Quantum dots can be used in white LEDs for lighting applications to fill the spectral gaps in the combined emission spectrum of the blue pumping LED and a broad band phosphor, in order to improve the source color rendering properties. Because quantum dots are low scattering materials, their use can also reduce the amount of backscattered light which can increase the overall efficiency of the white LED. The absorption spectrum and narrow emission spectrum of quantum dots can be easily tuned by altering their synthesis parameters. Due to the re-absorption events between the different luminescent materials and the light interaction with the LED package, determining the optimal quantum dot properties is a highly non-trivial task. In this paper we propose a methodology to select the optimal quantum dot to be combined with a broad band phosphor in order to realize a white LED with optimal luminous efficacy and CRI. The methodology is based on accurate and efficient simulations using the extended adding-doubling approach that take into account all the optical interactions. The method is elaborated for the specific case of a hybrid, remote phosphor white LED with YAG:Ce phosphor in combination with InP/CdxZn1−xSe type quantum dots. The absorption and emission spectrum of the quantum dots are generated in function of three synthesis parameters (core size, shell size and cadmium fraction) by a semi-empirical ‘quantum dot model’ to include the continuous tunability of these spectra. The sufficiently fast simulations allow to scan the full parameter space consisting of these synthesis parameters and luminescent material concentrations in terms of CRI and efficacy. A conclusive visualization of the final performance allows to make a well-considered trade-off between these performance parameters. For the hybrid white remote phosphor LED with YAG:Ce and InP/CdxZn1−xSe quantum dots a CRI Ra = 90 (with R9>50) and an overall efficacy of 110 lm/W is found.
© 2017 Optical Society of America
Light-emitting diodes (LEDs) provide an energy efficient alternative for classic light sources, and their application in the domain of general lighting is growing fast. A white LED is generally composed of one or more high energy blue pumping LEDs in combination with a wavelength conversion material [1, 2]. When this luminescent material, typically a phosphor, is in close contact with the pumping LED, it is referred to as an intimate phosphor. When the luminescent material is positioned further away from the LED, we speak of a remote phosphor LED [3–6].
The remote phosphor configuration has several important advantages. When exposed to heat, the phosphor can deteriorate or the luminescent characteristics can change . The blue pumping LED will heat up, so removing the phosphor away from the LED reduces the direct heat transfer to the phosphor layer. Because the flux density in the luminescent material is lower, remote phosphor LEDs allow lower phosphor temperatures . Remote phosphor LEDs also allow more design freedom. This makes it easier to customize the LED package by using different luminescent materials and at the end of life it becomes easier to repair or recycle the product. However, the larger the phosphor area, the larger the amount of luminescent material needed to obtain white light. More luminescent material increases the total cost of the white LED, so balancing cost and performance is a key aspect of a remote phosphor white LED.
Indoor lighting has a large impact on the well-being of people, influencing performance, stress-levels and mood [9, 10]. For this reason, it is important to design lighting to be energy efficient as well as providing to specific quality requirements. The performance of a white LED for general lighting applications is mainly determined by the luminous efficacy - the ratio of luminous flux to electrical power, the color rendering index (CRI) - determining the color appearance of objects that are illuminated by the light source, and the correlated color temperature (CCT) - a measure for the amount of long wavelength light versus short wavelength light, giving a warm or cold perception of the light . Additionally, the value of CRI R9 is also important when discussing the performance of LEDs. This value specifically determines the ability of the light source to render bright red objects, which can be a problem with LEDs.
The choice of the luminescent material(s) has a defining impact on the performance of the remote phosphor white LED. The absorption and emission spectrum of the luminescent material(s) determine the output spectrum of the white light, and the scattering and quantum efficiency have a large influence on the efficiency of the complete package. The amount of scattering for example affects the amount of backscattered light. This backscattered light is partially absorbed by the recycling cavity which lowers the overall efficiency . In earlier work, we found that scattering is necessary to avoid light trapping and ensure good angular color uniformity, but the amount of scattering should be fairly low to minimize the amount of backscattered light .
The luminescent materials traditionally used for white LEDs are phosphors. Generally, YAG:Ce is used because it has a broad greenish-yellow emission spectrum and a very high quantum efficiency . The luminescent layer is typically made by dispersing the phosphor powder into a binder and depositing the resulting mixture onto a substrate. However, such layers have a lot of scattering. Less scattering can be achieved by adjusting the particle sizes of the phosphor, thus tuning the Mie-scattering properties [15, 16] or by combining materials with different luminescent and scattering properties .
Quantum dots (QDs) are an alternative type of luminescent materials, which are increasingly used in lighting and display applications . These semiconductor nanoparticles are low scattering due to their small size and have a narrow emission spectrum of around 30 nm full width half maximum (FWHM) . This emission spectrum shifts when the size of the nanoparticles change . The ability to continuously tune the peak emission wavelength is one of the main advantages of QDs. For this reason QDs are used in displays, as the emission spectra can be tuned to fit the LCD color filters. In white LEDs, QDs are used to fill the spectral gaps in the combined spectrum of the blue LED and phosphor emission - for example in the red - and thus improve the CRI and especially R9 . The spectral tunability and low scattering behavior are the main advantages of QDs for this application. They typically have a lower quantum efficiency and are less stable compared to YAG:Ce, but perform similar or better compared to most small band phosphors .
Broad band phosphors have already been combined with quantum dots to improve color rendering [17, 21, 23–25]. It is however not self-evident to predict the individual emission spectra and necessary concentration of each luminescent material to yield the required optimal performance. In most studies the quantum dot emission spectrum is chosen in an experimental (trial & error) way [17, 24, 25] or by assuming that the combined emission spectrum is the weighted sum of both the emission spectrum of the phosphor and the quantum dot, neglecting re-absorption effects and interactions between the materials [21,23]. The first approach can take up a large amount of time and materials, and one is never sure to have the optimal configuration. The second approach dismisses scattering and re-absorption effects in the luminescent materials and/or interaction with the LED package or recycling cavity. These effects can have a profound impact on the resulting spectrum. For this reason an accurate simulation model is necessary to predict the performance of the complete white LED system and to be able to optimize these systems . No systematic optimization approach of the performance of a hybrid phosphor-QD white LED, based on accurate simulations, has been published before to our knowledge. Shimizu et al.  describes some results that were obtained with a proprietary spectrum based model, but no further details about the model are given. This paper tries to address this important issue for the case of a hybrid white remote phosphor LED.
The method commonly used for optical simulations is the Monte Carlo (MC) ray-tracing method. Geometrical rays are traced throughout the optical configuration and the performance of the system is examined in a stochastic way. There are few constraints on the complexity of the examined model, but accurate color simulations demand a very high number of rays. Modeling of more complex processes like luminescence typically result in a large simulation time . Another simulation tool is the Adding-Doubling (AD) method. This tool was developed to calculate intensity distributions by scattering materials by solving the radiative transfer equation (RTE) in a numerical way . The constraint for this method is that the system needs to be composed of planar rotationally symmetric components. The main advantage is that the method is quick and noise-free. The AD method was extended to include luminescent materials, taking into account not only scattering, but also wavelength conversion . Furthermore, we have also added the possibility to include recycling cavities . With this extended AD method we have the opportunity to quickly investigate the performance of a white LED system with one or more planar luminescent layers. This opens up the opportunity to scan various configurations and use optimization algorithms to find the ideal configuration.
In this paper we describe a methodology to select the best combination of a broad band phosphor with a narrow emitting quantum dot to realize a hybrid white remote phosphor LED with optimal performance. The method is elaborated for the specific case where YAG:Ce is combined with InP/CdxZn1−xSe QDs.
The used QDs can be altered by varying their core size and cadmium fraction. Both parameters determine the emission and absorption spectrum of the QD. Also the QD concentration and phosphor concentration can be varied. The performance of the hybrid remote phosphor white LED is quantified in terms of both luminous efficacy and CRI, for a fixed CCT. The R9 value is mentioned for all discussed cases. The simulation method takes into account all the interactions between the light and the recycling cavity as well as the re-absorption and re-emission of converted light within the wavelength conversion element.
2. Simulation method
Our simulation model uses the extended Adding-Doubling method for luminescent materials, with the ability to incorporate recycling cavities. The LED package that we simulate exists out of a cylindrical reflector cup with blue LEDs. The wavelength conversion element (WCE) is positioned at a remote location and contains two different luminescent materials, a phosphor and a quantum dot. A schematic depiction of the simulated LED package is shown in Fig. 1. To have an accurate prediction of the emitted spectral intensity distribution, accurate input data for the recycling cavity, the blue pumping LED and the luminescent materials are needed.
2.1. The input parameters
As a recycling cavity, we choose a cylindrical cavity with a complete Lambertian reflection and a reflection coefficient of 90% in agreement with a diffuse white recycling cavity. More information about the way this cavity is modeled can be found in .
The blue pumping LED is assumed to have a Lambertian intensity distribution. It has a maximum output power at 460 nm and a spectral width (FWHM) of 22 nm. For the calculation of the luminous efficacy we assume a radiant efficiency of 65% [31–33].
The luminescent materials are determined by a multitude of parameters: the absorption spectrum, which quantifies the absorption coefficient as a function of wavelength, the emission spectrum, which gives the wavelengths in which the absorbed light will be converted and its likelihood, the quantum efficiency (QE), which is a measure of how efficient the absorbed light is converted and how much light is lost, and finally the scattering parameters: the scattering coefficient per wavelength and the scattering phase function.
The phosphor material
The phosphor simulation parameters were derived from measurements of a YAG:Ce layer on a PET sample with an integrating sphere setup, using the “two measurement” method , and measurements in a BSDF setup .
The main difficulty to measure all the above parameters in the case of a phosphor material, is the fact that for simulations one needs the single-event parameters, e.g. the scattering phase function for a single scattering event, while in an experimental set-up we typically measure the result of multiple events, e.g. the scattering distribution from a sample with a certain thickness. In previous papers we have described in detail how to derive the scattering parameters from scattering samples using inverse methods [36–38]. With similar inverse modeling procedures all phosphor simulation parameters were derived. Since the exact measurement procedures are beyond the scope of this publication, they will be discussed in another paper.
The simulation input data for the phosphor material are shown in Fig. 2. As a phase function model we chose the two-parameter Gegenbauer function . This phase function is a more general version of the commonly used Henyey-Greenstein phase function as it introduces a second parameter α.
The absorption spectrum is linearly dependent on the concentration of the luminescent material. For that reason, the absorption spectrum of the phosphor (and any luminescent material discussed in this paper) is rescaled such that the absorption coefficient μa (@ 450 nm) = 1 mm−1. This makes it possible to translate the concentrations from the simulation into real life concentration, by using the Beer-Lambert law. The emission spectrum is normalized and the quantum efficiency has a maximum of almost 98%. The phase function parameter g is almost constant between 0.97 and 0.98, with a phase function parameter α between 0.75 and 0.55. The scattering coefficient is of the order 10 larger than the absorption coefficient, but the phase function is strongly forward scattering.
The quantum dot material
The considered quantum dots are InP type QDs with a ZnSe-shell with a small fraction of Cadmium in the shell to shift the absorption spectrum to the blue and reduce self-absorption . This type of QD is denoted as InP/CdxZn1−xSe. The quantum dot characteristics are dependent on the size of the QD core, as well as the amount of Cd in the shell. The thickness of the shell also has some smaller influence. To be able to include the continuous spectral tunability of the QD characteristics as a design freedom in our optimization study, we make use of a semi-empirical quantum dot model which generates the QD simulation input parameters (absorption coefficient and emission spectrum) as a function of three synthesis parameters (core size, Cd-fraction and shell thickness).
The empirical model was derived from experimental measurements of the absorption and emission spectra for various core sizes (dC), Cd-fractions (xCd) and shell thicknesses (dS) and a principle understanding of how the various synthesis parameters impact the optical characteristics. Experimental data suggests that the emission peak shape is determined by both dC and xCd. We approximate the emission peak by a Gaussian function . All synthesized QDs had emission spectra with the same FWHM and so the width of the Gaussian emission spectrum is kept constant. An increase of dC induces a redshift of the emission peak, because of the quantum confinement effect of the charge carriers. We use an experimental energy-size curve to take into account the dC impact on the emission spectrum. An increase of xCd in the shell induces a redshift of the emission. We use an empirical fit of the emission maximum as a function of the Cd-fraction to model this parameter influence. The absorption spectrum is approximated by a short-wavelength curve and a Gaussian curve with an empirical adjustment for the first excitation. The Gaussian function depends on dC and xCd in a similar way as for the emission spectrum. The short wavelength curve depends on the shell parameters: it is proportional to the shell thickness and its shape depends on xCd. An increase of Cd in the CdZnSe shell decreases the band gap of this alloy and induces a global redshift of the short wavelength absorbance curve, increasing the absorbance of the blue light compared to longer wavelengths, reducing re-absorption of converted light. An empirical fit is used to model the experimental data.
The influences of dC, xCd and dS on both the absorption and emission spectra of the InP/CdxZn1−xSe QDs are shown in Fig. 3. In Fig. 4 we see a comparison between the experimental data and the characteristics obtained from our QD model for a couple of QDs. We see that the model follows the general trends, especially the excitation peak and peak emission are predicted very well. However, in the low energy side of the emission spectrum, we see some deviations. These deviations can be attributed to emission defects originating from charge carriers traps. Because these defects are not controllable by synthesis parameters we’ve chosen to simulate the emission spectrum by a Gaussian, which corresponds with optimal synthesis performance. However we’ve investigated the influence on the resulting LED performance by comparing the results obtained with the QD model and results obtained with the experimentally measured characteristics. We found that the differences were within 4% for the efficacy (with an average of 1.7%) and 5% for the CRI (with an average of 3%). The quantum efficiency is assumed to be constant over the complete wavelength range and is equal to 70%.
To determine any possible scattering of the quantum dots, measurements were performed using the BSDF setup. With these measurements, we found that the QD scattering was completely negligible compared to the phosphor which exhibits high amounts of scattering. For that reason the QDs are modeled as non-scattering.
The important advantage of using a semi-empirical model for the quantum dot optical characteristics is the fact that the considered input parameters in the optical simulation are directly related to actual synthesis parameters. This means that when a QD with an ideal set of optical characteristics follows from our optimization procedure, the needed synthesis parameters to generate these characteristics are automatically known. This makes it more straightforward to produce these optimal QDs and assures a better predictability of the final white LED.
2.2. The extended adding-doubling method
The AD method is an algorithm that simulates the scattering behavior from a planar sample by solving the radiative transfer equation (RTE) in a numerical way within multiple thin infinitely-extended layers that comprise the full sample. Since no spatial information is considered, the output of an AD simulation is the transmitted and reflected intensity distribution of the scattered light. The incoming and scattered light within the sample is divided into a number of rotationally symmetric angular cones. The number of used cones determines the angular resolution of the adding-doubling method.
For (scattering) luminescent materials, the RTE takes the form shown in [Eq. (1)] for emission wavelength interval with central wavelength , where I(ν) is the flux in channel ν (= the cone with angle arccos(ν)). This equation exists out of a non-luminescent part, accounting for the loss of flux in channel ν due to absorption and scattering out of the channel. The second term calculates the flux gain of light scattered into channel ν from all other channels ν′. P(ν, ν′) is the phase function, which describes how the light is scattered and the probability that light from cone ν′ is scattered towards cone ν. The third term is the luminescent part, which takes into account the re-emission of light from all excitation wavelengths into a specific emission wavelength interval , with w being the emission spectrum and QE the quantum efficiency.
The RTE [Eq. (1)] is written to consider only one luminescent material. However, in this study we try to investigate the performance of a wLED using multiple luminescent materials. When the different luminescent materials are dispersed into separate layers, the above equation can be used with different luminescent characteristics for each material. When the different luminescent materials are mixed within a single layer, which is the case in this study, the combined luminescent characteristics have to be considered. The RTE for these combined luminescent characteristics has the same form as Eq. (1). The construction of these combined characteristics are explained in .
It is also implied that no up-conversion is possible: the emission for a wavelength equal to or smaller than the absorption wavelength is defined as zero. Since the QDs are non-scattering, the scattering properties of the phosphor-quantum dot mixture in the WCE will only depend on the scattering properties of the phosphor.
With this extended AD method, it is thus possible to simulate the WCE. However, to investigate the performance of the complete wLED, it is also important to include the impact of the recycling cavity. To do this, we developed an extension to the AD code that models the recycling properties of this cavity as a separate layer with specific angle-depending reflective properties. A more in-depth description of this method can be found in .
2.3. Confirmation of the simulation tool
We want to use the extended AD method to simulate an optical configuration where various aspects are combined (i.e. mixture of scattering and non-scattering luminescent materials, LED cavity interaction). For this reason, we need to confirm that the method works well and gives the correct results. To confirm this, we compare the results of a simulation with the AD tool implemented in MATLAB , with a simulation with the advanced commercial Monte Carlo (MC) ray-tracer, LightTools . This ray-tracer allows to implement all relevant physical phenomena of luminescent materials in a realistic manner.
We compare the optical configuration shown in Fig. 1 with the input parameters that were discussed in the previous sections, complemented with the parameters shown in Table 2.3. The total transmitted output spectrum and intensity distribution obtained with both the AD method and Monte Carlo simulations can be found in Fig. 5. From this we can see that there is a strong agreement between both results.
The AD simulations were run on an Intel(R) Xeon(R) CPU (E5-2630 v3 @ 2.40GHz). After performing 5 runs we found an average simulation time of 150 seconds to generate the results in Fig. 5. The MC simulations were run on the same machine and took approximately 1700 seconds, which is also an average of 5 simulations. This means that by using the AD simulation tool, the simulation time can be reduced considerably, eliminating the noise inherent to the MC approach. This makes it possible to model a large number of varying optical configurations in order to find the optimal wLED configuration.
The optimization methodology
While various aspects of a hybrid white remote phosphor LED for general lighting could be optimized, in this paper we focus on the following question: which InP/CdxZn1−xSe quantum dot should be selected in combination with a specific YAG:Ce phosphor to yield optimal performance, and secondly, what are the necessary concentrations for both luminescent materials to reach a desired CCT. As we explained before, the optical QD characteristics are fully determined by three synthesis parameters through a semi-empirical quantum dot model. Since the impact of the shell size (see Fig. 3) is limited, this parameter was not taken into account in our study. This leaves us with four parameters that can be varied to optimize the wLED performance: the size of the QD core, the amount of Cd in the shell, and the concentration of quantum dots and the phosphor.
To quantify the performance we calculate both the luminous efficacy and the CRI Ra value from the simulated spectral power distribution. Because both performance criteria cannot be optimized at the same time, meaning a high efficiency will not yield a high CRI and vice versa, we adopt an optimization strategy that visualizes this trade-off and allows to make a good choice in terms of each specific application.
The optimization methodology consists of three consecutive stages which are illustrated in Fig. 6 with a detailed flow chart. In the first stage, the range of values of the two QD synthesis parameters that will be analyzed, is selected. In the second stage, the needed concentrations of the phosphor and quantum dots to realize a certain CCT are determined with an optimization algorithm, for each combination of two QD synthesis parameters. This is by far the most time-consuming part. In the final stage, all results are visualized.
The optimization (Stage 2) starts with selecting an arbitrary QD and phosphor concentration for the WCE. The optical QD characteristics are calculated from the QD synthesis parameters with the semi-empirical QD model. These optical characteristics are rescaled for the chosen QD concentration. Also the phosphor input parameters are rescaled to account for the concentration. The phosphor and QD characteristics are then used in the AD simulation of the complete white LED configuration to calculate the resulting spectral power distribution. From this spectral power distribution the corresponding CCT can be calculated. Through a minimization routine, the combination of the phosphor and the quantum dot concentration that results in the desired CCT is determined. This is achieved by means of Matlab’s  fmincon interior point algorithm. This convergence routine stops when the simulated color point is within 1e-3 distance of the desired color point in CIE u’v’ space. This corresponds to 1 MacAdam ellipse as described in  and is smaller than the Just Noticeable Difference (JND). We have chosen to work in the CIE u’v’ space, because this space better represents the noticeable difference as observed by the human eye. This uniformity is also beneficial for the minimization routine, which is preferably used in continuous spaces.
This optimization method is repeated for every combination of two QD synthesis parameters and results (concentration, QD synthesis parameters, emitted spectrum) are saved. In the final stage we visualize the CRI and efficacy in a 2D grid for each combination of dC and xCd. This visualization enables to consider all the possible options and make a final choice of the best QD selection for a specific application, based on the luminous efficacy and color rendering index. The luminous efficacy is determined for a blue LED with a radiant efficiency of 65% and the CRI is calculated as defined by CIE 13.3-1995.
3. Results and discussion
We investigated an InP/CdxZn1−xSe type QD combined with YAG:Ce for a range of core sizes between 2.5 and 3.5 nm and cadmium fractions × between 0 and 0.15. As mentioned before, the shell thickness will not be varied and is fixed at 10 nm. The desired nominal CCT is 3500 K, which corresponds to a target CCT = 3465 ± 245 K and a target Duv = 0.000 ± 0.006 as described in ANSI C78.377-2008. The resulting CRIs and efficacies are shown in Fig. 7. The colorless regions correspond to combinations where the routine was unable to obtain the target CCT. The complete results for R9 are not shown, as they scale very well with CRI, especially when CRI is high.
In general the efficacy decreases when the core size increases. This can be attributed to the red-shift of the emission spectrum with increasing core size. When taking into account the eye sensitivity curve, the lumen output will decrease when shifting the emission spectrum to the red, thus lowering the efficiency. The cadmium has a more limited, but still noticeable influence on the emission spectrum, the related red-shift and efficiency. The CRI will be highest when the emission spectra of the phosphor and quantum dot complement each other. As the emission spectrum shifts to the red with increasing core size, we see an optimal emission spectrum for a core size around 3 nm. However, for the CRI the cadmium fraction has a non-negligible influence. It not only influences the emission spectrum of the QD, but also influences the absorption spectrum and thus which light is absorbed out of the phosphor spectrum, altering the final spectrum and thus CRI.
In order for the reader to be able to make a connection between the optimal QD synthesis parameters and the peak emission wavelength of this optimal QD, the peak emission wavelengths of the QDs are shown in Fig. 8. This plot shows the peak emission wavelength for each combination of dC and xCd.
We see that the optimal QD selection for achieving high efficacies is not the same choice we would make to have a high CRI. For this reason, a trade-off must be made when selecting the ideal QD. When we want the highest possible efficacy, a QD with dC = 2.7 nm and xCd = 0.145 would be the best choice, resulting in an efficacy = 128.82 lm/W. This system would however only have a CRI = 52.36 and an R9<0, which is too low for indoor lighting applications. When selecting the system with the highest CRI (= 96.59) we would choose the QD with dC = 3 nm and xCd = 0.08, which has an R9 as high as 93.52 and an efficiency = 101.01 lm/W, but such a high CRI is not necessarily needed. A good compromise can be made between both quality parameters by using the results in Fig. 7. All these luminous efficacies were calculated by using a radiant efficiency of 65% for the blue LED. Using a blue LED with a lower radiant efficiency would lead to lower luminous efficacies, but will have no influence on the resulting CRI and R9.
One way to make this compromise is by selecting a minimum required CRI and determining the iso-CRI-contour, as shown in Fig. 7 where CRI = 80 and CRI = 90 are indicated. When the CRI condition is fulfilled, one can search for the maximum efficacy in the area within the contour.
In this paper we present an optimization methodology, based on an efficient simulation tool for a remote phosphor type white LED which allows to find the optimal QD to pair with a specific phosphor. The methodology is elaborated for QDs of the InP/CdxZn1−xSe type which are characterized by three synthesis parameters: core size, shell size and cadmium fraction. These QDs are combined with a YAG:Ce phosphor.
In this example, a nominal CCT of 3500 K is targeted and we chose efficacy and CRI as quality parameters. These two parameters gave us a trade-off, but systems with a CRI of 90, an R9>50 and an efficacy of 110 lm/W were found for a blue pumping LED with a radiant efficiency of 65%. This method is versatile and can be used for any target CCT and different quality parameters.
The method can be adjusted to fit specific needs for a different application, using for example different performance parameters for the white LED, such as angular uniformity. Furthermore, also other variables can be varied and optimized, such as the amount of Ce doped in the YAG garnet.
Flemish agency for Innovation by Science and Technology (IWT) (501100003132) ‘LumiCoR’; KU Leuven (501100004040) ‘High-luminance solid-state white light sources (IMP/14/041)’
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