1. Introduction

White LEDs are potential candidates for replacing traditional lighting sources [1–4]. Compared to fluorescent and incandescent lamps, white LEDs have many advantages such as high efficiency, long lifetimes, and environmental friendliness [5,6].

Generally, the methods employed to obtain white LEDs are as follows: 1) color mixing using multiple single LEDs emitting red, green, and blue, 2) near-ultraviolet (UV) LEDs with different colors of phosphors (e.g. red, green, and blue), and 3) blue LEDs combined with a yellow phosphor [7–10]. The first method has the advantages of variable color points and higher efficiency than phosphor LEDs, but the color rendering index (CRI) is very low due to the narrow emission spectrum. Although the second approach achieves great color stability with broad emission, further improvement is needed with respect to the UV LED performance. From an industrial point of view, the most commonly used method for generating white light is the last approach.

Recently, various studies on methods for optically modeling phosphor-converted white LEDs have been published [11–13]. These reports have shown that the optical properties of white LED packages can be predicted by phosphor modeling. Especially, C.-C Sun et al. proposed the process for precise modeling of silicate phosphors applied to GaN-based white LEDs [11]. They measured a particle size and a density of the phosphor and evaluated scattering distribution, absorption coefficient, and conversion efficiency of the silicate phosphor plate sample. The spectrum and color coordinates of simulation based on the measured parameters has good agreement with experimental measurement. However, their model has obvious deviation when YAG phosphor instead of silicate phosphor is adopted. The reason has not been explored yet even though YAG phosphor is being popularly employed in white LED packages.

In this paper, we propose a method for improving the accuracy of phosphor modeling by considering spectra similar to the inherent emission of the phosphors. The light converted from a phosphor particle can be absorbed by nearby phosphors; thus, the emission spectrum may be distorted if the particles are aggregated. In this work, variations in the emission spectrum due to re-absorption are measured and analyzed by changing the phosphor concentration from 0.5 wt% to 6 wt% of silicone. The phosphors used in this study include a YAG:Ce³⁺ phosphor and a Eu-doped silicate phosphor. The former exhibits stronger absorption than the latter in the overlap region of the excitation and emission spectra. We demonstrate that the emission spectrum measured from phosphors in the powder state differs from that measured for a corresponding single phosphor. This difference depends on the phosphor composition and plays an important role in the accuracy of optical simulations for white LED packages with phosphors.

2. Experimental principle

The optical properties of a phosphor should be accurately measured and reflected in an optical simulation to predict the spectra and color coordinates of white LEDs. Conventionally, data such as the excitation, emission, and quantum yield spectra are collected by a photo-luminescence (PL) measurement system with a narrow band wavelength source. In Fig. 1(a), the schematic of the C9920 absolute PL quantum yield measurement system (Hamamatsu Photonics, Japan) is shown. The excitation wavelength is selected by a band-pass filter and a monochromator, and the phosphor sample is maintained as a powder in a 20-mm quartz Petri dish [14]. In this study, two types of phosphors, YAG:Ce³⁺ phosphor (Nemoto-81003) and a silicate-based phosphor (Intematix EY4453), were adopted for comparison. To measure the emission spectra as a function of phosphor concentration, the phosphors were mixed with a silicone binder (Dow Corning 6370HF) and then fabricated as an 800-μm-thick film by injection molding. The phosphor concentrations adopted in this experiment were 0.5 wt%, 2.5 wt%, and 6 wt%.

 

Fig. 1 Schematic diagram of (a) the system for measuring the excitation, quantum yield, and emission spectra of phosphors and (b) the interaction between the excitation light and a phosphor particle.

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Figure 1(b) illustrates the interaction between the excitation light and the phosphor particles. When the excitation light is introduced into the phosphor sample in the quartz dish, it is absorbed by a phosphor or scattered without being absorbed. Some of the absorbed blue light, photons with high energy, is down-converted to green-yellow light, photons with low energy, by the Stokes shift. However, the remaining light that is not converted to green-yellow is released as a non-radiative loss. Some of the converted light is absorbed again by neighboring phosphor particles. Scattered light without being absorbed is governed by the Mie theory because the phosphor particle size is 10 times larger than the wavelength of blue light. The scattered angular distribution depends on the particle size. The angular distribution is more similar to an isotropic pattern when the particle size is smaller [15].

3. Results and discussion

Figure 2(a) shows the excitation and emission spectra of YAG:Ce³⁺ phosphor powders (Nemoto-81003). The excitation spectrum is represented as the intensity of absorption by the phosphors, and the emission spectrum is the intensity of the light that is wavelength-converted by the phosphors. The excitation spectrum was measured by increasing the wavelength of the monochromatic light source from 430 nm to 600 nm in 10-nm intervals; this spectrum has a peak wavelength of 460 nm. The emission spectrum, with a peak wavelength of 550 nm, was measured for an excitation wavelength of 460 nm. Overlapping occurs between 475 nm and 545 nm, and the cross point between the excitation and emission spectra is located at 505 nm, with an absorption of 0.395%. When green-yellow light is emitted with an isotropic distribution from a phosphor particle, the light corresponding to the overlap zone is re-absorbed by surrounding phosphor particles. As a result, the emission spectrum of a powder state with a small distance between phosphor particles is distorted due to the increased possibility that the converted light will interact with other particles. Therefore, the emission spectrum without the effect of re-absorption among phosphor particles should be measured to obtain the original emission spectrum.

 

Fig. 2 Spectra from the YAG:Ce3 + phosphor: (a) excitation and emission spectra in the powder state; (b) comparison of emission spectra from 0.5 wt%, 2.5 wt%, and 6 wt% films and phosphor powder. The emission spectra are normalized with peak intensity.

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To identify the extent of the re-absorption effect on an emission spectrum with respect to the phosphor concentration, emission spectra from YAG:Ce³⁺ phosphor films with phosphor concentrations of 0.5 wt%, 2.5 wt%, and 6 wt% were measured with PL measurement system, as shown in Fig. 2(b). The phosphor film made of 0.5 wt% of silicone (hereafter, 0.5 wt% film) behaves as a transparent silicone specimen. The emission spectrum from the phosphor powder is approximately 12 nm narrower than that of the 0.5 wt% sample, with half of the normalized intensity, and the spectrum gradually broadens as the phosphor concentration decreases. This behavior indicates that the mean path between the phosphor particles has a strong influence on the emission spectrum. In other words, the inherent emission spectrum can be obtained if the effect of absorption is minimized by increasing the mean path between phosphor particles.

To investigate the effect of re-absorption on the emission spectrum, the excitation and emission spectra of a silicate-based phosphor (Intermatix EY4453) in the powder state as well as in a film were also measured. As shown in Fig. 3(a), the excitation spectrum has an absorption of 0.83 at 450 nm and extends to 530 nm. The emission spectrum has a peak wavelength of 565 nm. The overlap zone ranges from 473 nm to 530 nm, and the cross point at 496 nm has an absorption of 0.22, which is much lower than the YAG:Ce³⁺ phosphor absorption. Figure 3(b) shows the emission spectra for various phosphor concentrations. The spectrum from the powder is only 4 nm narrower than that of the 0.5 wt% sample, and there is little difference among the 0.5, 2.5, and 6 wt% samples.

 

Fig. 3 Spectra of the silicate-based phosphor: (a) excitation and emission spectra in the powder state; (b) comparison of emission spectra from 0.5 wt%, 2.5 wt%, and 6 wt% films and phosphor powder. The emission spectra are normalized with peak intensity.

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By comparing the results of Fig. 2 and Fig. 3, it is clear that a large distortion in the emission spectrum is generated when the phosphor has a wide overlap region for the excitation and emission spectra. This result is explained in Fig. 1(b). As the overlap region widens, more Stokes shifted light is absorbed by the phosphor, resulting in a selective reduction of the emission spectrum in the overlap region. As the phosphor concentration increases, the reduction becomes greater because the Stokes shifted light is more scattered then absorbed selectively by the neighboring phosphors.

4. Verification

White LED packages were fabricated with a lead frame, a blue LED chip, and an encapsulation including the phosphor; these packages were modeled in an optical simulation as shown in Fig. 4. The white LED simulation was conducted with LightTools 8.1 software based on Monte Carlo ray tracing and Mie scattering. For phosphor simulation, this simulation tool needs precise information about the phosphor density and particle size as well as spectra such as absorption, excitation and emission. The first step is to create physical model of the LED chip (0.97mm x 0.97mm x 0.105mm) and the lead frame (8.8mm x 7.6mm x 1.78mm). The optical properties of the blue LED chip (Cree EZ1000), such as the spectral power distribution and the angular intensity distribution, were measured. The lead frame was consisted of Ag-coated lead with Gaussian reflection of 90% and frame of Polyphthalamide (PPA) material with diffusion reflection of 95%. Next, the phosphor density and mean particle size were measured as 4.55 g/cm³ and ~8 µm for the YAG:Ce³⁺ phosphor, respectively, and 4.48 g/cm³ and ~15.5 µm for the silicate-based phosphor, respectively. The excitation, absorption, and emission spectra for each phosphor were determined by a quantum yield measurement system. All of LED chip, package, and phosphor parameters were inserted into the optical model, and the simulation was conducted with 3 million rays. The intensity distribution of unconverted light was based on Mie theory.

 

Fig. 4 Image and optical model of the LED package with silicone encapsulation including the phosphor.

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Figure 5 shows the simulated and experimental results of the YAG:Ce³⁺ and silicate-based phosphors for concentrations of 8 wt% and 9 wt%, respectively. As shown in Fig. 5(a), when the emission spectrum of the powder state is applied, a remarkable error between the simulation and the measurement is generated. However, the difference between the twospectra greatly decreases when the emission spectrum of the 0.5 wt% sample is applied. Thus, the optical properties of a phosphor with strong re-absorption must be measured in a state in which there is little interaction among the phosphor particles. As phosphor concentration increases, the distortion becomes serious as illustrated in Fig. 1(b). In contrast, the simulation error of the silicate-based phosphor is relatively small due to the weak re-absorption, as shown in Fig. 5(b). However, the proposed method still improves the agreement between the simulated and measured results.

 

Fig. 5 Comparison of emission spectra between fabricated samples (solid lines) and simulation results (dotted lines). (a), (b) are emission spectra from LED packages made of YAG:Ce3 + phosphor concentration of 8 wt%, and (c), (d) are those from LED packages made of silicate-based phosphor concentration of 9 wt%. Simulations are performed with emission spectrum from the powder state ((a), (c)) and the 0.5 wt% films ((b). (d))

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A comparison of the optical performance factors for the YAG:Ce³⁺ and silicate-based phosphors is presented in Table 1. Regardless of the phosphor type, the simulation accuracy based on the emission spectrum from the silicone film sample is higher than that of the powder sample with respect to the correlated color temperature (CCT), color rendering index (CRI), and chromaticity coordinates. Additionally, the simulation results employing the silicate-based phosphor data exhibit good agreement with the measurements compared to the YAG:Ce³⁺ phosphor, due to the weaker re-absorption effect.

Table 1. Comparison of chromatic performance factors for YAG:Ce³⁺ and silicate-based phosphors

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5. Conclusions

Improved phosphor modeling method for white LEDs by considering the effect of re-absorption by phosphor particles is proposed. According to the excitation and emission spectra measured by an absolute PL quantum yield measurement system, a high absorption rate exists in the overlap region of the two spectra. As a result, converted light by the phosphors is re-absorbed by other particles, and thus, the emission spectrum is distorted. As phosphor density increases, the distortion becomes greater. For further analysis, YAG:Ce³⁺ and silicate-based phosphor samples at different concentrations, with the same thickness, were evaluated, and the emission spectrum of the phosphor under weak re-absorption conditions was measured. The modified emission spectrum was incorporated in the optical simulation, and the simulation results showed better agreement with the measured parameters, e.g., the CCT, CRI, and chromaticity coordinates, of white LEDs in the optical spectrum compared to the previous method based on the emission spectrum of phosphors in the powder state. This research will contribute to the design of white LEDs for high chromatic performance with phosphors.