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A new method of creating a source model of a phosphor-converted white LED is demonstrated. It is based on a simple phosphor model, of which some key parameters have been obtained from measuring the near-field chromatic and luminance characteristics of a complete LED. The accuracy of the model is verified by measurements and simulations on an LED with a ball lens as primary optic.
©2013 Optical Society of America
1. Introduction
The light-emitting diode (LED) is the most promising light source, due to its environmental friendliness, energy saving, long life, high reliability, fast response, and high chromatic performance [1,2]. Thus LEDs for solid-state lighting (SSL) are targeted to replace traditional lighting, such as incandescent light bulbs, and are likely to enter the general illumination applications market [3]. Many applications of LED, such as outdoor lighting, vehicle headlamp, and smart lighting system, have been proposed and demonstrated [4–6].
The most common method to create high-quality white LEDs is based on mixing the short-wavelength blue light from a blue chip with the excited re-emission long-wavelength green-yellow light from a phosphor-silicone mixture [7–9]. The output intensity ratio of blue light and converted yellow light determines the overall chromatic performance of a white LED. Generally, the higher the concentration of the phosphor in the mixture, the lower the correlated color temperature (CCT), but other details of the LED package also decisive [10].
Optical design plays an important role in achieving high-quality SSL, and ray tracing programs based on Monte Carlo algorithms are commonly used to accelerate this process. A dome lens is often used in LED package optical design to change the light intensity distribution and enhance light output efficiency. However, the package structure not only changes the light distribution but dramatically influences the total color balance and the uniformity of the color over the emission angle because it changes the details of the blue light conversion.
To obtain a reliable simulation result requires a precise LED optical source model and a satisfactory phosphor characteristic model. Earlier studies have made progress in these areas. Sun et al. created a precise optical model for LED lighting in the mid-field region [11]. Chien et al. demonstrated a precise optical model of multi-chip white LEDs [12]. Moreno and Sun proposed a general and simple but accurate analytic representation for the radiation pattern of the light emitted from an LED [13]. Sun established the first precise phosphor model that accurately predicts the optical and chromatic performance of silicate phosphors applied to GaN-based white LEDs [14]. Hung and Tien introduced a different method to model the pc-LEDs by measuring the bidirectional scattering distribution functions of the phosphor layer [15]. Although these methods can precisely predict the performance of white LEDs, they involve time-consuming calculation and data collection. Therefore, we have attempted to formulate a simple but efficient method to model white LEDs using near-field chromatic luminance data to define the best phosphor parameters. The details are described in the following sections.
2. Optical modeling
2.1 Phosphor-converted white LEDs
Figure 1 describes the basic principle behind most white LEDs. The white light is obtained by coating a blue LED chip with a phosphor conversion layer, which consists of a powdered phosphor mixed with a silicone binder. Several phenomena occur in this layer. Some blue light does not encounter any phosphor particle and directly goes through the layer, which is called transmitted blue light. Some blue light with a wavelength in the excitation spectrum of the phosphor is converted to long-wavelength lights and is remitted isotropically. Some blue light is absorbed by phosphor particles and is transferred to heat. Some blue light encounters particles but is not absorbed. These rays will be scattered as described by Mie theory. The scattering effect also could happen when remitted yellow rays encounter phosphor particles. All the light rays mix into white light at the near-field and then spread into the far-field.
2.2 LED modeling
A white Luxeon-C LED from Philips Lumileds as shown in Fig. 2(a) is modeled in the optical software LightTools as Fig. 2(b) [16,17]. In this research, the LED is operated at 50 mA to avoid thermal effects.
Fig. 2 The appearance and structure of the LED used in the study. (a) Actual picture. (b) Optical model. (c) Schematic cross section diagram.
To model the blue LED chip, the first step is to create its physical model that includes its geometrical structures and optical properties. Figure 2(c) shows the schematic diagram of the Luxeon-C LED. Microscopic measurement determined the thickness of the phosphor layer and the silicone layer to be 50 µm. The top part of the chip is GaN of size 1mm × 1mm. The optical properties of the GaN surface are modeled as 80% reflection with scattering and 20% absorption. The second step is to set up an emission distribution from the LED chip. The blue chip is modeled as a Lambertian emitting surface with a measured spectrum from an integrating sphere. Characteristic for this LED is the array of 4x4 current contact dots on the surface, which are vias serving to spread the current evenly over the chip surface. These are modeled as non-emitting circles.
2.3 Phosphor conversion layer modeling
Modeling the behavior of the phosphor conversion layer is more complicated than of the LED chip. The former requires defining the excitation spectrum, emission spectrum, and quantum yield efficiency. Figure 3 shows the excitation and emission spectra of the phosphor and the spectrum of the blue LED chip used in this study. Data for the excitation and emission spectra of the phosphor are provided by Intematix [18]. The excitation and emission spectra may be considered as the probability that an incident photon of given shorter wavelength will be absorbed, and a photon of longer wavelength re-emitted. The emission spectrum describes the spectral power distribution of the re-emitted light. The quantum yield describes the percentage of absorbed energy that is converted to a longer wavelength. It is also a function of the wavelength of the incident photon. The other unconverted photons are converted to heat. The quantum yield is typically based on a theoretical value. In accordance with previous research, we use the value 0.92 for all blue light [19]. The energy loss due to the Stokes shift from blue to yellow photons is also considered in our ray tracing process.
2.4 The phosphor parameters
Next, the scattering parameters of a powdered phosphor mixed with a silicone binder will be defined. In our simple phosphor model, Mie theory is applied to describe light scattering by the phosphor particles. There are two unknown parameters: the effective phosphor particle radius, r, and the number density of these phosphor particles, N. Refractive indices of phosphor and silicone have significant effects on the radiant flux of pc-LEDs [20]. This study defines the refractive index of phosphor and silicone as 1.8 and 1.49, respectively. The influence of phosphor particle sizes on the lumen output and on the conversion efficiency has been documented [21]. The angular distribution of the scattered light for various phosphor radii is calculated by Mie theory and plotted in Fig. 4 . Figure 4 shows that large particles lead to weak scattering and that small particles enhance scattering significantly.
LED manufacturers are able to measure particle size distributions in test samples and define suitable density for their products. However, such phosphor test samples are not always available. Since the phosphor radii distribution was not available, it was infeasible to formulate a reasonable virtual phosphor radii distribution that reflects many unknown parameters such as radii distribution region and their corresponding weighting factors, which also would make the model more complicated and hard to use. Instead, our concept is to define an effective particle radius in the model that best describes the scattering effect of a real LED. Moreover, a single particle radius also makes the model simple and easy to use. The present paper will demonstrate how satisfactory data can be obtained from measurements on complete, widely available LED packages.
2.5 Research method
Figure 5 depicts the near-field, mid-field, and far-field of an LED. In the near-field, the CCT and spatial luminance vary with surface position and angle, due to the wavelength conversion and scattering effect of the phosphor layer. In the far-field, light intensity and CCT vary with angle only, since the light emitted from the LED spreads from near-field to far-field, a precise model of a white LED should describe well the optical and chromatic properties in both the near-field and far-field. The proposed method was formulated accordingly, and its flow chart is illustrated in Fig. 6 . We define the excitation and emission spectra of phosphor. Then we choose several sets of particle radii and densities for our simulations. The uncertainty of the parameters is then reduced step-by-step by comparing simulated and experimental results from integrated spectrum, far-field intensity, and color to near-field luminance and color. Finally, the obtained parameters are used to predict the optical and chromatic behaviors of LEDs.
2.6 Experimental measurement
The spectrum of the LED was measured by an integrating sphere. The far-field and near-field characteristics were obtained with a source imaging goniometer SIG300 from Radiant Zemax [22]. Figure 7 shows the SIG measurement schematic. The LED is aligned on a rotation stage plate and emitting upward. The SIG has a zoom lens combined with a CCD to focus on the emitting surface. The CCD captures real radiation images of the emitting surface, while the goniometer moves around the LED with a wide range of inclination and azimuthal angles (θ, φ). The near-field luminance L, color coordinate u’, and color coordinate v’ are recorded as four-dimensional data L(x,y,θ,φ), CIE u’(x,y,θ,φ), and CIE v’(x,y,θ,φ), respectively. Thus, the SIG performs near-field characteristics measurement by combing measured colorimetric images at many directional angles. The far-field intensity and color distribution can be calculated from near-field data because the near-field data were already recorded with angular information. We generated a ray set file from all measurement results using ProSource [23]. It is convenient and efficient to use a ray set file to design lighting such as street lamp and vehicle headlamp. However, it is difficult to change internal structures of the LED when using the ray set file. Thus the ray set file cannot be used to do optical design such as extracting more light from the LED, or to increase the angular color uniformity. However, a more detailed PC-LED model would support nearly all applications.
2.7 Using the far-field information
The first step is to compare the simulated and measured far-field averaged spectrum. The total wavelength-conversion ability is proportional to the total cross-section area of phosphor particles. Thus for a given spectrum, a small-radius parameter corresponds to a high-density parameter. In this study, we chose three small particle radii and three large particle radii, for which we figured out the possible related densities. Table 1 shows these particle radii and their corresponding densities to reconstruct the spectrum of the Luxeon-C LED. Figure 8(a) shows that all simulated spectra fit the measured spectra very well. Thus, comparing the far-field spectrum would not reduce the parameter uncertainty.
Table 1. Phosphor radii and densities used to reconstruct the Luxeon C spectrum
Fig. 8 Measured and simulated far-field parameters. (a) Averaged spectrum. (b) Intensity distribution. (c) Color coordinate u’. (d) Color coordinate v’.
The second step is to compare the simulated and measured far-field luminous intensity distributions, shown in Fig. 8(b). All simulated curves fit the measured curve perfectly. Thus, the far-field intensity information does not reduce parameter uncertainty.
The third step is to compare the simulated and measured far-field angular color distributions, shown in Fig. 8(c) and Fig. 8(d). Figure 8(c) indicates only a slight difference between these parameters. However, in Fig. 8(d), the simulation results indicate that large particle radius leads to a color coordinate's changing significantly over angle. After comparing the slopes of simulated and measured curves, we retained radius parameters 50 nm, 100 nm, and 1000 nm and excluded 200 nm, 3000 nm, and 5000 nm.
2.8 Using the near-field information
The fourth step is to compare the simulated and measured near-field luminance distribution over position. This involves analyzing two cross-section lines. One cross-section line is along the central part of the LED surface, as shown in the insert of Fig. 9(a) . Another line is along the conduction dots of the LED surface, as shown in the inserted picture of Fig. 9(b). Since the conduction dots area does not emit light, the scattering effect of phosphor causes light to emerge from the phosphor layer above the dots area. Thus, analyzing the near-field behavior along this line can help better model phosphor scattering effects. Figure 9(a) and Fig. 9(b) are the simulated and measured near-field luminance distributions over position of two cross-section lines. Because there is little differences between simulated and measured results in Fig. 9(a) and Fig. 9(b), we cannot reduce the parameter uncertainty in this step.
Fig. 9 The measured and simulated near-field. (a) Luminance along central line. (b) Luminance along dots line. (c) Color coordinate u’ along central line. (d) Color coordinate u’ along dots line. (e) color coordinate v’ along central line. (f) Color coordinate v’ along dots line.
The fifth step is to compare the simulated and measured near-field color distribution over position. Figure 9(c), Fig. 9(d), Fig. 9(e), and Fig. 9(f) depict the near-field color distributions of two cross-section lines. Figure 9(c) and Fig. 9(d) show that simulated and measured curves nearly coincide, which makes it unnecessary to delete any parameter. However, there are some differences in Fig. 9(e) and Fig. 9(f). Figure 9(e) shows that the simulated curves for particle radii 50 nm and 100 nm are an averaged difference of 0.01 from the experimental result, which is much closer than is the simulated curve for 1000 nm. Figure 9(f) confirms that the amplitude of the simulated curve for particle radius 1000 nm is much larger than the measured result. Therefore, the particle radius 1000 nm is excluded as a result of this step.
2.9 Define the best parameter using the information on a packaged LED
We reduce the uncertainty of parameters from six sets to two sets by comparing with careful optical and chromatic characterization of LEDs in both near-field and far-field. The parameters for particle radii 50 nm and 100 nm describe the measurement results well. In order to select the best parameter, we immersed the LED in a semi-spherical silicone dome for analysis. We measured and simulated the spectrum, far-field intensity distribution, and far-field angular color distribution. Figure 10(a) , Fig. 10(b), Fig. 10(c), and Fig. 10(d) indicate that the simulation results for radius 100 nm are closer to the experimental results than are those for radius 50 nm. Thus the best fit is achieved with a particle radius of 100 nm and density of 1.25e10 mm−3. In our model, this describes best the near-field luminance and color, as well as the emitted spectrum and the far-field intensity and color.
Fig. 10 (a) The LED immersed in a dome. (b) The corresponding optical model. (c) The measured and simulated far-field averaged spectrum. (d) Intensity distribution. (e) Color coordinate u’. (f) Color coordinate v’.
3. Verification
The phosphor model has been established. We then determined whether this model can predict the optical performance of an LED having an optical element. A Luxeon-C LED glued with a glass ball lens was used to examine the proposed model. The picture of this LED and the corresponding optical model are shown in Fig. 11(a) and 11(b), respectively. We compared the far-field intensity, angular color distribution, and spectrum between simulated and experimental results. The CCT and color rendering index (CRI) were also calculated from the spectrum, for confirmation. Figure 11(c) shows that the spherical lens converged the light. The far-field intensity collapses from a Lambertian distribution to a directional one with a Full Width at Half Maximum of 34°. The simulated and experimental results are almost identical. Figure 11(d) and Fig. 11(e) show the far-field color distribution versus angle. The data are plotted from 0 to 30 degrees because most of the light is in this range. The center of the distribution is slightly bluish, and at angles above 20° a slightly yellowish ring appears. The simulated and experimental results have an average difference smaller than 0.01. Figure 11(f) shows the simulated and experimental results of the total averaged spectrum. The simulation results are very similar to the measurement result, with a small difference in yellow wavelength range. We also calculated the CCT and CRI from the spectrum. The simulated and measured CCT are 6020 ± 50K and6260 ± 50K, respectively. The simulated and measured CRI are 73.0 ± 0.5 and 68.9 ± 0.5, respectively. These small differences indicate that the proposed model is very accurate.
Fig. 11 (a) The LED with a sphere lens. (b) The corresponding optical model. (c) The measured and simulated far-field intensity distribution. (d) Color coordinate u’. (e) Color coordinate v’. (f) Averaged spectrum.
It has been demonstrated how to improve an LED source model by using the spatial features on the LED surface, in the present case an array of electrical contact dots. In future work, this approach can be applied to other LED packages of other suppliers and to systems with a mixture of two phosphors.
4. Conclusion
This paper has proposed a new method for modeling white LEDs, using chromatic near-field data. We first built a theoretical model with phosphor parameters. Then we reduced the parameter uncertainty by comparing with careful optical and chromatic characterization of LEDs in both near-field and far-field. This research has demonstrated that the physical and chemical details of the phosphor need not be considered. Instead, we used the external measurement of LEDs to determine the best parameter. Based on this method, the far-field intensity distribution, far-field angular color distribution, total averaged spectrum, CCT, and CRI all can be predicted precisely. We believe this research can improve optical design of white LEDs.
References and links
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