Photo-Electro-Thermal Theory with Bidirectional Thermal Model

CHEN Huan-ting, LIN Shuo, HUANG Jun-xin, ZHOU Jin-rong, HE Zhong-quan， GAO Xi-qi

(1. College of Physics and Information Engineering, Minnan Normal University, Zhangzhou 363000, China;2. Fujian State Key Laboratory of LED Display and Lighting, Fushun Optoelectronics Science andTechnology Co., Ltd., Zhangzhou 363000, China;3. School of Information Science and Engineering, Southeast University, Nanjing 210000, China)



Photo-Electro-Thermal Theory with Bidirectional Thermal Model

CHEN Huan-ting1,2,3*, LIN Shuo1, HUANG Jun-xin1, ZHOU Jin-rong1, HE Zhong-quan2， GAO Xi-qi3

(1.CollegeofPhysicsandInformationEngineering,MinnanNormalUniversity,Zhangzhou363000,China;2.FujianStateKeyLaboratoryofLEDDisplayandLighting,FushunOptoelectronicsScienceandTechnologyCo.,Ltd.,Zhangzhou363000,China;3.SchoolofInformationScienceandEngineering,SoutheastUniversity,Nanjing210000,China)

An estimation method for the junction temperature of LED devices based on bidirectional thermal model was proposed in this paper. The bidirectional thermal model obtained in thermal measured procedure was applied to the original PET theory to predict the luminous flux. For the junction temperature, the average deviation between the unidirectional model and the measurement is about 11.2% and that between the bidirectional model and the measurement is 5.3%. For luminous flux, the average deviation between the PET theory with bidirectional model and the measurement is 6.3%. The calculated results are in good agreement with the measurements. These results confirm that the PET theory with bidirectional thermal model can provide accurate predictions for luminous flux.

light-emitting diode; photo-electro-thermal theory; bidirectional thermal model; junction temperature; luminous flux

1 Introduction

As the demands for light output increase, the driving power of the LED package increases continuously. The thermal management of LED package, which has great effect on electrical characterization and reliability, has become more and more important for these devices. The accurate prediction of junction temperature is limited by unidirectional thermal model for a variety of boundary conditions. This characterization usually consists of the junction-to-case or junction-to-ambient thermal resistance measured according to JEDEC51-1[1]. The unidirectional thermal model could not accurately describe the practical heat distribution in package[2-3]. Since LED modules can be used in various application situations, the junction temperature will be different for the same LED module if the heatsink is different. The thermal model can use an equivalent convective boundary condition to eliminate the effects of different application situations[4]. It could not accurately obtain the junction temperature. The interactions of photometric, electrical and thermal aspects have been described mathematically in a photo-electro-thermal (PET) theory[5-7]for LED systems. The PET theory can be used to optimize the design of an LED system and determine the operating point of maximum luminous flux per Watt. It can also be used to set criteria for the optimal thermal design for the appropriate heatsink for a given application. In addition, junction temperature is a critical parameter and affects luminous efficacy, maximum light output and reliability[8-14]. For the flat LED package with relatively large surface area, the heat flow from the device junction to the ambient through the silicone cover cannot be ignored[1]. This means that the bidirectional heat flow on both sides of the flat LED package should be considered. In fact, it will be shown that if such bidirectional heat flow is included, the theoretical prediction of the junction temperature and thus the luminous output would be much more accurate.

In this paper, the PET theory is extended with the use of bidirectional thermal model to determine the accurate junction temperature that is required in the theory. A fast measurement procedure consisting of a simple thermal measurement based on the use of the T3ster system is illustrated. Based on this procedure, bidirectional thermal model can extract the junction temperature that cannot be easily accessed in practice. The parameters obtained in this fast procedure are applied to the original PET theory to accurately predict the luminous flux.

2 Photo-Electro-Thermal Theory Based on Bidirectional Thermal Model

2.1 Bidirectional Thermal Model

The heat generated by the active layer of LED is first conducted to the heat sinkviasapphire, and then to MCPCB. In the end, heat is dissipated out to the ambient air by convection. Strictly speaking, heat flow from the device junction to the ambient through the silicone cover cannot be ignored. Therefore, two heat flow paths can be considered.

Fig.1(a) shows the heat flow path for unidirectional thermal model. The heat flow from the junction to the heatsink and then heatsink to the ambient can be respectively represented by the junction-to-case thermal resistanceRjcand the heatsink thermal resistanceRhs. Fig.1(b) shows the heat flow paths for bidirectional thermal model. The heat flow from the junction to the silicone cover should be included. For LED, the heat flow path is represented by the thermal resistanceRsiliconeas shown in Fig.1(b).

Fig.1 Unidirectional thermal model (a) and bidirectional thermal model (b) of LED

The model in Fig.1(b) will be used to demonstrate the heat trapping effects of the encapsulation layers in the flat LED package.

Based on the above unidirectional and bidirectional thermal model, the equivalent thermal resistance for LED can be expressed as

(1)

(2)

Where,Rjc,uis equivalent thermal resistance of unidirectional thermal model,Rjc,bis equivalent thermal resistance of bidirectional thermal model.

2.2 Junction Temperature

Based on the unidirectional and bidirectional thermal model described above, the thermal model for the LED can be expressed as

(3)

(4)

Where,Ruprefers to the total thermal resistance in the heat flow path from the junction through the surface of the LED package to the ambient, andRdownrefers to the total thermal resistance from the junction through the heatsink to the ambient. Based on Eq. (1) to (4), the junction temperatureTj,uandTj,bfor the unidirectional and bidirectional thermal model can be rewritten as

(5)

(6)

2.3 Photo-Electro-Thermal Theory

The total luminous fluxφvof a system consisting ofNLED devices can be expressed as

(7)

(8)

Where,Pdis electrical power,Eis luminous efficacy,keis a measure of the droop characteristic of the luminous efficacy with junction temperature,E0is the rated efficacy at the rated temperatureT0(typically 25 ℃ in some LED data sheets)[5-6].

Based on the junction temperature expression for Eq.(5) and (6), the luminous flux for unidirectional and bidirectional thermal model can be expressed as

(9)

(10)

The heat dissipation coefficientkhrepresents the portion of LED power that is dissipated as heat. It is related to the optical power and wall-plug efficiency that can be measured by combined thermal and radiometric measurement equipment. Therefore, it can be determined that lighting devices will generate more heat than the others by using comparing thekhfactor.

Several important observations can be made from Eq.(10):

(ⅰ)Eq.(10) relates the luminous fluxφvto the electrical powerPd, the thermal resistance of the heatsinkRhs, the deviceRjc, and the packageRsilicone. It is a model that integrates the photometric, electrical, thermal and package aspects of the LED system altogether.

3 Experimental Process

Luxeon K2 3WLED is mounted on heatsink. The optical measurements of the LED samples are performed under steady-state thermal and electrical conditions using the PMS-50 spectro-photocolorimeter with an integrating sphere (measured after 20 min of operation at different electrical power levels and at an ambient temperature of 20 ℃). The T3ster captures the thermal transient response in real time, records the cooling/heating curve, and then evaluates the cooling/heating curves for plotting the thermal characteristics. The heating current for the samples is 0.4 A and the heating/cooling time is 20 min. The measured current is 5 mA. The thermal resistance of the LED package could be extracted using the thermal structure function, which is based on the distribution RC networks[15-16]. The Peltier-cooled fixture was used to stabilize the LED temperature for the optical and electrical measurements and it also served as an actively temperature-controlled cold-plate.

4 Experimental Verification

Using the T3ster LED measurement system, the thermal resistance values of the LED samples (ⅰ) without silicone cover, (ⅱ) with silicone cover are measured. The total equivalent thermal resistance for the two samples (ⅰ) blue LED without silicone coverRjc,b′, (ⅱ) blue LED with silicone coverRjc,bare recorded in Fig.2. It is noted thatRjc,bis smaller thanRjc,b′because there is no silicone coating which generates and traps heat when the diode is in operation. Based on the thermal equivalent circuits in Fig.1 and Eq.(1) to (2), it can be found thatRsiliconeis about 35.4 ℃/W using by the measured results of Fig.2.

Fig.2 Thermal resistance and capacitance of the two samples (Blue LED without silicone package, blue LED with silicone package).

The coefficientkedefined in the PET theory is a measure of the droop characteristic of the luminous efficacy with junction temperature and is physically related to the characteristic temperature

(11)

Fig.3 shows the measured luminous efficacy of the LED sample with junction temperature. The luminous flux of the LED samples decrease with increasing junction temperature. By fitting the measured curve into the form of (8), thekeof the LED devices is -0.001 88 lm/(W·℃). The characteristic temperatureT1of the LED samples can be calculated by Eq.(11), which is 532 ℃. When projected to 25 ℃, the luminous efficacyEoof the LED sample is 22 lm/W.

Fig.3 Measured luminous efficacyversusjunction temperature

According to Fig.1, the bidirectional thermal resistance model is compared with the traditional unidirectional thermal resistance model. The LED samples are tested on two different heatsinks. The theoretical junction temperature of LED samples can be calculated based on unidirectional thermal model and bidirectional thermal model, as shown in Eq.(5) and (6). Fig.4 and Fig.5 show the theoretical values of the junction temperature of the LED sample based on the unidirectional and bidirectional models, respectively. The corresponding practical measurements are also plotted in the figures. While both models give the correct trend of the characteristics, the bidirectional thermal model offers a more accurate prediction than the unidirectional model. It can be seen that the bidirectional thermal model, which includes the heat flow through the surface area of the LED sample, offers a better prediction than the unidirectional model. The average deviation between the unidirectional model and the measurement is about 11.2% and that between the bidirectional model and the measurement is 5.3%. Therefore, the results in Fig.4 and Fig.5 confirm the validity of the bidirectional thermal model.

Fig.4 Calculated and measured junction temperatureversuselectrical power of LED based on unidirectional thermal model

Fig.5 Calculated and measured junction temperatureversuselectrical power of LED based on bidirectional thermal model

Based on Eq.(9) and (10), the calculated luminous flux curves are plotted along with the measured flux as functions of the electrical power in Fig.6. The required parameters of LED system are shown in following. With the electrical power of 0.45-2.26 W,E0is 22 lm/W at the junction temperature of 25 ℃,khandkeare related to the junction temperature and electrical power[6,13],khis from 0.52 to 0.63,keis from -0.001 9 to -0.002 8, N is 3.

Based on Eq.(9) and (10), the calculated luminous flux curves are plotted along with the measurements in Fig.6 and Fig.7 based on the unidirectional and bidirectional models, respectively. It can be seen that the PET theory with bidirectional thermal model offers a better prediction than the unidirectional model. The average deviation between the PET theory with unidirectional model and the measurement is about 10.8% and that between the bidirectional model and the measurement is 6.3%. The calculated results are in good agreement with the measurements. These results confirm that the PET theory with bidirectional thermal model can provide accurate predictions for luminous flux. The proposed model is a multi-physical one that provides physical insights for researchers and manufacturers. It can be used for analyzing the performance of LED structures in the context of a system, incorporating the interactions of heat, light and power.

Fig.6 Calculated and measured luminous fluxversuselectrical power of LED based on unidirectional thermal model

Fig.7 Calculated and measured luminous fluxversuselectrical power of the blue LED based on bidirectional thermal model

5 Conclusion

An estimation method for the junction temperature of LED devices based on bidirectional thermal model is proposed in this paper. The bidirectional thermal model obtained in thermal measured procedure is applied to the original PET theory to predict the luminous flux. The estimation method presented in this paper extends the original PET theory to covering luminous fluxφv, the electrical powerPd, the thermal resistance of the heatsinkRhs, the deviceRjc, and the packageRsilicone. It is a model that integrates the photometric, electrical, thermal and package aspects of the LED system altogether. It is envisaged that the extended theory can be used as a design tool for LED system designs.

[1] CHEN H T, LU Y J, GAO Y L,etal.. The performance of compact thermal models for LED package [J].Thermochim.Acta, 2009, 488(1-2):33-38.

[2] HUANG W, STAN M R, SKADRON K. Parameterized physical compact thermal modeling [J].IEEETrans.Compon.Packag.Technol., 2005, 28(4):615-621.

[3] SABRY M N. Compact thermal models for electronic systems [J].IEEETrans.Compon.Packag.Technol., 2003, 26(1):179-185.

[4] LUO X, MAO Z, YANG J,etal.. Engineering method for predicting junction temperatures of high-power light-emitting diodes [J].IETOptoelectron., 2012, 6(5):230-236.

[5] HUI S Y, QIN Y X. A general photo-electro-thermal theory for light emitting diode (LED) systems [J].IEEETrans.PowerElectron., 2009, 24(8):1967-1976.

[6] CHEN H T, TAO X H, HUI S Y R. Estimation of optical power and heat-dissipation coefficient for the photo-electro-thermal theory for LED systems [J].IEEETrans.PowerElectron., 2012, 27(4):2176-2183.

[7] CHEN H T, HUI S Y. Dynamic prediction of correlated color temperature and color rendering index of phosphor-coated white light-emitting diodes [J].IEEETrans.Ind.Electron., 2014, 61(2):784-797.

[8] 李艳菲,张方辉,张静. 大功率LED的电流老化特性分析 [J]. 发光学报, 2012, 33(11):1236-1240. LI Y F, ZHANG F H, ZHANG J. The accelerated aging characterization of high power LED [J].Chin.J.Lumin., 2012, 33(11):1236-1240. (in Chinese)

[9] 黄马连,陈焕庭,周小方,等. 利用相关色温和光通量优化白光LED光谱 [J]. 光子学报, 2015, 44(10):1030001-1-7. HUANG M L, CHEN H T, ZHOU X F,etal.. Optimization spectrum of white light emitting diodes based on correlated color temperature and luminous flux [J].ActaPhoton.Sinica, 2015, 44(10):1030001-1-7. (in Chinese)

[10] 汤英文,熊传兵,井晓玉. 量子垒结构对Si衬底GaN基绿光LED光电性能的影响 [J]. 发光学报, 2016, 37(3):327-331. TANG Y W, XIONG C B, JING X Y. Effect of quantum barrier structures on photoelectric properties of GaN-based green LED on si substrates [J].Chin.J.Lumin., 2016, 37(3):327-331. (in Chinese)

[11] CHEN H T, LIN D Y, TAN S C,etal.. Chromatic, photometric and thermal modeling of LED systems with nonidentical LED devices [J].IEEETrans.PowerElectron., 2014, 29(12):6636-6647.

[12] HAYASHI H, FUKUSHIMA D, NOMA T,etal.. Thermally engineered flip-chip InGaN/GaN well-ordered nanocolumn array LEDs [J].IEEEPhotonicsTechnol.Lett., 2015, 27(22):2343-2346.

[13] CHEN H T, TAN S C, HUI S Y R. Analysis and modeling of high-power phosphor-coated white light-emitting diodes with a large surface area [J].IEEETrans.PowerElectron., 2015, 30(6):3334-3344.

[14] 蔡嘉毅,陈焕庭,周小方,等. 三维空间下混合白光LED系统照度模型 [J]. 发光学报, 2015, 36(9):1088-1093. CAI J Y, CHEN H T, ZHOU X F,etal.. Illumination model of mixed white light-emitting diode system with three-dimensional conditions [J].Chin.J.Lumin., 2015, 36(9):1088-1093. (in Chinese)

[15] POPPE A, ZHANG Y, WILSON J,etal.. Thermal measurement and modeling of multi-die packages [J].IEEETrans.Compon.Packag.Technol., 2009, 32(2):484-492.

[16] SZÉKELY V. A new evaluation method of thermal transient measurement results [J].Microelectro.J., 1997, 28(3):277-292.

陈焕庭(1982-)，男，福建漳州人，博士，副教授，2010年于厦门大学获得博士学位，主要从事半导体照明技术的研究。

E-mail: htchen23@163.com

2016-05-19；

2016-06-21

国家自然科学基金(61307059)；中国博士后面上基金(2015M592075)； 福建省自然科学基金杰出青年项目(2016J06016)； 福建省高校新世纪优秀人才支持计划； 福建省区域重大项目(2015I1007)资助

基于双向热阻模型的光电热一体化理论

陈焕庭1,2，3*， 林 硕1， 黄俊鑫1， 周锦荣1, 何仲全2， 高西奇3

(1. 闽南师范大学 物理与信息工程学院， 福建 漳州 363000；2. 福建省LED显示屏及LED照明重点实验室 富顺光电科技股份有限公司， 福建 漳州 363000；3. 东南大学 信息科学与工程学院， 江苏 南京 210000)

通过双向热阻模型描述LED系统内部双向散热路径，进而构建光电热一体化模型。基于双向热阻模型参数，光电热一体化模型可高精度预测LED系统的结温以及光通量。实验验证结果表明，基于所提出的双向热阻模型的结温计算值和实验值的平均误差在5.3%之内，而采用传统的单向热阻模型的结温计算值和实验值的平均误差达到11.2%。基于双向热阻模型的光电热一体化理论，光通量的计算值与实验值的平均误差在6.3%之内。

LED； 光电热一体化理论； 双向热阻模型； 结温； 光通量

1000-7032(2016)11-1378-06

TN312+.8 Document code： A

10.3788/fgxb20163711.1378

*CorrespondingAuthor,E-mail:htchen23@163.com