Abstract

The design of white light-emitting diodes is carried out to achieve highly efficient white light emission with superior color quality, good vision performance, and healthy effect on human circadian rhythms. Here, the white light is obtained by combing five different emissions (blue, cyan, green, yellow, and red) from organolead halide perovskites [MAPb(BrxI1-x)3, MA-CH3NH3]. The color characteristics are evaluated by calculating the CIE coordinates, the correlated-color temperature (CCT), the color-rendering indices (CRI: Ra, R9-R15), and the Duv. Vision performance is evaluated by calculating the luminous efficacy of radiation. The effect of white light on human circadian rhythms is evaluated by calculating the circadian action factor (CAF). The results show that the white lights with a tunable CCT from 2851 K to 8315 K, extremely high CRI (up to 98.7), and small Duv (0.0002 – 0.0055) have been obtained by engineering the spectral power distributions. In addition, excellent vision performance and highly tunable CAF are demonstrated. These findings demonstrate that these types of materials are promising candidates to achieve highly efficient white light emission with excellent color quality and vision performance.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Light-emitting diodes (LEDs) have been developing for modern lighting and display technologies because of their high-energy efficacy, long lifespan, high color tunability, and robustness [110]. The development of highly efficient UV/blue LEDs coupled with the advances in the phosphor materials has directly resulted in the revolution of lighting technology. Lighting accounts for ∼10% of the total electricity consumed in the United States of America (U.S.) [11]. Based on a study by the U.S. Department of Energy (DOE), the U.S. would reduce its electricity for lighting by 50% in 2030 if conventional light bulbs are replaced with LEDs [12]. At the same time, significant greenhouse gas reductions would result [13]. Despite rapid advances, LED technology is still in its early stage, and continued innovation and breakthroughs are needed to achieve the full potential of this technology. The white LEDs are typically obtained by depositing yellow phosphors on the blue LEDs. However, the high correlated color temperature (CCT ∼ 6000 K) and the low color-rendering index (CRI < 75) are undesirable for indoor lighting applications [14,15]. To address this issue, the additional red phosphors were added to achieve warm white light [16]. Alternatively, highly efficient white LEDs with desired color quality were obtained by coating UV LEDs with blue, green, and red phosphors or coating blue LEDs with green and red phosphors [5,1722]. However, the limited material availability of the rare-earth elements [23,24] used in the current generation of down conversion phosphors for white LEDs increases the cost of white LEDs. Thus, developing low-cost and highly efficient color conversion materials has been listed as one of the Research & Development plans by DOE [25]. Searching for low-cost photon down conversion materials to couple with UV/blue LEDs is of paramount importance towards generating cost-effective white light.

Metal halide perovskites have attracted tremendous attention in recent years due to the earth-abundant elements, cost-effective production process, and remarkable structural, electrical, and optical properties [26,27]. The use of these materials as photon harvesters in solar cells has been extensively studied and the efficiency has been significantly increased [2730]. However, the application of these materials in light-emitting devices are less explored. Previous work showed that perovskite nanocrystals are of extremely high photoluminescence (PL) quantum yield (> 90%), tunable emission, and narrow full-width at half-maximum (FWHM) [26,3138]. These attributes place perovskites in a unique position to serve as color conversion layers in white LEDs. Applications of this type of materials in white LEDs have been experimentally demonstrated recently [33,3950]. Pathak et al. reported that by stacking green- and red-emitting organic metal halide perovskite thin films over a blue LED chip, white light with CRI of 86 and CCT of 5229 K was obtained [40]. Palazon et al. placed all-inorganic halide perovskites over a 365 nm UV LED chip to achieve white light emission with tunable CCT and higher stability upon continuous illumination at high power [41]. Zhang et al. coated halide perovskite composite films on a UV LED chip and obtained white light with CRI of 85 [45]. Ma et al. incorporated green-emitting CsPbBr3 perovskites and red-emitting CdSe quantum dots (QDs) to the blue LED chip to achieve white light emission with CRI of 89.2 and color coordinates of (0.34, 0.33) [44]. Yoon et al. reported the white LEDs with good color performance using the combination of six different colors [42]. Li et al. reported that the use of all-inorganic green and red halide perovskite QDs on a blue LED chip resulted in a tunable CCT between 2500 K and 11500 K, and the CIE coordinates have been optimized to (0.33, 0.30), which is very close to the coordinates of a standard neutral white light (0.33,0.33) [43].

The previous studies have focused on the applications of this type of materials in white LEDs and they have used the multilayer device structures. However, the halide perovskite is unstable in the ambient atmosphere and anion exchange exists among different color emitting halide perovskites within the layers [51]. In this work, we propose the multi-pixel designs for organolead halide perovskite-based white LEDs. Furthermore, we optimize spectral power distribution to achieve superior color quality and high vision performance. The color quality is evaluated by calculating CRI instead of other standard standards such as color fidelity score (Rf) [52,53] and color quality scale (CQS) [54] as the CRI is still widely used in the industry. The results show that white light with tunable CCT from 2851 K (warm white) to 8315 K (cool white) and extremely high CRI (> 98) could be achieved by the combination of perovskite materials with five different emissions in the multi-pixel design, which is much higher than four-emission configuration [55]. This work will provide guidelines for designing highly efficient halide perovskite QDs based white LEDs.

2. LED structure design and spectra optimization

2.1 Optical properties of MAPb(BrxI1-x)3 nanocrystals

The perovskite nanocrystals were synthesized using the modified ligand assisted re-precipitation method as reported in our previous work [56,57]. The band gaps of the obtained perovskite nanocrystals were calculated from the absorption spectra as shown in Fig. 1(a). The different band gaps for MAPbBr3 (2.83 eV and 2.73 eV) were obtained by controlling the amount of ligand [56,57]. A continuous decrease in the band gap of MAPb(BrxI1-x)3 nanocrystals was obtained by decreasing the Br/I ratio. The band gaps of 2.26 eV, 2.18 eV, and 2.0 eV were obtained from MAPb(Br0.9I0.1)3, MAPb(Br0.7I0.3)3, and MAPb(Br0.5I0.5)3 nanocrystals, respectively. The tunable band gap resulted in tunable emission (blue-cyan-green-yellow-red) [see Fig. 1(b)]. The peak emission wavelengths are 439.4 nm, 477.7 nm, 529.8 nm, 569.3 nm, and 627.8 nm with corresponding FWHM of 15.6 nm, 26.2 nm, 25.0 nm, 35.2 nm, and 41.4 nm, respectively. The combination of these narrow-band emissions to obtain white light will simultaneously achieve high color quality and vision performance. However, the white light with only high color quality can be obtained by employing broadband emissions. The optical properties of these nanocrystals are summarized in Table 1. The intensities in Table 1 are the integrated intensities of the emission spectra, which was calculated by integrating the area enclosed by x-axis and spectra. The excitation spectra [see Fig. 1(c)] obtained by monitoring the corresponding peak emission wavelength showed that the nanocrystals can be effectively excited by UV light to emit different colors. This indicates that this type of materials can serve as a photon down conversion materials in III-nitride based white LEDs. The schematics of the white LED device structure is shown in Fig. 1(d). Multi-pixel photon down conversion layer will be placed on top of UV LED instead of the multi-layered structure to minimize reabsorption.

 figure: Fig. 1.

Fig. 1. (a) UV-visible absorption spectra, (b) PL spectra, and (c) excitation spectra of blue-, cyan-, green-, yellow-, and red-emitting organolead halide perovskites. (d) Multi-pixel white LED device structure, which consists of a UV LED and a remote color conversion layer.

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Tables Icon

Table 1. The optical properties of MAPb(BrxI1-x)3 nanocrystals.

2.2 Spectral power distribution optimization

The perovskite multi-pixel color conversion layer will be incorporated with a UV LED chip through the remote phosphor approach. The conversion layer consists of many tiny boxes and the perovskite colloidal solutions with different emissions will be placed separately in these boxes [58]. To achieve high color quality and vision performance, extensive optimization was carried out by tuning the ratios of the amount of five different perovskites in these boxes, which corresponds to different spectral power distributions (SPDs). The combined SPDs were obtained by using the following equation:

$${S_{total}}(\lambda )= {r_B} \times {S_B}(\lambda )+ {r_C} \times {S_C}(\lambda )+ {r_G} \times {S_G}(\lambda )+ {r_Y} \times {S_Y}(\lambda )+ {r_R} \times {S_R}(\lambda ), $$
where,
$${r_B} = 0:0.1:1,{r_C} = 0:0.1:1,{r_G} = 0:0.1:1,{r_Y} = 0:0.1:1,{r_R} = 0:0.1:1.$$
The ratios (B: C: G: Y: R) shown in Table 3 were calculated using the following equation:
$$Ratios(B:C:G:Y:R) = ({r_B} \times {I_B}):({r_C} \times {I_C}):({r_G} \times {I_G}):({r_Y} \times {I_Y}):({r_R} \times {I_R}),$$
where, IB, IC, IG, IY, and IR are the integrated intensities of the corresponding SPDs of blue, cyan, green, yellow, and red emissions as shown in Fig. 1, respectively. Thus, in this work, the optimization starts with combining five different emission spectra with various power ratios (considering 11 different choices for each color spectrum), which results in 161051 different SPDs [$S(\lambda )$].

2.3 Color quality, vision performance, and circadian action factor calculation

The color quality, vision performance, and circadian action effect (health effect) are evaluated by calculating CCT, general CRI (Ra), CIE chromaticity coordinates (x, y), Duv, special CRIs (R9-R14), luminous efficacy of radiation (LER), circadian luminous efficacy of radiation (CER), and circadian action factor (CAF). The color of each combined SPD (${S_{total}}$) is determined by calculating the CIE 1931 (x, y) chromaticity coordinates. The color matching functions [$\overline x (\lambda ),\overline y (\lambda ),$ and $\overline z (\lambda )$] (see Fig. 2) were used to calculate the tristimulus values, $X,Y,$ and Z by using the following equations [59]:

$$X = \int_{380}^{780} {{S_{total}}(\lambda )} \overline x (\lambda )d\lambda ,\;$$
$$Y = \int_{380}^{780} {{S_{total}}(\lambda )} \overline y (\lambda )d\lambda ,$$
$$Z = \int_{380}^{780} {{S_{total}}(\lambda )} \overline z (\lambda )d\lambda .$$

 figure: Fig. 2.

Fig. 2. The color matching functions [$\overline x (\lambda )$,$\overline y (\lambda )$ and $\overline z (\lambda )$], spectral luminous efficiency function [$V(\lambda )$], and spectral circadian efficiency function [$C(\lambda )$] [62,63].

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The CIE 1931 $(x,y)$ coordinates were then calculated by using the following equations [59]:

$$x = \frac{X}{{X + Y + Z}},\;$$
$$y = \frac{Y}{{X + Y + Z}}.$$
The appearance of the color is characterized by CCT, which is a metric that relates to the appearance of a light source to the appearance of the black body [60]. The CCT of $S{(\lambda )_{total}}$ was then calculated by using [61]:
$$CCT = - 449{n^3} + 352{n^2} - 682.3n + 5520.33, $$
where, $n = {{(x - 0.3320)} \mathord{\left/ {\vphantom {{(x - 0.3320)} {(y - 0.1858)}}} \right.} {(y - 0.1858)}}$. The Duv was calculated to quantify the distance between the chromaticity of LED spectra and blackbody locus. General CRI (Ra) and special CRIs (R9 - R15) were calculated to measure the similarity of light source colors compared to black body source. Vision performance is evaluated by calculating LER. The CAF was calculated by adopting the circadian efficiency function ($C(\lambda )$) proposed by Gall [62] and luminous efficiency function ($V(\lambda )$). The luminous flux (${\Phi _V}$) is defined as
$${\Phi _V} = {K_m}\int_{380}^{780} {{S_{total}}(\lambda )V(\lambda )d\lambda } ,$$
where, ${K_m} = 683lm/W$ denotes maximum spectral luminous efficiency at 555 nm. The LER is defined as
$$LER(lm/W) = 683(lm/W)\frac{{\int_{380}^{780} {{S_{total}}(\lambda )V(\lambda )d\lambda } }}{{\int_{380}^{780} {{S_{total}}(\lambda )d\lambda } }}. $$
Circadian flux is defined as
$${\Phi _C} = {K_C}\int_{380}^{780} {{S_{total}}(\lambda )C(\lambda )d\lambda } ,$$
where, ${K_C} = 683blm/W$ is the maximum value of the circadian efficiency function [53].

The CER was calculated using the following equation [61]:

$$CER(blm/W) = 683(lm/W)\frac{{\int_{380}^{780} {{S_{total}}(\lambda )C(\lambda )d\lambda } }}{{\int_{380}^{780} {{S_{total}}(\lambda )d\lambda } }}, $$
and the CAF was calculated using the method proposed by Gall et al. [62] as the following:
$$CAF = \frac{{{K_C}\int_{380}^{780} {{S_{total}}(\lambda )C(\lambda )d\lambda } }}{{{K_m}\int_{380}^{780} {{S_{total}}(\lambda )V(\lambda )d\lambda } }}$$

3. Results and discussion

3.1 Color quality

One of the most important characteristics of light sources for general lighting and display is CRI. The CRIs of the resulting SPDs by combining five different emissions were calculated and the maximum CRI of 98.7 has been achieved by tuning the power ratios of five different emissions to 1: 1.2: 0.8: 1.2: 1.3. The corresponding CCT is 6344 K (see LED-7 in Table 2). Furthermore, the tunable CCT from warm white to cool white has been obtained. Based on LED color characteristic datasheet published by DOE, a light source with a CRI in the 90s is excellent for indoor lighting applications [60]. Therefore, white light with excellent color rendition and tunable CCT can be obtained by using these perovskite nanocrystals.

Tables Icon

Table 2. Color characteristics of selected LEDs with tunable CCT from warm to cool white.

The tunable CCT was achieved by combining different ratios of the integrated area of various emissions as shown in Fig. 3(a). The ratios presented in Fig. 3(a) were normalized based on the following equations:

$${R_{color}} = \frac{{{r_{color}} \times {I_{color}}}}{{{r_B} \times {I_B} + {r_C} \times {I_C} + {r_G} \times {I_G} + {r_Y} \times {I_Y} + {r_R} \times {I_R}}},$$
where the ${R_{color}}({{R_B},{R_C},{R_G},{R_Y},{R_R}} )$ is the ratio of the specific color determined by the corresponding ${r_{color}}({{r_B},{r_C},{r_G},{r_Y},{r_R}} )$ and ${I_{color}}({{I_B},{I_C},{I_G},{I_Y},{I_R}} ).$ Thus, the total power for each combination is equal to one and it can be written as:
$${R_{blue}} + {R_{cyan}} + {R_{green}} + {R_{yellow}} + {R_{red}} = 1. $$

 figure: Fig. 3.

Fig. 3. (a) The ratios of five different colors in the white light with various CCT (2827 K - 8315 K), (b) CCT with different relative power ratios of blue, cyan, and green to yellow and red emissions. The color bar indicates the CRI with corresponding CCT.

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The gradually increased CCT of white light is obtained by increasing the power ratios of blue, cyan, and green emissions and simultaneously decreasing the power ratios of yellow and red emissions as shown in Fig. 3(a). White lights with low CCT can be achieved by incorporating more yellow and red components and simultaneously lowering the content of blue, cyan and green components. The relation between ratios of the sum of blue, cyan, and green emissions to the sum of yellow and red emissions is also investigated and plotted in Fig. 3(b). The CCT increases with the increase in the ratios of blue, cyan, and green emissions to yellow and red emissions. Thus, the blue, cyan, and green emissions have more contribution to cool white light. However, the yellow and red emissions contribute more to warm the white light. The dependency of CCT on the ratio is well fitted using the following equations:

$$CCT(R) = 1800 + 2530R + 1110{R^2},$$
where, R is the ratios of the sum of blue, cyan, and green emissions to the sum of yellow and red emissions.

The color characteristics of selected LED spectra with tunable CCT ranging from 2851 K (warm white) to 8315 K (cool white) and corresponding CRI and Duv are summarized in Table 2. The special CRIs R9 to R12 represent four saturated colors (red, yellow, green, and blue). The R13, R14, and R15 represent Caucasian complexion, green leaf, and oriental complexion [64]. The R9 are especially pertinent, as the rendition of saturated red is particularly important for the appearance of skin tones. In general, an R9 score greater than zero is considered acceptable [60]. As seen in Table 2, the R9 is in the range of 82.3 - 98.3 for the selected eight LEDs. Furthermore, the R10-R15 are all above 94, which means that the color can be precisely reproduced for any color objects by using the white light obtained from organolead halide perovskites. As we discussed earlier, color temperature is an important aspect of color appearance related to how “cold’ (bluish) or how “warm” (yellowish) nominally white light appears. By tuning the power ratios of each emission, white lights with tunable CCT has been achieved. The corresponding spectra for selected eight LEDs are plotted in Fig. 4(a). Note that we have normalized the spectra by blue emission. Tunable CCT is especially important for practical applications. Light with low CCT creates a relaxing, cozy feeling, while light with high CCT is energizing and uplifting. Warm white lights are often preferred in living rooms and bedrooms to create a cozy atmosphere. Neutral and cool white lights have an energizing effect on people and are the good choice for homes, offices, and studies. Therefore, white light obtained using organic metal halide perovskites can be used in various lighting and display applications.

 figure: Fig. 4.

Fig. 4. (a) The spectral power distribution of white light with various CCTs (2827 K - 8315 K). (b) The chromaticity coordinates of white light in the CIE 1931 chromaticity diagram.

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Based on the previous discussion, the white light with tunable CCT and excellent CRI can be achieved by using halide perovskites. However, two light sources with the same CCT can look very different. Therefore, the American National Standards Institute (ANSI) has introduced the additional indices, Duv, to characterize light quality fully. The CIE coordinates (x, y) of these LEDs are shown in Table 3 and they are plotted in Fig. 4(b). The CIE coordinates we observed are very close to the Planckian Locus i.e. we have observed the small Duv for the selected LEDs ranging from 0.0002 to 0.0055. Therefore, the white light obtained from organolead halide perovskites are perceived as neutral in appearance, which indicates that the color temperature we obtained is comfortable to the human eyesight for a long time exposure. Furthermore, the CIE coordinates of the neutral white light (CCT ∼ 5603 K) is (0.33, 0.33), which is identical to the standard neutral white light (0.33, 0.33). Therefore, metal organic halide perovskites are promising materials to replace conventional phosphors in next-generation white LEDs. This type of materials has the potential of speeding up the widely spread adoption of LEDs in general illumination market.

Tables Icon

Table 3. Color characteristics of selected LEDs.

3.2 Vision performance

The vision performance of white lights is evaluated by calculating the LER of the corresponding SPD. The relation between the LER and CRI was investigated at four different color temperature ranges: 2700-2800 K, 3000-3100 K, 4000-4100 K, and 6500-6600 K. 2700 K is the typical color temperature of an incandescent light bulb (warm), which is suitable to be used as bedroom lighting. 3000 K is the color temperature of halogen light, which also creates a soft warm white. 4000 K is the color temperature of bright/cool white. The daylight has a color temperature of 6500 K. As shown in Fig. 5, the highest LER was obtained at a lower CRI and relatively lower LER was obtained at the highest CRI. There is a tradeoff between LER and CRI in general. It is not possible to achieve the highest LER and the highest CRI simultaneously at a specific CCT. In addition, the LER is highly tunable at lower CRI. Our results show that it is possible to achieve high CRI while having relatively high LER (in comparison to other QDs) [65] at any color temperature from warm white [see Figs. 5(a) and 5(b)] to cool white [see Figs. 5(c) and 5(d)].

 figure: Fig. 5.

Fig. 5. The LER as a function of CRI at different CCTs: (a) CCT = 2700-2800 K, (b) CCT = 3000-3100 K, (c) CCT = 4000-4100 K, and (d) CCT = 6500-6600 K.

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The CCT dependencies of LERs at various CRI ranges are plotted in Fig. 6. In general, the higher LER is obtained at lower CCT. This is because larger SPD in the blue region is necessary to obtain high CCT, while the blue component has a very low lumen contribution compared to green and red as we can see from color matching function [66]. At low CCT, an LER of 400 lm/W is obtained and at high CCT, an LER of ∼ 300 lm/W is obtained. Higher LERs over the range of cool white to warm white are obtained. The highest LER was obtained at a relatively low CRI [Fig. 6(a)]. Higher LER is achieved at lower CRI and CCT. In addition, the LER is highly tunable especially at relatively lower CRI [see Figs. 6(a) and 6(b)]. At a CCT of 3625 K and a CRI of 81.0-82.0, the lowest LER is 337 lm/W and the highest LER is 400 lm/W. The power ratios of five different emissions are 1:0:1.7:1.5:3.1 for LER of 337 lm/W, 1:0:2.9:2.8:4.8 for LER of 368 lm/W, and 1:0:11.8:10.6:16.9 for LER of 400 lm/W. Thus, the LER increases with the increase in the ratios of green, yellow, and red emissions.

 figure: Fig. 6.

Fig. 6. The LER as a function of CCT at various CRIs: (a) CRI = 81.0-82.0, (b) CRI = 85.0-86.0, (c) CRI = 90.0-91.0, (d) CRI = 95.0-97.8. The color of points represents corresponding CRI on the color bar.

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For the white light with CRI above 98, the maximum LER of 326 lm/W is obtained at CCT of 3310 K and the lowest LER is 278 lm/W at CCT of 8315 K. The power ratios of five different emissions to achieve different LERs at CRI above 98 were calculated. As shown in Fig. 7(a), LER increases with the increase in ratios of red and yellow emissions and the decrease in the ratios of blue, cyan, and green emissions. Thus, the ratio of the sum of blue, cyan, and green emissions to the sum of yellow and red directly affect the LER as shown in Fig. 7(b). The dependency of LER on the ratio is fitted using the following equation:

$$LER(R) = 333 + 22R - 9{R^2}.$$
The vision performance can be improved by increasing the yellow and red emissions or decreasing the blue, cyan, and green emissions, or by simultaneously increasing yellow, red emissions and decreasing the blue, cyan, and green emissions.

 figure: Fig. 7.

Fig. 7. (a) The ratios of spectral distribution of blue, cyan, green, yellow, and red emissions for obtaining white light with various LER, (b) LER as a function of ratios of blue, cyan, and green emissions to yellow and red emissions (the color of points represents CRI as labeled on color bar).

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3.3 Circadian action factor

In the previous sections, we have investigated the color quality and vision performance of white light obtained by combining five different emissions from organolead halide perovskite nanocrystals. We found that white lights with extremely high CRIs (above 98), tunable CCT (2827 - 8315 K), and high LER (above 300 lm/W) could be obtained by tuning the ratios of five different emissions. The effect of white light on human health is also investigated in this work. By combing five different emissions, the tunable CAF is obtained at fixed CCT. The CAFs as a function of CRIs at different CCT ranges are plotted in Fig. 8. The highest tunability of CAF was obtained at relatively lower CRIs (the 80s). The tunable CAF from 0.15 to 0.95 at CRI range of 80-81 and CCT range of 2700-2800 K are obtained as shown in Fig. 8(a). The tunable CAF from 0.16 to 0.99 at CRI range of 82-84 and CCT range of 3000-3100 K are obtained as shown in Fig. 8(b). Similarly, the tunable CAF from 0.27 to 1.06 at CRI range of 80 - 85 and CCT range of 4000-4100 K are obtained as shown in Fig. 8(c). The tunable CAF from 0.73 to 1.18 at CRI range of 80-82 and CCT range of 6500-6600 K are obtained as shown in Fig. 8(d). Thus, the CAFs of warm, neutral, and cool white are highly tunable at relatively low CRI (the 80s). However, the tunability of CAF become smaller with the increase in CRI. At high CCT, the tunability becomes smaller and CAF becomes higher.

 figure: Fig. 8.

Fig. 8. CAF as a function of CRI at various CCTs: (a) CCT = 2700–2800 K, (b) CCT = 3000–3100 K, (c) CCT = 4000–4100 K, and (d) CCT = 6500–6600 K.

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High tunability of CAF at a fixed CCT is also obtained at different CRI ranges: CRI = 80.0-82.0 [Fig. 9(a)], CRI = 85.0-86.0 [Fig. 9(b)], CRI = 90.0-91.0 [Fig. 9(c)], CRI = 95.0-96.0 [Fig. 9(d)], CRI = 97.0-98.0 [Fig. 9(e)], and CRI = 98.0-99.0 [Fig. 9(f)]. The highest tunability of CAF is obtained at low color temperature (CCT∼3000 K). The tunability decreases with the increase in the CCT. At lower CRIs [CRI = 80.0-81.0 in Fig. 9(a), CRI = 85.0-86.0 in Fig. 9(b), CRI = 90.0-91.0 in Fig. 9(c), and CRI = 95.0-96.0 in Fig. 9(d)], the higher tunability of CAF is obtained, especially at lower CCTs. At higher CRIs [CRI = 97.0-98.0 in Fig. 9(e) and CRI = 98.0-99.0 in Fig. 9(f)], the dependency of CAF on CCT is nearly linear and can be well fitted using the following equations:

$$CAF(CCT) = ( - 2.4 + 2.5CCT - 0.1CC{T^2}) \times {10^{ - 4}}, $$
and
$$CAF(CCT) = ( - 2.8 + 2.7CCT - 0.1CC{T^2}) \times {10^{ - 4}},$$
for CRI = 97.0-98.0 and CRI = 98.0-99.0, respectively. This indicates that at higher CRIs, the CAF increases with the increase in CCT. This is consistent with the previous report [6].

To find the power ratios of different emissions to achieve the high CRI (> 98) and tunable CAF, the power ratios were calculated at various CAFs while CRIs were kept above 98. The power ratios of five different emissions as a function of CAF are plotted in Fig. 10(a). CAF increases with the increase in ratios of blue, cyan, and green emissions and the decrease in the ratios of yellow and red emissions. The CAF dependency on ratios of the sum of blue, cyan, and green emissions to the sum of yellow and red emissions is plotted in Fig. 10(b). Almost a linear relationship was found. The relation between CAF and ratio can be fitted using the following equation:

$$CAF(R) = 0.08 + 0.87R - 0.15{R^2}.$$
The CAF dependency on the ratio is slightly different from CCT dependency on the ratio, but the trend is the same. However, the LER shows the opposite dependency. These findings will provide some guidelines to obtain white light with high quality, high LER, and desirable CCT and CAF.

 figure: Fig. 9.

Fig. 9. The CAF as a function of CCT at different CRIs: (a) CRI = 81.0 - 82.0, (b) CRI = 85.0 - 86.0, (c) CRI = 90.0 - 91.0, (d) CRI = 95.0 - 96.0, (e) CRI = 97.0 - 98.0, and (f) CRI = 98.0 - 99.0. The color of points represents corresponding CRI on the color bar.

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 figure: Fig. 10.

Fig. 10. (a) CAF changes with power ratios of five different emissions and (b) CAF as a function of ratios of the sum of blue, cyan, and green emissions to the sum of yellow and red emissions. The color of points represents corresponding CRI on the color bar.

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4. Conclusion

In summary, spectral optimization was carried out to study the color quality, vision performance, and circadian effect of the white light obtained from organolead halide perovskites. We demonstrated the tunability of CCT of white light from 2851 K (warm white) to 8135 K (cool white) by combining different power ratios of blue, cyan, green, yellow, and red emissions. The maximum CRI of 98.7 is obtained at a CCT of 6344 K. The significantly high special CRIs (R9-R15) are also obtained. This indicates that the color can be precisely reproduced for any color objects by using the white light obtained from organolead halides as the light source. In addition, the high LER above 300 lm/W indicates excellent vision performance. High tunability of CAF was also obtained, which indicates the dynamically modulated circadian efficacy of white light. The combination of the earth-abundant elements with superior optoelectronic properties places this type of materials in a unique position for the applications in next-generation of optoelectronic devices. The application of these materials in white LEDs will lead to a significant reduction in the cost of the white LEDs while having high-energy efficacy, superior color quality, and desirable circadian effect on human health. This will speed up the widespread adoption of white LEDs in general illumination market with the goal of achieving significant energy and budget saving. Note that the slight changes in peak wavelength of five different emissions (blue, cyan, green, yellow, and red) bands have no much effect on the color quality and vision performance and the model coefficients are pretty much the same. Thus, this work provides the guidelines to obtain highly efficient white LEDs based on halide perovskites.

Funding

University of Tulsa (TU) (Faculty Startup Fund).

References

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2. P. Zhao and H. P. Zhao, “Analysis of light extraction efficiency enhancement for thin-film-flip-chip InGaN quantum wells light-emitting diodes with GaN micro-domes,” Opt. Express 20(S5), A765–A776 (2012). [CrossRef]  

3. P. Pust, P. J. Schmidt, and W. Schnick, “A Revolution in Lighting,” Nat. Mater. 14(5), 454–458 (2015). [CrossRef]  

4. P. Zhu and N. Tansu, “Effect of Packing Density and Packing Geometry on Light Extraction of III-Nitride Light-Emitting Diodes with Microsphere Arrays,” Photonics Res. 3(4), 184–191 (2015). [CrossRef]  

5. J. Zheng, S. Wu, G. Chen, S. Dang, Y. Zhuang, Z. Guo, Y. Lu, Q. Cheng, and C. Chen, “Blue-emitting Ca5(PO4)3Cl:Eu2+ phosphor for near-UV pumped light emitting diodes: Electronic structures, luminescence properties and LED fabrications,” J. Alloys Compd. 663, 332–339 (2016). [CrossRef]  

6. L. Zheng, T. Wu, Y. Lu, Y. Gao, Y. Wang, L. Zhu, Z. Guo, and Z. Chen, “Spectral Optimization of Three-Primary LEDs by Considering the Circadian Action Factor,” IEEE Photonics J. 8(6), 1–9 (2016). [CrossRef]  

7. B. Janjua, H. Sun, C. Zhao, D. H. Anjum, D. Priante, A. A. Alhamoud, F. Wu, X. Li, A. M. Albadri, A. Y. Alyamani, M. M. El-Desouki, T. K. Ng, and B. S. Ooi, “Droop-free AlxGa1-xN/AlyGa1-yN quantum-disks-in-nanowires ultraviolet LED emitting at 337 nm on metal/silicon substrates,” Opt. Express 25(2), 1381–1390 (2017). [CrossRef]  

8. C. Liu, Y. K. Ooi, S. M. Islam, H. Xing, D. Jena, and J. Zhang, “234 nm and 246 nm AlN-Delta-GaN quantum well deep ultraviolet light-emitting diodes,” Appl. Phys. Lett. 112(1), 011101 (2018). [CrossRef]  

9. Y. K. Ooi and J. Zhang, “Light Extraction Efficiency Analysis of Flip-Chip Ultraviolet Light-Emitting Diodes With Patterned Sapphire Substrate,” IEEE Photonics J. 10(4), 1–13 (2018). [CrossRef]  

10. Z. Ren, Y. Lu, H. Yao, H. Sun, C. Liao, J. Dai, C. Chen, J. Ryou, J. Yan, J. Wang, J. Li, and X. Li, “III-Nitride Deep UV LED Without Electron Blocking Layer,” IEEE Photonics J. 11(2), 1–11 (2019). [CrossRef]  

11. “How much electricity is used for lighting in the United States?” (The U.S. Energy Information Administration (EIA), 2019), retrieved https://www.eia.gov/tools/faqs/faq.php?id=99&t=3.

12. “Solid-State Lighting Forecast Report,” (Solid-State Lighting Forecast Report, U.S. Department of Energy, 2016).

13. Y. J. Kim and M. Brown, “Impact of domestic energy-efficiency policies on foreign innovation: The case of lighting technologies,” Energy Policy 128, 539–552 (2019). [CrossRef]  

14. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007). [CrossRef]  

15. X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Sci. Appl. 2(1), e50 (2013). [CrossRef]  

16. K. T. Shimizu, M. Böhmer, D. Estrada, S. Gangwal, S. Grabowski, H. Bechtel, E. Kang, K. J. Vampola, D. Chamberlin, O. B. Shchekin, and J. Bhardwaj, “Toward commercial realization of quantum dot based white light-emitting diodes for general illumination,” Photonics Res. 5(2), A1–A6 (2017). [CrossRef]  

17. Y. Q. Li, A. C. A. Delsing, G. de With, and H. T. Hintzen, “Luminescence Properties of Eu2+-Activated Alkaline-Earth Silicon-Oxynitride MSi2O2-δN2+2/3δ(M = Ca, Sr, Ba): A Promising Class of Novel LED Conversion Phosphors,” Chem. Mater. 17(12), 3242–3248 (2005). [CrossRef]  

18. H. Xiao, Y.-J. Lu, T.-M. Shih, L.-H. Zhu, S.-Q. Lin, P. J. Pagni, and Z. Chen, “Improvements on Remote Diffuser-Phosphor-Packaged Light-Emitting Diode Systems,” IEEE Photonics J. 6(2), 1–8 (2014). [CrossRef]  

19. P. Pust, V. Weiler, C. Hecht, A. Tucks, A. S. Wochnik, A. K. Henss, D. Wiechert, C. Scheu, P. J. Schmidt, and W. Schnick, “Narrow-Band Red-Emitting Sr[LiAl3N4]:Eu2+ as a Next-Generation LED-Phosphor Material,” Nat. Mater. 13(9), 891–896 (2014). [CrossRef]  

20. V. Kumar, O. M. Ntwaeaborwa, T. Soga, V. Dutta, and H. C. Swart, “Rare Earth Doped Zinc Oxide Nanophosphor Powder: A Future Material for Solid State Lighting and Solar Cells,” ACS Photonics 4(11), 2613–2637 (2017). [CrossRef]  

21. Z. Zhou, Y. Li, M. Xia, Y. Zhong, N. Zhou, and H. T. Hintzen, “Improved luminescence and energy-transfer properties of Ca14Al10Zn6O35:Ti4+,Mn4+ deep-red-emitting phosphors with high brightness for light-emitting diode (LED) plant-growth lighting,” Dalton Trans. 47(38), 13713–13721 (2018). [CrossRef]  

22. P. Zhu, W. Wang, H. Zhu, P. Vargas, and A. Bont, “Optical Properties of Eu3+-Doped Y2O3 Nanotubes and Nanosheets Synthesized by Hydrothermal Method,” IEEE Photonics J. 10(1), 1–10 (2018). [CrossRef]  

23. D. B. Bauer, D. Diamond, J. Li, M. McKittrick, D. Sandalow, and P. Telleen, “2011 Critical Materials Strategy Summary,” 2011 Critical Materials Strategy Summary (2011).

24. N. A. Fromer and M. S. Diallo, “Nanotechnology and clean energy: sustainable utilization and supply of critical materials,” J. Nanopart. Res. 15(11), 2011 (2013). [CrossRef]  

25. “Solid-State Lighting Research & Development”, retrieved https://www.energy.gov/eere/ssl/research-development.

26. Q. Zhang and Y. Yin, “All-Inorganic Metal Halide Perovskite Nanocrystals: Opportunities and Challenges,” ACS Cent. Sci. 4(6), 668–679 (2018). [CrossRef]  

27. H. J. Snaith, “Present status and future prospects of perovskite photovoltaics,” Nat. Mater. 17(5), 372–376 (2018). [CrossRef]  

28. D. B. Khadka, Y. Shirai, M. Yanagida, T. Masuda, and K. Miyano, “Enhancement in Efficiency and Optoelectronic Quality of Perovskite Thin Films Annealed in MACl Vapor,” Sustainable Energy Fuels 1(4), 755–766 (2017). [CrossRef]  

29. J. Yan, W. Qiu, G. Wu, P. Heremans, and H. Chen, “Recent progress in 2D/quasi-2D layered metal halide perovskites for solar cells,” J. Mater. Chem. A 6(24), 11063–11077 (2018). [CrossRef]  

30. M.-C. Wu, W.-C. Chen, S.-H. Chan, and W.-F. Su, “The effect of strontium and barium doping on perovskite-structured energy materials for photovoltaic applications,” Appl. Surf. Sci. 429, 9–15 (2018). [CrossRef]  

31. L. Protesescu, S. Yakunin, M. I. Bodnarchuk, F. Krieg, R. Caputo, C. H. Hendon, R. X. Yang, A. Walsh, and M. V. Kovalenko, “Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut,” Nano Lett. 15(6), 3692–3696 (2015). [CrossRef]  

32. Y. Nagaoka, K. Hills-Kimball, R. Tan, R. Li, Z. Wang, and O. Chen, “Nanocube Superlattices of Cesium Lead Bromide Perovskites and Pressure-Induced Phase Transformations at Atomic and Mesoscale Levels,” Adv. Mater. 29(18), 1606666 (2017). [CrossRef]  

33. T. Guner and M. M. Demir, “A Review on Halide Perovskites as Color Conversion Layers in White Light Emitting Diode Applications,” Phys. Status Solidi A 215(13), 1800120 (2018). [CrossRef]  

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35. L. Zhang, L. Wang, K. Wang, and B. Zou, “Pressure-Induced Structural Evolution and Optical Properties of Metal-Halide Perovskite CsPbCl3,” J. Phys. Chem. C 122(27), 15220–15225 (2018). [CrossRef]  

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41. F. Palazon, F. Di Stasio, Q. A. Akkerman, R. Krahne, M. Prato, and L. Manna, “Polymer-Free Films of Inorganic Halide Perovskite Nanocrystals as UV-to-White Color-Conversion Layers in LEDs,” Chem. Mater. 28(9), 2902–2906 (2016). [CrossRef]  

42. H. C. Yoon, H. Kang, S. Lee, J. H. Oh, H. Yang, and Y. R. Do, “Study of Perovskite QD Down-Converted LEDs and Six-Color White LEDs for Future Displays with Excellent Color Performance,” ACS Appl. Mater. Interfaces 8(28), 18189–18200 (2016). [CrossRef]  

43. X. Li, Y. Wu, S. Zhang, B. Cai, Y. Gu, J. Song, and H. Zeng, “CsPbX3 Quantum Dots for Lighting and Displays: Room-Temperature Synthesis, Photoluminescence Superiorities, Underlying Origins and White Light-Emitting Diodes,” Adv. Funct. Mater. 26(15), 2435–2445 (2016). [CrossRef]  

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References

  • View by:

  1. J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
    [Crossref]
  2. P. Zhao and H. P. Zhao, “Analysis of light extraction efficiency enhancement for thin-film-flip-chip InGaN quantum wells light-emitting diodes with GaN micro-domes,” Opt. Express 20(S5), A765–A776 (2012).
    [Crossref]
  3. P. Pust, P. J. Schmidt, and W. Schnick, “A Revolution in Lighting,” Nat. Mater. 14(5), 454–458 (2015).
    [Crossref]
  4. P. Zhu and N. Tansu, “Effect of Packing Density and Packing Geometry on Light Extraction of III-Nitride Light-Emitting Diodes with Microsphere Arrays,” Photonics Res. 3(4), 184–191 (2015).
    [Crossref]
  5. J. Zheng, S. Wu, G. Chen, S. Dang, Y. Zhuang, Z. Guo, Y. Lu, Q. Cheng, and C. Chen, “Blue-emitting Ca5(PO4)3Cl:Eu2+ phosphor for near-UV pumped light emitting diodes: Electronic structures, luminescence properties and LED fabrications,” J. Alloys Compd. 663, 332–339 (2016).
    [Crossref]
  6. L. Zheng, T. Wu, Y. Lu, Y. Gao, Y. Wang, L. Zhu, Z. Guo, and Z. Chen, “Spectral Optimization of Three-Primary LEDs by Considering the Circadian Action Factor,” IEEE Photonics J. 8(6), 1–9 (2016).
    [Crossref]
  7. B. Janjua, H. Sun, C. Zhao, D. H. Anjum, D. Priante, A. A. Alhamoud, F. Wu, X. Li, A. M. Albadri, A. Y. Alyamani, M. M. El-Desouki, T. K. Ng, and B. S. Ooi, “Droop-free AlxGa1-xN/AlyGa1-yN quantum-disks-in-nanowires ultraviolet LED emitting at 337 nm on metal/silicon substrates,” Opt. Express 25(2), 1381–1390 (2017).
    [Crossref]
  8. C. Liu, Y. K. Ooi, S. M. Islam, H. Xing, D. Jena, and J. Zhang, “234 nm and 246 nm AlN-Delta-GaN quantum well deep ultraviolet light-emitting diodes,” Appl. Phys. Lett. 112(1), 011101 (2018).
    [Crossref]
  9. Y. K. Ooi and J. Zhang, “Light Extraction Efficiency Analysis of Flip-Chip Ultraviolet Light-Emitting Diodes With Patterned Sapphire Substrate,” IEEE Photonics J. 10(4), 1–13 (2018).
    [Crossref]
  10. Z. Ren, Y. Lu, H. Yao, H. Sun, C. Liao, J. Dai, C. Chen, J. Ryou, J. Yan, J. Wang, J. Li, and X. Li, “III-Nitride Deep UV LED Without Electron Blocking Layer,” IEEE Photonics J. 11(2), 1–11 (2019).
    [Crossref]
  11. “How much electricity is used for lighting in the United States?” (The U.S. Energy Information Administration (EIA), 2019), retrieved https://www.eia.gov/tools/faqs/faq.php?id=99&t=3 .
  12. “Solid-State Lighting Forecast Report,” (Solid-State Lighting Forecast Report, U.S. Department of Energy, 2016).
  13. Y. J. Kim and M. Brown, “Impact of domestic energy-efficiency policies on foreign innovation: The case of lighting technologies,” Energy Policy 128, 539–552 (2019).
    [Crossref]
  14. M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
    [Crossref]
  15. X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Sci. Appl. 2(1), e50 (2013).
    [Crossref]
  16. K. T. Shimizu, M. Böhmer, D. Estrada, S. Gangwal, S. Grabowski, H. Bechtel, E. Kang, K. J. Vampola, D. Chamberlin, O. B. Shchekin, and J. Bhardwaj, “Toward commercial realization of quantum dot based white light-emitting diodes for general illumination,” Photonics Res. 5(2), A1–A6 (2017).
    [Crossref]
  17. Y. Q. Li, A. C. A. Delsing, G. de With, and H. T. Hintzen, “Luminescence Properties of Eu2+-Activated Alkaline-Earth Silicon-Oxynitride MSi2O2-δN2+2/3δ(M = Ca, Sr, Ba): A Promising Class of Novel LED Conversion Phosphors,” Chem. Mater. 17(12), 3242–3248 (2005).
    [Crossref]
  18. H. Xiao, Y.-J. Lu, T.-M. Shih, L.-H. Zhu, S.-Q. Lin, P. J. Pagni, and Z. Chen, “Improvements on Remote Diffuser-Phosphor-Packaged Light-Emitting Diode Systems,” IEEE Photonics J. 6(2), 1–8 (2014).
    [Crossref]
  19. P. Pust, V. Weiler, C. Hecht, A. Tucks, A. S. Wochnik, A. K. Henss, D. Wiechert, C. Scheu, P. J. Schmidt, and W. Schnick, “Narrow-Band Red-Emitting Sr[LiAl3N4]:Eu2+ as a Next-Generation LED-Phosphor Material,” Nat. Mater. 13(9), 891–896 (2014).
    [Crossref]
  20. V. Kumar, O. M. Ntwaeaborwa, T. Soga, V. Dutta, and H. C. Swart, “Rare Earth Doped Zinc Oxide Nanophosphor Powder: A Future Material for Solid State Lighting and Solar Cells,” ACS Photonics 4(11), 2613–2637 (2017).
    [Crossref]
  21. Z. Zhou, Y. Li, M. Xia, Y. Zhong, N. Zhou, and H. T. Hintzen, “Improved luminescence and energy-transfer properties of Ca14Al10Zn6O35:Ti4+,Mn4+ deep-red-emitting phosphors with high brightness for light-emitting diode (LED) plant-growth lighting,” Dalton Trans. 47(38), 13713–13721 (2018).
    [Crossref]
  22. P. Zhu, W. Wang, H. Zhu, P. Vargas, and A. Bont, “Optical Properties of Eu3+-Doped Y2O3 Nanotubes and Nanosheets Synthesized by Hydrothermal Method,” IEEE Photonics J. 10(1), 1–10 (2018).
    [Crossref]
  23. D. B. Bauer, D. Diamond, J. Li, M. McKittrick, D. Sandalow, and P. Telleen, “2011 Critical Materials Strategy Summary,” 2011 Critical Materials Strategy Summary (2011).
  24. N. A. Fromer and M. S. Diallo, “Nanotechnology and clean energy: sustainable utilization and supply of critical materials,” J. Nanopart. Res. 15(11), 2011 (2013).
    [Crossref]
  25. “Solid-State Lighting Research & Development”, retrieved https://www.energy.gov/eere/ssl/research-development.
  26. Q. Zhang and Y. Yin, “All-Inorganic Metal Halide Perovskite Nanocrystals: Opportunities and Challenges,” ACS Cent. Sci. 4(6), 668–679 (2018).
    [Crossref]
  27. H. J. Snaith, “Present status and future prospects of perovskite photovoltaics,” Nat. Mater. 17(5), 372–376 (2018).
    [Crossref]
  28. D. B. Khadka, Y. Shirai, M. Yanagida, T. Masuda, and K. Miyano, “Enhancement in Efficiency and Optoelectronic Quality of Perovskite Thin Films Annealed in MACl Vapor,” Sustainable Energy Fuels 1(4), 755–766 (2017).
    [Crossref]
  29. J. Yan, W. Qiu, G. Wu, P. Heremans, and H. Chen, “Recent progress in 2D/quasi-2D layered metal halide perovskites for solar cells,” J. Mater. Chem. A 6(24), 11063–11077 (2018).
    [Crossref]
  30. M.-C. Wu, W.-C. Chen, S.-H. Chan, and W.-F. Su, “The effect of strontium and barium doping on perovskite-structured energy materials for photovoltaic applications,” Appl. Surf. Sci. 429, 9–15 (2018).
    [Crossref]
  31. L. Protesescu, S. Yakunin, M. I. Bodnarchuk, F. Krieg, R. Caputo, C. H. Hendon, R. X. Yang, A. Walsh, and M. V. Kovalenko, “Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut,” Nano Lett. 15(6), 3692–3696 (2015).
    [Crossref]
  32. Y. Nagaoka, K. Hills-Kimball, R. Tan, R. Li, Z. Wang, and O. Chen, “Nanocube Superlattices of Cesium Lead Bromide Perovskites and Pressure-Induced Phase Transformations at Atomic and Mesoscale Levels,” Adv. Mater. 29(18), 1606666 (2017).
    [Crossref]
  33. T. Guner and M. M. Demir, “A Review on Halide Perovskites as Color Conversion Layers in White Light Emitting Diode Applications,” Phys. Status Solidi A 215(13), 1800120 (2018).
    [Crossref]
  34. Q. A. Akkerman, G. Rainò, M. V. Kovalenko, and L. Manna, “Genesis, challenges and opportunities for colloidal lead halide perovskite nanocrystals,” Nat. Mater. 17(5), 394–405 (2018).
    [Crossref]
  35. L. Zhang, L. Wang, K. Wang, and B. Zou, “Pressure-Induced Structural Evolution and Optical Properties of Metal-Halide Perovskite CsPbCl3,” J. Phys. Chem. C 122(27), 15220–15225 (2018).
    [Crossref]
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  45. Y.-W. Zhang, G. Wu, H. Dang, K. Ma, and S. Chen, “Multicolored Mixed-Organic-Cation Perovskite Quantum Dots (FAxMA1−xPbX3, X = Br and I) for White Light-Emitting Diodes,” Ind. Eng. Chem. Res. 56(36), 10053–10059 (2017).
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2019 (7)

Z. Ren, Y. Lu, H. Yao, H. Sun, C. Liao, J. Dai, C. Chen, J. Ryou, J. Yan, J. Wang, J. Li, and X. Li, “III-Nitride Deep UV LED Without Electron Blocking Layer,” IEEE Photonics J. 11(2), 1–11 (2019).
[Crossref]

Y. J. Kim and M. Brown, “Impact of domestic energy-efficiency policies on foreign innovation: The case of lighting technologies,” Energy Policy 128, 539–552 (2019).
[Crossref]

G. C. Adhikari, P. A. Vargas, H. Zhu, and P. Zhu, “Saponification Precipitation Method for CsPbBr3 Nanocrystals with Blue-Green Tunable Emission,” J. Phys. Chem. C 123(2), 1406–1412 (2019).
[Crossref]

G. C. Adhikari, S. Thapa, H. Zhu, A. Grigoriev, and P. Zhu, “Synthesis of CsPbBr3 and Transformation into Cs4PbBr6 Crystals for White Light Emission with High CRI and Tunable CCT,” J. Phys. Chem. C 123(18), 12023–12028 (2019).
[Crossref]

Z. Guo, K. Liu, L. Zheng, T.-m. Shih, Y. Lu, T. Wu, Y. Lin, Y. Zhang, J. Zheng, and J. Chen, “Investigation on three-hump phosphor-coated white light-emitting diodes for healthy lighting by genetic algorithm,” IEEE Photonics J. 11(1), 1–10 (2019).
[Crossref]

P. Zhu, H. Zhu, G. C. Adhikari, and S. Thapa, “Spectral optimization of white light from hybrid metal halide perovskites,” OSA Continuum 2(6), 1880–1888 (2019).
[Crossref]

G. C. Adhikari, P. A. Vargas, H. Zhu, A. Grigoriev, and P. Zhu, “Tetradic phosphor white light with variable CCT and superlative CRI through organolead halide perovskite nanocrystals,” Nanoscale Adv. 1, 1791–1798 (2019).
[Crossref]

2018 (19)

G. C. Adhikari, H. Zhu, P. A. Vargas, and P. Zhu, “UV-Green Emission from Organolead Bromide Perovskite Nanocrystals,” J. Phys. Chem. C 122(26), 15041–15046 (2018).
[Crossref]

J. Sun, J. Yang, J. I. Lee, J. H. Cho, and M. S. Kang, “Lead-Free Perovskite Nanocrystals for Light-Emitting Devices,” J. Phys. Chem. Lett. 9(7), 1573–1583 (2018).
[Crossref]

M. D. Smith and H. I. Karunadasa, “White-Light Emission from Layered Halide Perovskites,” Acc. Chem. Res. 51(3), 619–627 (2018).
[Crossref]

S. W. Dai, B. W. Hsu, C. Y. Chen, C. A. Lee, H. Y. Liu, H. F. Wang, Y. C. Huang, T. L. Wu, A. Manikandan, R. M. Ho, C. S. Tsao, C. H. Cheng, Y. L. Chueh, and H. W. Lin, “Perovskite Quantum Dots with Near Unity Solution and Neat-Film Photoluminescent Quantum Yield by Novel Spray Synthesis,” Adv. Mater. 30(7), 1705532 (2018).
[Crossref]

M. He, Y. Cheng, R. Yuan, L. Zhou, J. Jiang, T. Xu, W. Chen, Z. Liu, W. Xiang, and X. Liang, “Mn-Doped cesium lead halide perovskite nanocrystals with dual-color emission for WLED,” Dyes Pigm. 152, 146–154 (2018).
[Crossref]

G. Lozano, “The Role of Metal Halide Perovskites in Next-Generation Lighting Devices,” J. Phys. Chem. Lett. 9(14), 3987–3997 (2018).
[Crossref]

B. J. Bohn, Y. Tong, M. Gramlich, M. L. Lai, M. Döblinger, K. Wang, R. L. Z. Hoye, P. Müller-Buschbaum, S. D. Stranks, A. S. Urban, L. Polavarapu, and J. Feldmann, “Boosting Tunable Blue Luminescence of Halide Perovskite Nanoplatelets through Postsynthetic Surface Trap Repair,” Nano Lett. 18(8), 5231–5238 (2018).
[Crossref]

T. Guner and M. M. Demir, “A Review on Halide Perovskites as Color Conversion Layers in White Light Emitting Diode Applications,” Phys. Status Solidi A 215(13), 1800120 (2018).
[Crossref]

Q. A. Akkerman, G. Rainò, M. V. Kovalenko, and L. Manna, “Genesis, challenges and opportunities for colloidal lead halide perovskite nanocrystals,” Nat. Mater. 17(5), 394–405 (2018).
[Crossref]

L. Zhang, L. Wang, K. Wang, and B. Zou, “Pressure-Induced Structural Evolution and Optical Properties of Metal-Halide Perovskite CsPbCl3,” J. Phys. Chem. C 122(27), 15220–15225 (2018).
[Crossref]

L. Zhang, C. Liu, L. Wang, C. Liu, K. Wang, and B. Zou, “Pressure-Induced Emission Enhancement, Band-Gap Narrowing, and Metallization of Halide Perovskite Cs3Bi2I9,” Angew. Chem., Int. Ed. 57(35), 11213–11217 (2018).
[Crossref]

Z. Zhou, Y. Li, M. Xia, Y. Zhong, N. Zhou, and H. T. Hintzen, “Improved luminescence and energy-transfer properties of Ca14Al10Zn6O35:Ti4+,Mn4+ deep-red-emitting phosphors with high brightness for light-emitting diode (LED) plant-growth lighting,” Dalton Trans. 47(38), 13713–13721 (2018).
[Crossref]

P. Zhu, W. Wang, H. Zhu, P. Vargas, and A. Bont, “Optical Properties of Eu3+-Doped Y2O3 Nanotubes and Nanosheets Synthesized by Hydrothermal Method,” IEEE Photonics J. 10(1), 1–10 (2018).
[Crossref]

Q. Zhang and Y. Yin, “All-Inorganic Metal Halide Perovskite Nanocrystals: Opportunities and Challenges,” ACS Cent. Sci. 4(6), 668–679 (2018).
[Crossref]

H. J. Snaith, “Present status and future prospects of perovskite photovoltaics,” Nat. Mater. 17(5), 372–376 (2018).
[Crossref]

J. Yan, W. Qiu, G. Wu, P. Heremans, and H. Chen, “Recent progress in 2D/quasi-2D layered metal halide perovskites for solar cells,” J. Mater. Chem. A 6(24), 11063–11077 (2018).
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M.-C. Wu, W.-C. Chen, S.-H. Chan, and W.-F. Su, “The effect of strontium and barium doping on perovskite-structured energy materials for photovoltaic applications,” Appl. Surf. Sci. 429, 9–15 (2018).
[Crossref]

C. Liu, Y. K. Ooi, S. M. Islam, H. Xing, D. Jena, and J. Zhang, “234 nm and 246 nm AlN-Delta-GaN quantum well deep ultraviolet light-emitting diodes,” Appl. Phys. Lett. 112(1), 011101 (2018).
[Crossref]

Y. K. Ooi and J. Zhang, “Light Extraction Efficiency Analysis of Flip-Chip Ultraviolet Light-Emitting Diodes With Patterned Sapphire Substrate,” IEEE Photonics J. 10(4), 1–13 (2018).
[Crossref]

2017 (8)

B. Janjua, H. Sun, C. Zhao, D. H. Anjum, D. Priante, A. A. Alhamoud, F. Wu, X. Li, A. M. Albadri, A. Y. Alyamani, M. M. El-Desouki, T. K. Ng, and B. S. Ooi, “Droop-free AlxGa1-xN/AlyGa1-yN quantum-disks-in-nanowires ultraviolet LED emitting at 337 nm on metal/silicon substrates,” Opt. Express 25(2), 1381–1390 (2017).
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K. T. Shimizu, M. Böhmer, D. Estrada, S. Gangwal, S. Grabowski, H. Bechtel, E. Kang, K. J. Vampola, D. Chamberlin, O. B. Shchekin, and J. Bhardwaj, “Toward commercial realization of quantum dot based white light-emitting diodes for general illumination,” Photonics Res. 5(2), A1–A6 (2017).
[Crossref]

V. Kumar, O. M. Ntwaeaborwa, T. Soga, V. Dutta, and H. C. Swart, “Rare Earth Doped Zinc Oxide Nanophosphor Powder: A Future Material for Solid State Lighting and Solar Cells,” ACS Photonics 4(11), 2613–2637 (2017).
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Y. Nagaoka, K. Hills-Kimball, R. Tan, R. Li, Z. Wang, and O. Chen, “Nanocube Superlattices of Cesium Lead Bromide Perovskites and Pressure-Induced Phase Transformations at Atomic and Mesoscale Levels,” Adv. Mater. 29(18), 1606666 (2017).
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D. B. Khadka, Y. Shirai, M. Yanagida, T. Masuda, and K. Miyano, “Enhancement in Efficiency and Optoelectronic Quality of Perovskite Thin Films Annealed in MACl Vapor,” Sustainable Energy Fuels 1(4), 755–766 (2017).
[Crossref]

K. Ma, X.-Y. Du, Y.-W. Zhang, and S. Chen, “In situ fabrication of halide perovskite nanocrystals embedded in polymer composites via microfluidic spinning microreactors,” J. Mater. Chem. C 5(36), 9398–9404 (2017).
[Crossref]

Y.-W. Zhang, G. Wu, H. Dang, K. Ma, and S. Chen, “Multicolored Mixed-Organic-Cation Perovskite Quantum Dots (FAxMA1−xPbX3, X = Br and I) for White Light-Emitting Diodes,” Ind. Eng. Chem. Res. 56(36), 10053–10059 (2017).
[Crossref]

W. Zhang, W. Yang, P. Zhong, S. Mei, G. Zhang, G. Chen, G. He, and R. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3076 (2017).
[Crossref]

2016 (6)

C.-W. Sher, C.-H. Lin, H.-Y. Lin, C.-C. Lin, C.-H. Huang, K.-J. Chen, J.-R. Li, K.-Y. Wang, H.-H. Tu, C.-C. Fu, and H.-C. Kuo, “A high quality liquid-type quantum dot white light-emitting diode,” Nanoscale 8(2), 1117–1122 (2016).
[Crossref]

F. Palazon, F. Di Stasio, Q. A. Akkerman, R. Krahne, M. Prato, and L. Manna, “Polymer-Free Films of Inorganic Halide Perovskite Nanocrystals as UV-to-White Color-Conversion Layers in LEDs,” Chem. Mater. 28(9), 2902–2906 (2016).
[Crossref]

H. C. Yoon, H. Kang, S. Lee, J. H. Oh, H. Yang, and Y. R. Do, “Study of Perovskite QD Down-Converted LEDs and Six-Color White LEDs for Future Displays with Excellent Color Performance,” ACS Appl. Mater. Interfaces 8(28), 18189–18200 (2016).
[Crossref]

X. Li, Y. Wu, S. Zhang, B. Cai, Y. Gu, J. Song, and H. Zeng, “CsPbX3 Quantum Dots for Lighting and Displays: Room-Temperature Synthesis, Photoluminescence Superiorities, Underlying Origins and White Light-Emitting Diodes,” Adv. Funct. Mater. 26(15), 2435–2445 (2016).
[Crossref]

J. Zheng, S. Wu, G. Chen, S. Dang, Y. Zhuang, Z. Guo, Y. Lu, Q. Cheng, and C. Chen, “Blue-emitting Ca5(PO4)3Cl:Eu2+ phosphor for near-UV pumped light emitting diodes: Electronic structures, luminescence properties and LED fabrications,” J. Alloys Compd. 663, 332–339 (2016).
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L. Zheng, T. Wu, Y. Lu, Y. Gao, Y. Wang, L. Zhu, Z. Guo, and Z. Chen, “Spectral Optimization of Three-Primary LEDs by Considering the Circadian Action Factor,” IEEE Photonics J. 8(6), 1–9 (2016).
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2015 (6)

P. Pust, P. J. Schmidt, and W. Schnick, “A Revolution in Lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref]

P. Zhu and N. Tansu, “Effect of Packing Density and Packing Geometry on Light Extraction of III-Nitride Light-Emitting Diodes with Microsphere Arrays,” Photonics Res. 3(4), 184–191 (2015).
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L. Protesescu, S. Yakunin, M. I. Bodnarchuk, F. Krieg, R. Caputo, C. H. Hendon, R. X. Yang, A. Walsh, and M. V. Kovalenko, “Nanocrystals of Cesium Lead Halide Perovskites (CsPbX3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut,” Nano Lett. 15(6), 3692–3696 (2015).
[Crossref]

J. H. Oh, H. Yoo, H. K. Park, and Y. R. Do, “Analysis of circadian properties and healthy levels of blue light from smartphones at night,” Sci. Rep. 5(1), 11325 (2015).
[Crossref]

S. Pathak, N. Sakai, F. Wisnivesky Rocca Rivarola, S. D. Stranks, J. Liu, G. E. Eperon, C. Ducati, K. Wojciechowski, J. T. Griffiths, A. A. Haghighirad, A. Pellaroque, R. H. Friend, and H. J. Snaith, “Perovskite Crystals for Tunable White Light Emission,” Chem. Mater. 27(23), 8066–8075 (2015).
[Crossref]

A. David, P. T. Fini, K. W. Houser, Y. Ohno, M. P. Royer, K. A. G. Smet, M. Wei, and L. Whitehead, “Development of the IES method for evaluating the color rendition of light sources,” Opt. Express 23(12), 15888–15906 (2015).
[Crossref]

2014 (3)

E. R. Dohner, E. T. Hoke, and H. I. Karunadasa, “Self-Assembly of Broadband White-Light Emitters,” J. Am. Chem. Soc. 136(5), 1718–1721 (2014).
[Crossref]

H. Xiao, Y.-J. Lu, T.-M. Shih, L.-H. Zhu, S.-Q. Lin, P. J. Pagni, and Z. Chen, “Improvements on Remote Diffuser-Phosphor-Packaged Light-Emitting Diode Systems,” IEEE Photonics J. 6(2), 1–8 (2014).
[Crossref]

P. Pust, V. Weiler, C. Hecht, A. Tucks, A. S. Wochnik, A. K. Henss, D. Wiechert, C. Scheu, P. J. Schmidt, and W. Schnick, “Narrow-Band Red-Emitting Sr[LiAl3N4]:Eu2+ as a Next-Generation LED-Phosphor Material,” Nat. Mater. 13(9), 891–896 (2014).
[Crossref]

2013 (2)

X. Li, J. D. Budai, F. Liu, J. Y. Howe, J. Zhang, X.-J. Wang, Z. Gu, C. Sun, R. S. Meltzer, and Z. Pan, “New yellow Ba0.93Eu0.07Al2O4 phosphor for warm-white light-emitting diodes through single-emitting-center conversion,” Light: Sci. Appl. 2(1), e50 (2013).
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N. A. Fromer and M. S. Diallo, “Nanotechnology and clean energy: sustainable utilization and supply of critical materials,” J. Nanopart. Res. 15(11), 2011 (2013).
[Crossref]

2012 (1)

2010 (1)

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010).
[Crossref]

2009 (1)

J. J. Wierer, A. David, and M. M. Megens, “III-nitride photonic-crystal light-emitting diodes with high extraction efficiency,” Nat. Photonics 3(3), 163–169 (2009).
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2007 (1)

M. R. Krames, O. B. Shchekin, R. Mueller-Mach, G. O. Mueller, L. Zhou, G. Harbers, and M. G. Craford, “Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting,” J. Disp. Technol. 3(2), 160–175 (2007).
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2005 (1)

Y. Q. Li, A. C. A. Delsing, G. de With, and H. T. Hintzen, “Luminescence Properties of Eu2+-Activated Alkaline-Earth Silicon-Oxynitride MSi2O2-δN2+2/3δ(M = Ca, Sr, Ba): A Promising Class of Novel LED Conversion Phosphors,” Chem. Mater. 17(12), 3242–3248 (2005).
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Adhikari, G. C.

G. C. Adhikari, P. A. Vargas, H. Zhu, and P. Zhu, “Saponification Precipitation Method for CsPbBr3 Nanocrystals with Blue-Green Tunable Emission,” J. Phys. Chem. C 123(2), 1406–1412 (2019).
[Crossref]

G. C. Adhikari, S. Thapa, H. Zhu, A. Grigoriev, and P. Zhu, “Synthesis of CsPbBr3 and Transformation into Cs4PbBr6 Crystals for White Light Emission with High CRI and Tunable CCT,” J. Phys. Chem. C 123(18), 12023–12028 (2019).
[Crossref]

P. Zhu, H. Zhu, G. C. Adhikari, and S. Thapa, “Spectral optimization of white light from hybrid metal halide perovskites,” OSA Continuum 2(6), 1880–1888 (2019).
[Crossref]

G. C. Adhikari, P. A. Vargas, H. Zhu, A. Grigoriev, and P. Zhu, “Tetradic phosphor white light with variable CCT and superlative CRI through organolead halide perovskite nanocrystals,” Nanoscale Adv. 1, 1791–1798 (2019).
[Crossref]

G. C. Adhikari, H. Zhu, P. A. Vargas, and P. Zhu, “UV-Green Emission from Organolead Bromide Perovskite Nanocrystals,” J. Phys. Chem. C 122(26), 15041–15046 (2018).
[Crossref]

Akkerman, Q. A.

Q. A. Akkerman, G. Rainò, M. V. Kovalenko, and L. Manna, “Genesis, challenges and opportunities for colloidal lead halide perovskite nanocrystals,” Nat. Mater. 17(5), 394–405 (2018).
[Crossref]

F. Palazon, F. Di Stasio, Q. A. Akkerman, R. Krahne, M. Prato, and L. Manna, “Polymer-Free Films of Inorganic Halide Perovskite Nanocrystals as UV-to-White Color-Conversion Layers in LEDs,” Chem. Mater. 28(9), 2902–2906 (2016).
[Crossref]

Albadri, A. M.

Alhamoud, A. A.

Alyamani, A. Y.

Anjum, D. H.

Bauer, D. B.

D. B. Bauer, D. Diamond, J. Li, M. McKittrick, D. Sandalow, and P. Telleen, “2011 Critical Materials Strategy Summary,” 2011 Critical Materials Strategy Summary (2011).

Bechtel, H.

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P. Zhu, H. Zhu, G. C. Adhikari, and S. Thapa, “Spectral optimization of white light from hybrid metal halide perovskites,” OSA Continuum 2(6), 1880–1888 (2019).
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L. Zhang, C. Liu, L. Wang, C. Liu, K. Wang, and B. Zou, “Pressure-Induced Emission Enhancement, Band-Gap Narrowing, and Metallization of Halide Perovskite Cs3Bi2I9,” Angew. Chem., Int. Ed. 57(35), 11213–11217 (2018).
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ACS Appl. Mater. Interfaces (1)

H. C. Yoon, H. Kang, S. Lee, J. H. Oh, H. Yang, and Y. R. Do, “Study of Perovskite QD Down-Converted LEDs and Six-Color White LEDs for Future Displays with Excellent Color Performance,” ACS Appl. Mater. Interfaces 8(28), 18189–18200 (2016).
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ACS Cent. Sci. (1)

Q. Zhang and Y. Yin, “All-Inorganic Metal Halide Perovskite Nanocrystals: Opportunities and Challenges,” ACS Cent. Sci. 4(6), 668–679 (2018).
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ACS Photonics (1)

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X. Li, Y. Wu, S. Zhang, B. Cai, Y. Gu, J. Song, and H. Zeng, “CsPbX3 Quantum Dots for Lighting and Displays: Room-Temperature Synthesis, Photoluminescence Superiorities, Underlying Origins and White Light-Emitting Diodes,” Adv. Funct. Mater. 26(15), 2435–2445 (2016).
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Adv. Mater. (2)

S. W. Dai, B. W. Hsu, C. Y. Chen, C. A. Lee, H. Y. Liu, H. F. Wang, Y. C. Huang, T. L. Wu, A. Manikandan, R. M. Ho, C. S. Tsao, C. H. Cheng, Y. L. Chueh, and H. W. Lin, “Perovskite Quantum Dots with Near Unity Solution and Neat-Film Photoluminescent Quantum Yield by Novel Spray Synthesis,” Adv. Mater. 30(7), 1705532 (2018).
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Appl. Phys. Lett. (1)

C. Liu, Y. K. Ooi, S. M. Islam, H. Xing, D. Jena, and J. Zhang, “234 nm and 246 nm AlN-Delta-GaN quantum well deep ultraviolet light-emitting diodes,” Appl. Phys. Lett. 112(1), 011101 (2018).
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Appl. Surf. Sci. (1)

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Z. Zhou, Y. Li, M. Xia, Y. Zhong, N. Zhou, and H. T. Hintzen, “Improved luminescence and energy-transfer properties of Ca14Al10Zn6O35:Ti4+,Mn4+ deep-red-emitting phosphors with high brightness for light-emitting diode (LED) plant-growth lighting,” Dalton Trans. 47(38), 13713–13721 (2018).
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Dyes Pigm. (1)

M. He, Y. Cheng, R. Yuan, L. Zhou, J. Jiang, T. Xu, W. Chen, Z. Liu, W. Xiang, and X. Liang, “Mn-Doped cesium lead halide perovskite nanocrystals with dual-color emission for WLED,” Dyes Pigm. 152, 146–154 (2018).
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Figures (10)

Fig. 1.
Fig. 1. (a) UV-visible absorption spectra, (b) PL spectra, and (c) excitation spectra of blue-, cyan-, green-, yellow-, and red-emitting organolead halide perovskites. (d) Multi-pixel white LED device structure, which consists of a UV LED and a remote color conversion layer.
Fig. 2.
Fig. 2. The color matching functions [$\overline x (\lambda )$,$\overline y (\lambda )$ and $\overline z (\lambda )$], spectral luminous efficiency function [$V(\lambda )$], and spectral circadian efficiency function [$C(\lambda )$] [62,63].
Fig. 3.
Fig. 3. (a) The ratios of five different colors in the white light with various CCT (2827 K - 8315 K), (b) CCT with different relative power ratios of blue, cyan, and green to yellow and red emissions. The color bar indicates the CRI with corresponding CCT.
Fig. 4.
Fig. 4. (a) The spectral power distribution of white light with various CCTs (2827 K - 8315 K). (b) The chromaticity coordinates of white light in the CIE 1931 chromaticity diagram.
Fig. 5.
Fig. 5. The LER as a function of CRI at different CCTs: (a) CCT = 2700-2800 K, (b) CCT = 3000-3100 K, (c) CCT = 4000-4100 K, and (d) CCT = 6500-6600 K.
Fig. 6.
Fig. 6. The LER as a function of CCT at various CRIs: (a) CRI = 81.0-82.0, (b) CRI = 85.0-86.0, (c) CRI = 90.0-91.0, (d) CRI = 95.0-97.8. The color of points represents corresponding CRI on the color bar.
Fig. 7.
Fig. 7. (a) The ratios of spectral distribution of blue, cyan, green, yellow, and red emissions for obtaining white light with various LER, (b) LER as a function of ratios of blue, cyan, and green emissions to yellow and red emissions (the color of points represents CRI as labeled on color bar).
Fig. 8.
Fig. 8. CAF as a function of CRI at various CCTs: (a) CCT = 2700–2800 K, (b) CCT = 3000–3100 K, (c) CCT = 4000–4100 K, and (d) CCT = 6500–6600 K.
Fig. 9.
Fig. 9. The CAF as a function of CCT at different CRIs: (a) CRI = 81.0 - 82.0, (b) CRI = 85.0 - 86.0, (c) CRI = 90.0 - 91.0, (d) CRI = 95.0 - 96.0, (e) CRI = 97.0 - 98.0, and (f) CRI = 98.0 - 99.0. The color of points represents corresponding CRI on the color bar.
Fig. 10.
Fig. 10. (a) CAF changes with power ratios of five different emissions and (b) CAF as a function of ratios of the sum of blue, cyan, and green emissions to the sum of yellow and red emissions. The color of points represents corresponding CRI on the color bar.

Tables (3)

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Table 1. The optical properties of MAPb(BrxI1-x)3 nanocrystals.

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Table 2. Color characteristics of selected LEDs with tunable CCT from warm to cool white.

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Table 3. Color characteristics of selected LEDs.

Equations (21)

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S t o t a l ( λ ) = r B × S B ( λ ) + r C × S C ( λ ) + r G × S G ( λ ) + r Y × S Y ( λ ) + r R × S R ( λ ) ,
r B = 0 : 0.1 : 1 , r C = 0 : 0.1 : 1 , r G = 0 : 0.1 : 1 , r Y = 0 : 0.1 : 1 , r R = 0 : 0.1 : 1.
R a t i o s ( B : C : G : Y : R ) = ( r B × I B ) : ( r C × I C ) : ( r G × I G ) : ( r Y × I Y ) : ( r R × I R ) ,
X = 380 780 S t o t a l ( λ ) x ¯ ( λ ) d λ ,
Y = 380 780 S t o t a l ( λ ) y ¯ ( λ ) d λ ,
Z = 380 780 S t o t a l ( λ ) z ¯ ( λ ) d λ .
x = X X + Y + Z ,
y = Y X + Y + Z .
C C T = 449 n 3 + 352 n 2 682.3 n + 5520.33 ,
Φ V = K m 380 780 S t o t a l ( λ ) V ( λ ) d λ ,
L E R ( l m / W ) = 683 ( l m / W ) 380 780 S t o t a l ( λ ) V ( λ ) d λ 380 780 S t o t a l ( λ ) d λ .
Φ C = K C 380 780 S t o t a l ( λ ) C ( λ ) d λ ,
C E R ( b l m / W ) = 683 ( l m / W ) 380 780 S t o t a l ( λ ) C ( λ ) d λ 380 780 S t o t a l ( λ ) d λ ,
C A F = K C 380 780 S t o t a l ( λ ) C ( λ ) d λ K m 380 780 S t o t a l ( λ ) V ( λ ) d λ
R c o l o r = r c o l o r × I c o l o r r B × I B + r C × I C + r G × I G + r Y × I Y + r R × I R ,
R b l u e + R c y a n + R g r e e n + R y e l l o w + R r e d = 1.
C C T ( R ) = 1800 + 2530 R + 1110 R 2 ,
L E R ( R ) = 333 + 22 R 9 R 2 .
C A F ( C C T ) = ( 2.4 + 2.5 C C T 0.1 C C T 2 ) × 10 4 ,
C A F ( C C T ) = ( 2.8 + 2.7 C C T 0.1 C C T 2 ) × 10 4 ,
C A F ( R ) = 0.08 + 0.87 R 0.15 R 2 .

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