Optimal spectra of white light-emitting diodes using quantum dot nanophosphors

Ping Zhong; Guoxing He; Minhao Zhang

doi:10.1364/OE.20.009122

1. Introduction

White LED lamps have promising features such as small size, safety, long lifetime, and are mercury-free, so they are expected to replace conventional incandescent and fluorescent lamps for general lighting applications in the near future [1]. The features of long lifetime and mercury-free would contribute to solving environmental problems. The widespread use of solid state lighting (SSL) is of great importance to significantly reduce the global electricity consumption and the use of fossil fuels. Today, the most commonly used SSL sources are based on the integration of traditional broadband phosphors on blue InGaN/GaN light emitting diodes (LEDs) [2]. Although traditional phosphor powders are able to generate a white spectrum with a high color rendering index (CRI) [3], simultaneously accomplishing a high luminous efficacy of radiation (LER) remains a challenge. Recently, nanocrystal based optoelectronic devices have made great progress in device research [4]. Nanocrystal emitters are particularly advantageous for use in white light sources because they feature tunable and relatively narrow emission across the visible spectral range and small overlap between their emission and absorption spectra, and also provide the ability to be easily and uniformly deposited in solid films with common techniques (e.g., spin casting and dip coating) [5–7]. Theoretical emission spectra of warm white LEDs (WWLEDs) using nanophosphors of semiconductor nanocrystal quantum dots (QD) have been investigated to achieve efficient solid-state lighting (SSL) with a high CRI approaching 90 and a LER higher than 380 lm/W at CCTs of 1500 K to 4000 K [8]. In Ref [8], however, the chromaticity difference condition dC <0.0054 and the rendering performance of other test color samples have not been considered. It has been observed that the spectra passing the thresholds given in Ref [8]. render the test color sample 9 with low success and the corresponding rendering index (R9) remains mostly around 30, while only one of these spectra could yield a R9 >70 [9]. This is mostly because of the large step sizes used in this previous study. It was experimentally demonstrated a WWLED combined with QD nanophosphors on LED chips to achieve LER > 350 lm/W with CRI = 89.2 at CCT < 3000 K [10]. However, these approaches could yield local results by reason of choosing a larger step size (10 nm) of wavelength and full-width-at-half-maximum (FWHM) intervals (6 nm) for each color source. The chromaticity difference condition dC ≤ 0.0054 [3] is not considered in Refs of [8] and [10]. So these WWLEDs do not satisfy the requirements recommended for general lighting with solid state lighting products [11–13]. It was reported that high CRI is not good color rendering for white LED sources [14, 15]. Poor color rendering of white LED with high CRI is due to low special CRIs of R9 to R12 for the four saturated colors (red, yellow, green, and blue) [16, 17]. An improved indicator, color quality scale (CQS), has recently been proposed by National Institute of Standards and Technology [18]. However, the CQS provides scores consistent with the CRI for the most recent phosphor type LED products, RGBA LEDs and traditional discharge lamps [19]. So the CRI as a metric for evaluating the color rendering abilities of white-light sources is suitable for the white LED with QD nanophosphors. The special CRI of R9 is very important to visual color rendering so that not only CRI but also R9 should be considered in simulation. The improved QD-WLED with CRI = 89.5. R9 = 83.0 and LER = 340lm/W at CCT = 4211 K within dC ≤ 0.0054 was reported [20]. Recently, the spectra combinations of QD-WLEDs with CRI ≥ 90, R9 ≥70 and LER ≥ 380 lm/W at 1500 K ≤ CCT ≤ 4000 K with dC ≤ 0.0054 were simulated [9]. White light sources with high CRIs and high LERs require the generation of a white emission spectrum by strategically selected colors with the lowest possible full-width-at-half-maximum (FWHM) values, as reported by Phillips et al. [21]. However, optical parameters including the peak emission wavelength (WL), FWHM, and the relative amplitude of each color component need to be carefully designed to achieve such high-quality white light generation which can compete with conventional phosphor-coated white LEDs (p-W LEDs) [21]. In this work, we investigate relationships of CRI vs. CCT, CRI vs. LER, and LER vs. CCT of the QD-WLED under condition of CRI ≥ 80 and LER ≥ 300 lm/W at CCTs of 1500 K to 6500 K with dC ≤ 0.0054, and obtain optimized peak WL and FWHM of each color component of for maximizing the LER of QD-WLED under conditions of CRI above 90 or 95, as well as, both CRI and R9 above 90 or 95 at CCTs of 2700 K to 6500 K with dC ≤ 0.0054.

2. Objective function of optimization

Consider a SPD that contains emission spectrum from green-, yellow-, and red-emitting QD, as well as a blue LED die of QD-WLED. The relative spectral power distribution (SPD) of the QD-WLED, S_QD-WLED(λ), is given by,

S_{Q D - W L E D} (λ) = q_{b} S (λ, λ_{b}, Δ λ_{b}) + q_{g} S (λ, λ_{g}, Δ λ_{g}) + q_{y} S (λ, λ_{y}, Δ λ_{y}) + q_{r} S (λ, λ_{r}, Δ λ_{r})

where S(λ, λ_b, ∆λ_b) refers to relative SPD of the blue spectrum transmitted through the QD nanophosphors, S(λ, λ_g, ∆λ_g), S (λ, λ_y, ∆λ_y),and S(λ, λ_r,∆λ_r) refer to the relative emission spectra of green, yellow and red QD nanophosphors, λ_b, λ_g, λ_y, λ_r refers to peak wavelengths of blue, green, yellow and red color components, ∆λ_b, ∆λ_g, ∆λ_y, ∆λ_r refers to FWHMs of blue, green, yellow and red color components, q_b, q_g, q_y and q_r are proportions of the relative spectra of S(λ, λ_b, ∆λ_g), S(λ, λ_g, ∆λ_g), S(λ, λ_y, ∆λ_y) and S(λ, λ_r,∆λ_r), respectively. The emission spectrum of each color source is modeled as a Gaussian function [22]. The chosen wavelength intervals for each color source are changed between 450 nm and 500 nm for blue, between 500 nm and 550 nm for green, between 550 nm and 600 nm for yellow, and between 600 nm and 650 nm for red. In addition, FWHM of each color component is changed between 30 nm and 54 nm. Subjecting the 3 × 4-dimensional parameter space to four color-mixing constrains results in the location of the feasible vectors on the hypersurface with 9 dimensionality [23]. In order to obtain relationships of the maximum obtainable CRI vs. CCT, the maximum obtainable CRI vs. LER, and the highest achievable LER vs. CCT under condition of CRI ≥ 80 and LER ≥ 300 lm/W at CCTs of 1500 K to 6500 K with dC ≤ 0.0054, we introduce three objective functions:

\begin{array}{l} F_{1} (λ_{b}, λ_{g}, λ_{y}, λ_{r}, Δ λ_{b}, Δ λ_{g}, Δ λ_{y}, Δ λ_{r}, q_{r}) = C R I \\ (under conditions of LER \geq 300 lm/W and dC \leq 0 .0054) \end{array}

\begin{array}{l} F_{2} (λ_{b}, λ_{g}, λ_{y}, λ_{r}, Δ λ_{b}, Δ λ_{g}, Δ λ_{y}, Δ λ_{r}, q_{r}) = C R I \\ (under conditions of 1500 K \leq CCT \leq 6500 K and dC \leq 0 .0054) \end{array}

\begin{array}{l} F_{3} (λ_{b}, λ_{g}, λ_{y}, λ_{r}, Δ λ_{b}, Δ λ_{g}, Δ λ_{y}, Δ λ_{r}, q_{r}) = L E R \\ (under conditions of CRI \geq 80 and dC \leq 0 .0054) \end{array}

In order to optimize spectra of the QD-WLED lamp with different requirements of color rendering at CCTs of 2700 K to 6500 K, we introduce two objective functions:

\begin{array}{l} F_{4} (λ_{b}, λ_{g}, λ_{y}, λ_{r}, Δ λ_{b}, Δ λ_{g}, Δ λ_{y}, Δ λ_{r}, q_{r}) = L E R \\ (under conditions of CRI \geq i at CCT = j with dC \leq 0 .0054) \end{array}

\begin{array}{l} F_{5} (λ_{b}, λ_{g}, λ_{y}, λ_{r}, Δ λ_{b}, Δ λ_{g}, Δ λ_{y}, Δ λ_{r}, q_{r}) = L E R \\ (under conditions of both CRI and R9 above i at CCT = j with dC \leq 0 .0054) \end{array}

i = (90, 95), j = (2700 K, 3000 K, 3500 K, 4000 K, 4500 K, 5000 K, 5700 K, 6500 K). Hence the optimization problem reduces to finding maxima of the objective function. The parameters in the objective function are dependent on not only the wavelength and FWHM but also the proportion of red color component. The proportions of blue, green and yellow are dependent on the proportion of red color component, CCT and dC. So the spectral optimization is carried out by optimizing the wavelength and FWHM of each color component, and also requires careful tuning of the amplitudes for each color component.

A common approach to such multi-objective problems, where the different objectives might be in trade-off, is to investigate the set of Pareto optimal solutions [24]. A Pareto optimal solution is optimal in the sense that improving one objective would degrade the performance for at least one other objective. This means that without any further information, one of these Pareto optimal solutions cannot be regarded as better than any other one. Although there are several global optimization algorithms available in the literature, in this work, genetic algorithms (GA) [25] were chosen because they are able to scan a vast set of solutions, they do not depend on a starting solution, they are very useful for complex problems, and most importantly, they can be easily modified to estimate the Pareto optimal set. For multi-objective problems, where there might not be one optimal solution, the single-objective GA is modified to evolve towards the Pareto optimal front. Several multi-objective evolutionary algorithms (MOEA) are described in literature [24]. The MOEA selected in this research is the non-dominated elitist NSGA-II genetic algorithm, a widely accepted benchmark in the MOEA research community [26]. A complete description of the NSGA-II algorithm is beyond the scope of this article, and the interested reader is kindly referred to the paper by Deb, et al [27].

3. Results

3.1 Relations between CRI vs. CCT, CRI vs. LER, and LER vs. CCT

The relationships of CRI vs. CCT, CRI vs. LER, and LER vs. CCT of the QD-WLED under conditions of CRI ≥ 80 and LER ≥ 300 lm/W at CCTs of 1500 K to 6500 K with dC ≤ 0.0054 have been obtained by nonlinear program for maximizing F₁, F₂ and F₃, respectively. The results are shown in Fig. 1(a) , 1(b) and 1(c), respectively. In Fig. 1(a), the maximum obtainable CRI value quickly increases to 99.6 from 1500 to 5000 K. After 5000 K, the CRI starts to decrease very slowly to 99.2. The simulation results show that the maximum obtainable CRIs are higher than 99 at CCTs of 2700 to 6500 K. In Fig. 1(b), the maximum obtainable CRI value decreases when increasing LER where the fundamental trade-off between CRI and LER appears. The high performance QD-WLEDs with CRI ≥ 90 and LER ≥ 400 lm/W as well as with CRI ≥ 95 and LER ≥ 380 lm/W could be achieved using QD nanophosphors. In Fig. 1(c), the highest achievable LER value increases at CCTs of 1500 to 2500 K. The LER value is 430 lm/W at 2500 K. After 2500 K, the LER value starts to decrease when increasing CCT where the fundamental trade-off between LER and CCT appears.

Fig. 1 Relationships of (a) CRI vs. CCT, (b) CRI vs. LER, and (c) LER vs. CCT with dC ≤ 0.0054.

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3.2 Optimal spectra of QD-WLEDs with excellent color rendering and high efficient

The optimal peak WL, FWHM and relative radiant flux (Φ_e%) of each color component as well as their performance of QD-WLEDs with CRIs above 90 or 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054) have been obtained by nonlinear program for maximizing F₄. The simulation results are shown in Table 1 and Table 2 , respectively. The simulation results show that the choice of optimal FWHM for each color component should be as narrow as possible (the smallest value in our simulations is 30 nm). Table 1 indicates that WLEDs with LER = 401 lm/W at CCT = 3000 K, LER = 372 lm/W at CCT = 4500 K, and LER = 355 lm/W at CCT = 5700 K for CRI = 90 could be achieved using QD nanophosphors. Table 2 indicates that WLEDs with LER = 382 lm/W at CCT = 3000 K, LER = 358 lm/W at CCT = 4500 K, and LER = 342 lm/W at CCT = 5700 K for CRI = 95 could be achieved using QD nanophosphors. Unfortunately, all special CRI of R9s of QD-WLED with the highest is below 56. The special CRI of R9 is very important to visual color rendering so that both CRI and R9 are considered in optimization of high color rendering QD-WLED. Excellent color rendering and high efficacy QD-WLEDs with both CRI and R9 above 90 or 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054) have been obtained by nonlinear program for maximizing F₅. The optimal peak WL, FWHMand relative radiant flux (Φ_e%) of each color component, and their performance of QD-WLEDs are given in Table 3 and Table 4 . The simulation results show that the optimal FWHM of each color component is still 30 nm. The optimal relative spectral powerdistributions (SPDs) of QD-WLEDs with CRI = 90 and R9 = 90, as well as CRI = 95 and R9 = 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054) are shown in Fig. 2 and Fig. 3 , respectively. The results show that high performance QD-WLEDs with CRI = 90, R9 = 90 and LER = 381 lm/W as well as CRI = 95, R9 = 95 and LER = 371 lm/W at a CCT of 3000 K, with CRI = 90, R9 = 90 and LER = 361 lm/W as well as CRI = 95, R9 = 95 and LER = 352 lm/W at a CCT of 4500 K, and with CRI = 90, R9 = 90 and LER = 346 lm/W as well as CRI = 95, R9 = 95 and LER = 338 lm/W at a CCT of 5700 K could be achieved using QD nanophosphors. The results in tables of 3 and 4 show that the CQS score is consistent with the CRI for QD-WLED with CRI = R9. Furthermore, their special CRIs of R13 and R15 corresponding to the colors of the skin on the face of European and Chinese women are also very high. Both R13 and R15 are especially important for interior lighting.

Table 1. Optimal peak WL, FWHM and Φ_e% of each color component, their performance of QD-WLEDs with CRI = 90 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054).

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Table 2. Optimal peak WL, FWHM and Φ_e% of each color component, their performance of QD-WLEDs with CRI = 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054).

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Table 3. Optimal peak WL, FWHM and Φ_e% of each color component, their performance of QD-WLEDs with CRI = 90 and R9 = 90 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054).

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Table 4. Optimal peak WL, FWHM and Φ_e% of each color component, their performance of QD-WLEDs with CRI = 95 and R9 = 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054).

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Fig. 2 Optimal relative SPDs of QD-WLEDs with CRI = 90 and R9 = 90 at CCTs of 2700 K to 6500 K (dC≤ 0.0054).

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Fig. 3 Optimal relative SPDs of QD-WLEDs with CRI = 95 and R9 = 95 at CCTs of 2700 K to 6500 K (dC≤ 0.0054).

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As compared with the traditional phosphor-coated white LEDs (p-W LEDs), the p-W LEDs consisting of a blue chip, green, yellow and red phosphors with at CCTs of 2700 K to 6500 K are simulated. Eleven green (507 nm~546 nm), nine yellow (554 nm~606 nm) silicate phosphors and six red (631 nm~667 nm) nitride phosphors are used in optimization [28]. The highest achievable LER values of QD-WLEDs with both CRI and R9 above 90 or 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054) are shown in Table 5 . The results show that LERs of WLEDs with QD nanophosphors increase by 13% to 32% compared with that of p-W LEDs with traditional phosphors.

Table 5. Highest achievable LER values of p-W LEDs with CRI = 90 and R9 = 90 as well as CRI = 95 and R9 = 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054).

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3.3 Effects of the deviations from peak emission wavelengths and FWHMs of the spectra

In order to achieve QD-WLEDs with high optical performance, we simulate the effect of the deviations from peak emission wavelengths and FWHMs of the spectra. Average and standard deviation (σ) values of peak wavelengths and FWHMs of the spectra satisfying the conditions of LER ≥ 370 lm/W at CCT = 2700 K, LER ≥ 370 lm/W at CCT = 3000 K, LER ≥ 365 lm/W at CCT = 3500 K, LER ≥ 360 lm/W at 4000 K, LER ≥ 350 lm/W at CCT = 4500 K, LER ≥ 345 lm/W at CCT = 5000 K, LER ≥ 335 lm/W at CCT = 5700 K and LER ≥ 325 lm/W at CCT = 6500 K for both CRI ≥ 90 and R9 ≥ 90 are shown in Table 6 . Those satisfying the conditions of LER ≥ 360 lm/W at CCT = 2700 K, LER ≥ 360 lm/W at CCT = 3000 K, LER ≥ 360 lm/W at CCT = 3500 K, LER ≥ 350 lm/W at CCT = 4000 K, LER ≥ 345 lm/W at CCT = 4500 K, LER ≥ 340 lm/W at CCT = 5000 K, LER ≥ 330 lm/W at CCT = 5700 K and LER ≥ 320 lm/W at CCT = 6500 K for both CRI ≥ 95 and R9 ≥ 95 are shown in Table 7 . The results show that the peak wavelength for each color component has a strong restriction, and that the choice of FWHM for each color component should be as narrow as possible (the smallest value in our simulations is 30 nm) for high performance QD-WLEDs. The relative radiant flux Φ_e% of each color component, and their performance of QD-WLEDs with ( $\bar{λ}$ , $\bar{Δ λ}$ ), ( $\bar{λ}$ + σ_λ, $\bar{Δ λ}$ + σ_∆λ) and ( $\bar{λ}$ - σ_λ, $\bar{Δ λ}$ - σ_∆λ) of each color component at CCTs of 2700 K to 6500 K under conditions of CRI ≥ 90 and R9 ≥ 90 are shown in Table 8 , Table 9 and Table 10 , respectively. Those under conditions of CRI ≥ 95 and R9 ≥ 95 are shown in Table 11 , Table 12 and Table 13 , respectively.

Table 6. Average and standard deviation (σ) values of the wavelength and FWHM of each color component satisfying the conditions of LER ≥ 370 lm/W at CCT = 2700 K, LER ≥ 370 lm/W at CCT = 3000 K, LER ≥ 365 lm/W at CCT = 3500 K, LER ≥ 360 lm/W at CCT = 4000 K, LER ≥ 350 lm/W at CCT = 4500 K, LER ≥ 345 lm/W at CCT = 5000 K, LER ≥ 335 lm/W at CCT = 5700 K, and LER ≥ 325 lm/W at CCT = 6500 K for both CRI ≥ 90 and R9 ≥ 90.

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Table 7. Average and standard deviation (σ) values of the wavelength and FWHM of each color component satisfying the conditions of LER ≥ 360 lm/W at CCT = 2700 K, LER ≥ 360 lm/W at CCT = 3000 K, LER ≥ 360 lm/W at CCT = 3500 K, LER ≥ 350 lm/W at CCT = 4000 K, LER ≥ 345 lm/W at CCT = 4500 K, LER ≥ 340 lm/W at CCT = 5000 K, LER ≥ 330 lm/W at CCT = 5700 K, and LER ≥ 320 lm/W at CCT = 6500 K for both CRI ≥ 95 and R9 ≥ 95.

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Table 8. Φ_e% of each color component, their performance of QD-WLEDs with $\bar{λ}$ and $\bar{Δ λ}$ of each color component at CCTs of 2700 K to 6500 K under conditions of CRI ≥ 90 and R9 ≥ 90.

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Table 9. Φ_e% of each color component, their performance of QD-WLEDs with $\bar{λ}$ + σ_λ and $\bar{Δ λ}$ + σ_∆λ of each color component at CCTs of 2700 K to 6500 K under conditions of CRI ≥ 90 and R9 ≥ 90.

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Table 10. Φ_e% of each color component, their performance of QD-WLEDs with $\bar{λ}$ - σ_λ and $\bar{Δ λ}$ - σ_∆λ of each color component at CCTs of 2700 K to 6500 K under conditions of CRI ≥ 90 and R9 ≥ 90.

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Table 11. Φ_e% of each color component, their performance of QD-WLEDs with $\bar{λ}$ and $\bar{Δ λ}$ of each color component at CCTs of 2700 K to 6500 K under conditions of CRI ≥ 95 and R9 ≥ 95.

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Table 12. Φ_e% of each color component, their performance of QD-WLEDs with $\bar{λ}$ + σ_λ and $\bar{Δ λ}$ + σ_∆λ of each color component at CCTs of 2700 K to 6500 K under conditions of CRI ≥ 95 and R9 ≥ 95.

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Table 13. Φ_e% of each color component, their performance of QD-WLEDs with $\bar{λ}$ - σ_λ and $\bar{Δ λ}$ - σ_∆λ of each color component at CCTs of 2700 K to 6500 K under conditions of CRI ≥ 95 and R9 ≥ 95.

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4. Conclusion

The relationship and trade-offs between the performance parameters including CRI, LER and CCT of WLEDs using QD nanophosphors are presented for CRI ≥ 80 and LER ≥ 300 lm/W at 1500 K ≤ CCT ≤ 6500 K with dC ≤ 0.0054. The optimal peak WL, FWHM and relative radiant flux (Φ_e%) of each color component of QD-WLEDs with both CRI and R9 above 90 or 95 at CCTs of 2700 K to 6500 K (dC ≤ 0.0054) are obtained. Furthermore, high performance QD-WLEDs with CRI = 90, R9 = 90 and LER = 381 lm/W as well as CRI = 95, R9 = 95 and LER = 371 lm/W at CCT = 3000 K, with CRI = 90, R9 = 90 and LER = 361 lm/W as well as CRI = 95, R9 = 95 and LER = 352 lm/W at CCT = 4500 K, and with CRI = 90, R9 = 90 and LER = 346 lm/W as well as CRI = 95, R9 = 95 and LER = 338 lm/W at CCT = 5700 K could be achieved using QD nanophosphors. The LERs of WLEDs with QD nanophosphors increase by 13% to 32% compared with that of p-W LEDs with traditional phosphors. Additionally, average and standard deviation values of peak wavelength and FWHM for each color component of QD-WLED are investigated in order to achieve QD-WLEDs with high optical performance,

Acknowledgments

This work was supported by Shanghai Science and Technology Committee (No.09DZ1141100) and the National “ITER” Project of Ministry of Science and Technology of P. R. China (No.2009GB107006 and No.2010GB107003).

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CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
λ_b	463.5	462.7	461.6	460.8	460.2	460.8	460.2	459.7
λ_g	529.0	528.9	528.8	528.7	528.7	528.7	528.7	528.8
λ_y	566.6	567.4	568.4	569.3	569.9	569.9	570.1	570.9
λ_r	614.0	613.0	611.7	610.8	610.0	609.5	608.7	608.2
∆λ_b	30	30	30	30	30	30	30	30
∆λ_g	30	30	30	30	30	30	30	30
∆λ_y	30	30	30	30	30	30	30	30
∆λ_r	30	30	30	30	30	30	30	30
Φ_eb (%)	9.0	11.9	16.5	20.5	24.0	26.3	29.8	33.1
Φ_eg (%)	20.9	23.4	26.3	28.0	29.2	30.6	31.0	31.2
Φ_ey (%)	19.3	18.3	16.6	15.1	13.8	12.6	11.4	10.3
Φ_er (%)	50.7	46.4	40.7	36.4	33.1	30.6	27.8	25.4
CRI	90	90	90	90	90	90	90	90
R9	−2	−4	−6	−7	−7	−8	−6	−4
LER(lm/W)	403	401	393	383	372	366	355	343

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
λ_b	461.2	460.9	460.4	459.7	459.2	460.2	459.6	459.0
λ_g	521.1	521.3	521.8	522.1	522.3	522.6	522.6	522.5
λ_y	567.3	567.3	567.5	567.9	568.2	567.9	568.3	568.7
λ_r	619.8	618.9	617.9	617.4	616.9	616.5	616.0	615.6
∆λ_b	30	30	30	30	30	30	30	30
∆λ_g	30	30	30	30	30	30	30	30
∆λ_y	30	30	30	30	30	30	30	30
∆λ_r	30	30	30	30	30	30	30	30
Φ_eb (%)	7.8	10.6	15.1	18.9	22.3	24.7	28.1	31.2
Φ_eg (%)	18.1	20.2	22.7	24.5	25.7	27.0	27.7	28.1
Φ_ey (%)	25.6	25.0	23.6	22.2	20.9	19.6	18.4	17.3
Φ_er (%)	48.4	44.2	38.6	34.3	31.1	28.7	25.8	23.4
CRI	95	95	95	95	95	95	95	95
R9	53	52	52	53	55	53	55	56
LER(lm/W)	383	382	376	369	358	353	342	332

	CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
CRI = 90, R9 = 90	LER (lm/W)	302	309	314	314	311	309	304	298
CRI = 95, R9 = 95	LER (lm/W)	281	290	297	299	297	296	292	288

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
LER (lm/W)	≥ 370	≥ 370	≥ 365	≥ 360	≥ 350	≥ 345	≥ 335	≥ 325
${\bar{λ}}_{b}$	468.9	467.9	466.6	465.0	464.6	465.0	464.2	463.5
${\bar{λ}}_{g}$	531.0	531.6	531.7	532.1	531.9	532.3	532.2	531.0
${\bar{λ}}_{y}$	563.7	564.5	565.1	565.8	566.8	567.2	568.5	567.3
${\bar{λ}}_{r}$	622.1	621.4	620.5	619.6	619.4	619.2	618.8	618.3
σ_λ,b	5.5	4.7	4.1	3.0	3.2	2.9	2.7	2.5
σ_λ,g	6.3	5.7	5.2	3.8	4.1	4.0	3.7	3.4
σ_λ,y	3.7	4.4	5.0	4.9	5.6	6.5	6.7	5.6
σ_λ,r	1.0	1.2	1.4	1.5	1.8	2.0	2.2	2.0
${\bar{Δ λ}}_{b}$	36.0	35.2	32.4	31.4	31.6	31.6	31.2	31.1
${\bar{Δ λ}}_{g}$	32.6	32.2	32.1	31.0	31.3	31.6	31.5	31.5
${\bar{Δ λ}}_{y}$	35.7	34.3	35.1	35.2	38.9	42.0	42.0	41.6
${\bar{Δ λ}}_{r}$	30.8	30.9	31.1	31.0	31.3	31.5	31.5	31.9
σ_∆λ,b	6.0	5.2	2.4	1.4	1.6	1.6	1.2	1.1
σ_∆λ,g	2.6	2.2	2.1	1.0	1.3	1.6	1.5	1.5
σ_∆λ,y	5.7	4.3	5.1	5.2	8.9	12.0	12.0	11.6
σ_∆λ,r	0.8	0.9	1.1	1.0	1.3	1.5	1.5	1.9

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
LER (lm/W)	≥ 370	≥ 370	≥ 365	≥ 360	≥ 350	≥ 345	≥ 335	≥ 325
${\bar{λ}}_{b}$	466.4	465.3	463.8	462.5	461.5	462.5	461.4	460.5
${\bar{λ}}_{g}$	520.9	521.6	522.7	522.7	522.5	523.2	523.0	523.3
${\bar{λ}}_{y}$	566.8	566.9	567.5	568.1	568.3	568.5	569.2	569.8
${\bar{λ}}_{r}$	624.1	623.4	622.5	622.1	621.7	621.7	621.6	621.3
σ_λ,b	4.9	3.9	2.6	2.0	1.6	1.5	1.1	0.8
σ_λ,g	3.9	3.5	2.4	2.4	2.0	2.0	1.8	1.3
σ_λ,y	1.5	1.6	1.6	1.6	1.3	1.7	1.7	1.3
σ_λ,r	0.6	0.7	0.7	0.8	0.9	1.0	1.0	0.9
${\bar{Δ λ}}_{b}$	36.0	36.0	32.6	33.4	31.7	31.6	31.5	31.5
${\bar{Δ λ}}_{g}$	36.0	35.6	31.6	32.8	31.7	31.5	31.7	32.0
${\bar{Δ λ}}_{y}$	32.5	32.8	31.5	33.5	32.9	34.4	36.0	36.0
${\bar{Δ λ}}_{r}$	31.3	31.7	31.0	32.2	31.6	31.6	32.1	32.8
σ_∆λ,b	6.0	6.0	2.6	3.4	1.7	1.6	1.5	1.5
σ_∆λ,g	6.0	5.6	1.6	2.8	1.7	1.5	1.7	2.0
σ_∆λ,y	2.5	2.8	1.5	3.5	2.9	4.4	6.0	6.0
σ_∆λ,r	1.3	1.7	1.0	2.2	1.6	1.6	2.1	2.8

Optimal spectra of white light-emitting diodes using quantum dot nanophosphors

Abstract

1. Introduction

2. Objective function of optimization

3. Results

3.1 Relations between CRI vs. CCT, CRI vs. LER, and LER vs. CCT

3.2 Optimal spectra of QD-WLEDs with excellent color rendering and high efficient

3.3 Effects of the deviations from peak emission wavelengths and FWHMs of the spectra

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (3)

Tables (13)

Equations (6)

Optics Express

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
λ_b	464.1	463.6	462.7	461.9	461.2	462.0	461.3	460.7
λ_g	527.5	528.5	529.4	530.1	530.5	530.8	531.2	531.4
λ_y	560.8	560.9	560.9	561.4	561.7	561.4	562.2	563.2
λ_r	621.7	620.9	619.8	619.0	618.3	618.0	617.4	616.8
∆λ_b	30	30	30	30	30	30	30	30
∆λ_g	30	30	30	30	30	30	30	30
∆λ_y	30	30	30	30	30	30	30	30
∆λ_r	30	30	30	30	30	30	30	30
Φ_eb (%)	8.79	11.76	16.37	20.40	23.89	26.32	29.90	33.14
Φ_eg (%)	12.81	15.18	18.32	20.88	22.71	24.49	25.91	27.04
Φ_ey (%)	26.85	25.78	23.69	21.41	19.41	17.76	15.75	13.87
Φ_er (%)	51.55	47.28	41.62	37.32	34.00	31.43	28.44	25.95
CRI	90	90	90	90	90	90	90	90
R9	90	90	90	90	90	90	90	90
R13	98	97	97	97	96	96	95	95
R15	93	92	92	91	91	91	90	90
CQS	89	89	88	88	88	88	87	87
LER(lm/W)	380	381	376	369	361	356	346	336

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
λ_b	462.5	462.3	461.6	460.9	460.2	461.1	460.4	459.7
λ_g	520.9	521.6	522.4	522.9	523.3	523.7	523.9	523.9
λ_y	566.0	566.0	566.2	566.6	567.0	566.7	567.4	568.2
λ_r	623.7	623.0	622.1	621.5	621.0	620.7	620.4	620.1
∆λ_b	30	30	30	30	30	30	30	30
∆λ_g	30	30	30	30	30	30	30	30
∆λ_y	30	30	30	30	30	30	30	30
∆λ_r	30	30	30	30	30	30	30	30
Φ_eb (%)	7.82	10.67	15.13	19.00	22.37	24.77	28.22	31.31
Φ_eg (%)	15.72	17.65	20.24	22.20	23.63	25.00	25.99	26.67
Φ_ey (%)	27.10	26.57	25.18	23.64	22.17	20.82	19.40	18.12
Φ_er (%)	49.36	45.11	39.46	35.16	31.83	29.42	26.40	23.90
CRI	95	95	95	95	95	95	95	95
R9	95	95	95	95	95	95	95	95
R13	96	96	96	96	97	97	97	97
R15	97	97	96	96	95	95	95	94
CQS	93	94	94	93	93	93	93	93
LER(lm/W)	370	371	367	360	352	347	338	327

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
${\bar{λ}}_{b}$ + σ_λ,b	474.4	472.6	470.6	468.0	467.8	467.9	466.9	466.0
${\bar{λ}}_{g}$ + σ_λ,g	537.3	537.3	536.9	535.9	535.9	536.3	535.9	534.5
${\bar{λ}}_{y}$ + σ_λ,y	567.4	568.9	570.1	570.6	572.5	573.6	575.3	572.9
${\bar{λ}}_{r}$ + σ_λ,r	623.1	622.5	621.9	621.0	621.2	621.2	621.0	620.4
${\bar{Δ λ}}_{b}$ + σ_∆λ,b	42.0	40.3	34.7	32.8	33.2	33.2	32.4	32.1
${\bar{Δ λ}}_{g}$ + σ_∆λ,g	35.3	34.5	34.2	32.0	32.5	33.1	33.0	33.0
${\bar{Δ λ}}_{y}$ + σ_∆λ,y	41.3	38.5	40.1	40.4	47.9	54.0	54.0	53.2
${\bar{Δ λ}}_{r}$ + σ_∆λ,r	31.7	31.8	32.3	32.0	32.6	33.1	33.0	33.7
Φ_eb (%)	11.56	14.80	19.43	22.94	26.86	29.32	32.82	35.84
Φ_eg (%)	17.59	20.41	23.12	24.25	27.24	29.52	31.04	32.14
Φ_ey (%)	21.69	20.17	18.93	17.69	17.85	16.87	16.22	15.87
Φ_er (%)	49.37	45.00	39.03	34.93	30.53	27.53	24.22	22.42
CRI	93	93	92	92	92	92	91	91
R9	90	90	90	90	90	90	90	90
R13	95	96	96	95	94	94	93	93
R15	93	93	92	91	90	90	89	88
CQS	90	90	89	89	89	89	89	89
LER(lm/W)	370	370	365	360	350	345	335	325

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
${\bar{λ}}_{b}$ - σ_λ,b	463.4	463.1	462.5	461.9	461.4	462.1	461.5	461.0
${\bar{λ}}_{g}$ - σ_λ,g	524.7	526.0	526.6	528.3	527.8	528.3	528.5	527.6
${\bar{λ}}_{y}$ - σ_λ,y	560.0	560.1	560.2	560.9	561.2	560.7	561.8	561.8
${\bar{λ}}_{r}$ - σ_λ,r	621.1	620.2	619.0	618.1	617.6	617.2	616.6	616.3
${\bar{Δ λ}}_{b}$ - σ_∆λ,b	30.0	30.0	30.0	30.0	30.0	30.0	30.0	30.0
${\bar{Δ λ}}_{g}$ - σ_∆λ,g	30.0	30.0	30.0	30.0	30.0	30.0	30.0	30.0
${\bar{Δ λ}}_{y}$ - σ_∆λ,y	30.0	30.0	30.0	30.0	30.0	30.0	30.0	30.0
${\bar{Δ λ}}_{r}$ - σ_∆λ,r	30.0	30.0	30.0	30.0	30.0	30.0	30.0	30.0
Φ_eb (%)	10.47	13.82	18.47	20.15	23.59	28.29	30.79	32.77
Φ_eg (%)	10.52	13.25	16.83	18.28	20.73	23.87	25.77	27.10
Φ_ey (%)	26.08	25.12	23.69	20.20	19.22	19.11	15.16	15.55
Φ_er (%)	51.25	46.96	41.42	37.85	34.32	31.54	29.44	26.05
CRI	92	92	93	91	92	93	91	92
R9	90	90	90	90	90	90	90	90
R13	95	95	95	94	95	95	90	94
R15	90	89	89	90	90	88	83	89
CQS	90	90	89	90	90	89	90	90
LER(lm/W)	371	370	365	367	359	345	335	332

CCT (K)	2700	3000	3500	4000	4500	5000	5700	6500
${\bar{λ}}_{b}$ + σ_λ,b	471.3	469.2	466.4	464.5	463.1	464.0	462.5	461.2
${\bar{λ}}_{g}$ + σ_λ,g	524.9	525.2	525.1	525.1	524.5	525.2	524.8	524.6
${\bar{λ}}_{y}$ + σ_λ,y	568.3	568.5	569.1	569.7	569.6	570.2	570.9	571.0
${\bar{λ}}_{r}$ + σ_λ,r	624.8	624.1	623.3	622.9	622.5	622.7	622.6	622.3
${\bar{Δ λ}}_{b}$ + σ_∆λ,b	42.0	42.0	35.3	36.8	33.5	33.2	33.0	32.9
${\bar{Δ λ}}_{g}$ + σ_∆λ,g	42.0	41.3	33.2	35.7	33.4	32.9	33.3	33.9
${\bar{Δ λ}}_{y}$ + σ_∆λ,y	35.0	35.6	32.9	36.9	35.7	38.8	42.0	42.0
${\bar{Δ λ}}_{r}$ + σ_∆λ,r	32.7	33.4	32.0	34.5	33.1	33.3	34.3	35.7
Φ_eb (%)	9.53	12.45	16.79	20.38	23.41	25.95	28.96	31.79
Φ_eg (%)	15.65	18.45	19.99	22.80	23.80	26.52	27.70	28.81
Φ_ey (%)	25.00	24.14	23.88	21.88	21.73	20.62	19.90	18.46
Φ_er (%)	48.67	44.48	38.66	34.66	31.13	28.36	25.24	23.17
CRI	96	96	96	96	96	96	96	96
R9	95	95	95	95	95	95	95	95
R13	98	98	98	97	98	97	96	96
R15	96	96	96	95	94	94	94	93
CQS	91	93	93	94	94	94	94	94
LER(lm/W)	361	361	360	351	345	340	330	321