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This paper demonstrates a novel retro-reflective dome that enhances the directionality of a light emitting diode (LED) by recycling photons reflected by a textured LED die surface. A simulation model is developed to describe both the photon recycling process within the dome and the role of specific pyramid patterns on the top surface of the LED die. Advanced simulations showed that a perfectly polished surface with 100% reflectivity potentially enhances the directionality of the dome by 340%, 250%, and 240% using reflective domes with 10°, 20°, and 30° light cones, respectively. In the experiment, the directionality of the domes exhibiting surface imperfections is enhanced by approximately 160%, 150%, and 130% using 10°, 20°, and 30° light cones, respectively. By incorporating a textured top surface on the LED die, the proposed dome effectively increases the directionality of the LED light source.
©2013 Optical Society of America
1. Introduction
Numerous previous studies have regarded light emitting diodes (LEDs) to be the most promising solid-state light source for next-generation lighting because of various advantages such as energy conservation, flexible design, superior color performance, high reliability, and other environmental benefits [1–4]. Flux density has been a primary obstacle in various practical LED applications. This is because the lumen per steradian of a white LED operating under high-power conditions is lower than that of certain traditional light sources. To solve this problem, maximizing the emitting efficiency or the external quantum efficiency of LEDs is necessary. Increasing the optical throughput of LEDs by using advanced optics has also been a common approach applied to projection systems. In the majority of cases, the far-field light distribution of LEDs has exhibited an almost Lambertian distribution. If a heavy injection current is incapable of meeting the flux demand of an optical system, the only alternative is to enlarge the surface area of the LED die. However, this approach causes an increase in the light source etendue and a reduction in the optical efficiency for collection of light by the LED [5–9]. Although LEDs have been considered as an alternative to the application of traditional discharge lamps in optical projectors, the discussed advantages of using LEDs are impractical for large surface areas because a large etendue renders solid-state light sources ineffective. Therefore, enhancing the directionality of LED light sources is a crucial technical task. Several approaches have been proposed to enhance the directionality of LEDs. For example, photonic crystals are periodic structures that have been used to extract light in the normal direction by causing a strong diffraction along the axial plane [10–14]. Another approach is to enhance the optical utilization efficiency by extracting the maximum amount of light from the LED crystal cavity rather than using a diffraction structure to enhance the directionality. This is achieved by implanting a microstructure either within the crystal (i.e., by using a sapphire substrate pattern) or by texturing the top surface of the LED die [15–18]. Using a microstructure for light extraction is advantageous because the reflected photons are recycled within the internal cavity of the LED. Other advantages include independence on emission wavelength, simple fabrication processes, and a light extraction efficiency approaching 90% [19]. However, the primary disadvantage of this approach is that no obvious enhancement of the directionality of the LED light source is observed. Therefore, this technology requires a novel approach to enhancing both the directionality and the light extraction efficiency of LEDs. In this paper, a novel approach to achieving both high directionality and high light extraction efficiency is proposed and demonstrated by applying a surface texture on the external cavity of an LED die.
2. Principle of photon recycling using an external cavity
The ideal conditions for producing a highly directional light source involve achieving maximum power efficiency and minimal etendue. Introducing a surface texture on an LED is generally an effective approach to increasing the light extraction, thereby maximizing the luminous efficacy. However, this potentially alters the light pattern. Although it is possible to enhance the light directionality by employing a specific textured structure, the light pattern becomes more dispersed under the majority of conditions if surface structures are added [20].
The principle of the proposed approach is to develop an external cavity for an LED that facilitates the recycling and redirecting of photons at large angles into a finite light cone in the normal direction. The geometry of the proposed external cavity for photon recycling in Fig. 1 shows an external cavity that contains a retroreflective dome (RRD) with an opening on the top surface. The RRD serves as a retroreflector that reflects the photons at wide angles back into the LED die. The texture on the top surface of the LED die not only greatly increases the light extraction efficiency but also alters the direction of the reflected photons, thereby increasing the probability of the light escaping through the opening. Any remaining photons are either absorbed or recycled between the RRD and the LED die for several runs before being redirected through the opening. This approach could increase the LED light intensity while achieving a tolerable etendue without increasing either the injection current or the emitting area.
Fig. 1 Schematic diagram of the RRD with an open hole on the top, where Ω is the half angle of the light cone.
Thus, the proposed RRD is theoretically capable of enhancing the directionality of an LED light source. However, because an LED die is not a point source, a key factor to optimizing the RRD is to cause all of the recycled photons to collide with the surface of the LED die. Moreover, the textural pattern on the top surface of the LED die should be designed so the photons are reflected into the opening of the RRD with a designed light cone.
3. LED die simulation
First, the light extraction efficiency simulation is based on Monte Carlo ray tracing for a thin-GaN LED [16–22]. The EZ-1000 LED dies used in this study were manufactured by CREE, as shown in Figs. 2 and 3. Figures 2(a) and 2(b) show the geometry and optical parameters of the LED die, respectively. Figures 3(b) and 3(c) show the detailed structure of textural patterns, which comprise various sizes of tightly grouped pyramids. Because the purpose of these structures is to extract light from the LED die and reflect it along the normal direction, producing an accurate simulation is necessary for both light extraction and spatial light distribution.
Fig. 3 The SEM image of EZ-1000. (a)The top view of the LED die, (b) top view of the surface texture, (c) side view of pyramids.
The simulation chip size is set at 980 × 980 um, the bottom reflectivity of the LED die is set at 90%, and the absorption coefficient of the active layer is 200 cm−1 (these values are selected based on practical experience). The images obtained using scanning electron microscopy (SEM, Fig. 3(c)) show that the apex angles of the pyramids range between 58° and 63°. The pyramids are divided into three groups. The first group is the largest pyramid (16.7 μm), the second group is the mid-size pyramid (8.3 μm), and the third group comprises the smallest pyramids (≤ 8.0 μm). The estimated filling factor of the pyramids is 97.5%. To form a simple combination of pyramid structures, an equivalent texture is produced by implanting the largest and the mid-size pyramids to cover 52.4% and 19.0% of the surface area, respectively. For the smallest pyramid group, the structure is simplified to a form triangular shape (8.3 μm) to cover 24.4% of the surface area (Fig. 4). No structures cover the remaining 2.5% of the surface area.
Fig. 4 (a) The geometry of the textured surface and (b) the detailed distribution of the different pyramids.
The simulation based on the specific patterns illustrated in Fig. 4 yields an increase in light extraction efficiency from 19.6% to approximately 83.6% using the flat top surface. Figure 5 shows a comparison between the spatial light distribution of the experimental measurements (Fig. 5(a)) and the simulation results (Fig. 5(b)) for the far-field intensity patterns. The emission patterns of the four measured LED dies are similar to a Lambertian distribution. The simulations based on the proposed structures shown in Fig. 4 produces similar distributions, although they deviate slightly from the Lambertian distribution along the normal direction. Such a difference causes no effect on the optimization of the RRD.
Fig. 5 The light distribution curve of EZ 1000. (a) Experimental measurement, (b) the simulation result.
4. Experimental design and results
The RRD design is critical for photon recycling. An incorrect shape or size would be incapable of directing the reflected photons toward the top surface of the LED die. To recycle the maximum amount of photons incident on the RRD, the photons must be reflected directly toward the LED die to reduce the etendue. The simulation for the optimized RRD size is performed as follows. A detailed definition of the geometry of the RRD is illustrated in Fig. 6. Figure 7 shows the simulation results for the received optical flux ratio as a function of the diameter of the RRD, where the dimensions of the LED die are 1 × 1 mm. The optical flux reflected onto the LED die increased in conjunction with the RRD diameter. At a diameter of 20 mm, approximately 95% of the photons are reflected onto the LED die. Because the miniature factor is also a key system requirement, a 20-mm diameter RRD is used as the ideal size for this study.
Fig. 7 Simulation of the received optical power ratio from the RRD to the LED die with respect to radius of the RRD.
To maintain the maximum optical flux and reduce the etendue, the following directionality enhancement ratio (DER) is defined
where and represent the flux confined by a specific light cone to be emitted by the die with and without the RRD, respectively. Figure 8 shows the experimental setup employed to measure the optical flux of the fixed light cone, which is controlled by the opening of the RRD. The optical flux was measured using a 12.5-inch integrating sphere with an iris attached to fit the light cone by the RRD opening to control the right angle of light cone. By fitting the LED die with an RRD, the size of the RRD opening could be manipulated to control the demanded light cone.Fig. 8 The schematic diagram of experiment for measuring the flux by the LED and RRD with a specific light cone.
For the experiments, three RRDs were produced exhibiting specific opening sizes to obtain 10°, 20°, and 30° light cones. Figure 9 shows the DER simulation and the corresponding experimental measurements, whereas Fig. 10 shows the measured light patterns and the corresponding simulations. For all three light cones, the measurements and simulations yield the highest DER when the light cone is slightly smaller than the designed one. In all three experiments, once the measured light cones become larger than the designed one, the DER decreases dramatically as the light cone increased. This implies that the design of the opening is crucial to obtaining the optimal light cone. The simulation results also show that the DER is greater when the designed light cone is smaller. For the 10° light cone, the simulation yields a maximum DEF of 340% when the surface reflectivity of the RRD is 100%, whereas the DER measured during the experiment is 160%. Similar differences are noted between the simulations and the experimental measurements for the maximum DER yielded by the 20° and 30° light cones. The light pattern simulations and measurements illustrated in Fig. 10 show similar differences to those shown in Fig. 9.
Fig. 9 Experimental measurement and the corresponding simulation for DER vs. half angle of the light cone under the designed light cones: (a) 10°, (b) 20°, (c) 30 o. Black dot: experimental measurement. Lines for simulation with reflectivity of 100% (red), 70% (blue), 60% (green) and 50% (pink).
Fig. 10 Experimental measurement and the corresponding simulation for light pattern vs. angle of the light cone under different light cones: (a) 10°, (b) 20°, (c) 30°. Black dot: experimental measurement. Lines for simulation with reflectivity of 100% (red), 70% (blue), 60% (green) and 50% (pink).
To clarify the differences between the experimental measurements and simulation results, additional simulations are performed after changing the surface reflectivity (Figs. 9 and 10). The simulation result for the DER at 60% reflectivity corresponds with those of the experimental measurements for the 10° light cone. However, an increase in the light cone causes a reduction in the reflectivity of lower fitting surface. The 30° cone yields a fitting surface reflectivity of approximately 50%. A further experiment was performed to measure the surface reflectivity using a blue laser as the light source (wavelength = 448 nm). The average surface reflectivity of the three RRDs is approximately 82%, which is typical of value obtained during general fabrication processes. Such reflectivity does not support the fitting reflectivity obtained during the simulations. Subsequently, an advanced study is conducted to examine the surface quality. An observation of the RRD surface reveals that it is not perfectly smooth. A collimated white light source was used instead of the laser to illuminate the surface, and a divergent spot filled with a speckle-like pattern was observed (Fig. 11). The pattern is not caused by interference, but by the surface being slightly roughened, which causes a serious degradation of the DER. To model this effect, an assumption is made in the simulation regarding the roughened surface, where an additional scattering light cone upon each reflection in the simulation and the surface reflectivity at 82% for the measurement are used. Subsequently, a similar DER is obtained for all three cases when the scattering light cone of half width is approximately 3°. Therefore, the difference between the original simulations and the experimental measurements caused by the surface imperfections can be imputed. Consequently, the directionality enhancement involving the RRD incorporated with a textured LED die surface is successfully modeled.
For the practical application of optical projection, the light source could be rectangular rather than square. Therefore, a large commercial LED (5.77 × 3.25 mm) was used as the light source. Figure 12 shows the measurements for the 30° RRD that is used to increase the DER in the experiment. The measured DER is approximately 1.23, which is slightly less than that obtained using the 1 × 1 mm LED die. The simulation in this case shows that the DER could be as high as 1.7 if the surface is perfectly polished and the reflectivity is 90%. This is a highly effective approach to enhancing the optical throughput in an optical projection system.
Fig. 12 Experimental measurement and the corresponding simulation for DER vs. the angle of the light cone with the 30° RRD for the case with the light source of a rectangle LED die. Black dot: experimental measurement. Lines for simulation with reflectivity of 90% (blue), 60% (red), and 50% (green).
5. Conclusion
In this paper, a novel retro-reflective dome is proposed and shown to recycle photons by using a textured LED die surface. A simulation model is successfully developed to describe the photon recycling process with the RRD incorporated with the pyramid patterns on the top surface of the LED die. First, the optimal RRD size is determined by considering both the optical flux ratio reflected back onto the LED die and the compact unit size. Second, the textural patterns are examined in detail using SEM. The textural patterns are categorized into three groups based on the various sizes and ratios. The simulations show that the modeled textural patterns enhanced the light extraction efficiency by up to 83.6%, and the simulation light pattern is similar to that observed in the experimental observations. Regarding the directionality enhancement, the advanced simulation shows that a perfectly polished surface with reflectivity of 100% obtains a DER of approximately 340%, 250%, and 240% using an RRD with 10°, 20°, and 30° light cones, respectively. The experimental measurement shows a DER of approximately 160%, 150%, and 130% for 10°, 20°, and 30° light cones, respectively. The differences between the original simulations and the experimental measurements that are caused by surface imperfections are imputed with a reflectivity of 82%. The simulations and the corresponding experiments show that the proposed retro-reflective dome can effectively increase the directionality of an LED light source incorporated with a surface texture on the top surface of the LED die.
Acknowledgment
This study was supported in part by the National Central University’s “Plan to Develop First-class Universities and Top-level Research Centers” (Grant numbers 995939 and 100G-903-2), the National Science Council of the Republic of China (contract numbers 99-2623-E-008-002-ET and NSC100-3113-E-008-001), and Delta Electronics-NCU joint project in 2010.
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