Dynamic prediction of optical and chromatic performances for a light-emitting diode array based on a thermal-electrical-spectral model

Jiajie Fan; Jiajie Fan; Jiajie Fan; Jiajie Fan; Wei Chen; Wei Chen; Weiyi Yuan; Xuejun Fan; Guoqi Zhang

doi:10.1364/OE.387660

Optics Express
Vol. 28,
Issue 9,
pp. 13921-13937
(2020)
•https://doi.org/10.1364/OE.387660

Dynamic prediction of optical and chromatic performances for a light-emitting diode array based on a thermal-electrical-spectral model

Jiajie Fan, Wei Chen, Weiyi Yuan, Xuejun Fan, and Guoqi Zhang

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Jiajie Fan, Wei Chen, Weiyi Yuan, Xuejun Fan, and Guoqi Zhang, "Dynamic prediction of optical and chromatic performances for a light-emitting diode array based on a thermal-electrical-spectral model," Opt. Express 28, 13921-13937 (2020)

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Abstract

Light-emitting diode (LED) arrays have attracted increased attention in the area of high power intelligent automotive headlamps because of their superiority in disposing of the power limit of an individual LED package and controllably luminous intensity and illumination pattern. The optical and chromatic performances of an LED array do not equal to the sum of individual LED packages’ performances, as the thermal interactions between individual LED packages can’t be ignored in the actual application. This paper presents a thermal-electrical-spectral (TES) model to dynamically predict the optical and chromatic performances of the LED array. The thermal-electrical (TE) model considering the thermal coupling effect in the LED array is firstly proposed to predict the case temperature of each individual LED package, and the Spectral power distributions (SPDs) of individual LED package is then decomposed by the extended Asym2sig model to extract the spectral characteristic parameters. Finally, the experimental measurements of the designed LED arrays operated under usage conditions are used to verify the TES model. Some validation case studies show that the prediction accuracy of the proposed TES model, which is expressed as a quadratic polynomial function of current and case temperature, can be achieved higher than 95%. Therefore, it can be concluded that this TES model offers a convenient method with high accuracy to dynamically predict the optical and chromatic performances of LED arrays at real usages.

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References

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Year
Author
Publication

M. Hamidnia, Y. Luo, and X. D. Wang, “Application of micro/nano technology for thermal management of high power LED packaging – A review,” Appl. Therm. Eng. 145, 637–651 (2018).
[Crossref]
Q. Wang, H. Xu, F. Zhang, and Z. Wang, “Influence of color temperature on comfort and preference for LED indoor lighting,” Optik 129, 21–29 (2017).
[Crossref]
T. Ouzounis, E. Heuvelink, Y. Ji, H. J. Schouten, R. G. F. Visser, and L. F. M. Marcelis, “Blue and red LED lighting effects on plant biomass, stomatal conductance, and metabolite content in nine tomato genotypes,” Acta Hortic. 1134(1134), 251–258 (2016).
[Crossref]
Z. Lu, P. Bai, B. Huang, A. Henzen, R. Coehoorn, H. Liao, and G. Zhou, “Experimental investigation on the thermal performance of three-dimensional vapor chamber for LED automotive headlamps,” Appl. Therm. Eng. 157, 113478 (2019).
[Crossref]
M. Roncati, D. Lauritano, F. Cura, and F. Carinci, “Evaluation of light-emitting diode (LED-835 NM) application over human gingival fibroblast: an in vitro study,” Journal of Biological Regulators & Homeostatic Agents 30, 161 (2016).
Y. Chien-Hung, L. Yen-Liang, and C. Chi-Wai, “Real-time white-light phosphor-LED visible light communication (VLC) with compact size,” Opt. Express 21(22), 26192–26197 (2013).
[Crossref]
I. E. Fragkos, V. Dierolf, Y. Fujiwara, and N. Tansu, “Physics of Efficiency Droop in GaN:Eu Light-Emitting Diodes,” Sci. Rep. 7(1), 16773 (2017).
[Crossref]
Y. Lee, C. Chen, and C. Lee, “Reduction in the Efficiency-Droop Effect of InGaN Green Light-Emitting Diodes Using Gradual Quantum Wells,” IEEE Photonics Technol. Lett. 22(20), 1506–1508 (2010).
[Crossref]
H. Y. Ryu, K. S. Jeon, M. G. Kang, H. K. Yuh, Y. H. Choi, and J. S. Lee, “A comparative study of efficiency droop and internal electric field for InGaN blue lighting-emitting diodes on silicon and sapphire substrates,” Sci. Rep. 7(1), 44814 (2017).
[Crossref]
K. Ben Abdelmlek, Z. Araoud, K. Charrada, and G. Zissis, “Optimization of the thermal distribution of multi-chip LED package,” Appl. Therm. Eng. 126, 653–660 (2017).
[Crossref]
H. Tang, H. Ye, X. Chen, C. Qian, X. Fan, and G. Zhang, “Numerical Thermal Analysis and Optimization of Multi-Chip LED Module Using Response Surface Methodology and Genetic Algorithm,” IEEE Access 5, 16459–16468 (2017).
[Crossref]
J. Zhou, J. Huang, Y. Wang, and Z. Zhou, “Thermal distribution of multiple LED module,” Appl. Therm. Eng. 93, 122–130 (2016).
[Crossref]
G. Elger, B. Spinger, N. Bienen, and N. Benter, “LED Matrix light source for adaptive driving beam applications,” in IEEE Electronic Components & Technology Conference (2013).
W. Chen, J. Fan, C. Qian, B. Pu, X. Fan, and G. Zhang, “Reliability Assessment of Light-Emitting Diode Packages With Both Luminous Flux Response Surface Model and Spectral Power Distribution Method,” IEEE Access 7, 68495–68502 (2019).
[Crossref]
C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]
J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]
M. W. Jeong, S. W. Jeon, and Y. Kim, “Optimal thermal design of a horizontal fin heat sink with a modified-opening model mounted on an LED module,” Appl. Therm. Eng. 91, 105–115 (2015).
[Crossref]
K. C. Yung, H. Liem, H. S. Choy, and Z. X. Cai, “Thermal investigation of a high brightness LED array package assembly for various placement algorithms,” Appl. Therm. Eng. 63(1), 105–118 (2014).
[Crossref]
H. Lu, Y. Lu, L. Zhu, Y. Lin, Z. Guo, T. Liu, Y. Gao, G. Chen, and Z. Chen, “Efficient Measurement of Thermal Coupling Effects on Multichip Light-Emitting Diodes,” IEEE Trans. Power Electron. 32(12), 9280–9292 (2017).
[Crossref]
J. Kang, J. Choi, D. Kim, J. Kim, Y. Song, G. Kim, and S. Han, “Fabrication and Thermal Analysis of Wafer-Level Light-Emitting Diode Packages,” IEEE Electron Device Lett. 29(10), 1118–1120 (2008).
[Crossref]
T. Treurniet and V. Lammens, “Thermal management in color variable multi-chip led modules,” in Twenty-Second Annual IEEE Semiconductor Thermal Measurement And Management Symposium (2006), pp. 173–177.
H. Zou, L. Lu, J. Wang, B. Shieh, and S. W. R. Lee, “Thermal characterization of multi-chip light emitting diodes with thermal resistance matrix,” in 2017 14th China International Forum on Solid State Lighting: International Forum on Wide Bandgap Semiconductors China (SSLChina: IFWS) (2017), pp. 32–37.
S. Y. Hui and Y. X. Qin, “A General Photo-Electro-Thermal Theory for Light Emitting Diode (LED) Systems,” IEEE Trans. Power Electron. 24(8), 1967–1976 (2009).
[Crossref]
S. Y. R. Hui, H. Chen, and X. Tao, “An Extended Photoelectrothermal Theory for LED Systems: A Tutorial From Device Characteristic to System Design for General Lighting,” IEEE Trans. Power Electron. 27(11), 4571–4583 (2012).
[Crossref]
H. T. Chen, X. H. Tao, and S. Y. R. Hui, “Estimation of Optical Power and Heat-Dissipation Coefficient for the Photo-Electro-Thermal Theory for LED Systems,” IEEE Trans. Power Electron. 27(4), 2176–2183 (2012).
[Crossref]
H. Chen, A. T. L. Lee, S. Tan, and S. Y. Hui, “Dynamic Optical Power Measurements and Modeling of Light-Emitting Diodes Based on a Photodetector System and Photo-Electro-Thermal Theory,” IEEE Trans. Power Electron. 34(10), 10058–10068 (2019).
[Crossref]
A. Lee, H. Chen, S. C. Tan, and S. Y. R. Hui, “Dynamic Photo-Electro-Thermal Modeling of Light-Emitting Diodes with Phosphor Coating as Light Converter,” IEEE Journal of Emerging and Selected Topics in Power Electronics, 1 (2018).
B.-J. Huang and C.-W. Tang, “Thermal–electrical–luminous model of multi-chip polychromatic LED luminaire,” Appl. Therm. Eng. 29(16), 3366–3373 (2009).
[Crossref]
C.-H. Lin, C.-H. Huang, Y.-M. Pai, C.-F. Lee, C.-C. Lin, C.-W. Sun, C.-H. Chen, C.-W. Sher, and H.-C. Kuo, “Novel Method for Estimating Phosphor Conversion Efficiency of Light-Emitting Diodes,” Crystals 8 (2018).
B. Sun, J. Fan, X. Fan, and G. Zhang, “A SPICE-based Transient Thermal-Electronic Model for LEDs,” in 2019 20th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE) (2019), pp. 1–5.
C. Negrea, P. Svasta, and M. Rangu, “Electro-thermal modeling of power LED using SPICE circuit solver,” in 2012 35th International Spring Seminar on Electronics Technology (2012), pp. 329–334.
K. Górecki and P. Ptak, “Modelling LED lamps in SPICE with thermal phenomena taken into account,” Microelectron. Reliab. 79, 440–447 (2017).
[Crossref]
P. Baureis, “Compact modeling of electrical, thermal and optical LED behavior,” in Proceedings of 35th European Solid-State Device Research Conference, 2005. ESSDERC 2005 (2005), pp. 145–148.
J. Fan, M. G. Mohamed, C. Qian, X. Fan, G. Zhang, and M. Pecht, “Color Shift Failure Prediction for Phosphor-Converted White LEDs by Modeling Features of Spectral Power Distribution with a Nonlinear Filter Approach,” Materials 10(7), 819 (2017).
[Crossref]
C. Qian, J. Fan, X. Fan, and G. Zhang, “Prediction of Lumen Depreciation and Color Shift for Phosphor-Converted White Light-Emitting Diodes Based on A Spectral Power Distribution Analysis Method,” IEEE Access 5, 24054–24061 (2017).
[Crossref]
H. T. Chen, D. Y. Lin, S. C. Tan, and S. Y. R. Hui, “Chromatic, Photometric and Thermal Modeling of LED Systems with Non-Identical LED Devices,” in IEEE Trans. Power Electron. (2014), pp. 6636–6647.
H. Chen and S. Y. Hui, “Dynamic Prediction of Correlated Color Temperature and Color Rendering Index of Phosphor-Coated White Light-Emitting Diodes,” IEEE Transactions on Industrial Electronics 61(2), 784–797 (2014).
[Crossref]
Y. E. Huaiyu, S. W. Koh, C. Yuan, H. van Zeijl, A. W. J. Gielen, S. W. R. Lee, and G. Zhang, “Electrical—thermal—luminous—chromatic model of phosphor-converted white light-emitting diodes,” Appl. Therm. Eng. 63(2), 588–597 (2014).
[Crossref]
K. F. Han, P. P. Yi, P. Y. Shang, T. T. Chen, C. P. Wang, C. L. Chen, and T. C. Pei, “The evaluation for the chromatic characteristics of LED module under electrical and thermal coupling analysis,” Microelectron. Reliab. 53(12), 1916–1921 (2013).
[Crossref]
H. Guoxing and Y. Huafeng, “Optimal spectra of the phosphor-coated white LEDs with excellent color rendering property and high luminous efficacy of radiation,” Opt. Express 19(3), 2519–2529 (2011).
[Crossref]

2019 (3)

Z. Lu, P. Bai, B. Huang, A. Henzen, R. Coehoorn, H. Liao, and G. Zhou, “Experimental investigation on the thermal performance of three-dimensional vapor chamber for LED automotive headlamps,” Appl. Therm. Eng. 157, 113478 (2019).
[Crossref]

W. Chen, J. Fan, C. Qian, B. Pu, X. Fan, and G. Zhang, “Reliability Assessment of Light-Emitting Diode Packages With Both Luminous Flux Response Surface Model and Spectral Power Distribution Method,” IEEE Access 7, 68495–68502 (2019).
[Crossref]

H. Chen, A. T. L. Lee, S. Tan, and S. Y. Hui, “Dynamic Optical Power Measurements and Modeling of Light-Emitting Diodes Based on a Photodetector System and Photo-Electro-Thermal Theory,” IEEE Trans. Power Electron. 34(10), 10058–10068 (2019).
[Crossref]

2018 (1)

M. Hamidnia, Y. Luo, and X. D. Wang, “Application of micro/nano technology for thermal management of high power LED packaging – A review,” Appl. Therm. Eng. 145, 637–651 (2018).
[Crossref]

2017 (10)

Q. Wang, H. Xu, F. Zhang, and Z. Wang, “Influence of color temperature on comfort and preference for LED indoor lighting,” Optik 129, 21–29 (2017).
[Crossref]

H. Y. Ryu, K. S. Jeon, M. G. Kang, H. K. Yuh, Y. H. Choi, and J. S. Lee, “A comparative study of efficiency droop and internal electric field for InGaN blue lighting-emitting diodes on silicon and sapphire substrates,” Sci. Rep. 7(1), 44814 (2017).
[Crossref]

K. Ben Abdelmlek, Z. Araoud, K. Charrada, and G. Zissis, “Optimization of the thermal distribution of multi-chip LED package,” Appl. Therm. Eng. 126, 653–660 (2017).
[Crossref]

H. Tang, H. Ye, X. Chen, C. Qian, X. Fan, and G. Zhang, “Numerical Thermal Analysis and Optimization of Multi-Chip LED Module Using Response Surface Methodology and Genetic Algorithm,” IEEE Access 5, 16459–16468 (2017).
[Crossref]

C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]

I. E. Fragkos, V. Dierolf, Y. Fujiwara, and N. Tansu, “Physics of Efficiency Droop in GaN:Eu Light-Emitting Diodes,” Sci. Rep. 7(1), 16773 (2017).
[Crossref]

H. Lu, Y. Lu, L. Zhu, Y. Lin, Z. Guo, T. Liu, Y. Gao, G. Chen, and Z. Chen, “Efficient Measurement of Thermal Coupling Effects on Multichip Light-Emitting Diodes,” IEEE Trans. Power Electron. 32(12), 9280–9292 (2017).
[Crossref]

K. Górecki and P. Ptak, “Modelling LED lamps in SPICE with thermal phenomena taken into account,” Microelectron. Reliab. 79, 440–447 (2017).
[Crossref]

J. Fan, M. G. Mohamed, C. Qian, X. Fan, G. Zhang, and M. Pecht, “Color Shift Failure Prediction for Phosphor-Converted White LEDs by Modeling Features of Spectral Power Distribution with a Nonlinear Filter Approach,” Materials 10(7), 819 (2017).
[Crossref]

C. Qian, J. Fan, X. Fan, and G. Zhang, “Prediction of Lumen Depreciation and Color Shift for Phosphor-Converted White Light-Emitting Diodes Based on A Spectral Power Distribution Analysis Method,” IEEE Access 5, 24054–24061 (2017).
[Crossref]

2016 (4)

J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]

J. Zhou, J. Huang, Y. Wang, and Z. Zhou, “Thermal distribution of multiple LED module,” Appl. Therm. Eng. 93, 122–130 (2016).
[Crossref]

T. Ouzounis, E. Heuvelink, Y. Ji, H. J. Schouten, R. G. F. Visser, and L. F. M. Marcelis, “Blue and red LED lighting effects on plant biomass, stomatal conductance, and metabolite content in nine tomato genotypes,” Acta Hortic. 1134(1134), 251–258 (2016).
[Crossref]

M. Roncati, D. Lauritano, F. Cura, and F. Carinci, “Evaluation of light-emitting diode (LED-835 NM) application over human gingival fibroblast: an in vitro study,” Journal of Biological Regulators & Homeostatic Agents 30, 161 (2016).

2015 (1)

M. W. Jeong, S. W. Jeon, and Y. Kim, “Optimal thermal design of a horizontal fin heat sink with a modified-opening model mounted on an LED module,” Appl. Therm. Eng. 91, 105–115 (2015).
[Crossref]

2014 (3)

K. C. Yung, H. Liem, H. S. Choy, and Z. X. Cai, “Thermal investigation of a high brightness LED array package assembly for various placement algorithms,” Appl. Therm. Eng. 63(1), 105–118 (2014).
[Crossref]

H. Chen and S. Y. Hui, “Dynamic Prediction of Correlated Color Temperature and Color Rendering Index of Phosphor-Coated White Light-Emitting Diodes,” IEEE Transactions on Industrial Electronics 61(2), 784–797 (2014).
[Crossref]

Y. E. Huaiyu, S. W. Koh, C. Yuan, H. van Zeijl, A. W. J. Gielen, S. W. R. Lee, and G. Zhang, “Electrical—thermal—luminous—chromatic model of phosphor-converted white light-emitting diodes,” Appl. Therm. Eng. 63(2), 588–597 (2014).
[Crossref]

2013 (2)

K. F. Han, P. P. Yi, P. Y. Shang, T. T. Chen, C. P. Wang, C. L. Chen, and T. C. Pei, “The evaluation for the chromatic characteristics of LED module under electrical and thermal coupling analysis,” Microelectron. Reliab. 53(12), 1916–1921 (2013).
[Crossref]

Y. Chien-Hung, L. Yen-Liang, and C. Chi-Wai, “Real-time white-light phosphor-LED visible light communication (VLC) with compact size,” Opt. Express 21(22), 26192–26197 (2013).
[Crossref]

2012 (2)

S. Y. R. Hui, H. Chen, and X. Tao, “An Extended Photoelectrothermal Theory for LED Systems: A Tutorial From Device Characteristic to System Design for General Lighting,” IEEE Trans. Power Electron. 27(11), 4571–4583 (2012).
[Crossref]

H. T. Chen, X. H. Tao, and S. Y. R. Hui, “Estimation of Optical Power and Heat-Dissipation Coefficient for the Photo-Electro-Thermal Theory for LED Systems,” IEEE Trans. Power Electron. 27(4), 2176–2183 (2012).
[Crossref]

2011 (1)

H. Guoxing and Y. Huafeng, “Optimal spectra of the phosphor-coated white LEDs with excellent color rendering property and high luminous efficacy of radiation,” Opt. Express 19(3), 2519–2529 (2011).
[Crossref]

2010 (1)

Y. Lee, C. Chen, and C. Lee, “Reduction in the Efficiency-Droop Effect of InGaN Green Light-Emitting Diodes Using Gradual Quantum Wells,” IEEE Photonics Technol. Lett. 22(20), 1506–1508 (2010).
[Crossref]

2009 (2)

B.-J. Huang and C.-W. Tang, “Thermal–electrical–luminous model of multi-chip polychromatic LED luminaire,” Appl. Therm. Eng. 29(16), 3366–3373 (2009).
[Crossref]

S. Y. Hui and Y. X. Qin, “A General Photo-Electro-Thermal Theory for Light Emitting Diode (LED) Systems,” IEEE Trans. Power Electron. 24(8), 1967–1976 (2009).
[Crossref]

2008 (1)

J. Kang, J. Choi, D. Kim, J. Kim, Y. Song, G. Kim, and S. Han, “Fabrication and Thermal Analysis of Wafer-Level Light-Emitting Diode Packages,” IEEE Electron Device Lett. 29(10), 1118–1120 (2008).
[Crossref]

Araoud, Z.

K. Ben Abdelmlek, Z. Araoud, K. Charrada, and G. Zissis, “Optimization of the thermal distribution of multi-chip LED package,” Appl. Therm. Eng. 126, 653–660 (2017).
[Crossref]

Bai, P.

Bao, W.-w.

J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]

Baureis, P.

P. Baureis, “Compact modeling of electrical, thermal and optical LED behavior,” in Proceedings of 35th European Solid-State Device Research Conference, 2005. ESSDERC 2005 (2005), pp. 145–148.

Ben Abdelmlek, K.

K. Ben Abdelmlek, Z. Araoud, K. Charrada, and G. Zissis, “Optimization of the thermal distribution of multi-chip LED package,” Appl. Therm. Eng. 126, 653–660 (2017).
[Crossref]

Benter, N.

G. Elger, B. Spinger, N. Bienen, and N. Benter, “LED Matrix light source for adaptive driving beam applications,” in IEEE Electronic Components & Technology Conference (2013).

Bienen, N.

G. Elger, B. Spinger, N. Bienen, and N. Benter, “LED Matrix light source for adaptive driving beam applications,” in IEEE Electronic Components & Technology Conference (2013).

Cai, Y.-x.

J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]

Cai, Z. X.

Carinci, F.

Charrada, K.

K. Ben Abdelmlek, Z. Araoud, K. Charrada, and G. Zissis, “Optimization of the thermal distribution of multi-chip LED package,” Appl. Therm. Eng. 126, 653–660 (2017).
[Crossref]

Chen, C.

Chen, C. L.

Chen, C.-H.

C.-H. Lin, C.-H. Huang, Y.-M. Pai, C.-F. Lee, C.-C. Lin, C.-W. Sun, C.-H. Chen, C.-W. Sher, and H.-C. Kuo, “Novel Method for Estimating Phosphor Conversion Efficiency of Light-Emitting Diodes,” Crystals 8 (2018).

Chen, G.

Chen, H.

A. Lee, H. Chen, S. C. Tan, and S. Y. R. Hui, “Dynamic Photo-Electro-Thermal Modeling of Light-Emitting Diodes with Phosphor Coating as Light Converter,” IEEE Journal of Emerging and Selected Topics in Power Electronics, 1 (2018).

Chen, H. T.

H. T. Chen, D. Y. Lin, S. C. Tan, and S. Y. R. Hui, “Chromatic, Photometric and Thermal Modeling of LED Systems with Non-Identical LED Devices,” in IEEE Trans. Power Electron. (2014), pp. 6636–6647.

Chen, T. T.

Chen, W.

Chen, X.

Chen, Z.

Chien-Hung, Y.

Y. Chien-Hung, L. Yen-Liang, and C. Chi-Wai, “Real-time white-light phosphor-LED visible light communication (VLC) with compact size,” Opt. Express 21(22), 26192–26197 (2013).
[Crossref]

Chi-Wai, C.

Y. Chien-Hung, L. Yen-Liang, and C. Chi-Wai, “Real-time white-light phosphor-LED visible light communication (VLC) with compact size,” Opt. Express 21(22), 26192–26197 (2013).
[Crossref]

Choi, J.

Choi, Y. H.

Choy, H. S.

Coehoorn, R.

Cura, F.

Dierolf, V.

I. E. Fragkos, V. Dierolf, Y. Fujiwara, and N. Tansu, “Physics of Efficiency Droop in GaN:Eu Light-Emitting Diodes,” Sci. Rep. 7(1), 16773 (2017).
[Crossref]

Elger, G.

G. Elger, B. Spinger, N. Bienen, and N. Benter, “LED Matrix light source for adaptive driving beam applications,” in IEEE Electronic Components & Technology Conference (2013).

Fan, J.

B. Sun, J. Fan, X. Fan, and G. Zhang, “A SPICE-based Transient Thermal-Electronic Model for LEDs,” in 2019 20th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE) (2019), pp. 1–5.

Fan, X.

Fragkos, I. E.

I. E. Fragkos, V. Dierolf, Y. Fujiwara, and N. Tansu, “Physics of Efficiency Droop in GaN:Eu Light-Emitting Diodes,” Sci. Rep. 7(1), 16773 (2017).
[Crossref]

Fujiwara, Y.

I. E. Fragkos, V. Dierolf, Y. Fujiwara, and N. Tansu, “Physics of Efficiency Droop in GaN:Eu Light-Emitting Diodes,” Sci. Rep. 7(1), 16773 (2017).
[Crossref]

Gao, Y.

Gielen, A. W. J.

Górecki, K.

K. Górecki and P. Ptak, “Modelling LED lamps in SPICE with thermal phenomena taken into account,” Microelectron. Reliab. 79, 440–447 (2017).
[Crossref]

Guo, Z.

Guoxing, H.

Hamidnia, M.

M. Hamidnia, Y. Luo, and X. D. Wang, “Application of micro/nano technology for thermal management of high power LED packaging – A review,” Appl. Therm. Eng. 145, 637–651 (2018).
[Crossref]

Han, K. F.

Han, S.

Henzen, A.

Heuvelink, E.

Huafeng, Y.

Huaiyu, Y. E.

Huang, B.

Huang, B.-J.

B.-J. Huang and C.-W. Tang, “Thermal–electrical–luminous model of multi-chip polychromatic LED luminaire,” Appl. Therm. Eng. 29(16), 3366–3373 (2009).
[Crossref]

Huang, C.-H.

Huang, J.

J. Zhou, J. Huang, Y. Wang, and Z. Zhou, “Thermal distribution of multiple LED module,” Appl. Therm. Eng. 93, 122–130 (2016).
[Crossref]

Hui, S. Y.

S. Y. Hui and Y. X. Qin, “A General Photo-Electro-Thermal Theory for Light Emitting Diode (LED) Systems,” IEEE Trans. Power Electron. 24(8), 1967–1976 (2009).
[Crossref]

Hui, S. Y. R.

Jeon, K. S.

Jeon, S. W.

Jeong, M. W.

Ji, Y.

Kang, J.

Kang, M. G.

Kim, D.

Kim, G.

Kim, J.

Kim, Y.

Koh, S. W.

Kuo, H.-C.

Lammens, V.

T. Treurniet and V. Lammens, “Thermal management in color variable multi-chip led modules,” in Twenty-Second Annual IEEE Semiconductor Thermal Measurement And Management Symposium (2006), pp. 173–177.

Lauritano, D.

Lee, A.

Lee, A. T. L.

Lee, C.

Lee, C.-F.

Lee, J. S.

Lee, S. W. R.

H. Zou, L. Lu, J. Wang, B. Shieh, and S. W. R. Lee, “Thermal characterization of multi-chip light emitting diodes with thermal resistance matrix,” in 2017 14th China International Forum on Solid State Lighting: International Forum on Wide Bandgap Semiconductors China (SSLChina: IFWS) (2017), pp. 32–37.

Lee, Y.

Li, H.-x.

J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]

Li, J.

C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]

Liao, H.

C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]

Liem, H.

Lin, C.-C.

Lin, C.-H.

Lin, D. Y.

Lin, Y.

Liu, Q.

J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]

Liu, T.

Lu, H.

Lu, L.

Lu, Y.

Lu, Z.

Luo, Y.

M. Hamidnia, Y. Luo, and X. D. Wang, “Application of micro/nano technology for thermal management of high power LED packaging – A review,” Appl. Therm. Eng. 145, 637–651 (2018).
[Crossref]

Marcelis, L. F. M.

Mohamed, M. G.

Negrea, C.

C. Negrea, P. Svasta, and M. Rangu, “Electro-thermal modeling of power LED using SPICE circuit solver,” in 2012 35th International Spring Seminar on Electronics Technology (2012), pp. 329–334.

Ouzounis, T.

Pai, Y.-M.

Pecht, M.

Pei, T. C.

Ptak, P.

K. Górecki and P. Ptak, “Modelling LED lamps in SPICE with thermal phenomena taken into account,” Microelectron. Reliab. 79, 440–447 (2017).
[Crossref]

Pu, B.

Qian, C.

Qin, Y. X.

S. Y. Hui and Y. X. Qin, “A General Photo-Electro-Thermal Theory for Light Emitting Diode (LED) Systems,” IEEE Trans. Power Electron. 24(8), 1967–1976 (2009).
[Crossref]

Rangu, M.

C. Negrea, P. Svasta, and M. Rangu, “Electro-thermal modeling of power LED using SPICE circuit solver,” in 2012 35th International Spring Seminar on Electronics Technology (2012), pp. 329–334.

Roncati, M.

Ryu, H. Y.

Schouten, H. J.

Shang, P. Y.

Sher, C.-W.

Shieh, B.

Song, Y.

Spinger, B.

G. Elger, B. Spinger, N. Bienen, and N. Benter, “LED Matrix light source for adaptive driving beam applications,” in IEEE Electronic Components & Technology Conference (2013).

Sun, B.

Sun, C.-W.

Svasta, P.

C. Negrea, P. Svasta, and M. Rangu, “Electro-thermal modeling of power LED using SPICE circuit solver,” in 2012 35th International Spring Seminar on Electronics Technology (2012), pp. 329–334.

Tan, S.

Tan, S. C.

Tang, C.-W.

B.-J. Huang and C.-W. Tang, “Thermal–electrical–luminous model of multi-chip polychromatic LED luminaire,” Appl. Therm. Eng. 29(16), 3366–3373 (2009).
[Crossref]

Tang, H.

Tansu, N.

I. E. Fragkos, V. Dierolf, Y. Fujiwara, and N. Tansu, “Physics of Efficiency Droop in GaN:Eu Light-Emitting Diodes,” Sci. Rep. 7(1), 16773 (2017).
[Crossref]

Tao, X.

Tao, X. H.

Treurniet, T.

van Zeijl, H.

Visser, R. G. F.

Wang, C. P.

Wang, J.

J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]

Wang, Q.

Q. Wang, H. Xu, F. Zhang, and Z. Wang, “Influence of color temperature on comfort and preference for LED indoor lighting,” Optik 129, 21–29 (2017).
[Crossref]

Wang, X. D.

M. Hamidnia, Y. Luo, and X. D. Wang, “Application of micro/nano technology for thermal management of high power LED packaging – A review,” Appl. Therm. Eng. 145, 637–651 (2018).
[Crossref]

Wang, Y.

C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]

J. Zhou, J. Huang, Y. Wang, and Z. Zhou, “Thermal distribution of multiple LED module,” Appl. Therm. Eng. 93, 122–130 (2016).
[Crossref]

Wang, Z.

Q. Wang, H. Xu, F. Zhang, and Z. Wang, “Influence of color temperature on comfort and preference for LED indoor lighting,” Optik 129, 21–29 (2017).
[Crossref]

Xiao, C.

C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]

Xu, H.

Q. Wang, H. Xu, F. Zhang, and Z. Wang, “Influence of color temperature on comfort and preference for LED indoor lighting,” Optik 129, 21–29 (2017).
[Crossref]

Ye, H.

Yen-Liang, L.

Y. Chien-Hung, L. Yen-Liang, and C. Chi-Wai, “Real-time white-light phosphor-LED visible light communication (VLC) with compact size,” Opt. Express 21(22), 26192–26197 (2013).
[Crossref]

Yi, P. P.

Yuan, C.

Yuh, H. K.

Yung, K. C.

Zhang, F.

Q. Wang, H. Xu, F. Zhang, and Z. Wang, “Influence of color temperature on comfort and preference for LED indoor lighting,” Optik 129, 21–29 (2017).
[Crossref]

Zhang, G.

Zhou, G.

Zhou, J.

J. Zhou, J. Huang, Y. Wang, and Z. Zhou, “Thermal distribution of multiple LED module,” Appl. Therm. Eng. 93, 122–130 (2016).
[Crossref]

Zhou, Z.

J. Zhou, J. Huang, Y. Wang, and Z. Zhou, “Thermal distribution of multiple LED module,” Appl. Therm. Eng. 93, 122–130 (2016).
[Crossref]

Zhu, L.

Zhu, W.

C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]

Zissis, G.

K. Ben Abdelmlek, Z. Araoud, K. Charrada, and G. Zissis, “Optimization of the thermal distribution of multi-chip LED package,” Appl. Therm. Eng. 126, 653–660 (2017).
[Crossref]

Zou, H.

Acta Hortic. (1)

Appl. Therm. Eng. (10)

M. Hamidnia, Y. Luo, and X. D. Wang, “Application of micro/nano technology for thermal management of high power LED packaging – A review,” Appl. Therm. Eng. 145, 637–651 (2018).
[Crossref]

K. Ben Abdelmlek, Z. Araoud, K. Charrada, and G. Zissis, “Optimization of the thermal distribution of multi-chip LED package,” Appl. Therm. Eng. 126, 653–660 (2017).
[Crossref]

J. Zhou, J. Huang, Y. Wang, and Z. Zhou, “Thermal distribution of multiple LED module,” Appl. Therm. Eng. 93, 122–130 (2016).
[Crossref]

C. Xiao, H. Liao, Y. Wang, J. Li, and W. Zhu, “A novel automated heat-pipe cooling device for high-power LEDs,” Appl. Therm. Eng. 111, 1320–1329 (2017).
[Crossref]

J. Wang, Y.-x. Cai, W.-w. Bao, H.-x. Li, and Q. Liu, “Experimental study of high power LEDs heat dissipation based on corona discharge,” Appl. Therm. Eng. 98, 420–429 (2016).
[Crossref]

B.-J. Huang and C.-W. Tang, “Thermal–electrical–luminous model of multi-chip polychromatic LED luminaire,” Appl. Therm. Eng. 29(16), 3366–3373 (2009).
[Crossref]

IEEE Access (3)

IEEE Electron Device Lett. (1)

IEEE Photonics Technol. Lett. (1)

IEEE Trans. Power Electron. (5)

S. Y. Hui and Y. X. Qin, “A General Photo-Electro-Thermal Theory for Light Emitting Diode (LED) Systems,” IEEE Trans. Power Electron. 24(8), 1967–1976 (2009).
[Crossref]

IEEE Transactions on Industrial Electronics (1)

Journal of Biological Regulators & Homeostatic Agents (1)

Materials (1)

Microelectron. Reliab. (2)

K. Górecki and P. Ptak, “Modelling LED lamps in SPICE with thermal phenomena taken into account,” Microelectron. Reliab. 79, 440–447 (2017).
[Crossref]

Opt. Express (2)

Y. Chien-Hung, L. Yen-Liang, and C. Chi-Wai, “Real-time white-light phosphor-LED visible light communication (VLC) with compact size,” Opt. Express 21(22), 26192–26197 (2013).
[Crossref]

Optik (1)

Q. Wang, H. Xu, F. Zhang, and Z. Wang, “Influence of color temperature on comfort and preference for LED indoor lighting,” Optik 129, 21–29 (2017).
[Crossref]

Sci. Rep. (2)

I. E. Fragkos, V. Dierolf, Y. Fujiwara, and N. Tansu, “Physics of Efficiency Droop in GaN:Eu Light-Emitting Diodes,” Sci. Rep. 7(1), 16773 (2017).
[Crossref]

Other (9)

G. Elger, B. Spinger, N. Bienen, and N. Benter, “LED Matrix light source for adaptive driving beam applications,” in IEEE Electronic Components & Technology Conference (2013).

P. Baureis, “Compact modeling of electrical, thermal and optical LED behavior,” in Proceedings of 35th European Solid-State Device Research Conference, 2005. ESSDERC 2005 (2005), pp. 145–148.

C. Negrea, P. Svasta, and M. Rangu, “Electro-thermal modeling of power LED using SPICE circuit solver,” in 2012 35th International Spring Seminar on Electronics Technology (2012), pp. 329–334.

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Fig. 1. Schematic diagram of (a) pc-WLED CSP and (b) LED array test samples used in this study.

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Fig. 2. Illustration the experimental setups for photoelectric parameters, SPD, and temperature measurements.

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Fig. 3. Schematic diagram of (a) pc-WLED CSP and (b) LED array test samples used in this study.

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Fig. 4. Equivalent thermal resistance network in (a) an individual LED and (b) a LED array

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Fig. 5. (a) ΔT v.s. total P_th of the Sample LED4 and(b) ΔT₁, ΔT₂ v.s. P_th of 1^st LED in the Sample LED4

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Fig. 6. Infrared measurement results: (a) Sample LED1; (b) Sample LED4; (c) Sample LED6; (d) Sample LED9 driven under the current of 125mA

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Fig. 7. The case temperature of the samples under different current: (a) Sample LED1; (b) Sample LED4; (c) Sample LED6; (d) Sample LED9.

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Fig. 8. The flowchart of prediction methodologies

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Fig. 9. (a) The measured temperature distribution of Sample LED1 under the current of 120 mA and the PCB temperature of 60°C and (b) The measured case temperatures of Sample LED1 under different operation conditions

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Fig. 10. The measured and fitted SPD data of Sample LED1 driven under the current of 120 mA with the case temperature of 64.8°C

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Fig. 11. (a) Superposition SPD of sample LED6 and verified by the measured SPDand (b) The predicted optical and chromatic parameters of Sample LED6

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Fig. 12. The prediction results of optical and chromatic parameters when all LEDs powered-on with same current: (a)luminous flux; (b)CCT; (c) chromaticity coordinate x; (d) chromaticity coordinate y

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Fig. 13. The prediction results of optical and chromatic parameters when parts of LEDs powered-on with same current: (a)luminous flux; (b)CCT; (c) chromaticity coordinate x; (d) chromaticity coordinate y

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Fig. 14. The prediction results of optical and chromatic parameters when LEDs powered-on with different currents: (a)luminous flux; (b)CCT; (c) chromaticity coordinate x; (d) chromaticity coordinate y

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Tables (10)

Table 1. The assumed Thermal Resistance Used in The FEA Simulation

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Table 2. The Key Material Parameters Used in The FEA Simulation

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Table 3. The Means and Variances of Prediction Errors for Different Test Samples

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Table 4. Experimental Scheme for Sample LED1

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Table 5. The Means and Variances of R² of Three Extends Models

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Table 6. The Fitting Results of Eight Spectral Characteristic Parameters with The Quadratic Polynomial Function

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Table 7. The Predicted Spectral Characteristic Parameters of Each LED in Sample LED6

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Table 8. The Operation Conditions for All Test Samples When All LEDs Powered-on with Same Current

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Table 9. The Operation Conditions for All Test Samples When Parts of LEDs Powered-on with Same Current

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Table 10. The Operation Conditions for All Test Samples When LEDs Powered-on With Different Currents

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Equations (15)

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T_{c} = T_{a} + P_{t h} (R_{a} + R_{b})

T_{c i} = T_{a} + P_{t h i} (R_{a i} + R_{b}) + Δ T_{c i}

Δ T_{c} = (\begin{matrix} Δ T_{c 1} \\ Δ T_{c 2} \\ \dots \\ Δ T_{c N} \end{matrix}) = (\begin{array}{cccc} 0 & {r_{1}}_{2} & \dots & {r_{1}}_{N} \\ r_{21} & 0 & \dots & r_{2 N} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ r_{N 1} & r_{N 2} & \dots & 0 \end{array}) (\begin{matrix} P_{t h 1} \\ P_{t h 2} \\ \dots \\ P_{t h N} \end{matrix})

T_{c} = (\begin{matrix} T_{c 1} \\ T_{c 2} \\ ⋮ \\ T_{c N} \end{matrix}) = T_{a} + (\begin{array}{cccc} R_{a 1} + R_{b} & {r_{1}}_{2} & \dots & {r_{1}}_{N} \\ r_{21} & R_{a 2} + R_{b} & \dots & r_{2 N} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ r_{N 1} & r_{N 2} & \dots & R_{a N} + R_{b} \end{array}) (\begin{matrix} P_{t h 1} \\ P_{t h 2} \\ ⋮ \\ P_{t h N} \end{matrix})

T_{c} = T_{a} + T_{a d} + P_{t h} (R_{a} + R_{b})

T_{c} = (\begin{matrix} T_{c 1} \\ T_{c 2} \\ ⋮ \\ T_{c N} \end{matrix}) = T_{a} + T_{a d} + (\begin{array}{cccc} R_{a 1} + R_{b} & {r_{1}}_{2} & \dots & {r_{1}}_{N} \\ r_{21} & R_{a 2} + R_{b} & \dots & r_{2 N} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ r_{N 1} & r_{N 2} & \dots & R_{a N} + R_{b} \end{array}) (\begin{matrix} P_{t h 1} \\ P_{t h 2} \\ ⋮ \\ P_{t h N} \end{matrix})

T_{c} = 22 + 1.10 + P_{t h} (68.69 + 17.57)

T_{c} = (\begin{matrix} T_{c 1} \\ T_{c 2} \\ {T_{c}}_{3} \\ T_{c 4} \end{matrix}) = 22 + 2.55 + (\begin{array}{cccc} 85.01 & 17.94 & 17.67 & 17.78 \\ 17.27 & 84.16 & 17.57 & 16.85 \\ 17.19 & 17.76 & 84.95 & 17.70 \\ 17.19 & 16.94 & 17.59 & 83.97 \end{array}) (\begin{matrix} P_{t h 1} \\ P_{t h 2} \\ P_{t h 3} \\ P_{t h 4} \end{matrix})

T_{c} = (\begin{matrix} T_{c 1} \\ T_{c 2} \\ T_{c 3} \\ \begin{array}{l} T_{c 4} \\ T_{c 5} \\ T_{c 6} \end{array} \end{matrix}) = 22 + 3.70 + (\begin{array}{cccccc} 83.17 & 15.40 & 13.76 & 13.41 & 14.51 & 15.34 \\ 16.80 & 82.49 & 14.70 & 13.90 & 14.87 & 13.88 \\ 13.60 & 14.80 & 83.14 & 14.91 & 14.01 & 12.95 \\ 13.18 & 14.22 & 13.96 & 70.71 & 15.03 & 13.54 \\ 14.06 & 14.92 & 13.96 & 14.73 & 83.13 & 14.90 \\ 14.96 & 14.12 & 13.08 & 13.39 & 15.11 & 83.07 \end{array}) (\begin{matrix} P_{t h 1} \\ P_{t h 2} \\ P_{t h 3} \\ \begin{array}{l} P_{t h 4} \\ P_{t h 5} \\ P_{t h 6} \end{array} \end{matrix})

\begin{array}{l} T_{c} = (\begin{matrix} T_{c 1} \\ T_{c 2} \\ T_{c 3} \\ \begin{array}{l} T_{c 4} \\ T_{c 5} \\ T_{c 6} \\ T_{c 7} \\ T_{c 8} \\ T_{c 9} \end{array} \end{matrix}) = 22 + 4.53 + \\ (\begin{array}{ccccccccc} 83.26 & 14.84 & 13.23 & 12.84 & 14.01 & 14.93 & 13.14 & 12.84 & 12.30 \\ 14.76 & 82.65 & 14.73 & 13.85 & 14.80 & 13.97 & 12.79 & 13.06 & 12.79 \\ 13.23 & 14.80 & 82.36 & 14.79 & 14.04 & 12.88 & 12.25 & 12.86 & 13.16 \\ 12.64 & 13.72 & 14.58 & 82.96 & 14.52 & 12.90 & 12.76 & 13.90 & 14.56 \\ 13.96 & 14.81 & 14.00 & 14.64 & 70.18 & 15.50 & 13.60 & 14.73 & 14.36 \\ 14.84 & 13.95 & 12.82 & 13.00 & 14.60 & 83.32 & 14.69 & 13.93 & 12.80 \\ 13.10 & 12.79 & 12.21 & 12.87 & 13.98 & 14.74 & 82.12 & 14.96 & 13.22 \\ 12.17 & 13.04 & 13.40 & 14.81 & 14.72 & 13.93 & 14.90 & 82.38 & 14.63 \\ 12.22 & 12.79 & 13.09 & 14.73 & 13.99 & 12.82 & 13.22 & 14.66 & 83.43 \end{array}) (\begin{matrix} P_{t h 1} \\ P_{t h 2} \\ P_{t h 3} \\ \begin{array}{l} P_{t h 4} \\ P_{t h 5} \\ P_{t h 6} \\ P_{t h 7} \\ P_{t h 8} \\ P_{t h 9} \end{array} \end{matrix}) \end{array}

S P D_{L E D} (λ) = a_{1} e x p [- 2 {(\frac{λ - {λ_{c}}_{1}}{w_{1}})}^{2}] + a_{2} e x p [- 2 {(\frac{λ - λ_{c 2}}{w_{2}})}^{2}]

S P D_{L E D} (λ) = b_{1} \frac{1 - \frac{1}{1 + e x p [- (λ - {λ_{c}}_{1}) / v_{1}]}}{1 + e x p [- (λ - {λ_{c}}_{1}) / u_{1}]} + b_{2} \frac{1 - \frac{1}{1 + e x p [- (λ - {λ_{c}}_{2}) / v_{2}]}}{1 + e x p [- (λ - {λ_{c}}_{2}) / u_{2}]}

S P D_{L E D} (λ) = \frac{2 a_{1}}{π} \times \frac{w_{1}}{4 (λ - {λ_{c}}_{1}) + {w_{1}}^{2}} + \frac{2 a_{2}}{π} \times \frac{w_{2}}{4 (λ - λ_{c 2}) + {w_{2}}^{2}}

z (I, T) = p_{1} + p_{2} I + p_{3} T + p_{4} I^{2} + p_{5} I T + p_{6} T^{2}

S P D_{A R R} (λ) = \sum_{i = 1}^{n} S P D_{L E D i} (λ)

Items	Descriptions
Thermal resistance of LED	From the junction to the PCB including the solder layer: 16 K/W
Thermal contact resistance	Between the underside of the LED and upside of PCB: 0.5 cm²·K/W

Materials	Density (g/cm³)	Thermal conductivity (W/cm·K)	Specific heat (J/g·K)
Air flow	/	2.563×10⁻⁴	1.004
PCB	3.89	1.109	0.454

Test samples	Means of prediction errors (%)	Variances of prediction errors
Sample LED1	1.78	1.19
Sample LED4	1.17	0.71
Sample LED6	2.03	0.87
Sample LED9	2.76	1.58

Factors	Schemes
Currents	From 40mA to 280mA with an interval of 20mA
PCB temperatures	From 20°C to 80°C with an interval of 10°C

SPD models	Means of R²	Variances of R²
Extended Gaussian SPD model	0.986061	0.003026
Extended Asym2sig SPD model	0.986359	0.002553
Extended Lorentzian SPD model	0.939333	0.006012

Spectral characteristic parameters	p₁	p₂	p₃	p₄	p₅	p₆	R²
b₁	-0.00015	2.61e-05	5.92e-06	-9.80e-09	-5.60e-08	-4.43e-08	0.9999
λ_c1	446.3	-0.0154	0.0175	2.85e-05	-4.28e-05	0.000210	0.9969
u₁	2.723	0.002938	0.01163	-1.89e-06	-6.74e-06	5.57e-05	0.9993
v₁	9.552	-0.01565	0.03463	2.57e-05	-7.94e-06	4.06e-05	0.9952
b₂	-1.28e-05	1.79e-05	3.04e-06	-1.04e-08	-2.96e-08	-3.02e-08	0.9999
λ_c2	565.4	-0.05124	0.08277	0.000154	-0.00051	0.000545	0.9808
u₂	45.9	-0.00757	0.02428	2.47e-05	-9.58e-05	-4.35e-05	0.956
v₂	51.87	0.01075	-0.02877	-4.49e-05	0.000177	-0.00025	0.9696

LED No.	b₁	λ_c1	u₁	v₁	b₂	λ_c2	u₂	v₂
1^st LED	0.00365	446.45	4.32	10.36	0.00252	563.61	45.62	51.07
2^nd LED	0.00364	446.47	4.33	10.39	0.00251	563.65	45.62	51.05
3^rd LED	0.00365	446.45	4.32	10.37	0.00252	563.62	45.62	51.06
4^th LED	0.00138	447.00	3.71	10.78	0.00100	567.58	46.45	50.49
5^th LED	0.00138	447.03	3.72	10.80	0.00100	567.65	46.46	50.46
6^th LED	0.00138	447.00	3.71	10.78	0.00100	567.58	46.45	50.49

Condition No.	Brief describes
Condition 1	Sample LED1: power-on with 65mA
Condition 2	Sample LED1: power-on with 125mA
Condition 3	Sample LED1: power-on with 185mA
Condition 4	Sample LED4: power-on with 65mA
Condition 5	Sample LED4: power-on with 125mA
Condition 6	Sample LED4: power-on with 185mA
Condition 7	Sample LED6: power-on with 65mA
Condition 8	Sample LED6: power-on with 125mA
Condition 9	Sample LED6: power-on with 185mA
Condition 10	Sample LED9: power-on with 65mA
Condition 11	Sample LED9: power-on with 125mA
Condition 12	Sample LED9: power-on with 185mA

Condition No.	Brief describes
Condition 1	Sample LED4: powering 1^st, 2^nd LED
Condition 2	Sample LED4: powering 1^st, 3^rd LED
Condition 3	Sample LED6: powering 1^st, 2^nd, 3^th LED
Condition 4	Sample LED6: powering 1^st, 3^rd, 5^th LED
Condition 5	Sample LED9: powering 1^st, 2^nd, 3^rd LED
Condition 6	Sample LED9: powering 1^st, 3^rd, 5^th, 7^th, 9^th LED
Condition 7	Sample LED9: powering 1^st, 2^nd, 3^rd, 4^th, 5^th, 6^th LED

Condition No.	Brief describes
Condition 1	Sample LED4: 1^st, 2^nd with 125mA; 3^rd, 4^th with 65mA
Condition 2	Sample LED4: 1^st, 2^nd with 185mA; 3^rd, 4^th with 65mA
Condition 3	Sample LED4: 1^st, 2^nd with 185mA; 3^rd, 4^th with 125mA
Condition 4	Sample LED6: 1^st, 2^nd, 3^rd with 125mA; 4^th, 5^th, 6^th with 65mA
Condition 5	Sample LED6: 1^st, 2^nd, 3^rd with 185mA; 4^th, 5^th, 6^th with 65mA
Condition 6	Sample LED6: 1^st, 2^nd, 3^rd with 185mA; 4^th, 5^th, 6^th with 125mA
Condition 7	Sample LED9: 1^st, 2^nd, 3^rd, 7^th, 8^th, 9^th with 125mA; 4^th, 5^th, 6^th with 65mA
Condition 8	Sample LED9: 1^st, 2^nd, 3^rd, 7^th, 8^th, 9^th with 185mA; 4^th, 5^th, 6^th with 65mA
Condition 9	Sample LED9: 1^st, 2^nd, 3^rd, 7^th, 8^th, 9^th with 185mA; 4^th, 5^th, 6^th with 125mA