Thermal Conductivity of Electric Molding Composites Filled with β-si 3 N 4
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1 22 Ê 6  ŠVol. 22, No à Journal of Inorganic Materials Nov., 2007 Ð ¹: X( β-si 3 N 4 / ¾Ú Đ Â ÉÓÅÖ ¼» 1, ³ º 1, µ² 2, ¹ 3 (1. ÅƱ ; ; 3. «« Û«º β-si 3N 4 ² ¼ SiO 2 Ý Ó ÑÕ ÛÄ Æ Í Áß Ò β-si 3N 4 SiO 2 Ó Ó ÛÄݱ µ «β-si 3N 4 Ù Ó ÛÄݱ Ø Ê Þ 50vol% β-si 3N 4 Ê Ó ÄÛ SiO 2 Ê Ó À 3.8 ºÈ ß Ó ÄÛ Õ ÏßÒ Ê Ó Ê Ó Agari ÄÛ Õµ Ò Ë «β-si 3N 4; Û Æ ÄÛ ± ¹«TB383 ÏÀ«A Thermal Conductivity of Electric Molding Composites Filled with β-si 3 N 4 ZHU Yuan 1, CHEN Ke-Xin 1, JIN Hai-Bo 2, FU Ren-Li 3 (1. State Key of New Ceramics and Fine Processing, Department of Materials Science & Engineering, Tsinghua University, Beijing , China; 2. Discipline of Materials Science & Engineering, Beijing Institute of Technology, Beijing , China; 3. Discipline of Materials Science & Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing , China Abstract: New electric molding composites were fabricated with hybridizing epoxy and β-si 3 N 4 instead of silica. The thermal conductivity of composites filled with β-si 3 N 4 was compared with that co-filled with β-si 3 N 4 and SiO 2. The results demonstrate that the thermal conductivity of the composite increases obviously with the increasing of β-si 3 N 4 content. Thermal conductivity of β-si 3 N 4 -filled composite is about 3.8 times as large as that of SiO 2 -filled one when the additional volume fraction achieves to 50%. Based on the experimental results, the discussion of calculating model for predicting thermal conductivity of composites shows that Agari model is more applicable to predict the thermal conductivities of β-si 3 N 4 filled and β-si 3 N 4 /SiO 2 co-filled composites. Furthermore, a common expression of Agari model for co-filled composites and its parameters are given. Key words: β-si 3 N 4 ; SiO 2 ; electric molding composite; thermal conductivity 1 Ý Æ» ±Í ÅÆ Å Æ Â Â½± ß³ Ë ÅÜ Å»ÏÌ ÆÌ ÑÅÁ ß ÏÅ ß³ Ë ß³Ñ Ü [1] Ü [2] ÌÇ , Ôµ ÌÇ Ä [3] Ôܺ [4] ÔÜ [5,6] Ü [6] [7] Ü Ï [8] ÔÜ Ï [9,10] ѼÓÏ / Ï [11] Þ» ÅÔÇ Ì ÑÑÏ Ò AlN BN Ñ Ú ÜÅß³ Ö± Ü» ß Al 2 O 3 Ñ SiO 2 ³ à  ( ß (1983, Ö Â Õ Ë Ã Ò Â kxchen@mail.tsinghua.edu.cn
2 1202  Š22 Ê ± ±» Ö Al 2 O 3 Ñ SiO 2 ÅÜ ¾ ³ Æ Û ±Í ÜÅß³ Å Ã β-si 3 N 4 Ó É 320W/m K ÅÜ [12], ÔÜ É AlN  ÆÀ Å»ÏÌ Ù Ü Á ßÑ Å ß ÆÛ Ü «ÔÅ ²³ º β-si 3 N 4 Å ³ β-si 3 N 4 Å Ó ÐÆ Ã» β-si 3 N 4 SiO 2 Þ Û Ô ÔÓÖÆ Ó Ë β-si 3 N 4 β-si 3 N 4 SiO 2 Ô Ë (ºÓ Ë Ô Ã Æ ÜÅß³Û Å ÅÜ Å»Ï ÑÉ Î ¾ ³ ¹ Ó Ë ÝIJ Ö ³»É Ë º Ó Ë ± Ì ³¹ Ä ³ Ñ É Ò Ä Maxwell Ñ Agari Û Ô Ü Å Ö Ó Ë Ô Ú» ß Û ¾» ºÓ Ë Ô ÅÜ Ö ÓÖÆ Å 2 ÎÙ ÅÃÑ ÆÒ» ¼ A Ö QSF Þ Þ ÙÝ 364, Ä ½ ß ÉÜ Ù Åà ŠÉÜ ÉÜ ÙÝ 182, Ð ½» β-si 3 N 4 ( ÆÛ Ñ SiO 2 ± ( Ä Ç. ß ³ 1. β-si 3 N 4 Ñ SiO 2 ± SEM ½Ë 1 2 Õ β-si 3 N 4 Â Ü Ñ± É ¾  SiO 2 Ê ¼Ù ± ÍÞ ±» Å Þ ÉÜ ÎÆ Ô ß ¹ Ý ÉÜ Ö ÃÅÈ φ12.5mm 1mm ½ÖÞ 1 ß ÒÄ Table 1 Properties of raw materials Raw material Epoxy Silica β-si 3N 4 Density/g cm Thermal conductivity 1 /W m 1 K β-si 3N 4 ÎØ Fig. 1 Micrograph of β-si 3N 4 powder 2 SiO 2 ÎØ Fig. 2 Micrograph of silica powder л Ï Ì ² Ï Þ Å Ï Þ ÅÜ ÀÇÓ (1 Û λ = 100 α ρ C p (1 ÓÒ λ ÅÜ (W/m K; α Å Ï (cm 2 /s; C p ÅÉ (J/g K; ρ (g/cm 3. ¾» ² Ý Ô ÅÜ ½Ü Å»Ï «ÅÉÐÝ Á Î ß C P = ÅÉ n ω i Cp i (2 i=1 Ò ω i «ÐÝ C i p «ÅÉ Ô A B Û«¹ Û É ± ¹ Ë 2 Õ A «Ó Ë β-si 3 N 4 Ô B «β-si 3 N 4 Ñ SiO 2 Ô Ë Ô ºÓ Ë Ô 3 ÎÙ º 3.1 ½ Ê 3 A «Ó Ë β-si 3 N 4 Ô ÅÜ β-si 3 N 4 ± ÍÌ Ò Ô ÅÜ β-si 3 N 4 Ë Ì
3 6 Þ «β-si 3N 4/ Ý Æ ÛÄݱ Á ³¼ ÍØÆ Table 2 Components of composites No. A B A1 A2 A3 A4 A5 B1 B2 B3 B4 B5 B6 Composition SiO /vol% β-si 3N ¾ 4 β-si 3 N 4 SiO 2 Đ Ò µ É Ò Ð Đ Ã Ú «Ý µé«(50vol% ¾ ² µé Ñ β-si 3 N 4 ĐË Ò Ð ĐÃÚ««Ë ¾ 4 Ñß ÏÎ µ É «Ì 50vol% β-si 3 N 4 Đ Ñ µ É Ò Ð Đ Ã Ú «Ñ µ É SiO 2 Đ 3.8 Ã Ú «Ø Đ ²Ç β-si 3 N 4 Đ ÃÚ«SiO 2, º ÁÛĐĐ β-si 3 N 4 ² È ½»Đ SiO 2 Đ Á Ø ² Đ Ò Á Á Ä Ã [16], Ò Ð Đ ÃÚ«3 Ò Ê β-si 3N 4 Ó ÄÛ β-si 3N 4 ƾ ËË Fig. 3 Thermal conductivities of β-si 3N 4-filled composites as a function of β-si 3N 4 volume fraction 4 Ó Ê Ó ÄÛ β-si 3N 4 ƾ ËË Fig. 4 Thermal conductivities of β-si 3N 4/SiO 2-filled composites as a function of β-si 3N 4 volume fraction 3.2 È ÁÐ Ê Ò ÐÃÚ«Ô ½«ÔĐ Maxwell Agari ÚÓ Ô ½ Ù ¹ ¾ºĐ Ð ÊÃÚ«Đ Maxwell ÁÐ [13] Maxwell ¹ (Potential theory Ú Þ Ç Ì Å Ö Đ Ñ ½ Ð Đ Ò Ð ÃÚ«ÆÑÅ [ λd + 2λ c + 2φ(λ d λ d ] λ e = λ c λ d + 2λ c φ(λ d λ c (3 ÑÑÅ λ e Ò ÐĐÃÚ«Æ λ c ÖĐ ĐÃ Ú «( ; λ d Ö Đ Đ Ã Ú «(µ Ð; φ ÖĐ Î ½ Agari ÁÐ [14,15] Agari Æ Ç Ò ÐÑ µ ÉÅ ½ ÅÄà ÚÅà Çà µ Ú (¹Ô Ú, ÃÚ«ÚÅ Ã Çà µ Ø Ô ( Ô Ú, Ã Ú «Ò Ð Đ Ã Ú «Í Ñ Ú Å Ñ lgλ c = Aφ + B (4 ( λd A = C f lg C p λ c (5 B = lg(c p λ c (6 ÑÑͳ e c d ½ Ô Ò Ð µð C f Ø µð ÄÃ Ç Đ ² 0 1 ² µðáè Äà C f Á 1. C p µç 1 ½ Ñ (4 Ï Î C f C p ¾ µð³ ÜĐ²Ú ÃÚ«Đ µ µðđ ½ Æ ÜÊÊ ÁÐ ÞÑ Maxwell Agari Ô Ø Ñ µé Ò Ð ÎĐ ßÎ ¹ β-si 3 N 4 Ñ µé Ò Ð Ã Ú «Æ (A Å Đ Ù ¹ Ü À ÒÇ Maxwell Ô Ý Ú ½ Ê ¾ 5 Ô Ò Ð Ã Ú «Đ Ý Ì β-si 3 N 4 µéü
4 1204  Š22 Ê Đ Ë Æ Ú Đ ² Ú Å ÕØ Maxwell Ô Ý β-si 3 N 4 µé«á Đ¼ Á Î Đ¼ Đ ² µ Ç Maxwell Ô µ É Đ Đ Å É Đ Ð À ³ Đ β-si 3 N 4 Ð ÁÛĐ Ð Æ [16], Ð (Ê Á Û Đ Ð Á È Ø Ä Ç º µ É «ÁÛĐ β-si 3 N 4 ÐÁ ÄÃ Ò ÐÃÚ«Đ ² Ò Ð ĐÃÚ«Maxwell Ô Maxwell ÔÆ µé Ø ÖĐĐ Ñ µé«50% Đ Ò ÐĐ ½ ¼ ² Ô Ù ¹ Ü ½ ¹ Agari Ô A Å Æ Ú½È Î Ã Ú«À Ò (µ¾ 6, ÐÝ A=2.22, B = ¾ (5 (6 ÚÑ Ð C p =1.13, C f =0.747, ÌÇ Agari ÔĐÒ ³ ² ¹ Agari Ô ½ Ñ µé Ò ÊĐ ÃÚ«²Ú Å Ñ µé β-si 3 N 4 Ò Ð Æ Đ Ò Ð Agari ÔÃÚ«Ñ Å logλ e = 2.22φ (7 Ñ λ e Ò ÐĐÃÚ«φ Ñ µ É Î ½ 3.3 Ü ²» È Þ Agari Ôµ¹Ý Ñ µé Ê Ð ÚÙ Đ Ù¹ Ñ µ É Ò Ð Ê Ã Ú «Đ Ú µ É Ò Ð Æ Agari Ô ¹Ô Ú Ñ Ô Å λ e = φ 1 λ d1 + φ 2 λ d2 + (1 φ 1 φ 2 λ c (8 Ñ φ 1, φ 2, λ d1, λ d2 ½ ÚÓµÉ Đ µé«ãú«ô Ú Ñ Ô Å 1 λ c = φ 1 λ d1 + φ 2 λ d2 + (1 φ 1 φ 2 λ c (9 (8 Ñ (9 Ñ» ÐÄ (10 ÑÅ λ n e = φ 1λ n d1 + φ 2λ n d2 + (1 φ 1 φ 2 λ n c (10 Ç (10 Ñ Ñ n=1 ¹ Ô Ú Ñ n = 1 Ô Ú Ñ Ì µ É Ä Ã Ç ² Ò ÐÃÈ ÉÚ µé Agari Ô Ô Å 5 β-si 3N 4 Ê Ó ÄÛ Maxwell Õ Fig. 5 Thermal conductivities of Maxwell model calculating and experiment results for β-si 3N 4-filled composites 6 Ò Ê β-si 3N 4 Ó ÄÛ Agari ÕµÓ Fig. 6 Linear fitting result with Agari model for thermal conductivity of β-si 3N 4-filled composites ( λe ( λd1 lg = φ 1 C f1 lg + C p λ c C p λ c ( λd2 φ 2 C f2 lg C p λ c (11 Ñ C f1, C f2 ½ Ú ÄÃ Ç Đ² C p Ò ÐĐÃÈ ( λd1 ( λd2 A 1 = C f1 lg, A 2 = C f2 lg, C p λ c C p λ c B = lg(c p λ c (12 É (11 Ñ ÐÄÅ lgλ e = A 1 φ 1 + A 2 φ 2 + B (13 Ç B Å Ñ φ 1 β-si 3 N 4 ½ φ 2 SiO 2 ½ É φ 1 + φ 2 =0.5. ² (13 Ñ Ú Å lgλ e = (A 1 A 2 φ 1 + (0.5A 2 + B (14
5 6 Þ «β-si 3N 4/ Ý Æ ÛÄݱ Á 1205 ¹ (14 Ñ B Å Ã Ú «Æ Ú Ò Ê ¾ 7 Ô Ñ A 1 A 2 =1.2623, 0.5A 2 +B= , Æ C p Ñ µé º É Æ (12 Ñ B 0.468, Ð A 2 = 1.07, C f2 = 0.662, A 1 = 2.287, C f1 =0.732, Ð Ç Ò Đ³ º C f1 Đ ¾ (5 Ñ Ð Đ C f C f Æ Ñ µé ÒÐ Ý Đ Ä Ã Ç Đ Ç Ñ µ É Ò Ð Ã Ú «Ç Ù ¹ Ü Ñ µé Ò ÐÐÝĐ C f Æ Ø² ÁÛĐ β-si 3 N 4 ÄÃ Đ Ò½ SiO 2 ½ ĐÒµÉ ÎÚÞ β-si 3 N 4 ÄÃ Đ¼ β-si 3 N 4 /SiO 2 ĐÒµÉ Ð Æ Đ Ò Ð Agari ÔÃÚ«Ñ Å lgλ e = 2.29φ φ (15 7 Ò Ê Ó Agari ÕµÓ Fig. 7 Linear fitting result with Agari model for thermal conductivity of co-filled composites 3.4 Agari ÁÐ ÏÎ Agari Ô µé«đ Ò ÐĐ ¹Ü½ ز Agari ÔØ Ó Þ ¹Ô ²Đ µ É Ü Ö ¾ ÑĐ Ü (, Õµ Ý Ñ µé Ê Agari ÔĐ ÙÜ ½ 4 1. β-si 3 N 4 Ø Ó Đ Ã Ú Ð Ð β-si 3 N 4 Ø Ò ÐĐÚÃÜ µé«ì 50% β-si 3 N 4 µé Ò Ð ĐÃÚ«Ø SiO 2 µéđ β-si 3 N 4 Ñ µ É Ò Ð Đ Ã Ú «Ò Agari Ô Maxwell Ô¾Ù¹ µ É ÃÚ«½ Đ Ò ÐĐÃÚ«3. Agari Ô ÚÙ ¹ Ñ µé Ò ÐĐÃÚ«¹ ÃÚ µé «Ð ÐĐ Ä Đ [1] Gonon P, Sylvestre A, Teysseyre J, Prior C. Journal of Materials Science: Materials in Electronics, 2001, 12: [2] Bujard P, Kuhnlein G, Ino S, et al. IEEE Trans. Components, Packaging, and Manu. Techno-part A, 1994, 17 (4: [3] Bajaj P, Jha N K, Kumar A. J. Appl. Polym. Sci., 1995, 56 (10: [4] Bujard P. Thermal conductivity of boron nitride filled epoxy resins: temperature dependence and influence of sample preparation. Inter Society Conference on Thermal Phenomena in the Fabrication and Operation of Electronic Components: I-THERM 88. New York, USA, [5] Xu Y S, Chung D D L, Mroz C. Composites, Part A: applied science and manufacturing, 2001, 32: [6] Li L, Chung D D L. Journal of Electronic Materials, 1994, 23 (6: [7] Lee W S, Han I Y, Jin Y, et al. Thermal characterization of thermally conductive underfill for a flip-chip package using novel temperature sensing technique. Proceedings of 6th Electronics Packaging Technology Conference, Piscataway, NJ, USA, [8] Bolt J D, Button D P, Yost B A. Mat. Sci. Eng. A, 1989, A109: [9] Æ ÕÐ Ø (WANG Yu-Di, et al. Ã«Đ (Journal of Inorganic Materials, 2000, 15 (6: [10] Æ ÕÐ Ø Ð 2001, 37: [11] Mclvor S D, Darby M I, Wostenholm G H, et al. J. Mat. Sci., 1990, 25: [12] Haggerty J S, Lightfoot A. Ceram. Eng. Sci. Proc., 1995, 16: 475. [13] Maxwell J C. A Treatise on Electricity and Magnetism. London, U. K.: Oxford Univ. Press, 1998, Ch9.1. [14] Agri Y, Uno T. J. Appl. Polym. Sci., 1986, 32: [15] Agri Y, Ueda A, Nagai S. J. Appl. Polym. Sci., 1993, 49: [16] ¹Í ĐÆ È - Þ²ÌÕ Å
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