White light-emitting diodes (WLEDs) that possess high luminous and energy efficiency, small volume, and green environment are good substitutions for conventional incandescent and fluorescent lamps [1]. However, improvements are still needed in light extraction and thermal conduction from the WLEDs packages [2, 3]. Blue or UV LEDs combined with phosphor materials can emit white light by converting the generated radiation to the complementary color. In general lighting applications, the phosphor-converted LEDs need to have a broadband spectrum which covers the visible region to achieve high color rendering index (CRI). Otherwise, a multilayer phosphor package with different emitting spectra should be selectable. However, due to the electron trapping phenomenon and the inelastic scattering between phosphor materials in the LED package, more emission power of the LED is lost as the phosphor concentration increases [4]. Phosphor arrangement and geometry can have a significant role in enhancing energy efficiency and reducing light trapping in the LED package. Novel phosphor configurations, e.g. scattered photon extraction (SPE) package [5], remote phosphor with a hemispherical dome [6, 7], as well as the method to enhance light extraction by using commercial YAG:Ce³⁺ (yellow) and SrS:Eu²⁺, Sr₂Si₅N₈:Eu²⁺ (red) phosphorus [9, 10] have been suggested and confirmed by ray-tracing analysis and experiments. Recently, some researchers have also recommended that a low-concentration phosphor mixture could provide improvement in the output luminous flux and the shift of color coordinates [11]. Other authors proposed an approach to enhance color homogeneity by adding SiO₂ [12] or using Y₂O₃:Eu³⁺ [8]. Another method to improve color quality is mixing a red phosphor like SrS:Eu²⁺ with a yellow or green phosphor, like YAG:Ce³⁺ or SrGa₂S₄:Eu²⁺ [13]. These studies are groundwork for the concept of reducing the backscattering light to an LED chip and improving the phosphor converted efficiency [14]. Single-layer, bi-layer or multi-layer structures with a different phosphor concentration at each layer have been reported in [15, 16].

This paper deploys a two-layer remote phosphor structure using a α-SrO·3B₂O₃:Sm²⁺ red phosphor layer above a YAG:Ce yellow phosphor layer, and investigates the variance of CRI, CCT deviation and luminous flux that can be caused by adjusting the concentration of red emitting α-SrO·3B₂O₃:Sm²⁺ phosphor. The characteristics of the proposed model are compared to a one-layer remote phosphor WLED (RP-WLED) package, which has been implemented in a previous study [18]. This investigation can be separated into two tasks: 1) analyzing the effect of α-SrO·3B₂O₃:Sm²⁺ concentration on the lighting performance of two-layer RP-WLED by combining Kubelka-Munk and Mie-Lorenz theories; 2) using the LightTools software to simulate the physical models of one-layer and two-layer RP-WLED.

Red-emitting α-SrO·3B₂O₃:Sm²⁺ phosphor, which has a peak wavelength of 680 nm, is a red polycrystalline phosphor. It is synthesized by three oxides including strontium oxide (SrO), samarium oxide Sm₂O₃, and orthoboric acid (H₃BO₃). Sm²⁺ ion is added to the polycrystalline phosphor for enhancing its absorbability at excitation spectrum region from 420 nm to 502 nm, which results in higher luminous efficiency [17]. Besides, with the advantage of excellent thermal and chemical stability, α-SrO·3B₂O₃:Sm²⁺ can be employed for compensating red light, and hence, increasing the color quality of LED lamps. However, until now, there has been no study that employs α-SrO·3B₂O₃:Sm²⁺ for two-layer RP-WLEDs.

The LightTools and SolidWorks are necessary to build the remote phosphor multi-chip WLEDs model, which is shown in Fig. 1. The RP-WLED reflector has a bottom length of 8 mm, a height of 2.07 mm and a length of 9.85 mm at its top surface. The one-layer remote phosphor configuration, which has a fixed thickness d = 1 mm, is mixed by α-SrO·3B₂O₃:Sm²⁺ red phosphor and YAG:Ce yellow phosphor and it is 0.8 mm far from the 9 LED chips as shown in Fig. 1(a). Each chip with a square base of 1.14 mm² and a height of 0.15 mm is bounded in the cavity of the reflector. The radiant flux of each blue chip is 1.16 W at wavelength 455 nm. Fig. 1(b) shows two-layer configuration with α-SrO·3B₂O₃:Sm²⁺ red phosphor layer having fixed thickness of 0.2 mm and YAG:Ce yellow phosphor layer having fixed thickness of 0.8 mm. In order to achieve light output and to investigate the effect of α-SrO·3B₂O₃:Sm²⁺ with the same CCT for both types of the studied RP-WLED packages, the amount of red-emitting phosphor-silicone mixture is adjusted while the concentration of yellow-emitting phosphor-silicone mixture is fixed at 15%. Also, the height of encapsulation is kept approximately the same in both configurations. Fig. 1(c) illustrates the package model and its real sample.

The two-flux model of Kubelka and Munk [19] is applied for two-layered structure in the analysis of light properties since it is simple and frequently yields fairly accurate results. We consider two fluxes across the x-direction through a thin layer of thickness x in YAG:Ce yellow phosphor layer of total thickness d as shown in Fig. 1(b).

The flux I₊(x) in the positive x-direction is decreased by absorption and backscattering inside the layer and is increased by backscattering of the intensity I₋(x) in the negative x-direction:

In contrast, the flux I₋(x) in the negative x-direction is decreased by absorption and backscattering inside the layer and is increased by backscattering of the intensity I₊(x) in the positive x-direction:

The above differential equations can be solved only for the ratio I₋(x)/ I₊(x). The results for x = 0 and x = d are of special interests. The ratio I₋(x = 0)/ I₊(x = 0) at x = 0 defines the diffuse reflectance R_KM of the two-layered structure:

Analogously, the ratio I₋(x = d)/ I₊(x = d) at x = d can be used to define the diffuse transmittance T_KM of this structure:

where and . The quantities K and S are related to the cross-sections for extinction and scattering, C_ext and C_sca, the asymmetry parameter g which presents the amount of back and forward scattered light, and the volume density V_d of phosphor particles [20-22]:

According to Mie-Lorenz theory [23], δ_sca is the reduced scattering coefficient. The extinction efficiency C_ext, the scattering efficiency C_sca, and the absorption efficiency C_abs are normally calculated by the following equations:

where k is the wave number (2π/λ), and a_n and b_n are the extension factors with even and odd symmetry, respectively, which are calculated by

where ψ_n(z) and ξ_n(z) are the Riccati - Bessel functions, z is relative to the size, which is calculated by Eq. (11), m is the refractive index of the particle which contains both the real and virtual term and depends on the ambient medium. In the WLEDs packaging, the ambient medium of phosphor particles is silicone glue. Thus the complex refractive index of a phosphor particle is calculated by m = n_phos/ n_sil;

where r is the equivalent spherical radius of phosphor particles, λ is the wavelength. n_phos and n_sil are the refractive indexes of phosphor and silicone gel, respectively.

For a two-layer structure, the transmission and reflection intensities of blue light and yellow light are most concerned, because the changes in diffuse reflectance R_KM and transmittance T_KM also result in changes in the optical properties of WLEDs. In Figs. 2 and 3, we can observe the interaction among the light scattering, reduced scattering, backscattering, and conversion inside two phosphor layers. These results are obtained by applying the above theoretical calculations with the variation of α-SrO·3B₂O₃:Sm²⁺ concentration from 2% to 35%, whereas YAG:Ce yellow phosphor concentration is chosen as 15%. The average radius of two types of phosphor configurations are set to 7.25 μm. The refractive indexes of silicone glue, α-SrO·3B₂O₃:Sm²⁺ and YAG:Ce particles are set to 1.5, 1.93, and 1.83, respectively [12].

In Fig. 2(a), it can be seen that the scattering and reduced scattering coefficients have a rapid rising trend for blue light (λ = 455 nm), yellow light (λ = 595 nm) and red light (λ = 680 nm). Moreover, scattering coefficient and reduced scattering coefficient of blue light increase higher than both yellow and red light in the yellow phosphor layer. Meanwhile, the scattering coefficient of blue light in the red phosphor layer also gets greater than for yellow light, but the reduced scattering coefficient is not much different (Fig. 2(b)). The backscattering coefficient at a wavelength of 455 nm is much larger than at the wavelength of 595 nm and 680 nm in yellow phosphor layer as shown in Fig. 3. For both blue and yellow lights in the red-emitting phosphor layer, the backscattering coefficient is much lower than the one of 680nm (red) light. These phenomena may be due to the following reasons: 1) when α-SrO·3B₂O₃:Sm²⁺ concentration rises, more blue, yellow and red light are absorbed and scattered. It becomes harder for blue and yellow light to penetrate the phosphor layer. Thus the light intensity changes extraordinarily, which implies a continuous variability of transmitted and reflected light in Fig. 4. 2) With the increasing of α-SrO·3B₂O₃:Sm²⁺ concentration, blue light is further backscattered to all directions in both yellow and red phosphor layers. Thus the reflected blue light tends to increase. The further increasing of α-SrO·3B₂O₃:Sm²⁺ concentration does not account for the rising of intensity at the incident surface, so the transmitted light intensity tends to decrease in Fig. 4. 3) When red phosphor concentration increases, at first more yellow light is converted. When concentration increases further, the effect of yellow light absorption and backscattering is the same as blue light, which explains for the increasing in transmitted light intensity in wavelength 595 nm (shown in Fig. 4). This increase leads to a trend of wider emitted spectrum at the wavelength approximate to 595 nm, similar to the theoretical calculation spectra for two-layer LED in Fig. 5, or the changes in diffuse refl ectance and transmittance also result in the color index variation of the WLEDs.

The emission spectra of two-layer and mixed one-layer WLED are obtained by running optical ray-tracing of LightTools^TM software at the same correlated color temperature (CCT) 8500 K. With the same concentrations of yellow and red phosphor particles, the experimental results are compared to the theoretical values by using Matlab software, as shown in Fig. 5. The emission spectra of the blue, yellow and red phosphors with the blue LED excitation light source are illustrated in Fig. 5(a). These spectral power distributions are measured using the optical simulation. Both YAG:Ce and α-SrO·3B₂O₃:Sm²⁺ phosphors are simulated based on the extended Gaussian model [25] described by (13). For multiple phosphor layers (yellow and red), converted yellow radiant power from the first layer is divided into Y₁ and Y₂. While Y₁ could be absorbed by the red phosphor because it lies within the absorption (extinction - C_ext) spectral range of red phosphor, Y2 cannot be absorbed by the red phosphor (Fig. 5(a)). The reflected and transmitted light would include some portion of the blue, red, and yellow (Y₁ and Y₂) radiations for blue radiant power incident on multiple phosphor layers. Therefore, the total spectral power distribution modeling for two-layer-coated phosphors white LED can be expressed as a tricolor spectrum (B-Y-R) (Fig. 5(b)).

The optical ray-tracing results matched well to the theoretical calculations in the two-layer structure. The spectral energy distributions in the WLEDs emission light and color features, in this case, are determined by the constitution of the relative luminous energy of the converted photons in phosphor layers. The reason for the disagreement in one-layer LED structure, a considerable percentage of the translated photons involved in backscattering are absorbed (flux I₋(x)) by the multichip LED. However, in the two-layer structure, these backscattering photons are taken out of the LED package, in addition to the total energy spectrum. Furthermore, the forward-emitted (flux I₊(x)) intensity from the first (YAG:Ce) layer will go through the second (α-SrO·3B₂O₃:Sm²⁺) phosphor layer and experience great scattering changes (Fig. 2(b)), while the second phosphor layer can absorb significant photon quality which drops in the excited energy band. However, the two-layer configuration attributes a higher percentage of photons to the total light energy than a single phosphor layer. For that reason, the first phosphor layer turns into the forceful layer. This leads to the result that the output luminous flux of two-layer LED is at least 17% higher than that of mixed one-layer LED. It has been demonstrated that high-concentration of red phosphor α-SrO·3B₂O₃:Sm²⁺ that exceeds 20% had disadvantages in output luminous flux as Fig. 6, due to the light scattering and absorption between phosphors’ materials as mentioned above.

The inelastic scattering of light reduces the efficiency since the increased light path length leads to higher possibility of re-absorption of the incident and emitted light. Light path randomization also increases the probability of light incident on high loss areas. Compared to the mixed one-layer LED at the same CCT 7700 K and 8500 K, the increased radiation flux of blue, yellow and red components in two-layer LED indicate the decreased scattering of light inside the package. To provide further proof that the total emission power (T_RP), including transmittance and reflectance, can be described in the spectral formula depending on wavelength (λ) and phosphor particles radius (r), from Eq. (3) to Eq. (11) as

From Eq. (12), the luminous flux (lumen) can be calculated from [24]

where Ψ_m is a constant, η(λ) is the relative photopic luminous efficiency function, and Δ(λ) is the wavelength interval.

The WLED color properties also depend on the spectral power distributions, which depend on the relative radiant power of the phosphor-converted photons in both layers. Figure 7 plots the CRIs of two-layer and mixed one-layer WLEDs with various red phosphor concentrations at correlated color temperature (CCT) 7700 K and 8500 K. Theoretical calculation and ray-tracing simulation spectra agree well. The CRIs values are quite different between two phosphor configurations, although the amount of yellow and red phosphors are equal in all cases. The two- layer package, which supports longer-wavelength red phosphor than the single-layer one, yields about 5% higher CRI output. With the increment of red phosphor concentration, the CRI moves up to the same extent in both two-layer and mixed one-layer LEDs under CCT modes. This indicates that their scattering and illumination characteristics are the same; however, for two-layer LED packages the chromaticity of LED can be efficiently adjusted by the ratio of blue to yellow and red components since the yellow phosphor does not absorb the backscattering of red emission from the upper red phosphor layer. This can confirm that the emission energy loss is associated with the re-absorption process by different phosphor emission spectrum within the LED packages.

One more improvement of the CRI is to overcome the derating of light sources at very low and very high CCTs below 3500 K and above 6500 K, respectively. The different CCT deviations should be required in various typical standards for WLED applications. The higher CCT deviation would lead to non-uniform white color at different angles because the light passes through the phosphor layer with higher concentration to be a smaller CCT deviation. As a result, the different lights could be mixed perfectly to form the uniform white light. That is the reason why CCT deviation in one-layer LED package decreases a little with the increment of α-SrO·3B₂O₃:Sm²⁺ concentration percentage in Fig. 8. Meanwhile, CCT deviation in two-layer LED package, where yellow phosphor layer concentration is fixed at 15% and α-SrO·3B₂O₃:Sm²⁺ concentration rises from 2% to 15%, changes insignificantly. However, with red phosphor concentration higher than 15%, CCT deviation tends to increase significantly due to scattering and backscattering in red phosphor layer with α-SrO·3B₂O₃:Sm²⁺ particles to be raised up as in Figs. 2(a) and 3. As a result, non-uniform WLED color is generated at different angles. These results are the different spectral power distribution of light from two different phosphor configurations such as Fig. 5.

Remote phosphor multi-chip WLEDs with separating α-SrO·3B₂O₃:Sm²⁺ (red) and YAG:Ce (yellow) phosphor layers are studied under different α-SrO·3B₂O₃:Sm²⁺ concentration conditions. It is found that this new packaging method with red-emitting α-SrO·3B₂O₃:Sm²⁺ phosphor leads to at least more than 17% increasing in lumen compared to traditional mixed red and a yellow phosphor packaging at the same correlated color temperature. The effect of higher additional concentration α-SrO·3B₂O₃:Sm²⁺ of two-layer RP-WLEDs is also observed. This improvement in uniform color properties is due to increased scattering and back reflection of light inside the packages. The CRI of two-layer remote phosphor white LEDs is almost 5% higher than mixed phosphor white LEDs in α-SrO·3B₂O₃:Sm²⁺ concentrating regulation condition. The technology of two-layer remote phosphor multi-chip WLED package that employs α-SrO·3B₂O₃:Sm²⁺ phosphor can give high lumen and color rendering index and allowable uniform color range. These results offer a prospective practical solution for manufacturing two-layer remote phosphor WLEDs. In further works, the influence of α-SrO·3B₂O₃:Sm²⁺ phosphor features on the lighting performance of RP-WLEDs will be more developed.