應用第一原理計算於摻鎳Cu6Sn5介金屬破裂韌性之研究

First-principles Calculations on Fracture Toughness Prediction of Ni-doped Cu6Sn5 Intermetallic Compounds

10.6342/NTU.2015.00013

林致淳

第一原理 ； 密度泛函理論 ； 虛擬晶體近似法 ； Cu6Sn5 ； 楊氏模數 ； 破裂韌性 ； DFT ； ab initio ； VCA ； Cu6Sn5 ； Fracture toughness

國立臺灣大學土木工程學系學位論文

2015年

碩士

陳俊杉

英文

介金屬化合物常見於電子構裝中的錫焊料及銅基板，並對電子構裝之品 質控制有莫大的影響。過往的研究中發現，在此系統中摻入鎳後，介金屬將會固定在eta相的Cu6Sn5，並能夠阻絕形成其他種類可能會造成介面劣化的介金屬。因此，了解eta相Cu6Sn5及其摻入鎳後的破裂性質(亦即破裂韌性)便極為重要。同時，由於缺乏摻鎳後的破裂韌性實驗數據，密度泛函理論的計算模擬在此問題上便為一方便而有效的工具。然而eta相Cu6Sn5本身在Sn位置的分數占據特性及摻入鎳後所形成的非整數化學當量使得密度泛函理論計算需建置一十分龐大的原子模型，並需要大量的計算時間。為了克服此問題，本研究採用混合非整數化學當量的原子之膺勢的虛擬晶體近似法以縮小模型，同時進一步驗證虛擬晶體近似法在此系統中之適用性。本研究藉由密度泛函理論結合虛擬晶體近似法研究eta相Cu6Sn5在摻入不同比例之鎳時的物理性質。首先本研究從驗證虛擬晶體近似法出發，接著討論eta相Cu6Sn5摻入不同比例鎳時的體積變化；隨後計算並討論計算破裂韌性時所需之楊氏模數在eta相Cu6Sn5中隨不同摻鎳比變化的趨勢；最後計算eta相Cu6Sn5在不同摻鎳比下之破裂韌性的變化情形。我們發現隨著摻鎳量的增加，eta相Cu6Sn5之體積會收縮，其彈性模數與破裂韌性亦有增加的趨勢；此趨勢將於正文中透過銅鎳間的鍵結增強加以解釋並討論。

Intermetallic compounds (IMC) which appear in the interface of Sn solders and Cu substrate play an important role in quality control in electronic packaging industry. In the system, it has been reported that IMC can be stabilized in eta phase Cu6Sn5 by adding Ni dopant. This can prevent the interface from being degraded by other IMCs. It is thus important to understand the fracture properties, i.e. fracture toughness, of eta-Cu6Sn5 and Ni-doped eta-Cu6Sn5. However, the fracture experiments in Ni-doped eta-Cu6Sn5 are lacking. Computational simulation with density functional theory (DFT) is thus a powerful tool to look into this system. Because of the fractional occupancy in eta-Cu6Sn5 and Nidoped eta-Cu6Sn5, it needs a large model to reproduce the fraction occupancy crystal, which requires tremendous computational efforts. Virtual crystal approximation (VCA) is thus involved to ease the computation in this research. However, the suitability of VCA to a system needs to be validated before conducting further computation. In this research, we conduct a DFT simulation. The suitability of VCA in eta-Cu6Sn5 with different amounts of Ni-dopant is first validated. Then the structural variations of eta-Cu6Sn5 under different percentages of Ni-dopant are also presented. The necessary mechanical properties to get fracture toughness, including Young’s modulus are examined. Finally, the fracture toughness of eta-Cu6Sn5 under different Ni-dopants is investigated. We found that eta-Cu6Sn5 experiences a shrinkage in volume and enhancement in Young’s modulus and fracture toughness as the percentage of Ni-dopant increases. The trend will be further discussed by the bond-strengthening mechanism between Cu and Ni atoms in this thesis.

1. 1. Lau, J.H., Overview and outlook of through‐silicon via (TSV) and 3D integrations. Microelectronics International: An International Journal, 2011. 28(2): p. 8-22.
   連結：
2. 5. European Union, Directive 2002/96/EC of the European Parliament and of the Council of 27 January 2003 on waste electrical and electronic equipment (WEEE), E. Union, Editor. 2002, Office for Official Publications of the European Communities: Brussels.
   連結：
3. 6. European Union., Directive 2002/95/EC of the European Parliament and of the Council of 27 January 2003 on the restriction of the use of certain hazardous substances in electrical and electronic equipment, E. Union, Editor. 2003, Office for Official Publications of the European Communities: Brussels.
   連結：
4. 7. Shapiro, A.A., et al. Pb-free microelectronics assembly in aerospace applications. in Aerospace Conference, 2004. Proceedings. 2004 IEEE. 2004.
   連結：
5. 10. Agarwal, R., et al., Cu/Sn microbumps interconnect for 3D TSV chip stacking, in Electronic Components and Technology Conference (ECTC), 2010 Proceedings 60th. 2010. p. 858-863.
   連結：
6. 11. Chao, B., et al., Investigation of diffusion and electromigration parameters for Cu–Sn intermetallic compounds in Pb-free solders using simulated annealing. Acta materialia, 2007. 55: p. 2805-2814.
   連結：
7. 12. Cherkaoui, M. and L. Capolungo, Atomistic and Continuum Modeling of Nanocrystalline Materials: Deformation Mechanisms and Scale Transition. MATERIALS SCIENCE, ed. R. Hull, et al. Vol. 112. 2009: Springer.
   連結：
8. 13. Nogita, K., et al., Kinetics of the η–η′ transformation in Cu6Sn5. Scripta Materialia, 2011. 65(10): p. 922-925.
   連結：
9. 14. Saunders, N. and A.P. Miodownik, The Cu-Sn (Copper-Tin) system. Bulletin of Alloy Phase Diagrams, 1990. 11(3): p. 278-287.
   連結：
10. 15. Bernal, J.D., The complex structure of the copper-tin intermetallic compounds. Nature, 1928. 122: p. 54-54.
    連結：
11. 16. Furtauer, S., et al., The Cu-Sn phase diagram, Part I: New experimental results. Intermetallics, 2013. 34: p. 142-147.
    連結：
12. 17. Dimcic, B., et al., Diffusion growth of Cu3Sn phase in the bump and thin film Cu/Sn structures. Microelectronics Reliability, 2012. 52: p. 1971-1974.
    連結：
13. 18. Chen, J., Y.S. Lai, and P.F. Yang, Structural and elastic properties of Cu6Sn5 and Cu3Snfrom first-principles calculations. Journal of Materials …, 2009.
    連結：
14. 19. Chen, H., et al., First principles study of anti-ReO3 type Cu3N and Sc-doped Cu3N on structural, elastic and electronic properties. Computational and Theoretical Chemistry, 2013. 1018(0): p. 71-76.
    連結：
15. 20. Bernal, J.D., The Complex Structure of the Copper–Tin Intermetallic Compounds. Nature, 1928. 122(3063): p. 54-54.
    連結：
16. 21. Tu, K.N., Interdiffusion and reaction in bimetallic Cu-Sn thin films. Acta Metallurgica, 1973. 21(4): p. 347-354.
    連結：
17. 22. Knodler, H., Der strukturelle Zusammenhang zwischen [gamma]- und [epsilon]-Phase im System Kupfer-Zinn. Acta Crystallographica, 1957. 10(1): p. 86-87.
    連結：
18. 23. Momma, K. and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. Journal of Applied Crystallography, 2011. 44(6): p. 1272-1276.
    連結：
19. 24. Gangulee, A., G.C. Das, and M.B. Bever, An x-ray diffraction and calorimetric investigation of the compound Cu6Sn5. Metallurgical Transactions, 1973. 4(9): p. 2063-2066.
    連結：
20. 25. Larsson, a.-K., L. Stenberg, and S. Lidin, The superstructure of domain-twinned η'-Cu 6 Sn 5. Acta Crystallographica Section B Structural Science, 1994. 50: p. 636-643.
    連結：
21. 26. Kang, J.S., et al., Isothermal solidification of Cu/Sn diffusion couples to form thin-solder joints. Journal of Electronic Materials, 2002. 31(11): p. 1238-1243.
    連結：
22. 27. Vianco, P., J. Rejent, and P. Hlava, Solid-state intermetallic compound layer growth between copper and 95.5Sn-3.9Ag-0.6Cu solder. Journal of Electronic Materials, 2004. 33(9): p. 991-1004.
    連結：
23. 28. Zeng, K., et al., Kirkendall void formation in eutectic SnPb solder joints on bare Cu and its effect on joint reliability. Journal of Applied Physics, 2005. 97(2): p. 024508.
    連結：
24. 29. Wang, Y.W., Y.W. Lin, and C.R. Kao, Kirkendall voids formation in the reaction between Ni-doped SnAg lead-free solders and different Cu substrates. Microelectronics Reliability, 2009. 49(3): p. 248-252.
    連結：
25. 30. Tsai, J.Y., et al., A study on the reaction between Cu and Sn3.5Ag solder doped with small amounts of Ni. Journal of Electronic Materials, 2003. 32(11): p. 1203-1208.
    連結：
26. 31. Ho, C.E., S.C. Yang, and C.R. Kao, Interfacial reaction issues for lead-free electronic solders, in Lead-Free Electronic Solders. 2007, Springer US. p. 155-174.
    連結：
27. 32. Wang, Y.W., et al., Effects of minor Fe, Co, and Ni additions on the reaction between SnAgCu solder and Cu. Journal of Alloys and Compounds, 2009. 478(1–2): p. 121-127.
    連結：
28. 33. Ghosh, G. and M. Asta, Phase Stability, Phase Transformations, and Elastic Properties of Cu6Sn5: Ab initio Calculations and Experimental Results. Journal of Materials Research, 2005. 20(11): p. 3102-3117.
    連結：
29. 34. Nogita, K., et al., Effect of Ni on phase stability and thermal expansion of Cu6−xNixSn5 (x = 0, 0.5, 1, 1.5 and 2). Intermetallics, 2012. 26(0): p. 78-85.
    連結：
30. 35. Born, M. and R. Oppenheimer, Zur Quantentheorie der Molekeln. Annalen der Physik, 1927. 389(20): p. 457-484.
    連結：
31. 36. Hohenberg, P. and W. Kohn, Inhomogeneous electron gas. Phys. Rev., 1964. 136: p. B864-B871.
    連結：
32. 37. Kohn, W. and L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev., 1965. 140: p. A1133-A1138.
    連結：
33. 38. Ceperley, D.M. and B.J. Alder, Ground State of the Electron Gas by a Stochastic Method. Physical Review Letters, 1980. 45(7): p. 566-569.
    連結：
34. 39. Perdew, J.P. and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems. Physical Review B, 1981. 23(10): p. 5048-5079.
    連結：
35. 40. Perdew, J.P., Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Physical Review B, 1986. 33: p. 8822.
    連結：
36. 41. Perdew, J.P., et al., Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Physical Review B, 1992. 46(11): p. 6671-6687.
    連結：
37. 42. Perdew, J.P., K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple. Physical Review Letters, 1996. 77(18): p. 3865-3868.
    連結：
38. 43. Payne, M.C., et al., Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Reviews of Modern Physics, 1992. 64(4): p. 1045-1097.
    連結：
39. 44. Hellmann, H., A New Approximation Method in the Problem of Many Electrons. The Journal of Chemical Physics, 1935. 3(1): p. 61-61.
    連結：
40. 45. Schwerdtfeger, P., The Pseudopotential Approximation in Electronic Structure Theory. ChemPhysChem, 2011. 12(17): p. 3143-3155.
    連結：
41. 47. Myers, E.R., V. Heine, and M.T. Dove, Thermodynamics of Al/Al avoidance in the ordering of Al/Si tetrahedral framework structures. Physics and Chemistry of Minerals, 1998. 25(6): p. 457-464.
    連結：
42. 48. Winkler, B., C. Pickard, and V. Milman, Applicability of a quantum mechanical virtual crystal approximation to study Al/Si-disorder. Chemical Physics Letters, 2002. 362(3–4): p. 266-270.
    連結：
43. 49. Ramer, N.J. and A.M. Rappe, Virtual-crystal approximation that works: Locating a compositional phase boundary in PbZr(1-x)TixO3. Physical Review B, 2000. 62(2): p. R743-R746.
    連結：
44. 50. Bellaiche, L. and D. Vanderbilt, Virtual crystal approximation revisited: Application to dielectric and piezoelectric properties of perovskites. Physical Review B, 2000. 61(12): p. 7877-7882.
    連結：
45. 52. Nordheim, L., Zur Elektronentheorie der Metalle. I. Annalen der Physik, 1931. 401(5): p. 607-640.
    連結：
46. 53. Giannozzi, P., et al., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 2009. 21(39): p. 395502.
    連結：
47. 54. Gonze, X., et al., First-principles computation of material properties: the ABINIT software project. Computational Materials Science, 2002. 25(3): p. 478-492.
    連結：
48. 55. Gonze, X., et al., A brief introduction to the ABINIT software package. Zeitschrift Fur Kristallographie, 2005. 220(5-6): p. 558-562.
    連結：
49. 56. Gonze, X., et al., ABINIT: First-principles approach to material and nanosystem properties. Computer Physics Communications, 2009. 180(12): p. 2582-2615.
    連結：
50. 57. Clark, S.J., et al., First principles methods using CASTEP. Zeitschrift Fur Kristallographie, 2005. 220(5-6): p. 567-570.
    連結：
51. 58. Hellmann, H., Einführung in die Quantenchemie. Angewandte Chemie, 1937. 54(11-12): p. 156.
    連結：
52. 59. Feynman, R., Forces in Molecules. Physical Review, 1939. 56: p. 340-343.
    連結：
53. 60. Anderson, T.L., Fracture mechanics : fundamentals and applications. 2005, Boca Raton, FL: Taylor & Francis.
    連結：
54. 61. Orowan, E., Fracture and strength of solids. Reports on Progress in Physics, 1949. 12(1): p. 185.
    連結：
55. 66. Sneddon, I.N., The Distribution of Stress in the Neighbourhood of a Crack in an Elastic Solid. Proceedings, Royal Society of London, 1946. A-187: p. 229-260.
    連結：
56. 67. Williams, M.L., On the Stress Distribution at the Base of a Stationary Crack. Journal of Applied Mechanics, 1957. 24: p. 109-114.
    連結：
57. 68. Caro, M.A., S. Schulz, and E.P. O’Reilly, Comparison of stress and total energy methods for calculation of elastic properties of semiconductors. Journal of Physics: Condensed Matter, 2013. 25(2): p. 025803.
    連結：
58. 69. Nogita, K., C.M. Gourlay, and T. Nishimura, Cracking and phase stability in reaction layers between Sn-Cu-Ni solders and Cu substrates. JOM, 2009. 61(6): p. 45-51.
    連結：
59. 71. Chen, S., W. Zhou, and P. Wu, The structural, elastic, electronic and thermodynamic properties of hexagonal η-Cu6−xNixSn5 (x = 0, 0.5, 1, 1.5 and 2) intermetallic compounds. Intermetallics, 2014. 54(0): p. 187-192.
    連結：
60. 72. Yu, C., et al., First-principles investigation of the structural and electronic properties of Cu(6−x)NixSn5 (x=0, 1, 2) intermetallic compounds. Intermetallics, 2007. 15(11): p. 1471-1478.
    連結：
61. 73. Haynes, W.M., CRC handbook of chemistry and physics. 2015-2016, CRC Press.
    連結：
62. 74. Nielsen, O.H. and R.M. Martin, Stresses in semiconductors: Ab initio calculations on Si, Ge, and GaAs. Physical Review B, 1985. 32(6): p. 3792-3805.
    連結：
63. 75. González-Díaz, M., P. Rodríguez-Hernández, and A. Muñoz, Elastic constants and electronic structure of beryllium chalcogenides BeS, BeSe, and BeTefrom first-principles calculations. Physical Review B, 1997. 55(21): p. 14043-14046.
    連結：
64. 76. Zoroddu, A., et al., First-principles prediction of structure, energetics, formation enthalpy, elastic constants, polarization, and piezoelectric constants of AlN, GaN, and InN: Comparison of local and gradient-corrected density-functional theory. Physical Review B, 2001. 64(4): p. 045208.
    連結：
65. 77. Bouamama, K., K. Daoud, and K. Kassali, Ab initio calculations in the virtual-crystal approximation of the structural and the elastic properties of BeS x Se 1− x alloys under high pressure. Modelling and Simulation in Materials Science and Engineering, 2005. 13(7): p. 1153.
    連結：
66. 78. Hill, R., The Elastic Behaviour of a Crystalline Aggregate. Proceedings of the Physical Society. Section A, 1952. 65(5): p. 349.
    連結：
67. 79. Ghosh, G., Elastic properties, hardness, and indentation fracture toughness of intermetallics relevant to electronic packaging. Journal of Materials Research, 2004. 19(05): p. 1439-1454.
    連結：
68. 80. Nogita, K. and T. Nishimura, Nickel-stabilized hexagonal (Cu, Ni)6Sn5 in Sn–Cu–Ni lead-free solder alloys. Scripta Materialia, 2008. 59(2): p. 191-194.
    連結：
69. 82. Balakrisnan, B., et al., Fracture toughness of Cu-Sn intermetallic thin films. Journal of Electronic Materials, 2003. 32(3): p. 166-171.
    連結：
70. 83. Hayes, S.M., N. Chawla, and D.R. Frear, Interfacial fracture toughness of Pb-free solders. Microelectronics Reliability, 2009. 49(3): p. 269-287.
    連結：
71. 84. Norman, L.T.S., Atomisitic Calculations of the Mechanical properties of Cu-Sn Intermetallic Compounds, in Department of Mechanical Engineering. 2008, National University of Singapore: Singapore.
    連結：
72. 2. Lau, J.H., Low Cost Flip Chip Technologies for DCA, WLCSP, and PBGA Assemblies. 1 ed. McGraw-Hill Professional Engineering. 2000: McGraw-Hill Professional.
73. 3. Bogatin, E., Roadmaps of Packaging Technology. 1997: Integrated Circuit Engineering Corporation.
74. 4. 白蓉生, PCB and Lead Free Soldering. 1 ed. 2006, Taoyung: Taiwan Printed Circuit Association.
75. 8. Internal discussion with the group of Professor Robert C. R. Kao, provided by ITRI, Taiwan.
76. 9. Abtew, M. and G. Selvaduray, Lead-free Solders in Microelectronics. Materials Science and Engineering: R: Reports, 2000. 27(5-6): p. 95-141.
77. 46. Lee, J.G., Computational Materials Science: An Introduction. 2011: CRC Press.
78. 51. Muto, T., On the Electronic Structure of Alloys. Scientific papers of the Institute of Physical and Chemical Research, 1938. 34: p. 377-390.
79. 62. Irwin, G.R., Fracture dynamics. Fracturing of metals, 1948. 152.
80. 63. Irwin, G.R., Onset of Fast Crack Propagation in High Strength Steel and Aluminum Alloys. Sagamore Research Conference Proceedings, 1956. 2: p. 289-305.
81. 64. Westergaard, H.M., Bearing Pressure and Cracks. Journal of Applied Mechanics, 1939. 6: p. 49-53.
82. 65. Irwin, G.R., Analysis of Stresses and Strains near the End of a Crack Traversing a Plate. Journal of Applied Mechanics, 1957. 24: p. 361-364.
83. 70. Fuchs, M., Comparison of exchange-correlation functionals: from LDA to GGA and beyond. 2005, Fritz-Haber-Institut der MPG: Los Angeles, USA.
84. 81. Kiejna, A. and K.F. Wojciechowski, Surface properties of alkali-metal alloys. Journal of Physics C: Solid State Physics, 1983. 16(35): p. 6883.