發光二極體(Light-Emitting Diodes, LEDs)是以半導體材料製作成具p-n接面之結構，將電能轉換成光能的元件。隨著磊晶技術的提升，發光效率已接近取代傳統照明元件的水準，然而成本及散熱問題是其進ㄧ步普及的關鍵。封裝結構可以保護晶片和其他內部材料、提供有效的導光路徑、多樣化的造型設計，同時為熱量傳遞的重要途徑，而良好的熱管理，能夠確保元件具有穩定的光、電、機械性質與可靠度。
本文以商業軟體ANSYS模擬5 mm燈泡型 LED及3W三晶片白光LED之穩態溫度場與熱應力分佈；前者與文獻上的結果比對，確認數值模型的準確性，接著以最佳化設計理論中的反應曲面法(Response Surface Methodology, RSM)，透過實驗設計法和最小平方迴歸分析，建立元件熱阻與所選擇設計變數之近似數學模型，討論可以有效增加結構散熱能力的參數，結果顯示採用熱傳導係數較高的材料製作導線架、加寬導線架至一臨界值，以及較高的封膠，可以有效地降低其熱阻。
白光LED則以紅外線熱像儀量測表面溫度、與二極體接面溫度之理論值比較，以光學軟體TracePro模擬照度分佈，並根據多目標值函數最佳化的理論，討論能同時增進熱傳與光學特性的封裝結構，由分析結果可知增加金屬散熱片及矽樹脂之高度、減少介電層之厚度，可增進其散熱能力，而提高矽樹脂的厚度、增加透鏡的厚度及半徑使其接近半球狀，可提升亮度。

Light-emitting diodes (LEDs) convert electrical current into light based on electroluminescence phenomenon and p-n junction. With the rapid improvement in epitaxial growth, luminous efficacy of LEDs already exceeded that of traditional incandescent bulbs. However, cost-effective and heat dissipation issues are still the main problems needed to overcome. Thus excellent thermal management plays an important role in package designs.
In this study, the steady-state temperature distribution and the corresponding thermal stresses of packaged lamp type and high power RGB LEDs were investigated numerically via three-dimensional finite element analysis. For LED lamps, the results were compared with available literature. Then the simulation-based design optimization method, the response surface methodology (RSM), was used to achieve the optimum design. It can be found that the junction-to-ambient thermal resistance was reduced by increasing thermal conductivity of lead frame material, by increasing the height of encapsulation, and by widening the cathode no more than a critical value.
For high power RGB LED, the surface temperature distribution was measured by a noncontact infrared thermography system to verify the numerical results. The junction temperature was compared with the theoretical value. Moreover, optical simulation was performed to investigate the illumination of RGB LED. Thereafter multiobjective optimization was adopted to improve the thermal and optical performances. Thermal resistance can be reduced by thinning the dielectric layer, and increasing the thickness of heat sink and silicone. Illumination can be enhanced by using spherical lens and by increasing the height of silicone.

1.S. M. Sze, Semiconductor Devices: Physics and Technology, 2nd ed., John Wiley and Sons, New York, 2001.
2.S. Chhajed, Y. Xi, Y. L. Li, Th. Gessmann and E. F. Schubert, “Influence of junction temperature on chromaticity and color-rendering properities of trichromatic white-light sources based on light-emitting diodes,” Journal of Applied Physics, Vol. 97, pp. 054506-1~8, 2005.
3.E. F. Schubert and J. K. Kim, “Solid-State Light Sources Getting Smart,” Science, Vol. 308, pp. 1274-1278, 2005.
4.N. Narendran, Y. Gu, J. P. Freyssinier, H. Yu and L. Deng, “Solid-state lighting: Failure analysis of white LEDs,” Journal of Crystal Growth, Vol. 268, pp. 449-456, 2004.
5.http://www.cie.co.at/cie
6.E. F. Schubert, Light-Emitting Diodes, Cambridge University Press, Cambridge, 2003.
7.S. Nakamura, T. Mukai and M. Senoh, “Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes,” Applied Physics Letters, Vol. 64, pp. 1687-1689, 1994.
8.D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin and S. L. Rudaz, “Illumination With Solid State Lighting Technology,” IEEE Journal on Selected Topics in Quantum Electronics, Vol. 8, pp. 310-320, 2002.
9.S. Muthu, F. J. P. Schuurmans and M. D. Pashley, “Red, Green, and Blue LEDs for White Light Illumination,” IEEE Journal on Selected Topics in Quantum Electronics, Vol. 8, pp. 333-338, 2002.
10.A. H. Mueller, M. A. Petruska, M. Achermann, D. J. Werder, E. A. Akhadov, D. D. Koleske, M. A. Hoffbauer and V. I. Klimov, “Multicolor Light-Emitting Diodes Based on Semiconductor Nanocrystals Encapsulated in GaN Charge Injection Layers,” Nano Letters, Vol. 5, pp. 1039-1044, 2005.
11.許榮宗, “白光製作技術走勢,” 工業材料雜誌, Vol. 220, pp. 143-154, 2005.
12.M. R. Krames, M. O. Holcomb, G. E. Hofler, C. C. Coman, E. I. Chen, I. H. Tan, P. Grillot, N. F. Gardner, H. C. Chui, J. W. Huang, S. A. Stockman, F. A. Kish, M. G. Craford, T. S. Tan, C. P. Kocot, M. Hueschen, J. Posselt, B. Loh, G. Sasser and D. Collins, “High-power truncated-inverted-pyramid (AlxGa1-x)0.5In0.5P/GaP light-emitting diodes exhibiting >50% external quantum efficiency,” Applied Physics Letters, Vol. 75, pp. 2365-2367, 1999.
13.D. H. Kim, C. O. Cho, Y. G. Roh, H. Jeon, Y. S. Park, J. Cho, J. S. Im, C, Sone, Y. Park, W. J. Choi and Q. H. Park, “Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns,” Applied Physics Letters, Vol. 87, pp. 203508-1~3, 2005.
14.R. Windisch, C. Rooman, B. Dutta, A. Knobloch, G. Borghs, G. H. Dohler and P. Heremans, “Light-Extraction Mechanisms in High-Efficiency Surface-Textured Light-Emitting Diodes,” IEEE Journal on Selected Topics in Quantum Electronics, Vol. 8, pp. 248-255, 2002.
15.P. C. P. Chao, L. D. Liao and C. W. Chiu, “Design of a Novel LED Lens Cap and Optimization of LED Placement in a Large Area Direct Backlight for LCD-TVs,” Proceedings of SPIE, Vol. 6196, pp. 61960N-1~9, 2006.
16.M. Achermann, M. A. Petruska, S. Kos, D. L. Smith, D. D. Koleske and V. I. Klimov, “Energy-transfer pumping of semiconductor nanocrystals using an epitaxial quantum well,” Nature, Vol. 429, pp. 642-646, 2004.
17.O. Kückmann, “High power LED arrays: Special requirements on packaging technology,” Proceedings of SPIE, Vol. 6134, pp. 613404-1~8, 2006.
18.M. R. Krames, J. Bhat, D. Collins, N. F. Gardner, W. Götz, C. H. Lowery, M. Ludowise, P. S. Martin, G. Mueller, R. Mueller-Mach, S. Rudaz, D. A. Steigerwald, S. A. Stockman and J. J. Wierer, “High-power III-Nitride Emitters for Solid-State Lighting,” physica status solidi (a), Vol. 192, pp. 237-245, 2002.
19.W. C. Peng and Y.C. S. Wu, “High-power AlGaInP light-emitting diodes with metal substrates fabricated by wafer bonding,” Applied Physics Letters, Vol. 84, pp. 1841-1843, 2004.
20.F. S. Hwu, G. J. Sheu and J. C. Chen, “Thermal Modeling and Performance of LED Packaging for Illuminating Device,” Proceedings of SPIE, Vol. 6337, pp. 63371J-1~7, 2006.
21.L. Kim, J. H. Choi, S. H. Jang and M. W. Shin, “Thermal analysis of LED array system with heat pipe,” Thermochimica Acta, Vol. 455, pp. 21-25, 2007.
22.V. Schwegler, S. S. Schad, C. Kirchner, M. Seyboth, M. Kamp, K. J. Ebeling, V. E. Kudryashov, A. N. Turkin, A. E. Yunovich, U. Stempfle, A. Link, W. Limmer and R. Sauer, “Ohmic Heating of InGaN LEDs during Operation: Determination of the Junction Temperature and Its Influence on Device Performance,” physica status solidi (a), Vol. 176, pp. 783-786, 1999.
23.L. Kim, G. W. Lee, W. J. Hwang, J. S. Yang and M.W. Shin, “Thermal analysis and design of GaN-based LEDs for high power applications,” physica status solidi (c), Vol. 0, pp. 2261-2264, 2003.
24.W. J. Hwang, T. H. Lee, L. Kim and M. W. Shin, “Determination of junction temperature and thermal resistance in the GaN-based LEDs using direct temperature measurement,” physica status solidi (c), Vol. 1, pp. 2429-2432, 2004.
25.T. H. Lee, L. Kim, W. J. Hwang, C. C. Lee and M. W. Shin, “Thermal analysis of GaN-based LEDs using the finite element method and unit temperature profile approach,” physica status solidi (b), Vol. 241, pp. 2681-2684, 2004.
26.M. Arik, S. Weaver, C. Becker, M. Hsing and A. Srivastava, “Effects of Localized Heat Generations Due to the Color Conversion in Phosphor Particles and Layers of High Brightness Light Emitting Diodes,” ASME International Electronic Packaging Technical Conference and Exhibition, Hawaii, 2003.
27.H. Wu, K. Qian and Y. Luo, “Research on Temperature Distribution of GaN-based High Power LED,” International Forum on Semiconductor Lighting, pp. 54-58, Shenzen, 2004.
28.M. Shatalov, A. Chitnis, P. Yadav, Md. F. Hasan, J. Khan, V. Adivarahan, H. P. Maruska, W. H. Sun and M. A. Khan, “Thermal analysis of flip-chip packaged 280 nm nitride-based deep ultraviolet light-emitting diodes,” Applied Physics Letters, Vol. 86, pp. 201109-1~3, 2005.
29.胡凡勳, 許國君, 周漢源, 鄭健宏, 陳志臣, “高功率LED之熱場模擬與封裝分析,” 中華民國第29屆全國力學會議, pp. L011-1~8, 新竹市, 12月16-17日, 2005.
30.M. Arik and S. Weaver, “Effect of chip and bonding defects on the junction temperatures of high-brightness light-emitting diodes,” Optical Engineering, Vol. 44, pp. 111305-1~8, 2005.
31.N. A. A. Karim, P. A. A. Narayana and K. N. Seetharamu, “Thermal analysis of LED package,” Microelectronics International, Vol. 23, pp. 19-25, 2006.
32.游晶瑩,昝世蓉, “發光二極體之熱傳分析,” 工業材料雜誌, Vol. 237, pp. 99-108, 2006.
33.L. Q. Yang, S. H. Jang, W. J. Hwang and M. W. Shin, “Thermal analysis of high power GaN-based LEDs with ceramic package,” Thermochimica Acta, Vol. 455, pp. 95-99, 2007.
34.P. P. Maaskant, M. Akhter, N. Cordero, D. P. Casey, J. F. Rohan, B. J. Roycroft and B. M. Corbett, “LED flip-chip assembly with electroplated AuSn alloy,” physica status solidi (c), Vol. 2, pp. 2907-2911, 2005.
35.C. Tsou, Y. S. Huang and G. W. Lin, “Silicon-based Packaging Platform for Light Emitting Diode,” IEEE 6th International Conference on Electronic Packaging Technology, 2005.
36.J. Hu, L. Yang, W. J. Hwang and M. W. Shin, “Thermal and mechanical analysis of delamination in GaN-based light-emitting diode packages,” Journal of Crystal Growth, Vol. 288, pp. 157-161, 2006.
37.H. Luo, J. K. Kim, E. F. Schubert, J. Cho, C. Sone and Y. Park, “Analysis of high-power packages for phosphor-based white-light-emitting diodes”, Applied Physics Letters , Vol. 86, pp. 243505-1~3, 2005.
38.C. M. Chang, Y. C. Fang and C. R. Lee, “A new design mixing R.G.B. LED (Red, Green, Blue Light Emitting Diode) for a modern LCD (Liquid Crystal Display) backlight system,” Proceedings of SPIE, Vol. 6338, pp. 63380Q-1~11, 2006.
39.S. J. Lee, “Study of photon extraction efficiency in InGaN light-emitting diodes depending on chip structures and chip-mount schemes,” Optical Engineering, Vol. 45, pp. 014601-1~14, 2006.
40.L. Xu, T. Reinikainen, W. Ren, B. P. Wang, Z. Han and D. Agonafer, “A simulation-based multi-objective design optimization of electronic packages under thermal cycling and bending,” Microelectronics Reliability, Vol. 44, pp. 1977-1983, 2004.
41.H. C. Cheng, W. H. Chen and I C. Chung, “Integration of Simulation and Response Surface Methods for Thermal Design of Multichip Modules,” IEEE Transactions on Components and Packaging Technologies, Vol. 27, pp. 359-372, 2004.
42.H. T. Chen, P. L. Chen, J. T. Horng and Y. H. Hung, “Design Optimization for Pin-Fin Heat Sinks,” ASME Journal of Electronic Packaging, Vol. 127, pp. 397-406, 2005.
43.J. H. Lienhard IV and J. H. Lienhard V, A Heat Transfer Textbook, 3rd ed., Phlogiston Press, Cambridge, 2003.
44.沈信安, 四方扁平薄型電子構裝(TQFP)之散熱效能分析, 國立清華大學動力機械工程學系碩士論文, 2001.
45.G. N. Ellison, Thermal Computations for Electronic Equipment, R. E. Krieger Publishing Company, Malabar, 1989.
46.M. Aghazadeh and D. Mallik, “Thermal Characteristic of Single and Multilayer High Performance PQFP packages,” IEEE Transactions on Components, Hybrids, and Manufacturing Technology-Part A, Vol. 13, pp. 975-979, 1990.
47.S. Mulgaonker, B. Chambers, M. Mahalingam, G. Ganesan, V. Hause and H. Berg, “Thermal Performance Limits of the QFP Family,” IEEE Transaction on Components, Packaging, and Manufacturing Technology-Part A, Vol. 17, pp. 573-581, 1994.
48.D. R. Edwards, M. Hwang and B. Stearns, “Thermal Enhancement of Plastic IC Packages,” IEEE Transactions on Components, Packaging, and Manufacturing Technology-Part A, Vol. 18, pp. 57-67, 1995.
49.G. Ridsdale, B. Joiner, J. Bigler and V. M. Torres, “Thermal simulation to analyze design features of plastic quad flat packages,” International Journal of Microcircuits and Electronic Packaging, Vol. 19, pp. 103-109. 1996.
50.W. H. Chen, H. C. Cheng and H. A. Shen, “An Effective Methodology for Thermal Characterization of Electronic Packaging,” IEEE Transactions on Components and Packaging Technologies, Vol. 26, pp. 222-232, 2003.
51.G. R. Blackwell, The Electronic Packaging Handbook, CRC Press, Boca Raton, 2000.
52.R. Remsburg, Thermal Design of Electronic Equipment, CRC Press, Boca Raton, 2001.
53.Release 10.0 Documentation for ANSYS, 2005.
54.R. D. Cook, D. S. Malkus, M. E. Plesha and R. J. Witt, Concepts and Applications of Finite Element Analysis, 4th ed., John Wiley and Sons, NewYork, 2002.
55.A. Link, K. Bitzer, W. Limmer, R. Sauer, C. Kirchner, V. Schwegler, M. Kamp, D. G. Ebling and K. W. Benz, “Temperature dependence of the E2 and A1(LO) phonons in GaN and AlN,” Journal of Applied Physics, Vol. 86, pp. 6256-6260, 1999.
56.J. H. Cho, C. S. Sone, Y. J. Park and E. J. Yoon, “Measuring the junction temperature of III-nitride light emitting diodes using electro-luminescence shift,” physica status solidi (a), Vol. 202, pp. 1869-1873 ,2005.
57.Y. Xi, J. Q. Xi, Th. Gessmann, J. M. Shah, J. K. Kim, E. F. Schubert, A. J. Fischer, M. H. Crawford, K. H. A. Bogart and A. A. Allerman, “Junction and carrier temperature measurements in deep-ultraviolet light-emitting diodes using three different methods,” Applied Physics Letters, Vol. 86, pp. 031907-1~3, 2005.
58.EIA/JESD51-1, “Integrated Circuits Thermal Measurement Method - Electrical Test Method (Single Semiconductor Device),” JEDEC Standard, December, 1995.
59.Y. Gu and N. Narendran, “A non-contact method for determining junction temperature of phosphor-converted white LEDs,” Proceedings of SPIE, Vol. 5187, pp. 107-114, 2004.
60.B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, John Wiley and Sons, New York, 1991.
61.“TracePro”, Version 3.3.7, Lambda Research Corporation, Littleton, 2006.
62.R. L. Mason, R. F. Gunst and J. L. Hess, Statistical Design and Analysis of Experiments with Applications to Engineering and Science, 2nd ed., John Wiley and Sons, New York, 2003.
63.W. D. van Driel, G. Q. Zhang, J. H. J. Janssen and L. J. Ernst, “Response Surface Modeling for Nonlinear Packaging Stresses,” ASME Journal of Electronic Packaging, Vol. 125, pp. 490-497, 2003.
64.H. T. Chen, J. T. Horng, P. L. Chen and Y. H. Hung, “Optimal Design for PPF Heat Sinks in Electronics Cooling Applications,” ASME Journal of Electronic Packaging, Vol. 126, pp. 410-422, 2004.
65.G. E. P. Box and D. W. Behnken, “Some New Three Level Designs for the Study of Quantitative Variables,” Technometrics, Vol. 2, pp. 455-476, 1960.
66.B. P. Wang, Z. X. Han, L. Xu and T. Reinikainen, “A Novel Response Surface Method for Design Optimization of Electronic Packages,” IEEE 6th International Conference on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-System, 2005.
67.D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers, 3rd ed., John Wiley and Sons, New York, 2002.
68.R. T. Haftka and G. M. L. Gladwell, Elements of Structural Optimization, 3rd ed., Kluwer Academic Publishers, Dordrecht, 2002.
69.W. Stadler, “Natural Structural Shapes of Shallow Arches,” Journal of Applied Mechanics, Vol. 44, pp. 291-298, 1977.
70.C. A. Coello and A. D. Christiansen, “Multiobjective optimization of trusses using genetic algorithms,” Computers and Structures, Vol. 75, pp. 647-660, 2000.
71.A. Kurpati, S. Azarm and J. Wu, “Constraint handling improvements for multiobjective genetic algorithms,” Structural and Multidisciplinary Optimization, Vol. 23, pp. 204-213, 2002.
72.“Matlab”, Version 7.3, The MathWorks, Incorporated, Natick, 2006.
73.EIA/JESD51, “Methodology for the Thermal Measurement of Component Packages (Single Semiconductor Device),” JEDEC Standard, December, 1995.
74.EIA/JESD51-3, “Low Effective Thermal Conductivity Test Board for Leaded Surface Mount Packages,” JEDEC Standard, December, 1995.
75.EIA/JESD51-2, “Integrated Circuits Thermal Test Method Environment Conditions -Natural Convection (Still Air),” JEDEC Standard, December, 1995.
76.M. G. Pecht, R. Agarwal, P. McCluskey, T. Dishongh, S. Javadpour and R. Mahajan, Electronic Packaging Materials and Their Properties, CRC Press, Boca Raton, 1998.
77.C. Zweben, “New material options for light-emitting diode packaging,” Proceedings of SPIE, Vol. 5366, pp. 173~182, 2004.
78.J. K. Park, H. D. Shin, Y. S. Park, S. Y. Park, K. P. Hong and B. M. Kim, “A Suggestion for High Power LED Package Based on LTCC,” IEEE Electronic Components and Technology Conference, pp. 1070-1075, 2006.
79.黃歆斐, 周榮華, “高功率LED封裝之熱分析,” 中華民國第30屆全國力學會議, 彰化縣, 12月15-16日, 2006.
80.http://www.dowcorning.com
81.Private communication.
82.L. Yang, J. Hu, L. Kim and M. W. Shin, “Variation of thermal resistance with input power in LEDs,” physica status solidi (c), Vol. 3, pp. 2187-2190, 2006.
83.http://www.uqgoptics.com/pdf/Schott%20BK7.pdf