of all nanowires (except the capping) are kept at the same height. In other words, n-GaN and p-GaN hexagonal prism (except the capping) change simultaneously, resulting in a varying vertical position of active layers. Thus, the 2-dimensional optimization is performed by sweeping the vertical position of the active layers with a 10-nm step and thickness of p-GaN capping from 0 to 300 nm with a 30-nm step (
Fig. 5. (a –c ) 2D colormap of angular FWHM as a function of n-GaN thickness and p-GaN capping height: (a) blue, (b) green, and (c) red nanowire LEDs. (d –f ) 2D colormap of effective LEE as a function of n-GaN thickness and p-GaN capping height: (d) blue, (e) green, and (f) red nanowire LEDs.
Based on the optimized geometry, we repeat the simulation of each case by 3D dipole cloud. Compared to the results in
Fig. 6. (a –c ) Normalized 2D angular distribution for optimized (a) blue, (b) green, and (c) red LEDs. (d ) Comparison of normalized 1D angular distribution between unoptimized (solid lines) and optimized (dashed lines) nanowire LEDs.
If the blue and green InGaN/GaN nanowire LEDs can achieve 58.5% IQE15 and red nanowire LED can achieve 32.2% IQE40, then the corresponding effective EQE for AR applications will be blue = 5.9%, green = 15.0%, and red = 10.6%. For µLEDs, its EQE decreases as the mesa size decreases due to sidewall defects and surface recombination. This dependency can be relieved by the potassium hydroxide (KOH) passivation treatment on the sidewall41, 42, while this method still requires validation for mass production. In comparison with the size-dependent blue9, 43 and green InGaN µLED43-47 and assuming 100% of the produced light can be coupled into the imaging system, our blue nanowire LED shows a better performance than µLED whose mesa size is smaller than 10 µm as shown in
Fig. 7. Comparison between calculated effective EQE of nanowire LED (horizontal dash lines) with measured EQE of (a ) blue InGaN µLEDs from ref.9,43, (b ) green InGaN µLEDs from ref.43-47 and (c ) red AlGaInP µLEDs from ref.48 as a function of mesa diameter. Vertical dash lines: EQE of µLEDs with 10-µm mesa size.
In contrast to
Fig. 8. (a ) Simulated angular color shift of 18 reference colors from 0° to 20° after optimization. (b ) Simulated average color shift from 0° to 30° viewing angle after optimization.
3 Conclusions
In conclusion, we have optimized full-color InGaN/GaN nanowire LEDs for AR/VR applications by 3D dipole cloud simulation. The simulation method is validated by matching with previous experimental data. By removing the p-GaN capping and modifying the position of active layers, the angular color shift within ±20° viewing cone is suppressed dramatically and the angular FWHM of [blue, green, red] nanowire LEDs is reduced from [48°, 47°, 35°] to [37°, 33°, 24°], respectively, which is favorable for near-eye displays. Meanwhile, the effective LEE of blue, green, and red is enhanced by 7.8%, 36.2%, and 7.4%, respectively.
4 Acknowledgements
The UCF group is grateful for the financial support of a.u.Vista Inc., and En-Lin Hsiang for valuable discussions.
Y. Z. Qian proposed the original idea and led the project. Z. Y. Yang helped to calculate color gamut and angular color shift. S. T. Wu supervised the project and edited the manuscript.
The authors declare no competing financial interests.
Supplementary information for this paper is available at
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Article Outline
Yizhou Qian, Zhiyong Yang, Yu-Hsin Huang, Kuan-Heng Lin, Shin-Tson Wu. Directional high-efficiency nanowire LEDs with reduced angular color shift for AR and VR displays[J]. Opto-Electronic Science, 2022, 1(12): 220021.