Single-step-fabricated disordered metasurfaces for enhanced light extraction from LEDs

While total internal reflection (TIR) lays the foundation for many important applications, foremost fibre optics that revolutionised information technologies, it is undesirable in some other applications such as light-emitting diodes (LEDs), which are a backbone for energy-efficient light sources. In the case of LEDs, TIR prevents photons from escaping the constituent high-index materials. Advances in material science have led to good efficiencies in generating photons from electron–hole pairs, making light extraction the bottleneck of the overall efficiency of LEDs. In recent years, the extraction efficiency has been improved, using nanostructures at the semiconductor/air interface that outcouple trapped photons to the outside continuum. However, the design of geometrical features for light extraction with sizes comparable to or smaller than the optical wavelength always requires sophisticated and time-consuming fabrication, which causes a gap between lab demonstration and industrial-level applications. Inspired by lightning bugs, we propose and realise a disordered metasurface for light extraction throughout the visible spectrum, achieved with single-step fabrication. By applying such a cost-effective light extraction layer, we improve the external quantum efficiency by a factor of 1.65 for commercialised GaN LEDs, demonstrating a substantial potential for global energy-saving and sustainability.

3. An Al layer was deposited on the PDMS.
4. After deposition of Al, the heated PDMS was cooled to ambient temperature by keeping the PDMS in the chamber for more than 30 min and venting to atmosphere.
5. The PDMS replica was formed by pouring PDMS materials over the buckled PDMS master and by curing at 100 o C for 1 h.
6. The PDMS replica was peeled off the PDMS master.
7. Second deposition of a 10-nm-thick Al layer on the buckled PDMS replica.
8. The buckling pattern of the replica was transferred to a glass substrate using UV curable resin with UV curing for 10 min.
9. The third deposition of a 10-nm-thick Al layer 2. The coated PDMS was cured at 100 o C for 1 h.
3. An Al layer was deposited on the PDMS.
4. After deposition of Al, the heated PDMS was cooled to ambient temperature by keeping the PDMS in the chamber for more than 30 min and venting to atmosphere.
5. The PDMS replica was formed by pouring PDMS materials over the buckled PDMS master and by curing at 100 o C for 1 h.
6. The PDMS replica was peeled off the PDMS master.
7. Second deposition of a 10-nm-thick Al layer on the buckled PDMS replica.
8. The buckling pattern of the replica was transferred to a glass substrate using UV curable resin with UV curing for 10 min.
9. The third deposition of a 10-nm-thick Al layer

Supplementary Note 2: Microstructures on the lantern cuticle of the fireflies
The firefly samples were treated under sonication to remove contaminant and further infiltrated with 2.3 mol/L sucrose overnight. The firefly samples were washed in distilled water to remove sucrose and then dehydrated through ethanol solutions of 50%, 70%, 90%, and 95% (vol/vol) twice for 10 min each and 100% three times for 10 min. Subsequently, the sample was treated with hexamethyldisilazane (HMDS; EMS) and air-dried overnight.
To observe the microstructures of the sample by using SEM, the gold thin layer was coated on the sample surface using thermal evaporation method. The prepared sample were then attached to a copper SEM stub by using carbon tape. A high-resolution field-emission scanning electron microscope (HITACHI S4800) was used for analyzing the nanostructures of firefly lantern as shown in Supplementary

Supplementary Note 3: Investigation of the impact of periodicity and particle size in light extraction
In the manuscript, the periodicity Λ is selected as 230nm (half of the wavelength blue light) and the particle size d is selected as 100 nm. To provide a comprehensive picture, we provide additional investigation to show how the periodicity and particle size impact the light extraction beyond the critical angle. For simplicity but without loss of generality, we investigate 2D periodic structures without disorder. Figure S4 summarises the influence of the periodicity at different incident angles above the critical angle. With the decrease of the periodicity, a blue shit of the transmission spectra is observed. Meanwhile, additional region with enhanced transmission is observed (comparing Figure S4c and b). Similarly, Fig. S5 summarises the influence of the periodicity at different incident angles above the critical angle. A blue shift of the transmission spectra is observed as the particle size decreases, due to the scalability of Maxwell's equations. With the variation of the size, regions with enhanced photon extraction are introduced and shifted, similar to the case of varying periodicity. Due to the complexed relationship between light extraction and periodicity/size even in 2D periodic structures, we directly optimise the metasurfaces from experiments, as shown in Supplementary Note 6.

Supplementary Note 4: Investigation of the impact of disorder in light extraction
Here we investigate how the magnitude of the fluctuations in size (∆ siz ) and position (∆ pos ) influences the transmission T TIR beyond total internal reflection. Transmission spectra at three different wavelengths are simulated, with the results summarised in Fig.  S6. To clarify the effect of disorder, we demonstrate the variation between the disordered and ordered structure, ∆T = T TIR −T TIR,0 . T TIR,0 is the transmission spectrum of ordered structure with the particle size of 100nm and a period of 230 nm. The incident angle is fixed to 32 o . The results are averaged from three different random sets. The disordered-induced transmission change ∆T has a strong dependence on the wavelength. While the disorder improves the transmission at 500nm (Fig. S6c), the enhancement at 400nm (Fig. S6a) or 450nm (Fig. S6b) is observed in specific regions with optimised values of ∆ siz and ∆ pos . Nevertheless, some regions with transmission enhancement (reddish-coloured area) coincide at three different wavelengths, illustrating a broadband improvement. In addition, the combination of disorder in position and size is desired for better transmission. We also investigate the impact of the density of NPs on the light extraction, with the results summarised in Fig. S7. Here, the fluctuations of the size of NPs ∆ siz is also included. We fix the disorder in position to 10% of the average distance among the NPs. The results are averaged from three different random sets. The density plays an important role in light extraction. There are optimised densities for outcoupling the photons, as shown in Fig. S7a-c. Such effect also has a strong wavelength-dependence. In addition, we observe a disorder enhanced transmission when magnitude of ∆ siz is moderate, similar to the results shown in Fig. S6.

Supplementary Note 5: Artificial design step for the disordered metasurface
In the main text, the simulations demonstrated the effect of light extraction based on the features from bio-inspiration. Here, the effect of structure extension is investigated, clarifying the pivotal of artificial design from Meta-III to Meta-V. Considering the limited computational resources, we investigate the periodic structures demonstrated in Supplementary Fig. 8a and b. The periodic stripes with a curved top surface are extended to a periodic structure composed of nanoparticles with a spherical surface on top. The effect of disorder is directly shown by the experimental results in the main text and Supplementary Note 5. Supplementary Fig. 8c compares the transmission T at normal incidence when the polarisation of the electric field varies in the x-y plane with different azimuthal angle φ. The difference in transmission clearly demonstrates another benefit from structure extension -the reduced coverage rate facilitates more photons to go outside the substate inside the light cone (no TIR occurs). Supplementary Fig. 8d investigates the case when incident angle θ changes. The azimuthal angle φ is set to 0 o when the stripe obtains maximum transmission. Even under this situation, the nanoparticle can extract more photons, owing to the enhanced capability for coupling light above the critical angle θ c .

Supplementary Note 6: Fabrication, characterisation and optimisation of disordered Ag metasurfaces
Ag metasurfaces were prepared by gas-phase nanocluster beam deposition method [2]. The nanocluster beam deposition system is composed of a cluster source, differential vacuum component, particle control component and a deposition chamber. In this fabrication, Ag clusters were generated in a magnetron plasma gas aggregation cluster source. The nanocluster beam was formed by differential pumping induced expansion, and then deposited onto the surface of the LED chips directly. The deposition was performed in a high-vacuum chamber equipped with the cluster source. An Ag target with high purity (99.999%) was used as the sputtering target. The magnetron discharge was operated in an argon stream at a pressure of about 90 Pa in a liquid nitrogen cooled aggregation tube. Ag atoms were sputtered out from the target and Ag nanoclusters were formed through the gas aggregation process in the argon gas. The clusters were swept by the gas stream into high vacuum through a nozzle and a skimmer, respectively, forming a collimated cluster beam with ultrasonic speed. Thus, the nanoparticles deposited and stuck on the substrate or LED chip surface firmly.
Supplementary Figure 9. (a) SEM images of disordered metasurfaces with different particle size. The scale bar represents 500nm. (b) Corresponding statistical analysis of the size of Ag nanoparticles in each metasurface. A Log-Normal fitting is also provided.
The gas-phase cluster beam technique provides the flexibility to form Ag nanoparticles with different sizes and coverage rate by simply tuning the deposition time and temperature. The deposition was carried out at a rate of 0.6 ± 0.1Å s −1 . The deposition time is 5 min, 9min, 12 min, 15 min, 18 min and 21 min. The post-deposition rapid annealing process was performed for 25 min in situ with a temperature of 400 o C. The structural properties of the metasurfaces were characterised by scanning electron microscopy (SEM, HITACHI S4800), as shown in Supplementary Fig. 9a. Due to the fact that silver nanoparticles have high mobilities on the surface of substrates [1], diffusion and coalescence of metallic nanoparticles on sapphire surface induce a significant increase in nanoparticle size with the deposition mass. The corresponding size distribution histograms of the deposited clusters are given in Supplementary Fig. 9b, which show that averaged size of Ag nanoparticles covers a range from 40 nm to 185 nm. Diameters of the deposited clusters observed from SEM are much larger than those of the clusters in the free beam, indicating that the clusters are effectively coalesced after they land on the surface.
Supplementary Figure 10. Schematic diagram of the light extraction measurement system We perform transmission measurement for each metasurface with the setup shown in Supplementary Fig. 10. The results are summarised in Supplementary Fig. 11. From the transmission spectra ( Supplementary Fig. 11a), the Meta-IV 6 is selected as the optimised structure for the light extraction. The performance of the metasurface can be evaluated from naked eyes through the images in Supplementary Fig. 11b. The transmitted light from Meta-IV 6 not only has a stronger intensity but also processes a white colour, implying a broadband light extraction.
We further increase the size of the NPs, with the results demonstrated in Fig. S12. An apparent degradation in light extraction is observed for the metasurface with an averaged NP size of 231nm, demonstrating the Meta-IV6 be the best one available for light extraction. NPs above 231nm can be fabricated at a high temperature. But the temperature may impair the performance of LEDs beneath the metasurfaces.
Due to the presence of several degrees of freedom in fabrication, there may be additional space to improve the extraction efficiency by seeking an optimised recipe. The recent development of deep-learning-aided recipe optimisation [3] may be utilised in future works for even better performance. The maximum transmission occurs around 600nm in the simulation, while the transmission peak was experimentally observed around 500nm. We attribute this blue shift to the deformation of the top half of real nanoparticles (compared to a hemisphere), as shown in Fig. 2c in the main text. We attribute the 100nm blue shift in the transmission spectrum to the volume reduction in real nanoparticles. Importantly, broadband transmission above the critical angle is demonstrated in both simulation and experiment. The maximum value of T TIR from experiments is larger than the simulated one, due to the shape variation of nanoparticles in fabrication. The moderate increment of the disorder resulted from fabrication imperfection can further enhance the transmission, matching the results shown in the main text and Supplementary Note 4. The angle dependence of the light extraction is investigated experimentally, with results summarised in Fig. S14 and Fig. S15. Figure S14a illustrates the setup. An integrating sphere is utilised to collect all the scattered photons. The transmission spectra are shown in Fig. S14b, with incident angles ranging from 50 o to 68 o . In spite of the decrease in transmission at larger incidence angles, photons in a broad spectral range can be extracted by utilising the disordered metasurface. Figure S15 summarises the light extraction below and above the critical angle at a fixed wavelength of 473nm. The transmission of a configuration without metasurface is also provided as a reference. Figure S15a and b show the photos for the setup with and without Meta-IV ,respectively. Figure S15c illustrates the relationship between the incident angle and transmission. Below the critical angle, a portion of photons is blocked by the nanostructure on top compared to the reference. But overall, the metasurface facilitates the light extraction, regarding the significant improvement of the transmission above the critical angle. This light extraction ability is also confirmed by the improvement of the EQE of LEDs.

Supplementary Note 11: Additional information for EQE measurement
After dicing and splitting, the LEDs were made into independent chips, and fixed with silver glue in the reflective bowl. Then the chips were connected with gold wires and covered the semi-circular epoxy resin filled it with silicone resin, and heat-cure to obtain the encapsulated LEDs. The relationship between light output power (LOP) and current(I) of encapsulated blank LED and encapsulated LED with Meta VI was measured and shown in Supplementary Fig. 18.
The external quantum efficiency (EQE) of LED can be calculated through The measurement was implemented with 75 independent chips, with statistical results demonstrated in Supplementary Fig. 19 -20. Supplementary Fig. 19 shows the statistics of LOP while Supplementary Fig. 20 shows the statistics of EQE. An EQE enhancement from 31.6(± 2.6)% to 51.5(± 3.8)% is observed by virtue of the light extraction structure.