Sub-Micron Monolithic Full-Color Nanorod LEDs on A Single Substrate

The extended reality (XR) display, including augmented reality (AR) and virtual reality (VR), requires ultrahigh-resolution and high-luminance pixel technology. GaN-based micro-LEDs are the most promising for high-density pixel applications. However, it is necessary to simultaneously fabricate full-color R/G/B emitters on a single substrate. Moreover, the efficiency droop at long wavelengths with high-indium InGaN still remains a challenge. The InGaN nanorod has the potential to realize monolithic R/G/B LEDs on a single substrate, and the Al reflector has a light reflectance that can dramatically improve light extraction efficiency. Here, we designed sub-micron monolithic full-color R/G/B nanorod LEDs with an Al core-shell reflector on single chip. The optimal structures for light confinement and vertical light extraction by single InGaN nanorod R/G/B LED structures were identified. The single nanorod with Al core-shell structure dramatically increased the light extraction efficiency, and showed an improvement of more than 20%, especially in the red wavelength. As a result, by introducing a long-length nanorod structure, we have successfully designed a new submicron pixel with full-color R/G/B LEDs operating within 1 μm × 1 μm size. This unique design will be a key factor in enabling the next generation of AR and VR displays that require ultra-small and compact pixels.


I. INTRODUCTION
S UB-MICRON light-emitting diode(LED) devices with enhanced light intensity are required to develop the ultrahighresolution and high-luminance displays for virtual reality (VR) and augmented reality (AR) applications [1], [2], [3]. Currently, LED displays have two approaches based on the type of emission: top-emitting LEDs, emitting vertically upwards from the substrate [4] and bottom-emitting LEDs, emitting toward the substrate [5], [6]. Because of the low aperture ratio caused by the electronic circuit configuration, conventional bottom-emitting LEDs typically have lower light emission efficiency than topemitting LEDs [7], [8]. Top-emitting LEDs, on the other hand, do not care about the electronic circuit configuration-dependent aperture ratio because they use the microcavity effect for smaller pixel display applications [9], [10], [11]. Although the topemitting LED devices have advantages, they are still difficult to apply to ultrasmall pixels, such as for VR or AR applications, due to their low heat dissipation and low light extraction. This problem highly degrades the LED efficiency. Therefore, there is still a need for the development of ultrasmall pixel devices with ultrahigh luminance. III-nitride based materials are suitable for multicolor emitting devices because they have wide range of emission wavelengths from ultraviolet (UV) to visible light and also offer some merit in containing low injection current and high brightness due to their direct bandgap [12], [13], [14], [15]. In particular, InGaN/GaN heterostructure based micro-LED and micro-laser diode (LD) are the most promising for high-resolution and high-density pixel displays. Some research groups have reported lasing structures based on GaN materials [16], [17], [18], [19]. The GaN-based nanostructure is emerging as a single-mode LD due to the small size and the large difference in refractive indices between the nanostructure and background [20], [21], [22]. When light is travelling from one medium to another medium, the angle of refraction follows Snell's law (1).
where the θ i and θ r are the angle of incidence and refraction, the n 1 and n 2 are the refractive indices of the two media, respectively. And two conditions for total internal reflection (TIR) are required: light travels from a dense medium to a less dense medium, and the angle of incidence should be bigger than the critical angle. The critical angle (θ c ) is defined by where the n 1 and n 2 are the refractive indices of the dense media and the less dense medium, respectively. Although the InGaN/GaN based heterostructure has many advantages, there is still a critical issue that the high indium concentration of the InGaN heterostructure causes the efficiency droop in the red wavelength of InGaN due to the large lattice mismatch between GaN and InN [23], [24], [25], [26]. The light efficiency of the LED is determined by the ratio of photons emitted from the LED to the number of electrons passing through the device, so-called external quantum efficiency (EQE). η EQE is determined by [27]  where η IQE is internal quantum efficiency (IQE) which is the ratio of the radiative recombination rate to all recombination rate during transition processes. η LEE is light extraction efficiency (LEE) which is the ratio of the number of photons emitted outside of LED to the number of photons generated inside the active region [28]. The rate of spontaneous emission in an LED is primarily determined by the optical density of state in the active layer. The short radiative lifetime and optical cavity can boost internal quantum efficiency, which is known as the Purcell effect [29]. The IQE is determined by [27], [30] where P active is the generated optical power from the active layer, R r and R nr are the radiative and nonradiative recombination rate, respectively. η LEE is determined by [28] η LEE = P out P active (5) where P out is the optical power emitted from LED device. To enhance the LEE, a few LED structures with metallic reflectors such as Ag, Au were demonstrated previously [31], [32], [33]. In particular, the Al reflector in nanostructure LED showed that can greatly improve the LEE [34]. For electrode, Al could be a best candidate as it exhibits high reflectance over a wide wavelength range [35], [36] and high electrical conductivity. The reflected light from the reflector results in a stronger emission intensity through constructive interference with the spontaneous emission in a nanostructure [37]. While a few basic designs of sub-micron scaled lasing structures based on GaN nanostructures have already been reported, a single nanorod lasing structure using Al core-shell reflector has not yet been presented.
In this study, we designed a sub-micron scaled bottomemitting LED structure with a metal reflector for each red, green, blue (R/G/B) sub-pixel. It consists of an InGaN/GaN nanorod heterostructure covered by a monolithic Al core-shell reflector, which can confine photons in the nanorod and strongly emit the light to the bottom direction of the substrate. We numerically investigated the LEE of Al core-shell nanorod LED using a threedimensional finite-difference time-domain (3D-FDTD) solver. In order to obtain luminous efficiency corresponding to lasing, we numerically investigated reflectance of the Al reflectors with various thicknesses. And optical properties of the Al core shell nanorod LEDs were analyzed under the various structural conditions, such as, the diameters and lengths of nanorods. As a result, it shows that the monolithic Al core-shell reflector greatly improved the LEE of the nanorod structure compared to the conventional nanorod structure in red wavelengths, in particular. Furthermore, we found optimal conditions for a single nanorod LED structure that can transmit and confine R/G/B wavelength ranges simultaneously.

II. RESULTS AND DISCUSSION
Firstly, to find a minimum thickness of Al reflector which can totally reflect the entire visible wavelength range, we designed a single nanorod LED structure with an Al reflector, as shown in Fig. 1(a). The light propagating to the substrate is expected to be totally reflected by the Al reflector, schematically shown in Fig. 1(b). The light reflectance of Al is calculated by the 3D-FDTD simulation using the commercial software package Ansys Lumerical FDTD. The nanorod of diameter 200 nm and overall layer thickness of about 760 nm (n-GaN -450 nm, InGaN multiple-quantum well (MQWs) -60 nm and p-GaN -250 nm) is subjected for simulation. The Al reflector with various thicknesses (10, 20, 40, and 60 nm) was located under the nanorod are also studied. A perfect matched layer (PML) was employed as a boundary condition to assume that light escaping the LED structure is perfectly absorbed without reflection. A transverse electric (TE) polarized dipole source was located in the center of the InGaN MQW with a wavelength range of 450 ∼ 650 nm. TE polarization is known to dominate in the entire visible wavelength range [38], [39]. The transmittance of propagating light is calculated by a transmittance monitor placed below the Al reflector. Reflectance is defined by where T is calculated transmittance in this simulation. The light intensity profiles showed that as the Al reflector becomes thicker, the transmitted light decreases. as shown in Fig. 1(c)-(f). About 10% of the light transmitted through the substrate results in optical loss. As shown in Fig. 1(g), about 27% of light in the blue wavelength range transmitted at 10 nm thick Al, which is attributed to the too thin Al thickness and large refraction angle at specific wavelength. But it showed that the reflectance remarkably increased as the Al thickness increased to 60 nm. In particular, high reflectance was shown near the wavelengths of blue (480 nm) and green (530 nm), suitable for display color. The reflectance of the lower part in the middle for 60 nm thick Al is expected to be ∼99.99%, as shown in inset of Fig. 1(g).
Knowing the reflectance information of nanoscale thick Al in nanostructures is very important for the application of the next generation of optoelectronic devices. As the results, the 60 nm thick Al was employed for the next light extraction simulations in this paper. After confirming the information of the nano-scaled Al reflector, we designed an InGaN/GaN based bottom-emitting LED structure with an Al core-shell reflector to improve the LEE of the nanorod LED. It consists of a nanorod p-i-n heterostructure and an Al core-shell reflector on a 1 μm thick GaN substrate, as shown in Fig. 2(a). The conditions of the nanorod p-i-n heterostructure were the same as those used in the previous simulation. The thickness of the Al core-shell and SiO 2 insulation layer covering the nanorod is defined as 60 nm and 20 nm, respectively, as schematically shown in Fig. 2(b). The Al core-shell reflector is expected to improve the LEE and luminance by confining the light generated in the active layer, resulting in constructive interference and stimulated emission. We investigated the wavelength most strongly emitted from the Al core-shell nanorod structure in the entire visible wavelength range by transmission box while increasing the nanorod diameter from 60 nm to 200 nm in 20 nm units. The notably emitted wavelengths for peak LEE are 541, 573, 610, and 629 nm at diameters of 140, 160, 180, and 200 nm, respectively, as shown in Fig. 2(c). The green wavelength was strongly emitted at a diameter of 140 and 160 nm and the red wavelength was strongly emitted at a diameter of 180 and 200 nm. The peak emission wavelength of the Al core-shell nanorod structure was redshifted as the diameter increased. Because the wavelength which can generate constructive interference becomes long along the increased diameter of the nanorod. The simulation result shows that the diameter of the nanorod considerably affects the LEE of the LED structure. Especially, it is an encouraging solution for the enhancement of the LEE of the high In content InGaN active layer, which has an extremely low LEE due to its poor crystallinity although it can emit in the long wavelength range. The result of the dramatically increased LEE can be utilized in the ≥540 nm wavelength range for the realization of R/G/B pixel in the future display. To find the optimal nanorod structure which can be used for red (∼620 nm), green (∼530 nm), and blue (∼480 nm) pixels, we calculated the LEE of nanorod structures of diameter from 60-200 nm, corresponding peak wavelength are depict in Fig. 2(c). As shown in Fig. 3(a), the values of LEE are 52.5%, 50.8%, 58.8%, 43.6%, and 46.2% at red (λ = 629 nm, diameter = 200 nm), orange (λ = 610 nm, diameter = 180 nm), yellow (λ = 573 nm, diameter = 160 nm), green (λ = 541 nm, diameter = 140 nm), and blue (λ = 465 nm, diameter). As shown in Fig. 3(b)-(f), each light intensity profile showed that light is strongly confined and emitted to the bottom direction at the wavelength of the best LEE of the nanostructures with different diameters. In particular, we obtained the LEE of over 52% at the red (λ = 629 nm) wavelength.
In order to further confirm the impact of the Al reflector, we compared the LEE for bottom-emitting passing through GaN substrate of the Al core-shell nanorod structure and the conventional nanorod structure with a diameter of 180 nm at 6 arbitrary visible wavelengths. As shown in Fig. 4(a), the LEE of the Al core-shell nanorod structure was ∼5% lower than that of the conventional nanorod structure in the blue wavelength range  Fig. 4(a). but increased by ∼20% in the red wavelength range. The Al core-shell reflector induced the redshift of the bottom-emitted peak wavelength.
The speed of light is proportional to the wavelength; that is, light with shorter wavelengths and higher frequencies has a higher refractive index. Therefore, the ratio of total internal reflection can be increased at shorter wavelengths, which have larger refraction angles at the same nanorod diameter. For this reason, as the wavelength increases, optical loss escaping from the side of the nanorod causes a reduction of the LEE in the conventional nanostructure, as schematically shown in Fig. 4(b)(A). In contrast, since all light is reflected inward, regardless of the rate of the diffuse reflection to the outside, the light extraction is simply related to the downward angle in the Al core-shell reflector nanostructure, as schematically shown in Fig. 4(b)(B). And light that cannot escape from the inside is expected to be related to light confinement. Since this behavior of light occurs in a nanorod diameter of several hundred nm, comparable to the wavelength of light, various conditions should be considered for showing periodicity such as the amplitude of the wavelength, the angular velocity, and the diameter and length depended on direction of propagation. As shown in Fig. 4(c)-(f), the light intensity profiles showed that red light at 610 nm is strongly bottom-emitted, whereas green light at 544 nm is weakly bottom-emitted. This result showed that the diameter of the nanorod is optimized at a red wavelength of 610 nm.
We confirmed that the LEE can be effectively controlled by changing the diameters of the nanorod. Furthermore, we have led to the result that the Al reflector can dramatically improve the LEE at the red wavelength of ∼610 nm. Based on these results, we investigated the LEE of nanorods with different lengths to realize a single full-color nanorod that can efficiently emit the R/G/B wavelengths and maximize LEE. In this simulation, we nearly doubled (1460 nm) and tripled (2510 nm) the elongated lengths of the Al core-shell nanorod structures along the z-axis. The thickness of the 60 nm InGaN active layer was fixed. Firstly, we also investigated the LEE of the light escaping from the Al core-shell nanorod structure with diameters of 160 and 180 nm in the entire visible wavelength range by transmission box. Fig. 5(a) showed the periodic light extraction characteristics depending on the wavelengths, as confirmed by the LEE simulations of the nanorod structures with various diameters. The result similar to R/G/B wavelengths consistent with display color was obtained at 1460 nm length and 180 nm diameter. And it showed the best value of LEE increased by ≥10% compared to other conditions. Likewise, we compared the LEE of the Al core-shell nanorod structure and the conventional nanorod structure at 1460 nm length and 180 nm diameter in the peak wavelength ranges of red (∼633 nm), green (∼544 nm) and blue (∼457 nm). The LEE of the Al core-shell nanorod structure increased by ∼7% in the red and green wavelength ranges, whereas it decreased by ∼4% in the blue wavelength range, compared to that of the conventional nanorod, as shown in Fig. 5(b). As shown in Fig. 5(c)-(e), the light intensity profiles showed that the R/G/B lights are strongly confined and propagated along the nanorod waveguide.
More optical loss, from the side of the conventional nanorod, occurred in the long wavelength range than in the short wavelength range. As mentioned earlier, this result is also because the Al reflector compensated for the light leakage with internal reflection. The reason that the LEE in the entire wavelength range is lower than that of nanostructures before the elongation of the length of the nanorod is expected because a part of the light propagating along the nanorod could not escape and was confined to the nanorod. Nonetheless, the designed Al core-shell nanorod structure achieved similar LEE across the entire R/G/B wavelength range, and it will contribute to the advancement of the uniform emission intensity R/G/B pixel targeting future displays. Through the various simulations, for the first time, we successfully designed a nano-scaled photonic device with the smallest R/G/B pixel on the size of ≤1 μm 2 single chip. These results will be the fundamental technology of the next-generation light source structures for future display applications such as AR, VR, and XR.

III. CONCLUSION
For the first time, we designed a sub-micron scaled monolithic bottom-emitting LED structure with Al core-shell reflector. We investigated the optical properties depending on wavelength and structural conditions by using FDTD simulation. The Al coreshell reflector improved the LEE of the nanorod by ∼20% in the visible red wavelengths compared to the conventional nanorod structure at 180 nm in diameter. It is implied that this unique nanostructure can overcome the efficiency droop in the high In content InGaN active layer and that strongly confined light in the nanorod can result in lasing. Furthermore, the elongated nanostructure showed the possibility of the development of the smallest R/G/B pixel with uniform emission intensity on the size of ≤1 μm 2 single chip. The results will pave a new path for bottom-emitting LED devices and will be a key factor in enabling the next generation AR, VR and XR displays that require ultrasmall and compact pixels.