1. Introduction

LEDs have been regarded as the most important and promising solid-state light source for the next generation lighting due to the advantages in efficiency, life time, chromatic performance, reliability and environmental protection [1–2]. Recently, white LEDs which are made by GaN covered with yellow phosphors have performed high energy efficiency caused by the great improvement in GaN epitaxy and package. The available commercialized high-power white LEDs achieve 100 lm/W in luminous efficiency [3], which is larger than most light sources in general lighting. However, the chromatic performance of LEDs is still not well controlled due to the variation in GaN chips and package structure [4]. In the package side, the geometry as well as phosphors are the both main issues impacting on the optical and chromatic performance. If we focus on the phosphors, the key parameters include the particle size, concentration, absorption coefficient [5–6], quantum efficiency and thickness. So far, there are several phosphors proposed to apply to GaN-based LED. The most attentions paid in the past years include YAG and silicate. Since different phosphors may perform different characteristics, the package parameters may completely different. Therefore, to the practical application, there is always a demand to white LEDs that should provide a precise and stable power and chromatic performance. Therefore, a precise optical model to simulate the optical effects caused by the phosphors and to describe the power efficiency and color presentation is necessary in LED package.

In this paper, as to our best knowledge, this is the first time to propose and demonstrate a precise phosphor model which accurately predicts the optical and chromatic performance of silicate phosphors applied to GaN-based white LEDs. In the following, we will start from the measurement of optical parameters of the phosphors, followed by the simulation with Monte-Carlo ray tracing [7–10] incorporated with Mie scattering [11–13]. Then we make the corresponding white LEDs with the parameters that we have figured out. Finally, a comparison between the experimental measurement and the simulation from the design will be made.

2. Optical modeling

The phosphor in the study is a silicate-based chemistry of (SrBaMg)₂S_iO₄:Eu²⁺, which absorbs blue light and emits the lights covering the spectrum in visible range but with green-yellow dominant and thus is useful for white light generation with blue GaN dies [14]. The optical modeling process in this study is illustrated in Fig. 1, where we did the measurement of the scattering lights, absorption coefficient, and conversion efficiency of the phosphor plate in different concentrations and thickness. Then we build up an optical simulation model with Mie scattering in a simulation program with Monte Carlo ray tracing. The model is aimed to simulate the outside power ratio of the blue light by the GaN die and the yellow light by the phosphor pumped by a blue light source. Finally, the successful model is applied to predict the color behavior of LEDs. In the following, we will describe the details.

The characterization of the phosphor starts from the measurement of the particle size, which is a key parameter in determining the fraction obscuration and the cross-sectional area of the phosphor mixed with silicone. The measured particle size is in a Gaussian distribution from 2 um to 30 um with the peak at around 17 um. Then we calculated the particle number and the concentration of the phosphor with the density of D_p=4.83g/cm³ [15]. Thus the parameters for Mie scattering are determined.

 

Fig. 1. The diagram of the process for phosphor modeling.

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Fig. 2. The measured scattering distribution and the corresponding simulation of the phosphor plates for the phosphor concentrations of 10% and 15%, respectively.

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The second step is to evaluate the validation of the scattering model in the simulation. Accordingly, measurement of the scattering light distribution of phosphor plates in various concentrations and thickness should be done. In the experiment, we made various phosphor plates with different concentrations (from 10% to 30%) and thickness (from 0.2 mm to 1.5 mm). In considering wavelength-independent property of the scattering and no photon conversion in the phosphor, we used a He-Ne laser as the light source, and the in-plane scattered light was measured. Figure 2 shows two of the simulated results for the concentration of 10% and 25% based on the measurement. Then the measured scattering characteristic is applied to fine-tune the phosphor parameters so the scattering model can describe the scattered light distribution for the same phosphor but at different concentration and thickness. The result as in Fig. 2 shows that the scattering model can be used to predict various phosphor plates with the same phosphor but with different concentration and thickness.

The third step is for the measurement of the absorption coefficient and conversion efficiency of the phosphors. In the experiment, we focused on the concentration of 10% and 15% respectively with the thickness from 0.2 mm to 1.5 mm. The measurements were done with phosphor plates attached on a GaN die attached on a metal slug (here called bare LED), as shown in Fig. 3. In order to effectively figure out these two parameters, we had to build up a precise optical model of the bare LED. The optical model of the bare LED was built with the optical modeling process described in Ref. 16–18. In order to make the LED be easily modeled, we darkened some reflection surfaces to reduce the number of the parameters in the LED. Then we obtained the power of the blue and yellow lights with the measurement by an integrating sphere, as shown in Fig. 4 [19]. The blue light power with and without phosphor plate were used to determine the absorption coefficient of the phosphor plate in the phosphor model with a fitting process. The fitting absorption coefficient for 10% and 15% concentration obtained in the experiment was obtained 0.51 and 0.88 mm-1, respectively. With the measurement result of the yellow light, we further determined the conversion coefficient, which was 0.58 for among our silicate phosphor samples. Thus all the optical parameters required in the phosphor model were determined.

 

Fig. 3. The phosphor plate covered a GaN die attached on a metal slug and its computer model in the simulation.

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Fig. 4. The measured blue (a) and yellow (b) lights with the structures shown in Fig. 3.

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Fig. 5. The forward/backward blue/yellow lights of a phosphor plate of the concentration of 15% for (a) experimental measurement and (b) the corresponding simulation.

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The final step in verifying the parameters is to compare forward and backward blue and yellow lights of the phosphor plates in the experiment [20–21] and in the simulation. In the simulation, the blue lights were absorbed by the phosphors and partially turned to yellow lights. The optical paths of the non-absorbed lights, including blue and yellow lights, were described by Mie scattering model. The forward lights were measured by locating the phosphor plates on the entrance face of an integrating sphere, where a laser at 448 nm illuminated the phosphor plates to obtain enough blue and yellow lights in the measurement. In contrast, the phosphor plates were located in center of the integrating sphere to measure the backward lights, where an absorption box attached on the back of the phosphor plates to remove all the forward lights. Figure 5 shows an example of the experimental result and the corresponding simulation with the phosphor model, where the concentration is 15% and the thickness was from 0.2 mm to 1.5 mm. Though there are some differences between the simulation and experimental measurement, we think that the model is good enough to describe the power distribution of the blue and yellow lights.

3. Verification with white LEDs

The phosphor model is aimed to precisely simulate the optical and color behavior of a practical LED with silicate phosphor. Therefore, we made a real package with GaN die covered with silicate phosphor, where the concentration was 10% and 15% respectively and the thickness of the phosphor was well controlled. In contrast to the model of the bare LEDs, here we had to put all the parameters of the package and phosphor in the optical model. In the simulation, the blue lights were emitted from the active layer and partially escaped from the die and went into the phosphor mixed with silicone. With the phosphor model based on Monte Carlo ray tracing and Mie scattering, we calculated the power of the blue and yellow lights. Fig. 6 shows both the LEDs with and without an encapsulating lens and the corresponding models in computer simulation. The emitting spectrum of the LEDs in the real samples and the corresponding simulation is shown in Fig. 7. Figure 8 and Table 1 show the comparison of the color coordinates of both cases in the experimental measurement and the simulation. We can find that the color differences (ΔxΔy) between the simulation and experimental measurement are almost within 0.004. Such small differences show that the developed phosphor model is accurate and successful.

 

Fig. 6. The picture and optical model of the white LEDs with (a) without (b) with encapsulation with a glass lens.

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5. Summary

In this paper, we present a phosphor modeling process to precisely simulate the power and chromatic performance with silicate phosphor covered on blue GaN dies. The process starts from the measurement of the particle size of the phosphor to determine some key parameters in Mie scattering model. Then scattering model of the phosphor plates in different concentrations and thickness was evaluated with the corresponding experimental measurement. The absorption coefficients and conversion efficient of the phosphor sample were determined with the measurement of the blue and yellow lights in a special experiment. The determined parameters incorporated with Monte Carlo ray tracing and Mie scattering model form the final phosphor model. In order to evaluate the developed model, we made comparisons between the simulated and measured the power ratio of the yellow and blue lights of the phosphor plates pumped by a blue laser. Finally, we applied the phosphor model to simulate the power and chromatic performance of packaged white LEDs with silicate phosphor covered on blue GaN LEDs. We can find that the color differences between the simulation and experimental measurement are almost within 0.004. The simulation by the phosphor model well predicts the color coordinates of the LEDs with and without lens encapsulation. Such a model will be helpful in determining the phosphor parameters in LED package and can also be useful to design a white LED in high optical and chromatic performance.

 

Fig. 7. The measured and simulated spectrum of the white LEDs with the phosphor concentrations of (a) 10% without encapsulation, (b) 10% with encapsulation with a glass lens,, (c) 15% without encapsulation, (d) 15% with encapsulation with a glass lens.

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Fig. 8. The measured and simulated chromatic performance of the white LEDs for the concentrations of 10% and 15%.

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Table 1. The comparison of the chromaticity coordinates for the LEDs with and without encapsulation with lens between simulation and experimental measurement.

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