A scattered volume emitter micropixel architecture for ultra efficient light extraction from DUV LEDs

Deep ultraviolet light-emitting diodes (DUV LEDs) typically suffer from strong parasitic absorption in the p-epitaxial layer and rear metal contact/mirror. This problem is exacerbated by a substantial portion of the multiple quantum well (MQW) emissions having a strong out-of-plane dipole component, contributing to emission in widely oblique directions outside the exit cone of the front semiconductor emitting surface. To address this, we propose an architecture that leverages such a heavily oblique angular emission profile by utilizing spaced-apart or scattered volume emitter micropixels that are embedded in a low-index dielectric buffer film with a patterned top surface. This approach achieves high light extraction efficiency at the expense of enlarging the effective emission area, however, it does not require a high-index (e.g., sapphire) substrate or a lens or a nanotextured epi for outcoupling purposes. Hybrid wave and ray optical simulations demonstrated a remarkable larger than three to sixfold increase in light extraction efficiency as compared to that of a conventional planar LED design with a sapphire substrate depending on the assumed epi layer absorption, pixel size, and ratio of light emission area to the MQW active area. An extraction efficiency three times greater than that of a recent nanotextured DUV LED design was also demonstrated. This architecture paves the way for DUV LEDs to have a plug efficiency comparable to that of mercury lamps while being significantly smaller.


Materials
. Epilayer thickness and optical properties of a "Reference" epi stack case.
We reproduced an LEE of 4.6% for the case of a semi-infinite LED stack with a sapphire superstrate considering an in-plane dipole emission only from multiple quantum wells (MQW).Instead, as shown in Fig. S1, considering the finite 1×1 mm 2 size of the chip and allowing rays to escape from the sidewalls and assuming an isotropic dipole orientation in the MQW, as explained in the main text, we obtained an LEE of 4.8%.Note that rays that exit the chip in the downward direction are also considered in the LEE calculation, as we assume these rays can be used.

Figure S1
. The 3-dimensional raytracing of 10 rays for the planar 1×1 mm 2 sapphire chip.(a) is the overall 3-dimensional view which is mostly sapphire block, and (b) is the magnified 2-dimensional XZ view where the thick, blue-colored block is sapphire, the purple block which is mostly AlN is the epilayers, and the thin gray layer is platinum.
The hybrid ray and wave optics LEEs for this simplified 1×1 mm 2 chip architecture for the three considered epistack cases are summarized in Table S2.As the referenced epilayer case is validated, the other two epilayer stack cases (as discussed in the main text) were chosen to further analyze the extraction capability of the SVEP architecture, i.e., a stack with a lower MQW refractive index and another stack with a lower p-side loss.For completeness, we include simulated LEE of the 1×1 mm 2 chip without the sapphire substrate on top.In a reference 1x1mm^2 chip, the main exit surface of light from the semiconductor epitaxial layers is only the top surface as not a lot of light emitted in the middle region of the chip will reach the epi sidewalls.With a thick sapphire substrate on top, one allows a major portion of the light which lies within the escape cone of epi to sapphire to be extracted and subsequently be outcoupled into air at the sapphire top and sidewall interfaces.The sapphire essentially act as a volume emitter.Without the sapphire, light will be confined within the lossy semiconductor DUV epi and a major portion of it will be lost.Although the "Low P-side Loss" epistack case has relatively less absorption than the "Reference" and "Low MQW RI" cases, its LEE is quite low.The main reason is that a large amount of power is sent to oblique angles in the n-epi at ~70 degrees beyond the escape cone of the n-epi to the sapphire.Because we only consider a planar chip structure, light beyond the nepi/sapphire escape cone remains trapped in the semiconductor epilayers.The SVEP architecture exploits this very same condition by considering small micropixels architecture where light can also escape from the sidewalls of the epi into the buffer layer region.

Geometric variations with negligible LEE enhancement
Table S3 summarizes what is studied for Figs.2-6 in the main text and other parameters that are kept constant for each figure.
The parameters and study set are to mainly highlight physics instead of providing an optimum structure.  ,   ,   , and   , are 8 µm, 14 µm, 1 µm, and 4 µm, respectively.
Table S3.The chip design variation approaches.Varying the buffer thickness, as depicted in Fig. S2, has a trivial effect on the LEE performance.This is true for all epistack cases.However, compared to their 1×1 mm 2 sapphire counterparts, our SVEP architecture outperforms the LEE by at least 3 folds.This is because the increased thickness is actually beneficial for sidewall extraction, but due to the large emission area compared to the MQW size, most of the rays are extracted upward rather than through the buffer sidewalls.Therefore, the effect of varying the buffer thickness alone on the LEE is negligible.
Buffer sheet air volume and percentage.In Fig. S3, similar to the buffer thickness variation, the a) air volume and b) percentage variations of the buffer sheet do not have a major effect on the LEE.Nonetheless, compared to a buffer sheet without volume scatterers (the volume and percentage of air particles are zero), when air particles are in the buffer sheet, there is a slight increase in the LEE by ~0.02 for all epilayer cases.This means that scattering slightly improves the extraction in this buffer medium, but increasing the scattering probability does not further increase the extraction efficiency.While the scattering increases the variety of rays' incident angles on the extraction surface, it also increases the TIR probability, which counteracts the efficiency by redirecting the rays into the absorbing layers.

Sample of data and results
The LEE ray-tracing calculations were performed with a minimum of 100,000 rays for each case of geometric and material epilayer property variations.We found that the LEE values converged with such a number of rays.The far-field shown in Figure 3 of the main paper was computed with 5 million rays.Fig. S4 shows an example of the SVEP's single-pixel ray tracing simulation with a 100-ray setting, where the gray block is platinum, and the red block is the SiO2 buffer layer covering that single pixel.
. Figure S4.A sample of SVEP ray tracing simulation with a sample of 100 rays.This is a YZ-axis 2-dimensional view.The gray-colored block is platinum, and the red block is the SiO2 buffer sheet covering the single pixel.
Notably, most variations of complex geometrical parameters require us to utilize design-based software, Solidworks-3D, in which the complete model can be exported into Lighttools for ray-tracing simulation afterward.For example, when the pixel size is varied, the changes in complex curves, filleting, and layers' subtraction can only be done in design-based softwarewithout error.As noted in the main text, the light tracing tool tracks both bulk absorption and surface losses, and also collects light that escapes the structure and propagate into the far-field in the ambient media (in our case we consider air as ambient except in Fig. 2(c) ).When light rays encounter most interfaces during the ray tracing, we simply consider Fresnel refraction laws.An exception is taken when light rays return from the n-side to the p-side of a pixel.There we consider the reflection response of a multilayer planar stack which comprise of the whole p-epi layers and p-contact, in an attempt to consider the wave-optical effect in the absorption as well.The more round trips occur in the absorbing layers due to Fresnel reflection and TIR, the more absorption takes place.We currently ignore photon recycling (reabsorption and reemission) processes in the MQWs as we consider at operational conditions the MQWs would be heavily pumped and be naturally less absorbing.In the considered epi stacks which exhibit large p-side losses, the effect of photon recycling would be overshadowed by the absorption losses in the surrounding material.Throughout the manuscript and supplementary the raytracing settings have been described, but for simplicity, they are arranged accordingly in Table S4.

Table S2 .
Simulation results of LEE based on our combined ray and wave optical modeling.