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ABSTRACT Quantum dots (QDs)-based white light-emitting diodes (QDs-WLEDs) have been attracting numerous attentions in lighting and flat panel display applications, by virtue of their high

luminous efficacy and excellent color rendering ability. However, QDs’ key optical parameters including scattering, absorption and anisotropy coefficients for optical modeling are still

unclear, which are severely against the design and optimization of QDs-WLEDs. In this work, we proposed a new precise optical modeling approach towards QDs. Optical properties of QDs-polymer

film were obtained for the first time, by combining double integrating sphere (DIS) system measurement with inverse adding doubling (IAD) algorithm calculation. The measured results show

that the typical scattering, absorption and anisotropy coefficients of red emissive QDs are 2.9382 mm−1, 3.7000 mm−1 and 0.4918 for blue light, respectively, and 1.2490 mm−1, 0.6062 mm−1 and

0.5038 for red light, respectively. A Monte-Carlo ray-tracing model was set-up for validation. With a maximum deviation of 1.16%, the simulated values quantitatively agree with the

experimental results. Therefore, our approach provides an effective way for optical properties measurement and precise optical modeling of QDs for QDs-WLEDs. SIMILAR CONTENT BEING VIEWED BY

OTHERS ADVANCES IN UNDERSTANDING QUANTUM DOT LIGHT-EMITTING DIODES Article 07 June 2024 ULTRABRIGHT AND STABLE TOP-EMITTING QUANTUM-DOT LIGHT-EMITTING DIODES WITH NEGLIGIBLE ANGULAR COLOR

SHIFT Article Open access 17 June 2024 ON THE ACCURATE CHARACTERIZATION OF QUANTUM-DOT LIGHT-EMITTING DIODES FOR DISPLAY APPLICATIONS Article Open access 03 June 2022 INTRODUCTION Colloidal

quantum dots (QDs), as emerging nanocrystals light conversion materials, have been attracted more and more attentions in displays and lighting1,2,3. Unlike the bulk semiconductor material

that has a fixed energy gap, the size range of QDs corresponds to the regime of quantum confinement for which electronic excitations feel the presence of the particle boundaries and respond

to changes in the particle size by adjusting their energy spectra. This phenomenon is known as the quantum size effect. Quantum confinement leads to a collapse of the continuous energy bands

of the bulk material into discrete ‘atomic’ energy levels. These well-separated QDs states can be labeled using atomic-like notations (1S, 1P, 1D, etc). Due to the strong quantum

confinement in three dimensions, QDs’ emission spectra can be easily tuned from ultraviolet to infrared by changing their particle size and chemical composition, and their full width at half

maximum (FWHM) is much narrower than that of conventional phosphor, leading to precise spectral control4,5,6,7. QDs can be excited by both photoluminescence and electroluminescence8,9,10.

With these extraordinary characteristics, QDs-based white light-emitting diodes (QDs-WLEDs) possess high luminous efficacy as well as high color rendering ability11,12,13, making them

promising candidates for next-generation solid-state lighting (SSL). In one QDs-WLED, blue light is firstly emitted from GaN LED chip by means of electroluminescence (EL), and then irradiate

on light conversion materials (e.g. phosphor, QDs). The mixture of transmitted blue light and long-wavelength light converted by QDs produces white light. Figure 1 shows the schematic of

all the possible behaviors between the incident blue photons and the QDs. The blue photons may either be scattered by QDs (light path (3)), resulting in a change of their movement direction,

or be absorbed by QDs (light path (2)), and their energy is converted into QDs emission light or transformed into heat energy. Besides, some of the blue photons may even pass the QDs layer

without been affected at all (light path (1)). Moreover, photons emitted from QDs also will have the chance to be scattered by other QDs during transmission (Inset). Therefore, photons’

behaviors, including absorbing, remitting, scattering and transmitting, are very complicated in QDs-WLED, and it is necessary and critical to build up an optical model of QDs-WLED for

further device optimization. Generally, three key optical parameters, absorption coefficient, scattering coefficient and anisotropy coefficient, are utilized to characterize the behaviors of

light absorption, conversion, scattering, and propagation in the QDs layer. Previous studies have presented some optical models of QDs to simulate their optical performances in various

optoelectronic devices14,15,16,17. In an approach, QDs are treated as dipoles and transfer matrix formalism11 is utilized to calculate the light out coupling and angular performance of

QDs-based device14,15. While there are difficulties in directly measuring the QDs’ microcosmic parameters such as power dissipation density, wave vector and intrinsic quantum yield _et al_.,

making this method impractical to simulate real QDs-polymer film. In another approach, Monte-Carlo ray-trace method is performed to theoretically evaluate the performance of QDs-based

materials16,17. Unlike the first method, this approach is conducted by inputting the absorption, PL spectra of QDs, the attenuation coefficient and QY of QDs, which are easier to be measured

and are practical to QDs devices. In previous literatures, before processing the Monte-Carlo ray-trace simulation, some assumptions have to be made to conduct the calculation, including

assuming that light scattering won’t occur in the QDs-polymer film due to the small size of QDs16,18,19. However, as far as we are concerned, this assumption is not always reasonable because

the scattering coefficient of QDs-polymer film is non-negligible, especially when scattering particles are doped in20,21,22,23. Therefore, a more precise optical model of QDs, including

coefficients of absorption, scattering and anisotropy, need to be developed for QDs-WLED design and optimization. Here, we reported on a precise optical model of QDs by combining double

integrating spheres (DIS) system with inverse adding-doubling (IAD) algorithm. The proposed model takes into account all the fate of incident photons, including transmittance, absorption and

scattering, which is compatible with the real situation. A series of QDs-polymer films samples with varying QDs concentrations were fabricated, and their transmittance, reflectance and

collimating transmittance were measured by the DIS system. Then their optical properties of scattering coefficient, absorption coefficient and anisotropy coefficient were calculated by the

IAD algorithm. Finally, these parameters were adopted in Monte-Carlo ray-tracing model to conduct the simulation, and the ray-tracing results were compared with the experimental results to

validate the feasibility of our model. EXPERIMENTAL SETUP DEFINITIONS As depicted in Fig. 1, the optical properties of QDs layer can be characterized by quantities as follows:

$${u}_{s}=1/{I}_{s},$$ (1) $${u}_{a}=1/{I}_{a}.$$ (2) where the scattering coefficient _µ_ s and the absorption coefficient _µ_ a are defined as the reciprocal of the average free path

between two scattering events (_I_ s) or two absorption events (_I_ a), respectively. If the QDs layer is highly absorbing, the number of absorption events will be big, leading to a small

average free path _I_ a, which yields a high absorption coefficient _µ_ a. Therefore, the higher the scattering or the absorption of a QDs layer is, the higher the respective coefficient

would become. In addition to the above two optical quantities, there is another parameter, single-scattering phase function _p_(_θ_), which characterizes the amount of light scattered at an

angle _θ_ from the incoming direction. It is often expressed in terms of the cosine of the scattering angle _θ_: $${\int }_{4\pi }p(v)d\omega =2\pi {\int }_{-1}^{1}p(v)dv=1,\,v=\,\cos

\,\theta .$$ (3) where _d_ω is a differential solid angle, and _v_ is the cosine of the scattering angle. The functional form of _p_(_v_) is usually unknown. While Jacques _et al_.24 and

Yoon _et al_.25 have demonstrated that Henyey-Greenstein function approximates single-particle light scattering in human dermis and aorta at 633 nm. Therefore, this phase function is adopted

in our calculation: $$p(v)=\frac{1}{4\pi }\cdot \frac{1-{g}^{2}}{{(1+{g}^{2}-2gv)}^{3/2}}.$$ (4) The Henyey-Greenstein phase function depends on the anisotropy coefficient _g_, which is

defined as: $$g={\int }_{4\pi }p(v)vd\omega =2\pi {\int }_{-1}^{1}p(v)vdv.$$ (5) The anisotropy coefficient _g_ ranges from −1 to 1. When _g_ = −1, scattering is all directed into reverse

direction, when _g_ = 1, scattering is all directed into forwarding direction, and when _g_ = 0, scattering is equally probable in all directions. Using the physical sample thickness _d_,

the coefficients _µ_ s and µa can be expressed by two dimensionless quantities, the albedo _a_ and the optical thickness _τ_ 26: $$a=\frac{{\mu }_{s}}{{\mu }_{s}+{\mu }_{a}}=\frac{{\mu

}_{s}d}{\tau },$$ (6) $$\tau =d\cdot ({\mu }_{s}+{\mu }_{a}).$$ (7) The albedo varies between 0 and 1, _a_ = 0 indicates that no scattering occurs in the sample, while _a_ = 1 indicates the

absence of absorption. The optical thickness is defined as the product of the physical sample thickness and the sum of the scattering and the absorption coefficient. For a sample with the

optical thickness _τ_ = 1, there is a probability of _e_ −1 = 37% that light will travel through it without being scattered or absorbed. In the following contents, the optical properties

will be calculated in terms of three dimensionless quantities _a_, _τ_, and _g_. MEASUREMENT SETUP The measurement of the optical properties of QDs samples can be achieved by the use of a

double integrating sphere set-up, which is schematically depicted in Fig. 2. The QDs sample is placed between two integrating spheres so that it is situated at the exit port of the

reflectance sphere (used to measure the reflectance _P_ r), and on the entrance port of the transmittance sphere (used to measure the transmittance _P_ t). These two ports have identical

sizes. Besides, the third integrating sphere (collimating transmittance sphere) is situated directly behind the transmittance sphere and is used to measure the light power _P_ ct that is

specularly transmitted through the sample. The entering light is incident perpendicularly upon the sample. To measure the reflectance and the transmittance of a sample, the photomultiplier

is usually used as detectors27. Theoretically, the voltage _V_ δ recorded by a detector is proportional to the light power _P_ δ incident upon it: $${V}_{\delta }=K{P}_{\delta }.$$ (8) where

_K_ is the constant proportionality, which depends on the detector characteristics. Due to the background signal _V_ 0, which occurs in all measurements and originates from noise in the

system and the presence of stray light, expression (9) has to be expanded as follows: $${V}_{\delta }=K{P}_{\delta }+{V}_{0}.$$ (9) Therefore, the detected power can be expressed as:

$${P}_{\delta }=\frac{1}{K}({V}_{\delta }-{V}_{0}).$$ (10) The constant _K_ can be eliminated by using reference measurements which conducted with a single integrating sphere set-up. For a

reference plate in the sample position, _P_ ref can be determined by: $${P}_{ref}=\frac{1}{K}({V}_{ref}-{V}_{ref,0}).$$ (11) Therefore, by conducting the reference measurements, the relative

values _V_ r%, _V_ t% and _V_ ct% can be calculated as: $${V}_{r} \% =\frac{{V}_{r}-{V}_{r,0}}{{V}_{ref}-{V}_{ref,0}};{V}_{t} \% =\frac{{V}_{t}-{V}_{t,0}}{{V}_{ref}-{V}_{ref,0}};{V}_{ct} \%

=\frac{{V}_{ct}-{V}_{ct,0}}{{V}_{ref}-{V}_{ref,0}}.$$ (12) where the values _V_ r,0, _V_ t,0 and _V_ ct,0 represent the background signals corresponding to the respective measurements _V_

r, _V_ t and _V_ ct. CALCULATION THEORY As mentioned above, the final aim is to obtain the optical properties given by _a_, _τ_, and _g_, respectively. While the DIS measurements do not

yield _a_, _τ_, and _g_ directly, several measurement values that depend on the reflectance and the transmittance of the sample. Therefore, we have to find a connection between the optical

properties and the measurement results. This can be done by the use of an appropriate model of radiative transfer. One of these models is used in the Adding Doubling (AD) Method27, which was

introduced by van de Hulst as one-dimensional numerical solution of the radiative transport equation. For given optical properties (albedo _a_, optical thickness _τ_, and anisotropy

coefficient _g_), the reflection factors (_R_ d, _R_ cd, _R_ c) and the transmission factors (_T_ d, _T_ cd, _T_ c) can be calculated by using this algorithm: $${f}_{AD}:(a,\tau ,g)\to

({R}_{d},{R}_{cd},{R}_{c},{T}_{d},{T}_{cd},{T}_{c}).$$ (13) where the reflection factor _R_ and the transmission factor _T_ are defined relative to the irradiance on the sample surface. They

vary between 0 and 1 and denote the fraction of the total incident light that is reflected or transmitted by the sample, respectively. For diffuse light incident upon the sample, the

diffuse reflection (transmission) factor _R_ d (_T_ d) denotes the fraction of light that is reflected (transmitted) diffusely by the sample. For collimated light incident upon the sample,

the diffuse reflection (transmission) factor _R_ cd (_T_ cd) denotes the fraction of light that is reflected (transmitted) diffusely by the sample. The collimated reflection (transmission)

factor _R_ c (_T_ c) denotes the fraction of light that is reflected (transmitted) specularly. The AD method assumes that the reflection function _R_(_ν_, _ν_’) and transmission function

_T_(_ν_, _ν_’) for light incident at an angle _ν_ and exiting at an angle _ν_’ are known for one layer. For two similar and adjacent slabs, the light traveling from left to right across the

boundaries 0, 1 and 2. The reflection and transmission of the two slabs can be derived from the results of the thin slab by using the AD equations28,29: $${R}^{02}={R}^{20}=T{(E-R\ast

R)}^{-1}R\ast T+R,$$ (14) $${T}^{02}={T}^{20}=T{(E-R\ast R)}^{-1}T.$$ (15) where _R_ 01 and _T_ 01 are defined as the reflection and transmission operators for light incident upon boundary 0

and moving towards boundary 1, respectively, and vice-versa. _E_ is the unity matrix. Beginning with the starting thickness _τ_ start, _R_ start and _T_ start, this doubling process

repeatedly doubles the slab thickness by using the expressions (14) and (15), until the desired slab thickness _τ_ has been reached. _τ_ start has to be far smaller than the thickness of QDs

sample d (_τ_ start = 2−_n_d, _n_ = 100~1000). After decided the _τ_ start, the _R_ start and _T_ start can be determined by the initialization routine29. The resulting _R_ and _T_ are

taken as the reflection matrix and the transmission matrix of the sample. The correlation between the measurement data and the reflection/transmission factor can be calculated by the ‘double

integrating sphere function’: $${f}_{DIS}:({R}_{d},{R}_{cd},{R}_{c},{T}_{d},{T}_{cd},{T}_{c})\to ({V}_{r} \% ,{V}_{t} \% ,{V}_{ct} \% ).$$ (16) With the expressions (13) and (16), we can

deduce that, the measurement results _V_ r%, _V_ t% and _V_ ct% can be predicted, if the optical properties _a_, _τ_ and _g_ of the sample are given, by a combination of the functions _f_ AD

and _f_ DIS: $${f}_{DIS}\cdot {f}_{AD}:(a,\tau ,g)\to ({V}_{r} \% ,{V}_{t} \% ,{V}_{ct} \% ).$$ (17) In our case, we want to perform the calculation in the other direction. An iterative

solution of the problem is given by the Inverse Adding Doubling (IAD) method, the function can be expressed as: $${f}_{IAD}={({f}_{DIS}\cdot {f}_{AD})}^{-1}:({V}_{r} \% ,{V}_{t} \% ,{V}_{ct}

\% )\to (a,\tau ,g).$$ (18) Figure 3 shows the correlations between the three levels of quantities. Consequently, the procedure to obtain the optical properties of a sample by the use of

DIS set-up and IAD algorithm is as follows: * (1) Conduct the reference measurements to calibrate the measurement set-up. * (2) Determine the three measurement values _V_ r%, _V_ t% and _V_

ct% for the sample. * (3) Calculate the optical properties _a_, _τ_ and _g_ with the IAD algorithm, by using the measurement data as the input of the program. * (4) Calculate _µ_ a and _µ_ s

from the returned values _a_ and _τ_. RESULTS AND DISCUSSION To verify the accuracy and effectiveness of our IAD algorithm, we performed an AD calculation for an ‘imaginary’ sample with the

optical properties _a_ = 0.8, _τ_ = 1, _g_ = 0.8 and a refractive index _n_ s = 1.5. The sample was situated between two ‘imaginary’ glasses with reflection factor _R_ g1 = _R_ g2 = 0.04

and transmission factor _T_ g1 = _T_ g2 = 0.96 (_n_ g = _n_ s = 1.5). By using the AD function described in expression (13), we can get the ‘measurement values’ $${V}_{r} \%

=0.0454;\,\,\,\,\,\,{V}_{t} \% =0.3039;\,\,\,\,\,\,{V}_{ct} \% =0.33911.$$ (19) In another direction, if we use above three values in equation (19) as the inputs for the IAD algorithm, we

should obtain the optical properties _a_ = 0.8, _τ_ = 1, _g_ = 0.8 as a result. As all three measurement values are known, all optical properties can be determined. Figure 4 shows the

development of _a_ and _g_ during the iteration. In our IAD program, the routine terminates after 145 iteration steps, returning the values of _a_ = 0.7999 and _g_ = 0.8001. Therefore, our

IAD algorithm has high accuracy and fast convergence speed. Without loss of generality, CdSe/ZnS core/shell QDs were used as the QDs-polymer film samples to validate our model. High-quality

red-emissive QDs with an optimized peak wavelength of 626 nm were prepared by the Tri-n-Octylphosphine (TOP)-assisted successive ionic layer adsorption and reaction (SILAR) method11,30.

According to our previous work31, adding QDs with a peak wavelength of 626 nm into phosphor-converted LEDs can greatly improve the color rendering index. Polymethyl methacrylate (PMMA) was

chosen as the polymer matrix of QDs film samples. The QDs-PMMA film was prepared with the _in-situ_ polymerization method32. Firstly 25 mL of MMA monomer and 0.2% wt/wt of

azodiisobutyronitrile (AIBN) with respect to MMA were mixed in a three-neck flask and kept stirring until the AIBN was dissolved completely. Then 3 mL of MMA-AIBN solution was transfer to a

cleaned centrifuge tube and 10 µL of QDs solution was added into the tube, and the mixture was homogeneously dispersed by the ultrasound treatment. After that, the tube was placed into the

thermostatic water bath at 70 °C for 15 min until the mixture reached certain viscosity, and then cooled to temperature. Then, the viscous liquid was introduced into the tailored mould. The

mould was placed in the vacuum oven at 45 °C and kept for 24 h. Finally, the resulting film was cut into circle and labeled as sample No. 1. Similarly, Nos 2–6 samples were prepared by

adding 20, 30, 40, 50 and 60 µL of QDs solution into 3 mL of MMA-AIBN solution. Figure 5(a) shows the high-resolution transmission electron microscope (HRTEM) images of the as-prepared QDs,

from which the average diameter of QDs is measured as 6.8 nm with uniform size distribution. Figure 5(b) depicts the absorption and PL spectra of the CdSe core and CdSe/ZnS core-shell QDs.

The narrow width at half maximum (FWHM) of near 31 nm from PL spectra has confirmed their uniform size distribution. Due to the TOP-assisted SILAR method, which removes the surface lattice

imperfections by the surface ions re-dissolution and lattice re-arrangement during the whole ZnS shell formation process, the absolute PL quantum yields (PLQY) was enhanced from 45% to 69%.

Figure 5(c) and (d) show the photographs of the QDs-PMMA film under daylight and UV light, respectively. The as-prepared film samples maintain high transparency and uniformity, and the

thickness of these films are measured as 0.41 to 0.44 mm. In QDs-LEDs packaging, the main concerns are the absorption and scattering properties of QDs film for blue light emitted from the

LED chip and converted red light emitted from itself. Therefore, in the DIS measurement, two diode lasers with peak wavelength of 450 nm and 650 nm were used as the light sources. The

optical power of these lasers is 20 mW, and their beam diameter is expanded to 8 mm to illuminate a sufficiently large area of QDs-PMMA film. Diameters of the reflectance, transmittance and

collimating transmittance spheres are 300 mm, 300 mm and 150 mm, respectively. Diameters of the apertures are 18 mm. For blue light (450 nm) excitation, the spectra of transmitted and

reflected light are divided into two parts at 500 nm. Light with spectra from 380 nm to 500 nm is defined as unconverted blue light. For red light (650 nm) excitation, since no converted

light is emitted from the QDs film, both the transmitted light and reflected light are sorted as the red light. Figure 6 shows the measured reflectance and transmittance of QDs-PMMA samples

based on blue and red light incidence. For simplicity, the reflectance, transmittance and collimating transmittance of the blue light and the red light are denoted as _V_ RB, _V_ TB, _V_

CTB, _V_ RR, _V_ TR and _V_ CTR. In the case of blue light incidence, _V_ RB only takes a very small proportion (1.04%~1.45%), and it varies little against the QDs concentration. This is

mainly because, during the light propagation, the backward scattered blue light is further absorbed by the QDs particles. It can be found that the QDs present remarkable high absorption and

scattering for the blue light, and cause rapid decrease of _V_ CTB and small reduction of _V_ TB when the QDs concentration increased. In the case of red light incidence, the results are

quite different from those of blue light. The _V_ RR and _V_ TR increased with the increasing QDs concentration, which depicts that the increase of QDs particles leads to the enhancement of

multiple scattering effects, and the backward scattered red light can emit out due to the weak absorption of the QDs. Consequently, the _V_ CTR decreased with the increasing QDs

concentration, because more and more light changed propagation direction. According to the measured reflectance and transmittance values, the optical properties (_µ_ s, _µ_ a and _g_) of

QDs-PMMA film samples are calculated by IAD algorithm, and the results are listed in Table 1. Measured results showed that the QDs present strong absorption for blue light, high reflection

for converted red light, and an anisotropic emission pattern of converted red light. It is seen that the scattering and absorption coefficients increase with the increasing QDs

concentration, while the anisotropy coefficient changes slightly with the QDs concentration. Under the same QDs concentration, the scattering and absorption coefficients toward blue light

incidence are large than that of red light incidence, which agrees with the measured results. To validate our calculated optical properties of QDs film, an optical model of DIS system, which

imitate the real DIS measurement system, was built up. The blue light (450 nm) is emitted out perpendicular to the laser aperture, with a beam divergence angle of 1.2 mrad. The inner

surfaces of the three integrating spheres are coated with a diffuse white material having optical properties of 11.1% absorption and 89.9% scattering, and are used as the receivers to

collect the transmitted and reflected light. The Monte Carlo method is applied for ray-tracing of the optical model. Total number of the traced rays is 2 million, of which 1 million rays are

the blue light and the other 1 million rays are the converted-red light. The threshold of light rays is 10–4. During the ray-tracing, the energy of light rays is calculated by optical power

in watts. Light rays with single wavelength are used to represent the blue light and the converted-red light, which are set to be 450 nm and 626 nm, respectively. This simplification has

been proven to be effective for the ray-tracing of light-emitting process33,34,35,36,37. Figure 7(a) shows the comparisons between the ray-tracing and experimental results of reflectance,

transmittance and collimating transmittance for the incident blue light. It can be seen that the simulated _V_ TB and _V_ CTB values agree well with the experimental results, with a maximum

deviation of 0.26%. The _V_ RB values in the ray-tracing are slightly larger than those in the experiments, with a maximum deviation of 0.32%, respectively. This larger difference is mainly

due to the relatively low value of _V_ RB. Figure 7(b) and (c) show the comparisons of those results for the converted red light. Note that the collimating transmittance values of the

converted red light are not displayed here due to their weak signals that can hardly be collected by the photodetector. With a maximum deviation of 1.16%, the simulated values quantitatively

agree with the experimental results. Therefore, the QDs optical properties can be measured and calculated precisely by our approach, which provides wide guidance for QDs-WLEDs design and

fabrication. CONCLUSION In summary, this work provides a precise optical modeling approach towards QDs-polymer materials. The optical properties of QDs-PMMA film were measured by a double

integrating sphere system and calculated by the inverse adding doubling algorithm. Measured results showed that the QDs present strong absorption for blue light, high reflection for

converted red light, and an anisotropic emission pattern for both blue light and converted red light. Based on the calculated results, the absorption coefficient, scattering coefficient, and

anisotropy coefficient were imported into the Monte-Carlo ray-tracing model for validation. With a maximum deviation of 1.16%, the simulated values quantitatively agree with the

experimental results. Therefore, our optical modeling approach can obtain the necessary optical properties of QDs-polymer film, and the parameters can be utilized to conduct the ray-tracing

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Lightwave Technol._ 26, 3556–3559 (2008). Article  ADS  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS This work was supported in part by the National Natural Science Foundation

of China (NFSC) (51625601, 61604135 and 51402148), in part by Fundamental Research Funds for the Central Universities (2016JCTD112), in part by Guangdong High Tech Project (2014A010105005,

2014TQ01C494), and in part by Shenzhen Innovation Project (JCYJ20150630145302223). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * School of Energy and Power Engineering, Huazhong University

of Science and Technology, Wuhan, 430074, China Bin Xie, Yanhua Cheng, Weicheng Shu & Xiaobing Luo * Department of Electrical and Electronic Engineering, Southern University of Science

and Technology, Shenzhen, 518055, China Bin Xie, Junjie Hao & Kai Wang Authors * Bin Xie View author publications You can also search for this author inPubMed Google Scholar * Yanhua

Cheng View author publications You can also search for this author inPubMed Google Scholar * Junjie Hao View author publications You can also search for this author inPubMed Google Scholar *

Weicheng Shu View author publications You can also search for this author inPubMed Google Scholar * Kai Wang View author publications You can also search for this author inPubMed Google

Scholar * Xiaobing Luo View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS B.X. and X.L. conceived the experiment, Y.C., W.S. and J.H.

conducted the experiment, B.X. and K.W. analyzed the results. All authors reviewed the manuscript. CORRESPONDING AUTHORS Correspondence to Kai Wang or Xiaobing Luo. ETHICS DECLARATIONS

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and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Xie, B., Cheng, Y., Hao, J. _et al._ Precise optical modeling of quantum dots for white light-emitting diodes. _Sci Rep_ 7, 16663 (2017).

https://doi.org/10.1038/s41598-017-16966-2 Download citation * Received: 02 October 2017 * Accepted: 15 November 2017 * Published: 30 November 2017 * DOI:

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