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Luminescent materials are widely used in white LEDs to convert part of the blue LED light into light with a longer wavelength, resulting in white light when both colors are well mixed. One way to integrate the luminescent material in the LED package is to deposit a thin luminescent layer on a planar carrier or disperse luminescent particles in the carrier material and then position the resulting wavelength conversion plate above one or more LEDs. It is very important that these wavelength conversion plates have the right properties to ensure homogeneous white light with a high efficiency and desired correlated color temperature (CCT). Key properties are the absorption and emission spectrum and the scattering and absorption coefficients. These properties strongly influence the color of the resulting light, but also the efficiency and the angular uniformity. This work describes an extensive study of the effect of the scattering and absorption coefficients in terms of the desired CCT. A computationally efficient extended Adding-Doubling method is used for the simulation of the light distribution and conversion in the planar wavelength conversion element. Ultimately an optimal combination with a high efficiency and low angular color deviation is desired. Different systems are investigated and optimal coefficients are found. With these findings a more targeted approach can be used in the manufacturing of wavelength conversion plates for white LEDs. The addition of scatterers or non-scattering luminescent particles can be used to obtain optimal scattering properties of the wavelength conversion plate.
© 2015 Optical Society of America
1. Introduction
Light emitting diodes (LEDs) are increasingly used in several applications, including lighting. Their popularity can be explained by their small size, high efficiency and long lifetime [1, 2]. LEDs intrinsically have a narrow emission spectrum. To obtain white light a number of methods can be used [3–5]. Combining LEDs with different colors, more specifically blue, green and red, will yield white light. Another approach uses one or more LED(s) that emit short-wavelength light, typically blue light, and a wavelength conversion element (WCE) to convert part of this emitted light into light with longer wavelengths, typically yellow. This WCE contains a luminescent material or a combination of different luminescent materials. These materials are typically phosphors, embedded in a transparent binder, but also quantum dots are increasingly considered [6]. The luminescent materials can be integrated in a LED package in different ways [7–9]. A first method is to deposit the phosphor directly onto the LED die. In this case it is possible that the luminescent material degrades faster and the luminescent properties are altered, because of the high temperatures when the LED is operated at high current densities [10]. A second method is to put the luminescent material on a remote location, which is often called a remote phosphor LED. This can avoid the heating of the phosphor, but more phosphor material is typically needed [11].
To guarantee the quality of a white LED, different properties must be controlled, including the correlated color temperature (CCT), the light extraction efficiency and the angular color uniformity. The CCT depends on the ratio between blue and yellow light, the light extraction efficiency describes the amount of generated light that escapes from the LED package and the angular color uniformity is a measure for the homogeneity of the emitted white light. Optimal characteristics of the emitted white light can be obtained by tuning the optical properties of the WCE, such as the amount of scattering and absorption.
A lot of scattering inside the WCE will lead to much back-reflected light [12, 13]. This understanding has initiated research on scatter-free phosphors for white LEDs [14]. On the other hand some scattering in the WCE will avoid light trapping in a planar luminescent layer and a sufficient amount of scattering is needed to ensure a good color mixing [15, 16]. This raises the question if there is an optimal amount of scattering to satisfy all requirements.
The scattering of the material influences the average optical path length that the excitation light travels before escaping the luminescent material. This means that the amount of scattering (quantified by the scattering coefficient µs) also determines the amount of absorption (quantified by the absorption coefficient µa) that is needed in the WCE to obtain a certain CCT. This paper therefore investigates the optimal amount of scattering (µs) in the WCE of a white LED in relation to the absorption coefficient (µa) to guarantee not only a good efficiency but also a good color uniformity.
The found optimum can be obtained in practice by changing the concentration(s) of the luminescent material(s), combining different luminescent materials (such as highly scattering phosphor with low scattering quantum dots) or adding extra volume scattering particles. It is also possible to tune the properties of a phosphor, such as particle size, adapt the refractive index of the binder material or change the concentration of the phosphor dopant to obtain optimal scattering/absorption properties. Furthermore, newly fabricated luminescent materials can quickly be evaluated and targeted development of new materials to reach this optimum is possible.
Several optical simulation studies have already been performed to analyze the impact of the optical parameters of a specific phosphor on the LED performance. Research has been done on the influence of the phosphor concentration and thickness of the WCE [7, 17–19] and of the phosphor particle size [9, 19–21] on the light quality. The starting point of these studies however is the assumption that spherical particles of a specific phosphor material are embedded in a binder material. Absorption and scattering properties are determined by the particle concentration and particle size as calculated by Mie-Lorenz theory. For these systems, scattering and absorption coefficients are directly coupled with one another. However, when combining multiple materials this tight coupling is not a necessity and a much broader range of optical properties is possible.
We propose a methodology that is based on the extended Adding-Doubling method [22]. This is a computationally efficient simulation approach that is well-suited for this optimization problem. The Adding-Doubling method is limited to infinite plane parallel layers which means that our methodology and study only covers white LEDs with a planar WCE. We remark that the used extended Adding-Doubling method could easily be adapted to specific situations where more parameter interdependencies are present, such as a varying emission spectrum or phase function.
2. Simulation method
The light distribution and conversion in the WCE are simulated using an Adding-Doubling method implemented in Matlab [23]. The Adding-Doubling method allows the determination of the angular distribution of light scattered by a sample, starting from the radiative transfer equation. This method can be extended to include luminescence and can be used for azimuthally symmetric light distributions within an infinite plane parallel WCE. This means that our study is limited to white LEDs with a planar WCE in which light guiding towards, and escape of light from the edges of the WCE can be neglected.
A schematic illustration of the simulated configuration is shown in Fig. 1. The fluxes are divided into conical segments to receive an angular intensity distribution for each wavelength both in transmission and reflection. Initially, the incident light will be blue and travels towards the WCE (shown in orange) in a Lambertian manner, this represents a small LED source emitting 1 Watt of blue light. As a result the spectral transmitted and reflected radiant intensity distribution for a certain incoming radiant intensity distribution are found. No spatial information of the light distribution is calculated or taken into account. All the optical parameters used in this simulation are defined in the extended radiative transfer equation: scattering coefficient (µs), phase function (P(ν,ν′)), absorption coefficient (µa), quantum efficiency (QE) and emission spectrum of the luminescent material. A more comprehensive description of this modeling approach is given in [22].
Fig. 1 Schematic representation of the setup simulated with the extended Adding-Doubling method. The radiant intensity distributions consist out of radially symmetric conical segments.
The simulations are run with only two wavelengths to reduce the calculation time: a source wavelength of 450 nm and an emission wavelength of 540 nm. This two wavelength approximation is valid when there is no significant overlap between the excitation and emission spectrum of the luminescent material in the WCE [24]. After the simulation and before doing the color calculations, the two discrete wavelengths are converted in two continuous spectra while maintaining the radiant flux ratio between source and emission wavelengths. The used spectra are shown in Fig. 2.
The aim of this study is to investigate if there are optimal combinations of µs and µa to have both high efficiency and color uniformity. This means that we keep all other simulation parameters constant. For each combination of µs and µa, the transmitted spectral radiant intensity distribution is saved, from which it is possible to determine the angular color characteristics and the total transmitted flux.
As a first case, we consider a WCE with a thickness of 3 mm and a refractive index n = 1.5 corresponding to a typical resin in which the luminescent material is embedded. The WCE is illuminated by a Lambertian point source emitting light with a wavelength of 450 nm. The WCE absorbs part of that source light with a probability depending on the µa(@450 nm) and emits light with a longer wavelength with a probability equal to the QE = 0.9. The absorption of converted light is assumed to be 10 times lower than the amount of absorption of excitation light, µa(@540 nm) = 1/10 µa(@450 nm) [25]. For converted light no re-emission of the light occurs. The volume scattering is defined by the Henyey-Greenstein phase function, with an anisotropy factor g = 0.9 and µs(@450 nm) = µs(@540 nm). These values were chosen to be in fair agreement with values reported in the literature for practical phosphors [25–27]. From this point on given values for µs and µa are referring to µs and µa(@450 nm).
To find optimal (µs,µa) combinations, simulations are run with µs and µa varying from respectively 0 to 10 mm−1 and 0 to 20 cm−1. The results of each simulation are saved to compare them in terms of CCT, light extraction efficiency and angular color uniformity. All these properties can be plotted in a µsµa-plot to draw conclusions.
After analyzing the aforementioned system with anisotropy factor g = 0.9, the same method is used to analyze a system with an anisotropy factor g = 0.5. In the first case the light is strongly forward-scattered, while in this second case the light is more diffusely scattered. In this way the influence of the anisotropy factor on the optimal amount of scattering is roughly investigated. All other simulation parameters are kept the same.
As a second case, the simulation method is adapted to include recycling of the reflected light. In a realistic LED package the light reflected by the WCE is partially recycled and send back onto the WCE. This results in a higher efficiency and better mixing of the light. The recycled blue light also gets an extra opportunity to be converted, so the amount of luminescent material can be reduced to achieve the same CCT, which reduces the overall cost.
In the Adding-Doubling model the complete LED package can be simulated by adding an additional layer to the WCE model (Fig. 1) which represents a diffuse reflecting plate with a certain reflectivity. This plate partially recycles light that is reflected back by the upper layers and can be implemented as an additional reflection matrix. This simple way of including recycling can be a sufficiently good approximation of a reflector cup, which is for example used in white remote phosphor LEDs as a mixing chamber. The advantage of using the Adding-Doubling method to simulate the LED package is the small computational time compared to the Monte Carlo method. To verify to what extend the Adding-Doubling method with inclusion of light recycling approximates a realistic reflector cup with a WCE, the results are compared to results obtained with a Monte Carlo ray-tracer, which has no restrictions on the simulated configuration. The commercial Monte Carlo ray-tracer used for this is TracePro [28]. The WCE has the same optical properties as described in the first case, with an anisotropy factor g = 0.9.
In the Monte Carlo simulation, the WCE has a radius of 25 mm and is embedded inside a cylindrical reflector cup with a height of 25 mm with a blue LED on the bottom of this cup in the center, as shown in Fig. 3. The walls of the reflector cup are Lambertian reflective with a reflection coefficient of 95%.
The only variable in our simplified light recycling model for the extended Adding-Doubling simulations is the reflection coefficient. In the reflector cup the light can hit the walls multiple times before it falls back onto the WCE, which lowers the overall recycling efficiency. We assume an average of 2 interactions before hitting the WCE again. This results in an effective reflection coefficient of 90% (= (95%)2) for the light recycling in the Adding-Doubling model.
The results of the comparison between the complete reflector cup (simulated in TracePro) and the simplified light recycling (simulated with the extended Adding-Doubling method) are shown in Fig. 4. The Monte Carlo simulations were run with 5·106 rays and took up to 35 times more time than the Adding-Doubling method. Moreover there is still a significant amount of noise present. We can see an overall good agreement between both simulations, only for the light transmitted under very small scattering angles there are some deviations. From these results we suggest that using the extended Adding-Doubling method to simulate a complete LED package with planar WCE including light recycling is permitted, provided that a good corresponding effective reflection coefficient is used.
Fig. 4 Comparison of the transmitted excitation (left) and converted (right) light of the LED package with a reflector cup (simulated in TracePro) and the LED package with simplified light recycling (simulated with the Adding-Doubling method).
3. Results and discussion
3.1. Anisotropy factor g = 0.9, without light recycling
In Fig. 5, the color of the light transmitted along the normal direction of the WCE is depicted for different (µs,µa). The results are very diverse. For example: for a WCE with small µa, most of the blue incident light propagates through the plate without conversion, resulting in transmitted blue light. On the other hand, when the luminescent material strongly absorbs the incoming blue light, the light escaping the plate is mainly converted light. Furthermore, it can be noted that by increasing the scattering light remains longer inside the WCE which increases the probability of conversion. The fraction of converted light is therefore larger when µs increases.
Fig. 5 True color of the light transmitted along the normal direction of the WCE of a system with g = 0.9 for different scattering and absorption coefficients. Black lines: iso-CCT lines for CCT = 5000 K, 6000 K and 8000 K.
The black lines shown on Fig. 5 connect different (µs,µa) combinations that yield the same CCT. Only (µs,µa) combinations lying on the same iso-CCT line are compared with each other, to ensure meaningful conclusions when analyzing system performance and efficacy.
The performance of the system is first analyzed in terms of the total amount of transmitted light. This is the amount of light escaping the WCE in forward direction and it quantifies the light extraction efficiency of the LED package when no light recycling is present. The transmission (in Watt) for the different (µs,µa) combinations is shown in Fig. 6 (a). The same iso-CCT lines are also shown in this plot. The trend followed by the transmission is deviating from the color-trend, indicating that for a specific CCT an optimal (µs,µa) combination, for which the transmission is maximal, exists.
Fig. 6 (a) Total amount of transmitted light (in Watt) of systems with g = 0.9 for different scattering and absorption coefficients. Yellow lines: iso-CCT lines for CCT = 5000 K, 6000 K and 8000 K. (b) Total amount of transmitted light (in Watt) of systems with g = 0.9 for different scattering and absorption coefficients resulting in transmitted light with a CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. Systems with maximum transmission are indicated with a red dotted line.
If we now plot the transmission as a function of the scattering coefficient for a fixed CCT, which is done in Fig. 6 (b) for CCT = 5000 K, CCT = 6000 K and CCT = 8000 K, the optimal scattering coefficients can be directly seen. Along one CCT-line every scattering coefficient corresponds with one absorption coefficient, so that the (µs,µa) combination yields the specific CCT. For example, for a CCT = 6000 K a maximum transmission 25% is found for µs = 6.1 mm−1 and µa = 0.27 mm−1. A first important observation is the fact that maximal transmission is not reached at very low µs values. This is because a certain amount of scattering is needed to avoid light trapping in the planar WCE by total internal reflection.
To analyze the system in terms of the angular color uniformity, the same technique is used. The deviation in color between the transmitted light in the center and light at the edge of the distribution, where the intensity is 10% of that in the center, is determined in the u′v′-plane (CIELUV). This color deviation Δu′v′ is plotted in a µsµa-plot shown in Fig. 7 (a). Again this can be plotted as a function of µs resulting in a fixed CCT as shown in Fig. 7 (b). The systems resulting in an optimal transmission are also indicated on these plots and the corresponding color deviation can be read from this graph. For a system with CCT = 6000 K the corresponding color deviation Δu′v′ = 0.015.
Fig. 7 (a) Color deviation in u′v′-plane (CIELUV) between center and edge of the transmitted light distribution of systems with g = 0.9 for different scattering and absorption coefficients. Yellow lines: iso-CCT lines for CCT = 5000 K, 6000 K and 8000 K. (b) Color deviation in u′v′-plane (CIELUV) between center and edge of the transmitted light distribution of systems with g = 0.9 for different scattering and absorption coefficients resulting in transmitted light with a CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. Systems with maximum transmission are indicated with a red dotted line.
In Fig. 7 (b) it is seen that the angular color deviation drops significantly with increasing scattering coefficient. This means that the optimal amount of scattering to reach a high light extraction efficiency might not be the amount in order to have a sufficiently good color uniformity. It is therefore necessary to make a trade-off between those two performance parameters. The graphs depicted in Fig. 6 (b) and Fig. 7 (b) directly allow us to make a suitable trade-off. For example, if we demand an Δu′v′ = 0.01 for a CCT = 6000 K, the system requires a WCE with µs = 8.1 mm−1 corresponding with a µa = 0.22 mm−1. This results in a system with a total transmission of 24 %. Which is only slightly less than the optimal transmission in this case.
3.2. Anisotropy factor g = 0.5, without light recycling
The analysis is repeated for a scattering WCE with anisotropy factor g = 0.5. The light will remain forward-scattered, albeit more diffusely. This change in g influences the resulting color as shown in Fig. 8, where the true color of the light transmitted along the normal direction of the WCE is shown. When comparing this to Fig. 5 we can see that there is more converted light present for the same (µs,µa) combinations when the light is scattered more diffusely. This is explained by the longer optical path length of the excitation light inside the plate for g = 0.5 compared to g = 0.9, increasing the chance for absorption and thus conversion.
Fig. 8 True color of the light transmitted along the normal direction of the WCE of a system with g = 0.5 for different scattering and absorption coefficients. Black lines: iso-CCT lines for CCT = 5000 K, 6000 K and 8000 K.
To find the optimal amount of scattering in order to obtain a system with maximum transmission for a specific CCT, the same technique is used as before. The transmission for systems with a fixed CCT (CCT = 5000 K, CCT = 6000 K and CCT = 8000 K) is shown in Fig. 9. The maximum transmission is slightly lower than the optimal transmission for the case where g = 0.9 (Fig. 6) and there is a stronger decrease of the transmission if we deviate from the optimal amount of scattering. For the system with g = 0.5 and CCT = 6000 K the maximum transmission of 23 % is found for (µs,µa) = (1.48,0.26) mm−1. The desired scattering coefficient in this case is significantly lower than in the previous case.
Fig. 9 (a) Total amount of transmitted light (in Watt) for different scattering and absorption coefficients of systems with g = 0.5. Yellow lines: iso-CCT lines for CCT = 5000 K, 6000 K and 8000 K. (b) Total amount of transmitted light (in Watt) of systems with g = 0.5 for different scattering and absorption coefficients resulting in transmitted light with a CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. Systems with maximum transmission are indicated with a red dotted line.
The color deviation for the system with g = 0.5 and fixed CCT (CCT = 5000 K, CCT = 6000 K and CCT = 8000 K) is shown in Fig. 10. When investigating the situation with maximum transmission for a system with CCT = 6000 K, (µs,µa) = (1.48,0.26) mm−1, the corresponding color deviation (Δu′v′ = 0.019) is slightly larger than it was the case for the optimal system with g = 0.9. Again in this case a suitable trade-off between light extraction efficiency and angular color uniformity can be selected based on Fig. 9 and Fig. 10.
Fig. 10 (a) Color deviation in u′v′-plane (CIELUV) for different scattering and absorption coefficients of systems with g = 0.5. Yellow lines: iso-CCT lines for CCT = 5000 K, 6000 K and 8000 K. (b) Color deviation in u′v′-plane (CIELUV) between center and edge of the transmitted light distribution of systems with g = 0.5 for different scattering and absorption coefficients resulting in transmitted light with a CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. Systems with maximum transmission are indicated with red dotted line.
3.3. Anisotropy factor g = 0.9, with light recycling
The results for the system with light recycling are shown in Fig. 11–13. In Fig. 12 (b) we can see that the total amount of transmitted light along a CCT-line increases rapidly with increasing scattering coefficient, but then slowly decreases over a long range of µs. The reason for this is because a higher µs is accompanied with a lower µa (for a fixed CCT), decreasing the amount of absorbed light in the WCE, but on the other hand a higher µs increases the amount of reflected light, increasing the amount of light absorbed by the reflector cup. These two processes are partially canceling each other out. For a system with a CCT = 6000 K the maximal amount of transmitted light is 52 % for a (µs,µa) = (9.9,0.12) mm−1. This is, as expected, much larger compared to the systems without recycling.
Fig. 11 True color of the light transmitted along the normal direction of the WCE of a system with g = 0.9 and simplified recycling for different scattering and absorption coefficients. Black lines: iso-CCT lines for CCT = 5000 K, 6000 K and 8000 K.
Fig. 12 (a) Total amount of transmitted light (in Watt) of systems with g = 0.9 and simplified recycling for different scattering and absorption coefficients. Yellow lines: iso-CCT lines for CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. (b) Total amount of transmitted light (in Watt) of systems with g = 0.9 and simplified recycling for different scattering and absorption coefficients resulting in transmitted light with a CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. Systems with maximum transmission are indicated with a red dotted line.
Fig. 13 (a) Color deviation in u′v′-plane (CIELUV) between center and edge of the transmitted light distribution of systems with g = 0.9 and simplified recycling for different scattering and absorption coefficients. Yellow lines: iso-CCT lines for CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. (b) Color deviation in u′v′-plane (CIELUV) between center and edge of the transmitted light distribution of systems with g = 0.9 and simplified recycling for different scattering and absorption coefficients resulting in transmitted light with a CCT = 5000 K, CCT = 6000 K and CCT = 8000 K. Systems with maximum transmission are indicated with a red dotted line.
The angular color deviation is shown in Fig. 13. The systems with a maximum transmission are indicated and for a CCT = 6000 K a Δu′v′ = 0.0067 is found. From this it is seen that recycling the reflected light can not only improve the efficiency, but also the angular color uniformity of the system. Again, it is possible to select a system in terms of the desired color uniformity by using Fig. 13 (b). As the total amount of transmitted light varies only little, this is a favorable approach.
Our results can be used to guide new luminescent material developments or evaluate existing luminescent materials. YAG:Ce, for example, is the most commonly used phosphor in white LEDs. The scattering and absorption coefficients of this materials, for several concentrations, are experimentally determined in [27]. From these experimentally obtained properties we see that the optimal values found by our simulations are not obtained by changing the concentration of this single phosphor. We only compare the results of YAG:Ce with the cases where the anisotropy factor g = 0.9 (without and with light recycling), as this is a relevant value for this phosphor. In concrete terms, for both the cases, there is more scattering required in order to obtain the desired angular color uniformity. White LEDs with a YAG:Ce luminescent plate often have an extra diffusor plate, which is necessary in order to comply with this need of additional scattering.
4. Conclusion
The amount of scattering relative to the luminescent absorption in the WCE has a significant impact on both the light extraction efficiency and angular color uniformity. Possible ways to change the ratio between scattering and absorption coefficient are adding extra non or low scattering luminescent materials or adding extra volume scattering particles to the WCE. In this paper we proposed a methodology to investigate the optimal amount of scattering in a WCE and applied this methodology to different cases. In most cases there is a trade-off between a high light extraction efficiency and a good angular color uniformity, both properties cannot be optimized at the same time. This is especially true for systems with a lower anisotropy factor.
The used simulation method is considerably faster than the Monte Carlo simulation method which is an important issue for optimization problems as the one tackled in this paper. The proposed general methodology in this paper can be adapted to different specific optical configuration and luminescent materials.
Acknowledgments
This research was supported by IWT (Flemish agency for Innovation by Science and Technology) through the IWT-SBO project ‘LumiCoR’, and the Impulse Fund KU Leuven through the project ‘High-luminance solid-state white light sources ( IMP/14/041)’.
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