Simulation of Phosphor Converted LED Packaging with Considerations on Phosphor Settling

Transcription

1 Simulation of Phosphor Converted LED Packaging with Considerations on Phosphor Settling Ph. D., Kit Cheong, Breault Research Organization, USA, Tucson Abstract Settling of phosphor particles in PC-LED packaging is a common nuance observed in the manufacturing process. The settling alters the optical behaviour of the phosphor-rich encapsulant and consequently the emission behaviour of the LED. In this paper, we model the encapsulant with phosphor settling as a volumetric scattering medium with spatial inhomogeneities in its scattering and absorption behaviour. Such a spatially inhomogeneous scattering medium can be studied using Monte Carlo ray tracing method and a mathematical model that reflects the spatial variations in the scattering and absorption coefficients of the encapsulant. We will present simulation results of LEDs emission properties with different levels of settling. 1. Introduction Solid-state lighting using LEDs is gaining popularities because of its higher light conversion efficiencies, longer lifetime, and environmental benefits. LED by itself emits narrow spectrum around its nominal emission wavelengths. For general lighting purposes, light sources with broader spectrums that better correlate the natural white light are desirable. Different methods have been developed to generate broad spectrum light from LEDs. One of these methods relies on the down conversion mechanism of phosphors. White LEDs operated under such principle are called the Phosphor Converted-LED (PC-LED). This paper will describe the use of an optical design software (ASAP, Advanced System Analysis Program, Breault Research Organization) in investigating packaging design issues surrounding PC-LEDs, specifically the settling effect of phosphors. In the manufacturing of PC-LED, phosphor powders are mixed with an adhesive carrier (usually silicone) to form viscous fluids to encapsulate the LED chips through curing. Some of the shorter wavelength photons emitted by the chip (excitation photons) experience down-conversions when propagating through the encapsulant through interactions with the suspended phosphor particles in the carrier. Longer wavelength photons (emission photons) are thus generated in accordance to the phosphor emission spectrum. The mixing of the residual excitation photons with the phosphor emission photons creates the desired broad spectrum light. Due to the relatively large specific gravity of the phosphor particles (~4.3), they tend to settle during the silicone curing process when manufactured (Ref. 1). Such settling alters the spatial concentration of the phosphors from the original design and renders differences in the predicted chromatic and illumination characteristics. In this paper, we will study the effect of phosphor settling on the performance of a simple PC-LED with a blue chip as the excitation source. We will look at the extracted light spectra of samples with and without phosphor settling, as well as the effect of settling on the angular distribution of the extracted light. We will show that versatile optical design software can provide a convenient virtual platform for the PC-LED packaging engineers to gain better understanding of the physics happening within the package and probe the different optical effects that are difficult to access in experimental setting.

2 2. Method 2-1. Reflector cup model The reflector cup structure and coating properties for this simulation is shown in Image 1. The square reflector cup sits in a metal housing with an opening of mm 2 at the top, an area of mm 2 at the bottom, and a thickness of 0.5mm. The center dark grey region is the LED chip mounted on a thin bottom substrate with silver coating (reflectivity of 85%). The white stripe around the chip shows the extension of this bottom substrate beyond the chip width. The light grey area next to the bottom substrate is a coating of AuSn with a reflectivity of 50%. The adjacent dark grey stripes are silicon coating (reflectivity of 30%). The white area in the cavity is the aluminum coating of 85% reflectivity. Image 1: Reflector cup structure and different coatings 2-2. Chip model Image 2. Chip model (not to exact dimensions) and emitting surfaces Image 2 shows the blue LED chip on a silver coated bottom substrate. The surface area of this substrate is mm 2 with a thickness of 20µm. The chip size is mm 2 and its thickness is 150µm. We have adopted a simplified blue chip architecture based on the description in Ref. 2 for the simulation. The P-type GaN layer is assumed to have a thickness of 200nm, the active region is 42nm, and the N-type GaN layer is 3µm. The GaN layers and the active region are assumed to have the same refractivity (n=2.45) and absorption coefficient (α=8mm -1, Ref. 3). Such configuration is described as the homogeneous chip model in Ref. 4. However, in this simulation, we modify the homogeneous model described in Ref. 4 by moving the emitting sources from the chip surfaces into the GaN layers. Two isotropic planar emitting sources are defined at the boundaries between the active region and the GaN layers to mimic photon emission from the multi-qw. The total flux of these two emitting surfaces is 1080mW for the simulation. The planar source at the top emits rays in the upward direction, and the

3 Absorption Coefficient (1/mm) bottom source in the downward direction (see Image 2). The Sapphire substrate has a thickness of µm and a refractivity of Phosphor model The absorption and emission spectra of the phosphor used in this simulation are shown in Image 3 (a). The absorption spectrum is measured between 399nm and 525nm and the emission spectrum from 415nm to 730nm. The particle size distribution of the yellow phosphor (YAG:CE) powder is shown in Image 3(b). The solid dots are the measured particle size distribution with its peak around 8 µm. The minimum radius is 1µm and the maximum about 16µm. This measured distribution is fitted using a Gaussian distribution with its mean at 7.95 µm and width (σ) of 2.3µm. Image 3. (a) Absorption and emission spectra of the yellow phosphor (b) Particle size distribution of the phosphor The phosphor then was dispersed in a silicone adhesive (n=1.54) to form a phosphor-rich encapsulant for packaging purpose. The density of the YAG is 4.3 mg/mm 3 and the weight percentage of the phosphor in the encapsulant is 20%. The absorption coefficients (in mm -1 ) of this phosphor-rich encapsulant are calculated using the Mie model for wavelengths from 415nm to 525nm as shown in Image 4. The conversion efficiency (CEFF) of the phosphor is set to be Wavelength (nm) Image 4. Simulation result of the phosphor encapsulant absorption coefficients (in 1/mm), with a phosphor weight percentage of 20%

4 2-4. Settling function and settling scale We define an exponential decaying function to describe the settling of the phosphor particles within the silicone adhesive. We assume that, due to gravity pull, the phosphor particle concentration decays exponentially as the vertical coordinate (the z-direction) moves away from the bottom of the container while the concentration remains uniform in the horizontal plane. Therefore, the settling function is a function of the z-coordinate only: z z0 SF( z) c exp( ), zs where c is the normalization constant, z 0 is the z-coordinate of the container bottom, and zs is a parameter to describe the settling degree, and it will be referred to as the settling scale in the rest of this paper. Image 5. Showing the chip and the bottom substrate in the reflector cup. The dark grey area represents the region above the chip with its settling function described by SF 1. The rest of the volume inside the cup is treated as one region with a settling function SF 2 In order to account for the discontinuity at the reflector cup bottom due to the height of the chip and other structures, we further divide the reflector cup into different regions. For simplicity, we have neglected the small step at the cup bottom due to the height of the bottom substrate. Thus, the reflector cup is divided into two distinct regions as shown in Image 5. Each region has its own settling function to describe the inhomogeneity of the phosphor concentration in the z-direction: z zc z zb SF 1( z) c exp( ), SF 2( z) c exp( ), zs zs where z b =0.15mm is the z-coordinate of the cup bottom in the simulation, and z c =0.32mm the coordinate of the chip top. Then the total settling function can be written as SF( x, y, z) SF 1( z) rect( x ) rect( y ) SF 2( z) (1 rect( x ) rect( y )), W W W W c c c c where W c =1.143mm is the width of the chip. The normalization constant c is determined by preserving the total volume of the phosphor particles (V ph ) with and without settling: V VCON d r= VCON SF( x, y, z)d r, 3 3 ph 0 0 V V where VCON 0 is the phosphor volume concentration without settling, and the integration volume V is the reflector cup volume excluding the chip and the modified bottom contact volume (using the chip width instead of the real width, 1.3mm, of the bottom contact). The settling functions for settling scales zs=0.1mm, zs=0.3mm, and zs=10mm are plotted in Image 6. The effects of the spatial inhomogeneity of the particles on the scattering and absorption coefficients of the encapsulant can then be described as: ( x, y, z) SF(,, ), abs abs,0 x y z scat x y z scat,0 (,, ) SF( x, y, z), where µ abs,0 and µ scat,0, respectively, are the absorption and scattering coefficient for the phosphor-rich encapsulant without settling. The spatially varying scattering and absorption coefficients of the encapsulant are implemented in the simulation by using the built-in medium property modification functionality in ASAP.

5 Image 6. (a) Settling function SF 1 plotted with respect to the z-coordinate. The starting point in this plot is 0.35mm just above the top surface of the chip (b) Settling function in region 2. It is plotted from z=0.15mm (cup bottom) to 0.65mm (cup top) 2-5. Ray tracing The ray tracings are carried out with a phosphor-in-cup configuration as shown in Image 7. We perform the ray tracings first without settling. Then we repeat the ray tracings with a similar set-up except that the encapsulant is modified to show different degrees of settling. Image 7. Phosphor-in-cup configuration used in simulation In each of the ray traces, the excitation source is assumed to emit excitation wavelength (EWL) between 416nm and 515nm at 1nm increments in accordance to the spectral power distribution of the LED chip as shown in Image 8. For each EWL, we monitor the power absorbed in the GaN inside the chip (GAN_ABS_EWL), the power absorbed by the yellow phosphor (YAG_ABS_EWL), and the power of the nonconverted blue light escaped the encapsulant and propagated in the upward direction. Image 8. Measured emission spectrum of the blue LED from 416nm to 515nm

6 For the fluorescent process, at each EWL, we trace fluorescent wavelengths (FWL) from 470nm to 730nm at an increment of 1nm. The phosphor encapsulant volume is converted into a volumetric emitting source to simulate the fluorescence. The strength of the source is determined by the following factors: the excitation power absorbed by the phosphor at the particular EWL (YAG_ABS_EWL), the CEFF of the phosphor, and the spectrum power density at the particular FWL in accordance to the phosphor emission spectrum. During the fluorescent ray trace process, we record the fluorescent power absorbed by the GaN (GAN_ABS) and the power escaping the package in the upward direction. The total fluorescent spectrum being extracted is obtained by summing up the individual fluorescent extraction spectrum at each EWL. We calculate the volumetric scattering models of the enscapsulant for the whole spectrum of the EWL and the FWL. The appropriate volumetric model is assigned to the phosphor encapsulant for each EWL and FWL being traced. However, during the fluorescent ray trace, the absorption coefficient of the encapsulant is reset to zero. As seen in Image 3a, there is an overlapping between the phosphor absorption and emission spectra. It means that part of the fluorescent light will be absorbed by the phosphor and stimulates the phosphor to an excited state that will emit another photon, which probably will be absorbed again. Such chain events happen quickly in the phosphor and the effect is accounted for by the measured CEFF. However, in a simulation, we cannot perform ray tracing of such chain events in a time effective manner. Therefore, we will approximate this complex process by considering the overall effect of the CEFF on the source strength of the fluorescent light, and turn off the absorption during the fluorescent ray trace while keeping the scattering property of the encapsulant unchanged. 3. Results and discussions 3-1. Spectra, CCT, and CRI of the PC-WLED of different settling scales Image 9 shows the emission spectra of the PC-WLED for the two phosphor encapsulants where one exhibits no settling and the other with a settling scale zs=0.1mm. It is shown that the peak strength of the blue band as well as the total power carried by the blue light (the non-converted light ) is decreased due to settling while the total fluorescent light power in the yellow light (the converted light) is increased with settling. Image 9. Simulation result of the extraction spectra of the PC-LED with and without settling The simulation results of all the samples with different levels of settling are summarized in the Tables 1-3 below. Table 1 summarizes the spectral properties of the encapsulants at different zs. It shows that as zs increases (i.e., a lesser degree of settling), the power carried by the blue band as well as its peak value increases toward the values at no settling.

7 Table 1 zs (mm) power_blue_peak blue_flux yellow_flux total_flux total_lumen No Settling Table 2 summarizes the amounts of power of the excitation radiation being absorbed in GaN (GAN_ABS_EWL) and the phosphor YAG (YAG_ABS). It also lists the amount of fluorescent power being absorbed by the GaN inside the excitation LED chip. It shows that YAG_ABS in general increases when the phospor enscapsulant exhibits a larger degree of settling, and the absorption of the fluorescent light at the GaN layers also increase. Table 2 zs (mm) GAN_ABS_EWL YAG_ABS Total_ABS GAN_ABS_FWL No Settling Table 3 shows the color properties of these samples. We see that in general the CCT (Correlated Color Temperature) and the CRI of the PC-LED increase with zs (i.e., lesser degree of settling). When the tristimulus coordinates (X, and Y) of these samples are plotted in Image 10, it shows that the data points spread out along a straight line with the no-settling result at the lower left corner and the result of zs=0.1 at the upper right. Table 3 Zs(mm) CCT (K) CRI Tri-stimulus X Tri-stimulus Y No Settling

8 Image 10. Tri-stimulus X and Y for the samples with different settling degrees 3-2. A closer look at the effect of settling In order to understand better the effect of settling, we focus on just two scenarios, no settling and the sample with a settling scale of zs=0.1mm, and perform another simulation with a sufficient larger set of rays (2M rays) on these two samples for the excitation wavelength EWL=450nm (the blue light) and the fluorescent wavelength FWL=547nm (the yellow light) Absorption of excitation energy at different depths We set up a 3D voxels that includes 101 slices along the z-direction in the reflector cup to monitor the amount of excitation energy absorbed at different depths. The result is shown in Image 11. It shows that, with settling, more energy is absorbed below the top surface of the chip around the cup bottom because more phosphor particles are deposited there. The jump around z=0.35mm corresponds to the sediment of phosphors at the top surface of the chip. Compared to the no settling sample, actually, the settling makes it more efficient for the phosphor to absorb the excitation energy. This is shown in Table 2, where the YAG_ABS for the sample with zs=0.1mm is mW and mW for the sample without settling: an increase of about 10%. However, this increase does not translate effectively into the increase of usable extracted yellow light: the amount of extracted yellow light for the sample with zs=1mm is mW and mW for the sample with no settling. This corresponds to an increase of only about 5%. In an attempt to find an explanation for this, we examine the amount of the fluorescent energy being absorbed by the different surfaces inside the reflector cup. We notice that there is an increase in the absorption of the fluorescent energy in the range of 20% to 30% by the bottom contact surfaces, especially where it comes into contact with the sapphire substrate. We contend that, with settling, though the absorption of the excitation energy is increased, however, an important portion of this absorption happens around the bottom of the cup and a larger amount of the fluorescent light therefore is actually absorbed by the structures at the bottom, especially the contact substrate, once the light is emitted by the phosphor and before it can escape the package. This effect, together with the increase in the absorption of the fluorescent light by the GaN layers in the chip (see Table 2), explain why the enhancement in excitation energy absorption for the sample with settling does not have an equivalent impact in the light extraction.

9 Image 11. Power absorbed by the yellow phosphor at different depths inside the encapsulant Angular distribution of the extract fluxes One of the major concerns in the PC-WLED packaging is the angular distribution of the extracted light, especially the mixing of the yellow and blue light. In this part, we look at the fluxes of the blue and yellow light and their ratio at different angles for the two samples. All the rays selected in this analysis propagated within -5 o and +5 o of the polar angles with respect to the upward z-axis, at the different azimuths indicated in the plot (from 0 o to 80 o, at every 10 o with an angular width of ±5 o around the plotted azimuths). It is shown in Image 12 (a) and (b) that the settling has a greater impact on the angular distribution of the radiant flux of the blue light than the yellow. Image 12 (c) shows the ratios of the yellow flux to the blue flux normalized to 1 at 0 o azimuth for the two samples. It shows that, when there is no settling, the ratio maintains around 1 up to the angle about 30. Then the yellow light starts to overpower the blue light. However, when there is settling, the change of the ratio is in a smoother fashion which indicates probably a similar effect in the angular distribution of the CCT of the extraction light spectrum. Image 12. (a) Extracted power of the yellow light at different azimuths (b) Extracted power of the blue light at different azimuths (c) Yellow-to-blue ratio at different azimuth, with the ratio at 0 o normalized to 1 5. Conclusion In this paper, we have investigated the effect of phosphor settling on PC-LED by employing a simple mathematical model. We assume that settling causes an inhomogeneity in the spatial distribution of the phosphor particles and this will in turn affect the scattering and absorption properties of the random medium comprised of the phosphor and silicone adhesive. We have seen that, with this simple mathematical model described by a single parameter, the settling scale zs, we are able to examine the changes in the extract light spectra of samples with different degrees of settling. We also investigate the impact of phosphor settling on the angular distribution of the extracted light, and the absorption of the

10 excitation energy at different depths inside the reflector cup. We have shown that the settling actually increased the phosphor absorption of the excitation light, however, this increase in absorption fails to translate into a greater extraction of the yellow fluorescent light because of the spatial distribution of the phosphor in relation to the other structures in the PC-LED. Light propagation in random medium such as the phosphor-rich encapsulant studied in this paper is a complex process that is difficult to visualize or assess with the traditional deterministic optics theory because of the stochastic nature of volumetric scattering. A flexible optical simulation tool with a reliable Monte Carlo ray trace engine can help us better understand such stochastic system with the wealth of information obtainable through simulations that are carefully designed to probe the system. Such understanding will eventually lead to a better design of the solid-state lighting based on PC-LEDs. Perhaps one day we can learn to harness the inhomogeneity in the phosphor distribution to create sources with richer colours and higher efficiencies. Acknowledgement We want to express our gratitude to Mr. Song-Chun Wu, Siliconware Precision Industries Co., Ltd., Taiwan, for providing us the measured data for this simulation, especially the detailed reflector cup structure. This contribution has allowed us to carry out the simulation on a solid footing that is more relevant to a real design project. [1]. R. Elgin et. al., Evaluation of phosphor settling rate in silicone encapsulant, NuSil Technology LLC. [2]. M. V. Bogdanov et. al., Effect of ITO spreading layer on performance of blue light-emitting diodes, Phys. Stat. Solidi (c) 7, No 7-8, (2010) [3]. Z. Liu et. al., Optical analysis of phosphor s location for high-power light-emitting diodes, IEEE Transactions on device and materical reliability, Vol. 9, No. 1, 65-73, March 2009 [4]. S Liu and X Luo, LED Packaging for Lighting Application: Design, Manufacturing, and Testing, John Wiley & Sons, Inc