Planar Compound Eye Lens for Enhanced Light Extraction Efficiency in AlGaN‐Based Deep Ultraviolet LEDs

Total internal reflection prevents photons from escaping deep‐ultraviolet (DUV) LED, resulting in serious energy waste and reduced service life. To lift the limitation of extraction ability of AlGaN‐based DUV LEDs, an inspiration was drawn from biological visual systems with wide field, which have obtained highly optimized features through evolution. By reconfiguring planar compound eye lens (PCEL) on the n‐AlGaN surface utilizing bio‐inspired features acquired from praying mantis, light extraction efficiency (LEE) enhancement over 180% is demonstrated both for transverse electric (TE) and magnetic fields by finite difference‐time domain (FDTD) simulation. Owing to its ultrathin planar structure and compatibility of material, PCEL provides a pathway to improve energy utilization efficiency of DUV‐LED utilizing one‐step nanoimprint.


Introduction
Since the outbreak of COVID-19 and signature of Minamata Convention on Mercury, it is urgently required to develop an environmentally friendly deep-ultraviolet (DUV) light source.[3][4] However, AlGaN-based LEDs still suffer from relatively low external quantum efficiency (EQE), especially for the wavelength shorter than 280 nm.According to tremendous efforts, the EQE has been mainly increased by improving crystalline defects and light extraction efficiency (LEE).Most of these defects originate from high dislocation densities of Al x Ga 1Àx N active layers in the epitaxy growth processes and act as nonradiative recombination centers, leading to poor radiative efficiencies of multiple quantum wells (MQWs).Although the defects can be improved by adopting high quality substrate materials or optimizing the epitaxy growth processes, [5,6] the threading dislocation density in AlGaN MQWs tends to increase with the proportion of Al compositions, which results in low radiative efficiency for deep ultraviolet region with high Al compositions.Furthermore, LEEs of these DUV-LEDs are considerably lower than visible-light LEDs due to the anisotropic optical property of AlGaN MQWs and intense DUV absorption in p-GaN ohmic contact layer.Particularly, the polarized light with transverse magnetic (TM) field, which mainly propagates in the lateral direction becomes dominant as emission wavelength decreases.Owing to the large refractive index contrast between AlGaN and air, the electric field components with emission angles beyond the critical angle are unable to escaping from LED structure by total internal reflection (TIR).Hence, a large fraction of generated photons is trapped inside the high-index material of DUV-LEDs, and converts to a lot of heat by materials absorption, resulting in serious energy waste and a reduced service life.Substantial efforts have been proposed to enhance LEEs of the DUV-LEDs, mainly by reducing absorption of materials and by breaking boundary conditions at the air/dielectric interface to attenuate TIR, such as utilizing p-AlGaN with low absorption, [7][8][9] Micro/nano structured LEDs, [10][11][12][13] patterned sapphire substrate (PSS), [14][15][16][17][18] inclined/rough sidewall, [19][20][21] plasmonic nanoparticles, [22][23][24][25] optimized metallic reflector etc. [26][27][28][29] However, the AlGaN-based deep ultraviolet LEDs still suffer from limited LEE with multiple fabrication steps.
To lift the limitation of extraction ability of AlGaN-based deep ultraviolet LEDs, we draw inspiration from biological visual systems with wide field, which have highly optimized features through evolution.By reconfiguring planar compound eye lens (PCEL) on the n-AlGaN surface utilizing bio-inspired features acquired from a praying mantis, LEEs of DUV-LEDs are significantly enhanced both for TE and TM fields by utiziling 3D finite difference-time domain (FDTD) simulation.Owing to its ultrathin planar structure and compatibility of material, the PCEL provides a pathway to improve energy utilization efficiency DOI: 10.1002/adpr.202300309Total internal reflection prevents photons from escaping deep-ultraviolet (DUV) LED, resulting in serious energy waste and reduced service life.To lift the limitation of extraction ability of AlGaN-based DUV LEDs, an inspiration was drawn from biological visual systems with wide field, which have obtained highly optimized features through evolution.By reconfiguring planar compound eye lens (PCEL) on the n-AlGaN surface utilizing bio-inspired features acquired from praying mantis, light extraction efficiency (LEE) enhancement over 180% is demonstrated both for transverse electric (TE) and magnetic fields by finite difference-time domain (FDTD) simulation.Owing to its ultrathin planar structure and compatibility of material, PCEL provides a pathway to improve energy utilization efficiency of DUV-LED utilizing one-step nanoimprint.and service life of DUV-LED utilizing one-step nanoimprint.Moreover, the functional biomimetic method utilizing bioinspired features have potential applications on wide field of vision, structured illumination, and bionic structure.

Bio-Inspired Features
Specialized organs of creatures usually have extremely high energy utilization efficiency through millions of years of evolution and natural survival law.Here, the Tenodera sinensis which living in east Asia with ultraviolet-sensitive vision is selected for investigation.Its compound eyes exhibit extraordinary performance on wide-field optical imaging, especially for the near-distance information collection under low-light intensity environment. [30,31]According to the principle of optical reversion in linear systems, biomimetic structures based on the features of compound eyes have great potential to improve energy utilization efficiency of DUV-LED.We reconfigure the biological characteristics to enhance LEE of DUV-LED utilizing metasurface.As a planar integrated optics platform, metasurface consisting of ultrathin plasmonic or dielectric resonators have been designed to exhibit exotic electromagnetic properties and functionalities, which significantly enhanced the control of the propagation of electromagnetic waves, [32] and developed various applications such as metalenses, [33] subdiffractional imaging, [34] optical sensing, [35] and so forth.
The microscopic images of the compound eye of Tenodera sinensis are illustrated in Figure 1b,c.Its compound eye is composed by thousands of uniformly arranged ommatidia.And each ommatidium consists of a corneal lens focusing light on its receptor cells.By incorporating the morphologies of ommatidia and their compact arrangement, the biological features of Tenodera sinensis's compound eyes can be summarized as micro-lenses arranged on a curved surface with honeycomb lattices.To transfer these features on a flat substrate, we design a honeycomb array consisting of eye-like microstructures, which is depicted in Figure 1e.Its geometry is formed by two stackable semi-ellipsoids with different eccentricities and dimensions, which can be optimized by FDTD calculation.The eccentricities of semi-ellipsoids are defined as η ¼ ðr L À r S Þ=ðr L þ r S Þ, where r L and r S are the lengths of major and minor axes for each ellipsoid, respectively.
However, although these features may have the potential to improve LEE, it is still a significant challenge to accurately fabricate the eye-like microstructures utilizing existing processing technology.To avoid this trap, we further reconfigure the bio-inspired features on dielectric/air interface utilizing PCEL, as shown in Figure 1f.Owing to its ultrathin planar structure and compatibility of material, the metasurface-based configuration has inherent advantages to be integrated in DUV-LED utilizing one-step nanoimprint.

Transmission Properties of Interface
As a wide band gap semiconductor with a high refractive index, Al x Ga 1Àx N suffers from low light extraction because of its minor critical angle of TIR.TIR prevents photons from escaping the constituent high-index materials.Micro/nano structures create new outcoupling channels for light by breaking the local boundary conditions at the air/dielectric interface, releasing a portion of otherwise trapped photons into air, as shown in Figure 2a.The transmission spectra T at different incident angles θ are investigated, providing quantitative comparisons of light extraction for different structures, as summarized in Figure 2b-d.The honeycomb-arranged structures with the same period p = 1.91 μm are adopted to calculate transmission spectra escaping from the AlGaN substrate.For the AlGaN material with a refractive index n = 2.6, its critical angle θ c is equal to 22.6°.Thus, most of photons generated from MQWs are unable escape into the air.As a typical structure employed in the LED research, a honeycomb array consisting of hemispheric microstructures provides a wide-range transmission enhancement beyond the critical angle.However, transmission obviously decreases for light with small incident angles, which is caused by TIR on the off-centered arc surface of hemisphere, as shown in Figure 2b.
By comparison, the optimized eye-like microstructures exhibit a more effective improvement of light extraction, as shown in Figure 2c.Although its transmission enhancement cannot cover such a wide range as the hemispheric dielectric array beyond critical angle, and the light with a small incident angle achieves a high transmittance.And, its performance is mainly determined by eccentricities η of the two stackable semi-ellipsoids.Here, the optimized eccentricities of 0.55 and 0.58 respectively for the bottom and upper semi-ellipsoids are chosen for simulation.Eyelike microstructures are helpful to improve the light extraction, but the machining of irregular curved surface in nanoscale is an enormous challenge.
To obtain the similar bio-inspired function, we reconfigure the features utilizing a planar dielectric metasurface.By etching ultrathin nano patterns on AlGaN surface, the transmission spectra exhibit further enhancement of light extraction, especially for the incident angles beyond critical angle compared with that of Meta-I.The field distributions as shown in Figure 2e-h demonstrate the gradual improvement of light extraction.The plane wave is adopted to illuminate the substrate with an incident angle θ i = 25°.And wavelength of incident light is set as 280 nm.Because the incident angle is beyond the critical angle, no photons can escape from the substrate, as shown in Figure 2e.The micro/nano structures couple the light to air by breaking the TIR condition in local space.As shown in Figure 2f, partial light couples to air from the localized curved surface of the hemispheres.However, its enhancement efficiency is limited because of the unsuitable curvature.By introducing the bio-inspired eye-like structure, the coupling region of interface obviously increases, leading to release more photons into air, as shown in Figure 2g.Besides, the reconstructed metasurface PCEL exhibits similar field regulation with Meta-I owing to its effective phase modulation and light scattering of nanoparticles, as shown in Figure 2h.All FDTD simulations were performed based on a commercialized software (LUMERICAL, FDTD Solution).

Reconfiguration of Planar Compound-Eye Lens
To reconfigure the biomimetic structure Meta-I, nanorods with equal ultra-thin thickness are adopted to form the PCEL.Each nanorod modulates local field as an optical antenna by exciting waveguide mode.By arranging different nanorod structures in an array with honeycomb lattice as shown in Figure 3a, space modulation of light field can be realized on the flat substrate surface.Figure 3b shows the transition spectra of nanorods with different diameters R, indicating high transmissivity (>82%) in a broad spectral range.Meanwhile, each kind of nanorod introduces different phase delay covering the range from 0 to 2π, as shown in Figure 3c.Thus, the AlGaN-based nanorods provide a platform to modulate local field effectively for DUV light.The optical characteristics of nanorods were calculated with the following parameters: d = 100 nm, h = 300 nm.And, light beams incident normally from the AlGaN substrate onto the nanorods.The diameters R of nanorods range from 40 to 90 nm to realize modulation of local fields.
The desired phase distribution, which is essential to reconstruct the planar metasurface, can be calculated from the biomimetic structure.The structural profile of Meta-I has an optimized curvature for external coupling compared with hemisphere.And, the corresponding phase distribution φðx, yÞ of the curve-shaped profile can be calculated as: where f z ðx, yÞ is the spatial distribution of the curve-shaped profile; n d and λ 0 represent the refractive index of dielectric and operating wavelength, respectively.Figure 3d shows the structural profiles (top) and their corresponding phase distributions (bottom) of the curve-shaped structures along x direction.By matching the desired phase distribution φðx, yÞ and appropriate local phase shifts of nanorods, the metasurface with biomimetic function can be reconstructed by a nanorod array.On this basis, one unit cell of the PCEL is reconfigured for the operating wavelength λ 0 = 280 nm, as shown in Figure 3e.Owing to its periodic distribution, the PCEL can be simply formed utilizing tightly arranged units with a honeycomb lattice, as shown in Figure 3f.

LEE Improvement of DUV-LED
The frequently used flip-chip LED structure [36,37] is adopted to investigate the LEE enhancement, as shown in Figure 4a.As the TIR exists extensively at the interface between the dielectrics with different refractive indices, the substrate-free AlGaN-based structure with thin epitaxial layers is selected to accelerate the simulation process.The MQWs layer with 100 nm thickness is sandwiched between AlGaN layers with n/p-type doping.
The thicknesses of the n-AlGaN and p-AlGaN layers are assumed to be 1 and 0.1 μm, respectively.In order to enhance ohmic contact, the p-GaN and metal electrodes are essential for the flipchip.And, the thicknesses of the p-GaN and metal electrodes are 100 and 305 nm, respectively.Wherein, the metal electrodes are composed by 5 nm Ni and 300 nm Al, showing a reflectivity over 67% in the DUV band.Apart from the TIR, the material absorption in p-GaN and MQWs layers tend to restrict the LEE of DUV-LED intensely, especially for the TM-polarized light.
The absorption coefficients of the MQWs and p-GaN layers are assumed to be 1 Â 10 3 and 1.7 Â 10 5 cm À1 , respectively.And, their corresponding refractive indices are set as 2.6 and 2.9, respectively. [36]wing to the periodic structure of the biomimetic structures, several units of compound eye can be picked to economize time of computation in the LEE simulation. [37,38]Boundary configuration in the LEE simulation was adopted: perfect mirror for lateral dimension and perfectly matched layer (PML) for vertical dimension respectively, as shown in Figure 4b.And the perfect mirror configuration has been frequently employed to extend the propagation of electromagnetic fields by 100% reflection.The DUV light emits from dipole sources laying in the center of MQWs active region with a peak wavelength 280 nm.The polarized direction of dipole source either parallel or perpendicular to the MQWs plane indicates the TE or TM mode, respectively.The monitor is placed 1 μm above n-AlGaN surface to calculate LEE, avoiding the influence caused by evanescent wave.Thus, photons exciting from MQWs region propagate in multiple directions, and have opportunities to escape from n-AlGaN/air interface directly, or after several times of reflection by perfect mirror boundaries and NiþAl reflector.Otherwise, the photons trapping inside the DUV-LEDs are absorbed by lossy materials.
On this foundation, the LEEs of DUV-LEDs with different surface patterns can be calculated through 3D-FDTD.The PCEL is reconfigured by corresponding phase distribution φðx, yÞ of curve-shaped profile, its performance is mainly determined by the eccentricities η of eye-like microstructure Meta-I.Figure 4c shows the corresponding LEEs of PCELs reconstructed by eye-like microstructures with different eccentricities, where α and β indicate the eccentricities for bottom and upper semiellipsoids, respectively.And, the subscripts TE and TM indicate the polarized directions of dipole sources.In particular, the PCEL is reconstructed by a flat surface without phase variation when η = 1, its LEEs decrease obviously both for TE and TM modes.And, the optimized performance appears when eccentricities are equal to 0.55 and 0.58 for bottom and upper semi-ellipsoids, respectively.Figure 4d shows the comparison of LEEs with different surface patterns.The LEEs of DUV-LED with unstructured plate are 3.34% and 0.48% for TE and TM modes, fitting well with the previous works. [36,39]By etching optimized PCEL on the n-AlGaN surface, the LEEs rise to 9.37% and 2.1% respectively for the TE and TM modes, indicating the corresponding improvement as 181% and 337%, respectively.As expected, the LEEs of PCEL are quite similar with Meta-I, especially for the TE mode (the deviation is 1.7%), indicating the superiority of functional reconfiguration by metasurface.
Figure 5 shows the distributions of normalized field intensity at the XZ-plane cutting the middle of y-axis for TE and TM modes, respectively.Compared with the unstructured LED under the TE source as shown in Figure 5a, the coupling regions for light significantly increase at the n-AlGaN/air interface, especially for the bio-inspired structures Meta-I as shown in Figure 5e,g.This can be mainly attributed to efficiency improvement of phase modulation originating from the highly optimized features by biological evolution.Because the PCEL is constituted by discontinuous antenna arrays, its corresponding field modulation is not as homogeneous as Meta-I.However, its LEE improvement is not significantly affected for the TE mode.As the field modulation efficiency significantly decreases with the incident angles θ, the outcoupling field becomes disorganized, as shown in Figure 5f,h.In the case, waveguide mode is difficult to excite by optical antenna, and scattering turns to be dominant for the TM mode.Owing its rougher surface morphology, more photons release into air by scattering of nano antennas.

Conclusion
We drew inspiration from biological visual systems with wide field, and reconfigured the highly optimized features with metasurface to enhance LEE of DUV-LEDs.By etching PCEL on the n-AlGaN surface utilizing bio-inspired phase distribution, LEEs are significantly enhanced both for the TE and TM modes.Owing to its ultrathin planar structure and compatibility of material, PCEL provides a pathway to improve energy utilization efficiency and service life of DUV-LED utilizing one-step nanoimprint.Moreover, the functional reconfiguration method utilizing bioinspired features has potential applications on wide field of vision, structured illumination and bionic structure.

Figure 1 .
Figure 1.Bio-inspired design of PCEL for light extraction.a) Photo images of a Tenodera sinensis, b) Microscopic image and c) enlarged view of its compound eye, d-f ) the design flow of honeycomb-arranged compound eye lens; d) Hemisphere, e) Meta-I, f ) PCEL.Their corresponding cross-sections of unit cells are illustrated in dashed frames.

Figure 2 .
Figure 2. FDTD simulation for the bio-inspired light extraction.a) The diagram of light transmission from high refractive index material (AlGaN) to air.b-d) Transmission spectra of light from the substrate into air at different incident angles θ; b) Hemisphere, c) Meta-I, d) PCEL.The white dashed line indicates the critical angle of TIR θ c = 22.6°.e-f ) Field distributions E y for e) AlGaN f ) Hemisphere, g) Meta-I, h) PCEL.The incident angle is chosen as θ i = 25°.

Figure 3 .
Figure 3. Reconfiguration method of bio-inspired features utilizing planar dielectric metasurface.a) Nanorods with honeycomb lattice.b-c) optical characteristics of nanorods with different diameters R. b) transmitted intensity, c) phase.d) Structural profile (top) and corresponding phase distribution (bottom) of the curve-shaped structures.e) Top view of single planar eye lens.f ) Top view of PCEL.

Figure 4 .
Figure 4. Simulation scheme of the DUV-LED.a) A flip-chip DUV-LED structure, b) cross-sectional view of a 3D-FDTD computational model, c) the LEEs depend on eccentricities of reconfigured semi-ellipses.d) Corresponding LEEs for the structures with different surface patterns.