Effect of Quantum Dot-Based Remote Lenses on the Emission Properties of White LED Lighting Studied by Optical Simulation and Experiment

Abstract

The introduction of side-emitting lenses into white light-emitting diodes (LEDs) has enabled thin panel lighting technology based on LED technology, but also presents the disadvantage of low color rendering due to insufficient red components in the spectra of typical white LEDs. Additional application of remote quantum dot (QD) components such as QD films or caps presents the issues of increased numbers of components and higher costs. In this study, we incorporated red QDs directly into a lens placed on white LEDs and analyzed the effects of QD lenses on the optical characteristics of a lighting device through experiments and simulations. By incorporating red CdSe/ZnS QDs into UV-curable resin to fabricate QD lenses and applying them to white LEDs, we significantly improved the color rendering index and were able to adjust the correlated color temperature over a wide range between 2700 and 9900 K. However, as the concentration of QDs in the lens increased, scattering by the QD particles was enhanced, strengthening the Lambertian distribution in the intensity plot. Following the development of optical models for QD lenses under experimental conditions, comprehensive optical simulations of white LED lighting systems revealed that increasing the device height proved more effective than modifying TiO₂ scattering particle concentration in the diffuser plate for mitigating QD-induced bright spots and enhancing illumination uniformity.

1. Introduction

The 2023 Nobel Prize in Chemistry was awarded to three scientists who studied quantum dots (QDs). QDs are semiconducting nanomaterials whose properties depend on their size due to the quantum confinement effect [1,2,3]. QDs have been widely used in various applications, such as general lighting, display technology, biomedical imaging, solar cells, etc. In particular, the use of QDs in white light-emitting diodes (LEDs) has been a promising way to improve the color rendering properties of conventional white LEDs [4,5,6]. In addition, the combination of blue LEDs and red/green QDs has been adopted in backlight units for liquid crystal displays (LCDs), and this has proven effective in improving the color gamut [7,8,9,10,11,12,13].

Conventional LEDs for general lighting consist of blue LED chips and yellow phosphors, such as YAG (Y₃Al₅O₁₂:Ce³⁺) [14,15]. The typical emission spectrum lacks deep red, which is the reason for the relatively low color rendering index (CRI) of white LEDs. QDs can be used to precisely tune the emission spectrum in the long wavelength range without significantly reducing luminous efficacy. In particular, QDs have been integrated into remote-type components, such as QD films and QD caps, to enhance long-term stability [16,17,18,19,20,21,22]. QD-embedded glass or polymer components are the most commonly used designs for remote-type applications [23,24,25,26,27,28,29]. Remote designs have been shown to demonstrate high CRI values of above 90 by us [30,31,32,33,34] and by other groups [35,36,37,38].

Flat light sources are extensively used in LCD backlights and various general lighting applications. These sources can be developed through two primary methods: one involves using a light guide plate, which is a crucial optical component in edge-lit LCD backlights [39]; the other method involves the integration of LEDs and side-emitting lenses, which homogenize light across two dimensions without the need for a light guide [40]. While the latter provides a cost-effective approach to creating two-dimensional light sources, the former offers a superior solution for developing ultra-thin backlights for LCDs.

The combination of white LEDs and side-emitting lenses offers a straightforward approach to achieving homogeneous flat light sources; however, the insufficiency of the red component remains a limitation in general lighting applications. Various remote red QD components, including QD films and QD caps, have been developed to enhance the red spectral component of white LEDs [30,31,32,33,34]. However, incorporating additional remote quantum dot (QD) components also increases both the number of parts in the lighting devices and the overall cost. Red QDs can be directly integrated into side-emitting lenses to achieve flat light sources with enhanced color rendering properties. The purpose of this study was to fabricate QD-embedded lenses and evaluate their feasibility for application in flat light sources through experiments and optical simulations.

2. Experiment and Simulation

An injection molding method was used to fabricate the QD lens. The lens, whose shape is illustrated in Figure 1, was manufactured from polycarbonate. The quantum dots (QDs) used were CdSe/ZnS with a core/shell structure; these were mixed with irregular hollow silica particles (SG-HS40, Sukgyung AT Co., Ansan, Republic of Korea) to achieve homogeneous dispersion and long-term stability [30]. The lens mold was placed on a petri dish into which PDMS (Polydimethylsiloxane) hardener was poured at a ratio of 10:1 between the base material and the curing agent. The hardening process required 24 h under ambient conditions. After removing the lens mold, a mixture of UV curing agent (Miracle UV resin) and QD particles at an appropriate ratio was dispensed into the mold using dispensing equipment (Super Sigman CMIII-V5, Musashi Engineering Inc., Tokyo, Japan). The QD lens was then irradiated at 50 mW/cm² for one minute using a UV curing system (MSUV-L400L, MS Tech Co., Hwaseong, Republic of Korea). A detailed description of the complete fabrication process is provided in Ref. [41].

Figure 1a shows the four QD lenses fabricated for this study. The left lens did not include red QD particles. The second, third, and fourth lenses included QD particles with concentrations of 0.5 wt%, 1.0 wt%, and 1.5 wt%, respectively. The QD concentration was determined through an iterative trial-and-error approach to encompass the widest possible correlated color temperature (CCT) range. The QD lenses had a specific shape, with dimensions of 13.6 mm width and 4.5 mm height, as shown in Figure 1b. The inner parabolic cavity, with a height of 4 mm, a curvature of −2.88 mm⁻¹ and a conic constant of −1, was designed to redirect the light from LED via total internal reflection. The bottom shape of the cavity was a circle with a radius of 1.68 mm. The white LEDs, with an area of 2.86 mm × 2.86 mm, were fabricated by coating a blue LED chip (IWS-L5056-UB-K3, ITSWELL Co., Incheon, Republic of Korea) with YAG phosphors and resin. The angular dependence of the luminous intensity of the LED with four lenses was measured using a goniophotometer (LED626, Everfine Co., Hangzhou, China), and the results were compared with the simulation results. The color coordinates and the color rendering index (CRI) were measured using a digital illuminance meter (CL-500A, Konica Minolta, Tokyo, Japan) and the spectrum was measured using a spectroradiometer (PR670, Photo Research, Chatsworth, CA, USA).

The simulation model incorporated the same dimensions and material properties as the actual lenses (resin, n = 1.5), with QD concentrations matching those used in the fabricated lenses. The emission spectrum of the W-LED in the simulation model was set to match that of the W-LED used in the experiment. Figure S1 in the Supplementary Information displays the emission spectrum of white LEDs used in the experiment; this was subsequently utilized as input for the simulation model.

Figure 2 illustrates the test lighting device, comprising four white LEDs, which was used in the simulation study. The overall dimensions and optical properties are shown in

Table 1. The dimensions and optical properties of each optical component.

Variable	Lighting Frame	Diffuser Plate	Quantum-Dot Lens
Size (mm2)	100 × 100	97 × 97	Freeform
Thickness (mm)	15 (Height)	1.5	4.3
Material	Aluminum	Polycarbonate and $\mathrm{T}\mathrm{i}{\mathrm{O}}_2$ (n = 1.5896 and n = 2.4358)	Resin and red quantum dot (n = 1.4936)
Optical property	Inner bottom and side reflectance: 85% Optical smoothing (Fresnel loss)	Optical smoothing (Fresnel loss)	Optical smoothing (Fresnel loss)

. Four white LEDs were placed at equal distances apart. Total luminous flux was 100 lm. The material property of the lighting box, the dimensions of which were 100 × 100 × 15 mm³, was aluminum. The lighting box functions as an inner reflector; therefore, aluminum is an optimal material choice due to its high reflectivity. For homogenization of the emitted light, a polycarbonate diffuser plate of 0.1 mm thickness and with TiO₂ particles embedded was placed over the lighting box. The side-emitting lens was modeled using the shape parameters illustrated in Figure 1b. Several parameters of the lighting device were adjusted in the simulation model: the QD concentration in the lens, the height of the lighting box, and the concentration of the TiO₂ scattering particles. The TiO₂ particles, with an average diameter of 225 nm, were incorporated into the diffuser plate at several concentrations between 1.0 and 5.0 wt%, and were treated as Mie particles. The size distribution of the Mie particles is shown in the Supplementary Materials (Figure S2). The basic structure is represented by a lighting box with a height of 15 mm and a scattering particle concentration of 1 wt% in the diffuser plate. The commercial simulation tool LightTools (ver. 2024.09, Synopsys Co.) was used for the optical simulation. A detector with a 21 × 21 mesh grid was positioned 2.5 mm above the diffuser plate. Each mesh had an area of 4.619 mm × 4.619 mm. The CCT, two color rendering indices (Ra and Re), and illuminance were obtained from the simulation for comparison. Here, Ra and Re represent the average values of R1–R8 and R1–R15, respectively, where Ri (i = 1–15) denotes the individual color rendering index (CRI). The simulation was conducted under the condition of five million rays, but ten million rays was used for certain conditions to reduce the error rate below 5%. Figure S3 in the Supplementary Information illustrates one example of the ray tracing results within the lens. The figure demonstrates how both the inner cavity and outer surface effectively redirect emitted rays toward horizontal directions, enhancing the homogenization of light generated from small LED chips.

3. Results and Discussion

Figure 3a–d present intensity polar plots, illustrating the angular dependence of luminous intensity for four QD concentrations—0, 0.5, 1.0 and 1.5 wt, respectively, from left to right—obtained from simulation. Figure 3a illustrates the intensity of the original white LED with a transparent lens that does not contain any quantum dots (QDs). The twelve curves in the figure represent the luminous intensity distribution measured at 5-degree intervals of polar angle from −90° to 90°, across azimuthal angles from 0° to 180° divided into 15-degree increments. The intensity distribution exhibits rotational symmetry with respect to the normal direction. This symmetry likely results from the rotational symmetry inherent in both the inner cavity and the outer surface structures. The luminous intensity reaches its peak at high angles, ranging from 75° to 85°, as indicated by two red arrows in Figure 3a. This phenomenon is primarily attributed to the side-emitting lens, where light rays undergo double refraction toward high angles of approximately 80°. This side-emitting distribution is advantageous for achieving two-dimensional homogeneous light. Such side-emitting lenses are widely employed in LCD backlights and flat light sources. As shown in Figure 3b–d, the red QDs embedded in the lens enhance light scattering. Consequently, the luminous intensity exhibits forward emission, which becomes increasingly pronounced with higher QD concentrations.

The left of Figure 4 compares the emission spectra of white LEDs with QD concentrations in the lens ranging from 0 to 1.5 wt%, as recorded on the diffuser plate. The spectrum of the original white LED with a bare lens, free of QD particles, displays a sharp blue peak and a broad yellow peak. With increasing QD concentration in the lens, the intensities of the blue and green components decrease, whereas the red component near 620 nm exhibits a substantial enhancement. These changes were expected to have a significant impact on both the color temperature and the color rendering performance. The color coordinates (x, y) and (u’, v’) are shown on the CIE1931 and CIE1976 chromaticity diagrams, respectively.

Table 2. The dependence of CCT, CRI, and color coordinates (x, y) on the QD concentration in the lens, obtained from experiment.

QD Concentration (wt%)	CCT (K)	CRI (Ra)	CRI (Re)	CRI (R9)	CIE x	CIE y
0	9876	78	68	−12	0.280	0.292
0.5	5471	79	71	0	0.333	0.347
1.0	3634	82	75	17	0.399	0.390
1.5	2769	84	79	25	0.451	0.403

shows the dependence of CCT, CRI, and color coordinates (x, y) on the QD concentration in the lens. Figure 5 shows the same data on the rectangular graph and the CIE1931 chromaticity diagram. Figure 5 illustrates the dependence of the CCT on the QD concentration, in addition to the change in the color coordinates on the chromaticity diagram (CIE1931). For the side-emitting lens without any QD particles, the CCT is 9876 K, which is relatively high for general lighting applications, indicating insufficient color conversion by the yellow phosphor. The CCT significantly decreases to 2769 K at a QD concentration of 1.5 wt%, which correlates with a substantial shift in the color coordinates. This is consistent with the color changes observed in the four white LEDs with varying QD concentrations shown in Figure 4, where the emitted light shifts from bluish cool white to yellowish warm light as the QD concentration increases. The most appealing aspect of using the QD lens is its enhancement of color rendering performance. The CRI value of Ra increases from 78 to 84 at a QD concentration of 1.5 wt% due to the enhanced red component in the spectrum. Notably, the R9 value, corresponding to the deep red color, increased from −12 to 25 as the QD concentration increased.

Figure 3e–h present intensity polar plots, illustrating the angular dependence of luminous intensity for four QD concentrations—0, 0.5, 1.0 and 1.5 wt%, respectively, from left to right—obtained from optical simulation. Despite slight differences, the overall intensity distributions in the experiment and simulation are similar. As the QD concentration in the lens increases, the Lambertian component in the overall intensity distribution becomes more pronounced. This result confirms that the simulation model adopted in this study is reliable and suitable for further in-depth analysis.

Figure 6a presents the LED emission spectrum of the lighting device obtained from the simulation. As the QD concentration increases, the sharp peak near 630 nm grows significantly, while the blue and green peaks decrease. The spectra of QD-integrated white LEDs differ from the measured spectra shown in Figure 4 at the same QD concentration. The QD parameters employed in the simulation only partially reproduce the experimental spectra. This discrepancy may be attributed to the omission of certain experimental conditions in the simulation model, such as the irregular morphology of hollow silica and potential absorption by the host matrix. Figure 6b illustrates the dependence of CCT and CRI (Ra) on QD concentration. In the low concentration range, the overall trends of CCT and Ra resemble those observed in the experiment. As the QD concentration increases, the CCT decreases while Ra improves. The CCT decreases from 5662 K to 2016 K, indicating the high color conversion efficiency of the red QDs and, consequently, a significant red proportion in the emission spectrum. However, Ra reaches a maximum of ~92 at a QD concentration of 0.5 wt% and then decreases to ~74 as the QD concentration increases further. Figure 6a shows that the red peak becomes unusually high at the high QD concentrations of 1.0 and 1.5 wt% used in the simulation, disrupting the spectral balance in the visible range. This spectral imbalance causes the decrease in Ra at the highest QD concentration. The R9 value was significantly low (−63) in the absence of QD particles in the lens. However, with the incorporation of QD particles at concentrations ranging from 0.5 to 1.5 wt%, the R9 value improved considerably, reaching a range of 50 to 89. This indicates that an appropriate amount of red QDs should be incorporated into the remote QD component to maintain a balanced visible spectrum, thereby achieving high color rendering performance.

The results demonstrate that incorporating QD lenses can significantly enhance the color rendering properties of general lighting. Notably, compared with QD films, the QD lens design requires a considerably smaller quantity of QD particles within the lighting device, as they can be compactly positioned closer to the LED chips within a much smaller space, i.e., the lens. However, the incorporation of QD particles into the lens can lead to excessive light scattering, resulting in a pronounced forward scattering component and shifting the light intensity profile closer to a Lambertian distribution. This was confirmed by the luminous intensity profile shown in Figure 3. The increased forward scattering induced by the QD particles may result in bright spots on the target surface, thereby degrading light uniformity.

Figure 7a–d present luminance and illuminance profiles for four QD concentrations—0, 0.5, 1.0 and 1.5 wt%—in the lens, with luminance values measured along the optical axis. The bright spots become increasingly prominent as the QD concentration in the lens increases. Uniformity was calculated as the ratio of the minimum value to the maximum value. The luminance and illuminance uniformities exhibited a significant decreasing trend with increasing QD concentration as shown in Figure 7e. This phenomenon can be primarily attributed to the strong forward scattering caused by the isotropic emission profile of QDs, which resulted in insufficient light homogenization within the lighting box.

One approach to mitigate this disadvantage of using QD lenses on white LEDs is to ensure sufficient light mixing to prevent the formation of bright spots. Two commonly employed methods for light homogenization are increasing the height of the light box and enhancing the concentration of scattering particles in the diffuser plate. First, the height of the lighting box was varied to 15, 25, and 35 mm. Figure 8a shows the illuminance distributions of nine configurations formed by four QD concentrations and three heights of the lighting device. Table S1 in the Supplementary Information presents the CRI values (Ra, Re, and R9) and the maximum, minimum, and average illuminance values, as well as the CCT, for the four QD concentrations in the lens and the three frame heights (15, 25, and 35 mm) of the lighting device. Figure 8b shows the dependence of the uniformity on the height and the QD concentration. The illuminance uniformity improves as the height increases. When the height is 15 mm, the illuminance uniformity exhibits significant variation, with the highest value observed for the bare lens without any QD particles. At a height of 35 mm, the uniformity becomes comparable across different QD concentrations, consistently showing values between 60% and 65%. Figure 8 clearly demonstrates that at a height of 35 mm the light emitted from each lens is substantially dispersed, leading to more homogeneous illumination regardless of the QD concentration in the lens. As the height of the lighting box increases, the forward-emitted light from the QD lens spreads more effectively, enhancing light uniformity. The CRI values remain nearly identical regardless of device height, indicating that the color conversion efficiency of the QDs within the lens was nearly the same.

Second, the concentration of the scattering particles in the diffuser plate was varied between 0.1 wt% and 5 wt%. Table S2 in the Supplementary Information presents the CRI (Ra, Re, and R9), as well as the maximum, minimum, and average illuminance values, along with the CCT, for the two QD concentrations in the lens and the five TiO₂ concentrations in the diffuser plate. Figure S4a,b in the Supplementary Information show the dependence of the illuminance uniformity and CCT, respectively, on the TiO₂ concentration. It is evident that the TiO₂ concentration has a minimal effect on the uniformity and CCT. The increase in TiO₂ concentration significantly reduced the illuminance due to decreased transmittance; however, the uniformity showed no notable improvement. This outcome may be attributed to the relatively small height (15 mm) of the lighting box and the thin diffuser plate (thickness 0.1 mm). Although the light experiences stronger scattering within the diffuser plate at higher TiO₂ concentration, its relatively thin structure inhibits adequate light homogenization and leads to low transmittance, resulting in only a marginal improvement in uniformity. The marginal effect of TiO₂ concentration on the CCT suggests that the color conversion efficiency of QD particles in the lens remains nearly constant.

Our study demonstrates that high color rendering performance can be achieved through a simple and cost-effective approach utilizing QD-integrated remote lenses. Notably, the correlated color temperature could be flexibly tuned over a wide range—from bluish cool white to yellowish warm light. However, certain challenges remain, including long-term stability and more precise control over the emission wavelength and spectral width, both of which are crucial for fine-tuning the target color to maximize CRI while minimizing efficiency loss [42,43]. A more thorough investigation of the various configurations of LED chips, color conversion components, and their spatial arrangements may offer deeper insights into optimizing the optical structures of general lighting devices, as well as QD-based displays, including electroluminescent devices [44,45].

4. Conclusions

The incorporation of side-emitting lenses has been pivotal in the development of thin panel lighting systems using white LEDs. However, these systems typically suffer from poor color rendering performance due to the inherent lack of red spectral components in conventional white LEDs. While existing solutions such as remote quantum dot films or caps can address this limitation, they inevitably increase component complexity and manufacturing costs. Through our experimental work and simulation studies, we have thoroughly investigated how the integration of red quantum dots directly into the lens structure affects the optical properties of LED lighting systems. Our findings provide valuable insights into improving color quality while maintaining cost-effectiveness in LED lighting applications. Our incorporation of red CdSe/ZnS quantum dots into UV-curable resin to create quantum dot lenses for white LEDs resulted in a remarkable enhancement of the color rendering index. Additionally, this approach enabled us to effectively tune the correlated color temperature across a substantial range from 2700 to 9900 K, demonstrating the versatility and effectiveness of our method for advanced LED lighting applications. Our findings revealed that increasing the concentration of quantum dots within the lens structure enhanced scattering effects, resulting in a more pronounced Lambertian distribution in the intensity profile. To investigate practical applications, we developed computational models of these quantum dot lenses under consistent parameters and conducted comprehensive optical simulations of white LED lighting systems incorporating these designs. The simulation results demonstrated that to effectively mitigate bright spots generated by quantum dots and enhance overall lighting uniformity, increasing the height of the lighting fixture proved to be substantially more effective than modifying the concentration of scattering particles within the diffuser plate. This insight provides valuable design guidance for optimizing quantum dot-enhanced LED lighting systems.