摘要
准确描述电子封装焊点微观力学及热学行为是解决电子器件可靠性问题的基本前提。近年来,为满足电子器件微小化要求,焊点尺度持续减小,金属间化合物在其内所占的体积百分比越来越大,因此已不能把焊点简化成各向同性、均匀无结构的钎料合金整体。另一方面,传统的实验研究以大块材料作为试样,采用自上而下的研究范式,着重于宏观现象描述,已不太适用于目前和未来的小尺度焊点。本文通过第一性原理方法在原子尺度上系统地研究了焊点内金属间化合物的基本物性,同时构建了能够准确反映β-Sn晶体金属共价混合成键特性的原子间相互作用势,为深入研究焊点可靠性提供了基本数据和理论基础。本文包含以下主要内容。
根据研究对象的特点选取了合适的计算参数,并详细考察了两个关键参量截断能和k点间距与计算收敛性之间的关系,论证了计算结果的可靠性。在此基础上,基于真实的晶体结构构建了计算初始构型,经几何优化得到了各金属间化合物的平衡晶体结构。结果表明,计算结果同试验数据吻合良好,进一步证实了计算的可靠性。
对几何优化后的构型施加了特定的变形,计算了应力矩阵。获得一系列变形-应力数据后,用最小二乘法拟合得到了单晶体的弹性刚度系数和弹性柔度系数。运用Voit、Reuss、Voit-Reuss-Hill以及Hashin-Shtrikman理论推导出了多晶体的弹性性质,并利用Pugh判据评估了韧脆性。同时,根据已得到的弹性常数预测了金属间化合物的Debye温度及热导率。
通过分析不同晶向上的体变模量和杨氏模量,研究了金属间化合物的各向异性力学行为。结果表明,几乎所有的金属间化合物都表现出强烈的弹性各向异性,而且晶体学对称性高低并不完全决定IMC的各向异性程度。各向异性是造成弹性性质试验数据分散的主要原因。
结合虚拟静水压力试验,确定了IMC的状态方程,研究了IMC的成键状态和电子结构及其压力响应。结果表明,IMC晶体具有共价性或共价-金属混合性的原子结合,弹性各向异性本质上是由其内共价键的方向性引起的。
在Tersoff-Brenner键级势模型基础上,建立了Sn原子间相互作用势;并结合分子动力学方法预测了β-Sn和bct-Sn的晶体结构、结合能、键距、键能以及体变模量,计算了α-Sn和β-Sn的晶体振动模式密度和热容,研究了Sn的α?β相变。结果表明,构建的Sn的原子间相互作用势很好地反映了各种Sn相的成键状态,且具有良好的可移植性。
Micro-mechanical behavior and thermal property of solder joints should be accurately characterized to resolve the problem about electronics reliability. Recently, solder joints become increasingly small to meet the need of electronics miniaturization, and the volume fraction of intermetallics in solder joints increase. As a result, the solder joint cannot be simplified to an isotropy and homogenous solder alloy. In addition, conventional experimental researches utilize bulk materials as test samples; these researches emphasize the description of macro-phenomena using the top-down mode. However, this type of research has not been enough to obtain insightful view on the properties of micro-scale joints. In this paper, we determined the basic physical properties of the several intermetallics that exist in solder joints on an atomic level using the first-principles method, and established the interatomic potentials that can capture the metallic-covalent bonding characteristics ofβ-Sn crystal exactly; the results enriched the fundamental data and basic theory to investigate the reliability of solder joints. This paper includes the following contents.
According to the characteristic of research object, we selected suitable calculation parameters; investigated in detail the relationship between the convergence of calculations and two key parameters, viz. energy cutoffs and k-point divisions; demonstrated the calculation results reliable. Initial geometrical configurations of the intermetallics were proposed by virtue of their real crystal structures, and these configurations were optimized to achieve the equilibrium structures with the predetermined sets of calculation parameters. The calculations showed good agreement with the experimental results, which proves their accuracy further.
We set the strain of the optimized equilibrium cells to a finite value by applying a given homogeneous deformation to optimize the internal atomic coordinates and calculate the resulting stress; each of the second-order elastic constants of the single crystals was determined by means of a least-squares linear fit of stress against strain. Polyscrystalline elastic moduli were estimated from the compliance tensor components using the Voit, Reuss, and Voit-Reuss-Hill method, and the Hashin-Shtrikman scheme; the toughness (or brittleness) of the intermetallics was evaluated using the Pugh criterion. At the same time, the Debye temperatures and thermal conductivities were predicted from the calculated elastic constants.
Anisotropic mechanical behaviors of these intermetallics were investigated by analyzing the directional dependence of bulk modulus and Young’s modulus. The results indicated that virtually all intermetallics possess strong elastic anisotropy, and the anisotropy is not exactly attributable to the crystal symmetry, meaning that the elastic anisotropy of the compounds may be partially responsible for the discrepancy in the reported experimental results.
Hydrostatic pressure test was simulated with first-principles method to determine IMC’s equation of state, and to investigate the bonding characteristics, electronic structure, and their responses to applied pressures. The results showed that the IMCs are composed of the special interatomic combinations that encompasse both covalent and metallic characteristics, and the elastic anisotropy is caused by the directional character of the covalent bond.
An analytical bond-order potential of Sn was proposed on the basis of Tersoff-Brenner model, and that was used to predict the crystal structures, binding energies, bond distances and strengths, and bulk modulus ofβ-Sn and bct-Sn. the potential was also used to calculate phonon DOS and heat capacity ofα-Sn andβ-Sn, and to investigate theα?βphase transition of Sn. All results indicated that the proposed interatomic potential can describe the bonding states of different phases of Sn accurately, and have a good transferability.
引文
1 Y. Ding, C. Wang, Y. Tian, M. Li. Influence of Aging Treatment on Deformation Behavior of 96.5Sn3.5Ag Lead-Free Solder Alloy During in Situ Tensile Tests. J. Alloys Compd. 2007, 428(1-2):274-285.
2 Y. Ding, C. Wang, M. Li. Scanning Electron Microscope in-Situ Investigation of Fracture Behavior in 96.5Sn3.5Ag Lead-Free Solder. J. Electron. Mater. 2005, 34(10):1324-1335.
3 H.K. Kim, H.K. Liou, K.N. Tu. Three-Dimensional Morphology of a Very Rough Interface Formed in the Soldering Reaction between Eutectic Snpb and Cu. Appl. Phys. Lett. 1995, 66(18):2337-2339.
4 K.N. Tu, T.Y. Lee, J.W. Jang, L. Li, D.R. Frear, K. Zeng, J.K. Kivilahti. Wetting Reaction Versus Solid State Aging of Eutectic Snpb on Cu. J. Appl. Phys. 2001, 89(9):4843-4849.
5 K. Tu, F. Ku, T. Lee. Morphological Stability of Solder Reaction Products in Flip Chip Technology. J. Electron. Mater. 2001, 30(9):1129-1132.
6 H.K. Kim, K.N. Tu. Kinetic Analysis of the Soldering Reaction between Eutectic Snpb Alloy and Cu Accompanied by Ripening. Phys. Rev. B. 1996, 53(23):16027-16034.
7 A. Kumar, M. He, Z. Chen. Barrier Properties of Thin Au/Ni-P under Bump Metallization for Sn-3.5Ag Solder. Surf. Coat. Technol. 2005, 198(1-3):283-286.
8 P.G. Kim, J.W. Jang, T.Y. Lee, K.N. Tu. Interfacial Reaction and Wetting Behavior in Eutectic SnPb Solder on Ni/Ti Thin Films and Ni Foils. J. Appl. Phys. 1999, 86(12):6746-6751.
9 M. He, Z. Chen, G. Qi. Solid State Interfacial Reaction of Sn-37Pb and Sn-3.5Ag Solders with Ni-P under Bump Metallization. Acta Mater. 2004, 52(7):2047-2056.
10 P.L. Liu, Z. Xu, J.K. Shang. Thermal Stability of Electroless-Nickel/Solder Interface: A. Interfacial Chemistry and Microstructure. Metall. Mater. Trans. A-Phys. Metall. Mater. Sci. 2000, 31A(11):2857-2866.
11 H. Matsuki, H. Ibuka, H. Saka. Tem Observation of Interfaces in a Solder Joint in a Semiconductor Device. Sci. Technol. Adv. Mater. 2002, 3(3):261-270.
12 M. He, A. Kumar, P.T. Yeo, G.J. Qi, Z. Chen. Interfacial Reaction between Sn-Rich Solders and Ni-Based Metallization. Thin Solid Films. 2004, 462-463:387-394.
13 P.G. Kim, K.N. Tu. Morphology of Wetting Reaction of Eutectic SnPb Solderon Au Foils. J. Appl. Phys. 1996, 80(7):3822-3827.
14 C. Ho, Y. Chen, C. Kao. Reaction Kinetics of Solder-Balls with Pads in BGA Packages During Reflow Soldering. J. Electron. Mater. 1999, 28(11):1231-1237.
15 C.E. Ho, S.Y. Tsai, C.R. Kao. Reaction of Solder with Ni/Au Metallization for Electronic Packages During Reflow Soldering. IEEE Trans. Adv. Packag. 2001, 24(4):493-498.
16 M. Zequn, M. Kaufmann, A. Eslambolchi, P. Johnson. Brittle Interfacial Fracture of Pbga Packages Soldered on Electroless Nickel/Immersion Gold. Proceedings of the 48th Electronic Components and Technology Conference, Seattle, WA, USA, 1998:952-961.
17 A. Minor, J. Morris. Growth of a Au-Ni-Sn Intermetallic Compound on the Solder-Substrate Interface after Aging. Metall. Mater. Trans. A-Phys. Metall. Mater. Sci. 2000, 31(3):798-800.
18 A. Minor, J. Morris. Inhibiting Growth of the Au0.5Ni0.5Sn4 Intermetallic Layer in Pb-Sn Solder Joints Reflowed on Au/Ni Metallization. J. Electron. Mater. 2000, 29(10):1170-1174.
19 C. Ho, R. Zheng, G. Luo, A. Lin, C. Kao. Formation and Resettlement of (AuxNi1?X)Sn4 in Solder Joints of Ball-Grid-Array Packages with the Au/Ni Surface Finish. J. Electron. Mater. 2000, 29(10):1175-1181.
20 X. Liu, M. Kinaka, Y. Takaku, I. Ohnuma, R. Kainuma, K. Ishida. Experimental Investigation and Thermodynamic Calculation of Phase Equilibria in the Sn-Au-Ni System. J. Electron. Mater. 2005, 34(5):670-679.
21 J.-H. Lee, J.-H. Park, Y.-H. Lee, Y.-S. Kim. Effects of Cu and Ni Additions to Eutectic Pb-Sn Solders on Au Embrittlement of Solder Interconnections. J. Mater. Res. 2001, 16(5):1249-1251.
22 C. Ho, L. Shiau, C. Kao. Inhibiting the Formation of (Au1?XNix)Sn4 and Reducing the Consumption of Ni Metallization in Solder Joints. J. Electron. Mater. 2002, 31(11):1264-1269.
23 M. Abtew, G. Selvaduray. Lead-Free Solders in Microelectronics. Mater. Sci. Eng. R-Rep. 2000, 27:95–141.
24 K. Suganuma. Advances in Lead-Free Electronics Soldering. Curr. Opin. Solid State Mat. Sci. 2001, 5(1):55-64.
25 C.M.L. Wu, D.Q. Yu, C.M.T. Law, L. Wang. Properties of Lead-Free Solder Alloys with Rare Earth Element Additions. Mater. Sci. Eng. R-Rep. 2004, 44(1):1-44.
26 C.M.L. Wu, Y.W. Wong. Rare-Earth Additions to Lead-Free Electronic Solders. J. Mater. Sci.: Mater. Electron. 2006:1-15.
27 A. Sharif, Y.C. Chan. Dissolution Kinetics of Bga Sn-Pb and Sn-Ag Solderswith Cu Substrates During Reflow. Mater. Sci. Eng. B-Solid State Mater. Adv. Technol. 2004, 106(2):126-131.
28 D.Q. Yu, C.M.L. Wu, C.M.T. Law, L. Wang, J.K.L. Lai. Intermetallic Compounds Growth between Sn-3.5Ag Lead-Free Solder and Cu Substrate by Dipping Method. J. Alloys Compd. 2005, 392(1-2):192-199.
29 J. Tsai, Y. Hu, C. Tsai, C. Kao. A Study on the Reaction between Cu and Sn3.5Ag Solder Doped with Small Amounts of Ni. J. Electron. Mater. 2003, 32(11):1203-1208.
30 M.O. Alam, Y.C. Chan, K.N. Tu. Effect of 0.5 Wt% Cu Addition in Sn-3.5%Ag Solder on the Dissolution Rate of Cu Metallization. J. Appl. Phys. 2003, 94(12):7904-7909.
31 M. He, W.H. Lau, G. Qi, Z. Chen. Intermetallic Compound Formation between Sn-3.5Ag Solder and Ni-Based Metallization During Liquid State Reaction. Thin Solid Films. 2004, 462-463:376-383.
32 Z. Chen, M. He, G. Qi. Morphology and Kinetic Study of the Interfacial Reaction between the Sn-3.5Ag Solder and Electroless Ni-P Metallization. J. Electron. Mater. 2004, 33(12):1465-1472.
33 Z. Kejun, V. Vuorinen, J.K. Kivilahti. Interfacial Reactions between Lead-Free Snagcu Solder and Ni(P) Surface Finish on Printed Circuit Boards. IEEE Trans. Electron. Packag. Manuf. 2002, 25(3):162-167.
34 V. Vuorinen, T. Laurila, H. Yu, J.K. Kivilahti. Phase Formation between Lead-Free Sn–Ag–Cu Solder and Ni(P)/Au Finishes. J. Appl. Phys. 2006, 99:023530.
35 C. Ho, R. Tsai, Y. Lin, C. Kao. Effect of Cu Concentration on the Reactions between Sn-Ag-Cu Solders and Ni. J. Electron. Mater. 2002, 31(6):584-590.
36 C.E. Ho, Y.L. Lin, C.R. Kao. Strong Effect of Cu Concentration on the Reaction between Lead-Free Microelectronic Solders and Ni. Chem. Mater. 2002, 14(3):949-951.
37 W.T. Chen, C.E. Ho, C.R. Kao. Effect of Cu Concentration on the Interfacial Reactions between Ni and Sn-Cu Solders. J. Mater. Res. 2002, 17(2):263-266
38 P.G. Kim, K.N. Tu. Fast Dissolution and Soldering Reactions on Au Foils. Mater. Chem. Phys. 1998, 53(2):165-171.
39 L.C. Shiau, C.E. Ho, C.R. Kao. Reactions between Sn-Ag-Cu Lead-Free Solders and the Au/Ni Surface Finish in Advanced Electronic Packages. Solder. Surf. Mount Technol. 2002, 14(3):25-29.
40 K. Lee, M. Li. Formation of Intermetallic Compounds in Snpbag, Snag, and Snagcu Solders on Ni/Au Metallization. Metall. Mater. Trans. A-Phys. Metall. Mater. Sci. 2001, 32(10):2666-2668.
41 K. Lee, M. Li. Interfacial Microstructure Evolution in Pb-Free SolderSystems. J. Electron. Mater. 2003, 32(8):906-912.
42 T. Laurila, V. Vuorinen, T. Mattila, J. Kivilahti. Analysis of the Redeposition of Ausn4 on Ni/Au Contact Pads When Using SnPbAg, SnAg, and SnAgCu Solders. J. Electron. Mater. 2005, 34(1):103-111.
43 K.N. Tu, K. Zeng. Tin–Lead (SnPb) Solder Reaction in Flip Chip Technology. Mater. Sci. Eng. R-Rep. 2001, 34:1-58.
44 K. Zeng, K.N. Tu. Six Cases of Reliability Study of Pb-Free Solder Joints in Electronic Packaging Technology. Mater. Sci. Eng. R-Rep. 2002, 38:55-105.
45 T. Laurila, V. Vuorinen, J.K. Kivilahti. Interfacial Reactions between Lead-Free Solders and Common Base Materials. Mater. Sci. Eng. R-Rep. 2005, 49(1-2):1-60.
46 R. Darveaux, K. Banerji. Constitutive Relations for Tin-Based Solder Joints. IEEE Trans. Compon. Hybrid. Manuf. Technol. 1992, 15(6):1013-1024.
47 A.J. Rafanelli. Ramberg-Osgood Parameters for 63-37 Sn-Pb Solder. J. Electron. Packag. 1992, 114:234-238.
48 J.H. Lau, D.W. Rice. Solder Joint Fatigue in Surface Mount Technology: State of the Art. Solid State Technol. 1985, 28(10):91-104.
49 H.K. Charles, G.V. Clatterbaugh. Solder Joint Reliability-Design Implications from Fem and Experimental Testing. J. Electron. Packag. 1990, 112(2):135-146.
50 J.H. Lau, D. Rice, P. Avery. Elastoplastic Analysis of Surface-Mount Solder Joints. IEEE Trans. Compon. Hybrid. Manuf. Technol. 1987, 10(3):346-357.
51 E.E. de Kluizenaar. Reliability of Soldered Joints: A Description of the State-of-the-Art. I. Solder. Surf. Mount Technol. 1990, 4(4):27-38.
52 J. Weertman. Dislocation Climb Theory of Steady-State Creep. ASM Trans. Quart. 1968, 61(4):681-694.
53 J. Weertman, J.R. Weertman. Elementary Dislocation Theory. Macmillan, 1964:213.
54 H.U. Akay, H. Zhang, N.H. Paydar. Experimental Correlations of an Energy-Based Fatigue Life Prediction Method for Solder Joints, Advance in Electronic Packaging. Proceedings of the of the Pacific Rim/ASME International Intersociety Electronic and Photonic Packaging Conference, InterPack'97, New York, 1997, ASME:1567-1574.
55 F.Garofalo. An Empirical Relation Defining the Stress Dependence of Minimum Creep Rate in Metals. Trans. Metall. Soc. AIME. 1963, 227(2):351-355.
56 J.H. Lau, S.-W.R. Lee, C. Chang. Solder Joint Reliability of Wafer Level Chip Scale Packages(WLCSP): A Time-Temperature-Dependent Creep Analysis. J. Electron. Packag. 2000, 122(4):311-317.
57 W. Jung, J.H. Lau, Y.-H. Pao. Nonlinear Analysis of Full-Matrix and Perimeter Plastic Ball Grid Array Solder Joints. J. Electron. Packag. 1997, 119(3):163-170.
58 M.C. Shine, L.R. Fox. Fatigue of Solder Joints in Surface Mount Devices. ASTM Spec. Tech. Publ. 1988(942):588-610.
59 J.H.L. Pang, C.W. Seetoh, Z.P. Wang. Cbga Solder Joint Reliability Evaluation Based on Elastic-Plastic-Creep Analysis. J. Electron. Packag. 2000, 122(3):255-261.
60 J.H.L. Pang, Y.T. Kwok, C.W. SeeToh. Temperature Cycling Fatigue Analysis of Fine Pitch Solder Joints. ASME Advances in Electronic Packaging. 1997, 19(2):1495-1498.
61 V. Sarihan. Temperature Dependent Viscoplastic Simulation of Controlled Collapse Solder Joint under Thermal Cycling. J. Electron. Packag. 1993, 115(3):16-21.
62 K. Iwasaki, Y.H. Pao. Fatigue-Creep Crack Propagation Path in Solder Joints under Thermal Cycling. ASME Advances in Electronic Packaging. 1997, 19(2):1058-1064.
63 A.K. Miller. Unified Constitutive Equations for Creep and Plasticity. Elsevier Applied Science Publishers. 1987:273-285.
64 S.R. Bodner. Unified Plasticity for Engineering Applications. Kluwer Academic/Plenum Punlishers, 2002:97-99.
65 L. Anand. Constitutive Equations for Hot-Working of Metals. Int. J. Plast. 1985, 1(3):213-231.
66 E.P. Busso, M. Kitano, T. Kumazawa. Modeling Complex Inelastic Deformation Processes in Ic Packages. J. Electron. Packag. 1994, 116(3):6-15.
67 E.P. Busso, M. Kitano. A Visco-Plastic Constitutive Model for 60/40 Tin-Lead Solder Used in Ic Package Joints. ASME J. Eng. Mater. Technol. 1992, 114:331-337.
68 A.F. Skipor, S.V. Harren, J. Botsis. On the Constitutive Response of 63/37 Sn/Pb Eutectic Solder. ASME J. Eng. Mater. Technol. 1996, 118(1):1-11.
69 S.E. Yamada. The J-Integral for Augmented Double Cantilever Beams and Its Application to Bonded Joints. Eng. Fract. Mech. 1988, 29(6):673-682.
70 G.Z. Wang, Z.N. Cheng, K. Becker, J. Wilde. Applying Anand Model to Represent the Viscoplastic Deformation Behavior of Solder Alloys. J. Electron. Packag. 2001, 123(3):247-253.
71 W.W. Lee, L.T. Nguyen, G.S. Selvaduray. Solder Joint Fatigue Models: Review and Applicability to Chip Scale Packages. Microelectron. Reliab. 2000, 40(2):231-244.
72 H.D. Solomon. Fatigue of 60/40 Solder. IEEE Trans. Compon. Hybrid. Manuf. Technol. 1986, 9(4):423-432.
73 T.J. Kilinski. Solder Joint Reliability: Theory and Applications. Van Nostrand Reinhold, 1991:389-395.
74 W. Engelmaier. Surface Mount Solder Joint Long-Term Reliability: Design, Testing, Prediction. Solder. Surf. Mount Technol. 1989, 1(1):14-22.
75 W. Engelmaier. Generic Reliability Figures of Merit Design Tools for Surface Mount Solder Attachments. IEEE Trans. Compon. Hybrid. Manuf. Technol. 1993, 16(1):103-112.
76 P.C. Paris. Fracture Mechanics and Fatigue. Fatigue Fract. Eng. Mater. Struct. 1998, 21(5):535-540.
77 Y.H. Pao, S. Badgley, E. Jih, R. Govila, J. Browning. Constitutive Behavior and Low Cycle Thermal Fatigue of 97 Sn-3 Cu Solder Joints. J. Electron. Packag. 1993, 115(22):1-8.
78 J.H. Lau. Solder Joint Reliability: Theory and Applications. Van Nostrand Reinhold, 1991:389-412.
79 J.M. Hu. An Empirical Crack Propagation Model and Its Alication for Solder Joints. J. Electron. Packag. 1996, 118(2):1001-1005.
80 J.H. Lau. Thermal Fatigue Life Prediction of Flip Chip Solder Joints by Fracture Mechanics Method. Eng. fract. mech. 1993, 45(5):643-654.
81 Y.H. Pao. A Fracture Mechanics Approach to Thermal Fatigue Life Prediction of Solder Joints. IEEE Trans. Compon. Hybrid. Manuf. Technol. 1992, 15(4):559-570.
82 A.R. Syed. Creep Crack Growth Prediction of Solder Joints During Temperature Cycling—an Engineering Approach. J. Electron. Packag. 1995, 117(2):116-122.
83 Z. Guo, H. Conrad. Fatigue Crack Growth Rate in 63Sn37Pb Solder Joints. J. Electron. Packag. 1993, 115(2):159-164.
84 H. Krishnamoorthy, H.V. Tippur. Evaluation of Elastic-Plastic Interfacial Fracture Parameters in Solder-Copper Bimaterial Using Moire Interferometry. J. Electron. Packag. 1998, 120(3):267-274.
85 S.H. Ju, B.I. Sandor, M.E. Plesha. Life Prediction of Solder Joints by Damage and Fracture Mechanics. J. Electron. Packag. 1996, 118(4):193-200.
86 Z. Guo, A.F. Sprecher, H. Conrad. Plastic Deformation Kinetics of Eutectic Pb-Sn Solder Joints in Monotonic Loading and Low-Cycle Fatigue. J. Electron. Packag. 1992, 114(2):112-117.
87 E. Levine, J. Ordonez. Analysis of Thermal Cycle Fatigue Damage in Microsocket Solder Joints. IEEE Trans. Compon. Hybrid. Manuf. Technol. 1981, 4(4):515-519.
88 H.D. Solomon. Strain-Life Behavior in 60/40 Solder. J. Electron. Packag. 1989, 111:75-82.
89 A. Dasgupta, C. Oyan, D. Barker, M. Pecht. Solder Creep-Fatigue Analysis by an Energy-Partitioning Approach. J. Electron. Packag. 1992, 114(2):152-160.
90 T.Y. Pan. Critical Accumulated Strain Energy Failure Criterion for Thermal Cycling Fatigue of Solder Joints. J. Electron. Packag. 1994, 116(3):163-170.
91 C. Barasan, C.Y. Yan. Thermodynamic Framework for Damage Mechanics of Solder Joints. J. Electron. Packag. 1998, 120(4):379-384.
92李云卿,唐祥云,马莒生,黄乐. 62Sn-36Pb-2Ag SMT封装焊点的等温剪切低周疲劳特征.金属学报. 1994, 30(4):164-169.
93 S.M. Lee, D.S. Stone. Deformation and Fracture of Pb-Sn-Eutectic under Tensile and Fatigue Loading. J. Electron. Packag. 1992, 114:118-121.
94 H.D. Solomon. High and Low Temperature Strain-Life Behavior of a Pb Rich Solder. J. Electron. Packag. 1990, 112:123-128.
95 H.D. Solomon. Low Cycle Fatigue of Sn96 Solder with Reference to Eutectic Solder and a High Pb Solder. J. Electron. Packag. 1991, 113:102-108.
96 J. Liang, N. Gollhardt, P.S. Lee, S.A. Schroeder, W.L. Morris. A Study of Fatigue and Creep Behavior of Four High Temperature Solders. Fatigue Fract. Eng. Mater. Struct. 1996, 19(11):1401-1409.
97 C. Kanchanomai, Y. Miyashita, Y. Mutoh. Strain-Rate Effects on Low Cycle Fatigue Mechanism of Eutectic Sn-Pb Solder. Int. J. Fatigue. 2002, 24(9):987-993.
98 C. Kanchanomai, Y. Miyashita, Y. Mutoh. Low Cycle Fatigue Behavior and Mechanisms of a Eutectic Sn-Pb Solder 63Sn/37Pb. Int. J. Fatigue. 2002, 24(6):671-683.
99 C. Kanchanomai, S. Yamamoto, Y. Miyashita, Y. Mutoh, A.J. McEvily. Low Cycle Fatigue Test for Solders Using Non-Contact Digital Image Measurement System. Int. J. Fatigue. 2002, 24(1):57-67.
100 J. Zhao, Y. Miyashita, Y. Mutoh. Fatigue Crack Growth Behavior of 95Pb-5Sn Solder under Various Stress Ratios and Frequencies. Int. J. Fatigue. 2000, 22(8):665-673.
101 J. Zhao, Y. Miyashita, Y. Mutoh. Fatigue Crack Growth Behavior of 96.5Sn-3.5Ag Lead-Free Solder. Int. J. Fatigue. 2001, 23(8):723-731.
102 C. Kanchanomai, Y. Miyashita, Y. Mutoh, S.L. Mannan. Influence of Frequency on Low Cycle Fatigue Behavior of Pb-Free Solder 96.5Sn-3.5Ag. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 2003, 345(1-2):90-98.
103 C. Kanchanomai, Y. Miyashita, Y. Mutoh. Low-Cycle Fatigue Behavior andMechanisms of a Lead-Free Solder 96.5Sn/3.5Ag. J. Electron. Mater. 2002, 31(2):142-151.
104 C. Kanchanomai, Y. Mutoh. Effect of Temperature on Isothermal Low Cycle Fatigue Properties of Sn-Ag Eutectic Solder. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 2004, 381(1-2):113-120.
105 R.B. Vastava, T.G. Langdon. An Investigation of Intercrystalline and Interphase Boundary Sliding in the Superplastic Pb-62% Sn Eutectic. Acta Metallurgica. 1979, 27(2):251-257.
106 V. Raman, T. Reiley. Cyclic Deformation and Fracture in Pb-Sn Solid Solution Alloy. Metall. Mater. Trans. A-Phys. Metall. Mater. Sci. 1988, 19(6):1533-1546.
107 S. Vayman, M. Fine, D. Jeannotte. Isothermal Fatigue of Low Tin Lead Based Solder. Metall. Mater. Trans. A-Phys. Metall. Mater. Sci. 1988, 19(4):1051-1059.
108 M.E. Fine, V. Stolkarts, L.M. Keer. Fatigue Crack Nucleation Assisted by Thermal Activation. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 1999, 272(1):5-9.
109 K. Tanaka, T. Mura. A Dislocation Model for Fatigue Crack Initiation. J. Appl. Mech. 1981, 48(1):97-103.
110T. Mura, Y. Nakasone. A Theory of Fatigue Crack Initiation in Solids. J. Appl. Mech. 1990, 57:1-6.
111 B. Wong, D.E. Helling. A Mechanistic Model for Solder Joint Failure Prediction under Thermal Cycling. J. Electron. Packag. 1990, 112:104-109.
112 A.I. Attarwala, J.K. Tien, G.Y. Masada, G. Dody. Confirmation of Creep and Fatigue Damage in Pb/Sn Solder Joints. J. Electron. Packag. 1992, 114:109-111.
113 M. Nowottnick, W. Scheel, K. Wittke, U. Pape. Method for Rapid Testing of Thermo-Mechanical Characteristics of Solder Joints. Microelectron. Reliab. 2000, 40(7):1135-1146.
114 J.H. Lau, S.W.R. Lee. Reliability of Wafer Level Chip Scale Package (Wlcsp) with 96.5Sn-3.5Ag Lead-Free Solder Joints on Build-up Microvia Printed Circuit Board. S.W.R. Lee. Electronic Materials and Packaging, 2000. (EMAP 2000). International Symposium on, 2000:55-63.
115 J.H. Lau, S.H. Pan, C. Chang. Creep Analysis of Wafer Level Chip Scale Package (WLCSP) with 96.5Sn-3.5Ag and 100in Lead-Free Solder Joints and Microvia Build-up Printed Circuit Board. J. Electron. Packag. 2002, 124(2):69-76
116 S. Wiese, F. Feustel, E. Meusel. Characterisation of Constitutive Behaviour of Snag, SnAgCu and SnPb Solder in Flip Chip Joints. Sens. Actuator A-Phys.2002, 99(1-2):188-193.
117 J. Villain, O.S. Brueller, T. Qasim. Creep Behaviour of Lead Free and Lead Containing Solder Materials at High Homologous Temperatures with Regard to Small Solder Volumes. Sens. Actuator A-Phys. 2002, 99(1-2):194-197.
118 R. McCabe, M. Fine. Creep of Tin, Sb-Solution-Strengthened Tin, and Sbsn-Precipitate-Strengthened Tin. Metall. Mater. Trans. A-Phys. Metall. Mater. Sci. 2002, 33(5):1531-1539.
119 H. Song, J. Morris, F. Hua. The Creep Properties of Lead-Free Solder Joints. JOM. 2002, 54(6):30-32.
120 S. Jadhav, T. Bieler, K. Subramanian, J. Lucas. Stress Relaxation Behavior of Composite and Eutectic Sn-Ag Solder Joints. J. Electron. Mater. 2001, 30(9):1197-1205.
121 K. Chen, A. Telang, J. Lee, K. Subramanian. Damage Accumulation under Repeated Reverse Stressing of Sn-Ag Solder Joints. J. Electron. Mater. 2002, 31(11):1181-1189.
122 M. Kerr, N. Chawla. Creep Deformation Behavior of Sn-3.5Ag Solder/Cu Couple at Small Length Scales. Acta Mater. 2004, 52(15):4527-4535.
123R. Cabarat, L. Guillet, R.L. Roux. The Elastic Properties of Metallic Alloys. J. Inst. Met. 1949, 75:391-402.
124 B. Subrahmanyan. Elastic Moduli of Some Complicated Binary Alloy Systems. Trans. Jpn. Inst. Met. 1972, 130:93-95.
125 L.M. Ostrovskaya, V.N. Rodin, A.I. Kuznetsov. Soviet J. Non-Ferrous Metall. (TSVETNYE METALLY). 1985, 26:90-96.
126 R.J. Fields, S.R. Low. http://www.metallurgy.nist.gov/mechanical_properties /solder_paper.html.
127 R. Chromik, R. Vinci, S. Allen, M. Notis. Measuring the Mechanical Properties of Pb-Free Solder and Sn-Based Intermetallics by Nanoindentation. JOM. 2003, 55(6):66-69.
128 R.R. Chromik, R.P. Vinci, S.L. Allen, M.R. Notis. Nanoindentation Measurements on Cu–Sn and Ag–Sn Intermetallics Formed in Pb-Free Solder Joints. J. Mater. Res. 2003, 18(9):2251-2261.
129 G. Ghosh. Elastic Properties, Hardness, and Indentation Fracture Toughness of Intermetallics Relevant to Electronic Packaging. J. Mater. Res. 2004, 19(5):1439-1454.
130 X. Deng, M. Koopmanb, N. Chawla, K.K. Chawla. Young's Modulus of (Cu, Ag)–Sn Intermetallics Measured by Nanoindentation. Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 2004, 364:240-243.
131 X. Deng, N. Chawla, K.K. Chawla, M. Koopman. Deformation Behavior of (Cu, Ag)–Sn Intermetallics by Nanoindentation. Acta Mater. 2004,52(14):4291-4303.
132 M. Dao, N. Chollacoop, K.J. Van Vliet, T.A. Venkatesh, S. Suresh. Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation. Acta Mater. 2001, 49(19):3899-3918.
133 R.R. Chromik, D.-N. Wang, A. Shugar, L. Limata, M.R. Notis, R.P. Vinci. Mechanical Properties of Intermetallic Compounds in the Au–Sn System. J. Mater. Res. 2005, 20(8):2161-2172.
134 F.G. Yost, M.M. Karnowsky, W.D. Drotning, J.H. Gieske. Thermal Expansion and Elastic Properties of High Gold-Tin Alloys. Metall. Mater. Trans. A-Phys. Metall. Mater. Sci. 1990, 21:1885-1889.
135 J. Ciulik, M.R. Notis:. Phase Equilibria and Physical Properties in the Au–Sn System. Proceedings of the 2nd ASM International Electronic Materials and Processing Congress, OH, 1989, ASM International:57-61.
136 A. Vicenzo, M. Rea, L. Vonella, M. Bestetti, P.L. Cavallotti. Electrochemical Deposition and Structural Characterization of Au-Sn Alloys. J. Solid State Electrochem. 2004, 8(3):159-166.
137 B.H. Cheong, K.J. Chang. First-Principles Study of the Structural Properties of Sn under Pressure. Phys. Rev. B. 1991, 44(9):4103-4108.
138 N.E. Christensen, M. Methfessel. Density-Functional Calculations of the Structural Properties of Tin under Pressure. Phys. Rev. B. 1993, 48(9):5797-5807.
139 T. Brudevoll, D.S. Citrin, M. Cardona, N.E. Christensen. Electronic Structure of Alpha -Sn and Its Dependence on Hydrostatic Strain. Phys. Rev. B. 1993, 48(12):8629-8635.
140 P. Pavone, S. Baroni, S. de Gironcoli. Alpha-Beta Phase Transition in Tin: A Theoretical Study Based on Density-Functional Perturbation Theory. Phys. Rev. B. 1998, 57(17):10421-10423.
141 A. Aguado. First-Principles Study of Elastic Properties and Pressure-Induced Phase Transitions of Sn: Lda Versus Gga Results. Phys. Rev. B. 2003, 67(21):212104.
142 C.Q. Wang, W.F. Feng. Selecting Cluster Model in Alloy Designing Calculation with Discrete Variational Xa Method. Acta Metallurgica Sinica (English Letters). 2000, 13(1):84-88.
143 W.F. Feng, C.Q. Wang, M. Morinaga, H. Yukawa, Y. Liu. Electronic Structure Calculation for Properties of Sn-Based Solder Alloys with the Relativistic Dv-Xa Method. Modell. Simul. Mater. Sci. Eng. 2002, 10(2):121-129.
144 W.F. Feng, C.Q. Wang, M. Morinaga. Electronic Structure Mechanism for the Wettability of Sn-Based Solder Alloys. J. Electron. Mater. 2002, 31(3):185-190.
145 G. Ghosh, M. Asta. Phase Stability, Phase Transformations, and Elastic Properties of Cu6sn5: Ab Initio Calculations and Experimental Results. J. Mater. Res. 2005, 20(11):3102-3117.
146 N.T.S. Lee, V.B.C. Tan, K.M. Lim. First-Principles Calculations of Structural and Mechanical Properties of Cu6Sn5. Appl. Phys. Lett. 2006, 88:031913.
147 N.T.S. Lee, V.B.C. Tan, K.M. Lim. Structural and Mechanical Properties of Sn-Based Intermetallics from Ab Initio Calculations. Appl. Phys. Lett. 2006, 89:141908.
148R. Hill. The Elastic Behaviour of a Crystalline Aggregate. Proc. Phys. Soc. A. 1952, 65(5):349-354
149 R. Ravelo, M. Baskes. Equilibrium and Thermodynamic Properties of Grey, White, and Liquid Tin. Phys. Rev. Lett. 1997, 79(13):2482-2485.
150 S. Bernard, J.B. Maillet. First-Principles Calculation of the Melting Curve and Hugoniot of Tin. Phys. Rev. B. 2002, 66(1):012103.
151 H. Dong, K.-S. Moon, C. Wong. Molecular Dynamics Study of Nanosilver Particles for Low-Temperature Lead-Free Interconnect Applications. J. Electron. Mater. 2005, 34(1):40-45.
152 H. Dong, L. Fan, K.-s. Moon, C.P. Wong, M.I. Baskes. Meam Molecular Dynamics Study of Lead Free Solder for Electronic Packaging Applications. Modell. Simul. Mater. Sci. Eng. 2005, 13(8):1279-1290.
153 M. Born, J.R. Oppenheimer. On the Quantum Theory of Molecules. Inc Bell Telephone, 1954:89-96.
154 D.R. Hartree. The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I-Theory and Methods. Proceedings of the Cambridge Philosophical Society, 1928:89-110.
155 V. Fock. N?herungsmethode Zur L?sung Des Quantenmechanischen Mehrk?rperproblems Zeits. f. Physik. 1930, 61(1-2):126-148.
156 J.C. Slater. Atomic Shielding Constants. Phys. Rev. 1930, 36(1):57-64.
157 D.R. Hartree. The Calculation of Atomic Structures John Wiley & Sons, Inc, 1957:58-59.
158 J.A. Pople, M. Head-Gordon, K. Raghavachari. Quadratic Configuration Interaction. A General Technique for Determining Electron Correlation Energies. J. Chem. Phys. 1987, 87(10):5968-5975.
159 P. Hohenberg, W. Kohn. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136(3B):B864 - B871.
160 W. Kohn, L.J. Sham. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140(4A):A1133-A1138
161 D.C. Langreth, J.P. Perdew. Theory of Nonuniform Electronic Systems. I. Analysis of the Gradient Approximation and a Generalization That Works.Phys. Rev. B. 1980, 21(12):5469-5493.
162 D.C. Langreth, M.J. Mehl. Beyond the Local-Density Approximation in Calculations of Ground-State Electronic Properties. Phys. Rev. B. 1983, 28(4):1809-1834.
163 J.P. Perdew, W. Yue. Accurate and Simple Density Functional for the Electronic Exchange Energy: Generalized Gradient Approximation. Phys. Rev. B. 1986, 33(12):8800-8802.
164 J.P. Perdew. Density-Functional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Phys. Rev. B. 1986, 33(12):8822-8824.
165 T. Koopmans. ber Die Zuordnung Von Wellenfunktionen Und Eigenwerten Zu Den Einzelnen Elektronen Eines Atoms. Physica. 1934, 1(1-6):104-113.
166 J.C. Slater. A Simplification of the Hartree-Fock Method. Phys. Rev. 1951, 81(3):385-390.
167 D.M. Ceperley, B.J. Alder. Ground State of the Electron Gas by a Stochastic Method. Phys. Rev. Lett. 1980, 45(7):566-569.
168 J.P. Perdew, A. Zunger. Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems. Phys. Rev. B. 1981, 23(10):5048-5079.
169 J.P. Perdew, Y. Wang. Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy. Phys. Rev. B. 1992, 45(23):13244-13249.
170 A. Rosén, D.E. Ellis, H. Adachi, F.W. Averill. Calculations of Molecular Ionization Energies Using a Self-Consistent-Charge Hartree-Fock-Slater Method. J. Chem. Phys. 1976, 65(9):3629-3634.
171 D.E. Ellis, H. Adachi, F.W. Averill. Molecular Cluster Theory for Chemisorption of First Row Atoms on Nickel /100/ Surfaces. Surf. Sci. 1976, 58(2):497-510.
172 R.M. Martin. Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press, 2004:156-159.
173 W. Kohn. Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms. Phys. Rev. Lett. 1996, 76(17):3168.
174 W. Kohn. Nobel Lecture: Electronic Structure of Matter—Wave Functions and Density Functionals. Rev. Mod. Phys. 1999, 71(5):1253-1266.
175 A.D. Becke. Density-Functional Thermochemistry. I. The Effect of the Exchange-Only Gradient Correction. J. Chem. Phys. 1992, 96(3):2155-2160.
176 A.D. Becke. Density-Functional Thermochemistry. Ii. The Effect of the Perdew-Wang Generalized-Gradient Correlation Correction. J. Chem. Phys. 1992, 97(12):9173-9177.
177 A.D. Becke. Density-Functional Thermochemistry. Iii. The Role of Exact Exchange. J. Chem. Phys. 1993, 98(7):5648-5652.
178 A.D. Becke. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A. 1988, 38(6):3098-3100.
179 J.P. Perdew, Y. Wang. Pair-Distribution Function and Its Coupling-Constant Average for the Spin-Polarized Electron Gas. Phys. Rev. B. 1992, 46(20):12947-12954.
180 J.P. Perdew, K. Burke, M. Ernzerhof. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77(18):3865-3868.
181 C. Lee, W. Yang, R.G. Parr. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B. 1988, 37(2):785-789.
182 C. Filippi, C.J. Umrigar, M. Taut. Comparison of Exact and Approximate Density Functionals for an Exactly Soluble Model. J. Chem. Phys. 1994, 100(2):1290-1296.
183 X. Xu, W.A. Goddard III. The X3LYP Extended Density Functional for Accurate Descriptions of Nonbond Interactions, Spin States, and Thermochemical Properties. Proc. Natl. Acad. Sci. U. S. A. 2004, 101(9):2673-2677.
184 A.E. Mattsson, P.A. Schultz, M.P. Desjarlais, T.R. Mattsson, K. Leung. Designing Meaningful Density Functional Theory Calculations in Materials Science—a Primer. Modell. Simul. Mater. Sci. Eng. 2005, 13:R1-R31.
185 J.P. Perdew, S. Kurth, A. Zupan, P. Blaha. Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation. Phys. Rev. Lett. 1999, 82(12):2544-2547.
186 J. Tao, J.P. Perdew, V.N. Staroverov, G.E. Scuseria. Climbing the Density Functional Ladder: Nonempirical Meta;Generalized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91(14):146401.
187 A.D. Becke. A New Mixing of Hartree--Fock and Local Density-Functional Theories. J. Chem. Phys. 1993, 98(2):1372-1377.
188 U.v. Barth, L. Hedin. A Local Exchange-Correlation Potential for the Spin Polarized Case. I. J. Phys. C: Solid State Phys. 1972, 5(13):1629-1642.
189 J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais. Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B. 1992, 46(11):6671-6687.
190 V.I. Anisimov, J. Zaanen, O.K. Andersen. Band Theory and Mott Insulators: Hubbard U Instead of Stoner I. Phys. Rev. B. 1991, 44(3):943-954.
191 B.A. Hess. Relativistic Electronic-Structure Calculations Employing a Two-Component No-Pair Formalism with External-Field Projection Operators. Phys. Rev. A. 1986, 33(6):3742-3748.
192 E. van Lenthe, E.J. Baerends, J.G. Snijders. Relativistic Regular Two-Component Hamiltonians. The Journal of Chemical Physics. 1993, 99(6):4597-4610.
193 T. Nakajima, T. Suzumura, K. Hirao. A New Relativistic Scheme in Dirac-Kohn-Sham Theory. Chem. Phys. Lett. 1999, 304(3-4):271-277.
194 T. Nakajima, K. Hirao. A New Relativistic Theory: A Relativistic Scheme by Eliminating Small Components (Resc). Chem. Phys. Lett. 1999, 302(5-6):383-391.
195 E. Runge, E.K.U. Gross. Density-Functional Theory for Time-Dependent Systems. Phys. Rev. Lett. 1984, 52(12):997-1000.
196 E.K.U. Gross, W. Kohn. Local Density-Functional Theory of Frequency-Dependent Linear Response. Phys. Rev. Lett. 1985, 55(26):2850-2852.
197 G. Vignale, M. Rasolt. Density-Functional Theory in Strong Magnetic Fields. Phys. Rev. Lett. 1987, 59(20):2360-2363.
198 S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi. Phonons and Related Crystal Properties from Density-Functional Perturbation Theory. Rev. Mod. Phys. 2001, 73(2):515-562.
199 R. Car, M. Parrinello. Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Lett. 1985, 55(22):2471-2474.
200 R. Car, M. Parrinello. Structural, Dymanical, and Electronic Properties of Amorphous Silicon: An Ab Initio Molecular-Dynamics Study. Phys. Rev. Lett. 1988, 60(3):204-207.
201 T.L. Beck. Real-Space Mesh Techniques in Density-Functional Theory. Rev. Mod. Phys. 2000, 72(4):1041-1080.
202 W.A. Harrison. Electronic Structure and the Properties of Solids. Freeman, 1980:278-295.
203黄昆,韩汝琦.固体物理学.高等教育出版社, 1988:189-196.
204 D.E. Ellis, G.S. Painter. Discrete Variational Method for the Energy-Band Problem with General Crystal Potentials. Phys. Rev. B. 1970, 2(8):2887-2898.
205李正中.固体物理.高等教育出版社, 2002:135-137.
206 C. Herring. A New Method for Calculating Wave Functions in Crystals. Phys. Rev. 1940, 57(12):1169-1177.
207 M.L. Cohen, V. Heine, D. Weaire. Solid State Physics. Academic, 1970:38-249.
208 C.F. Melius, W.A. Goddard. Ab Initio Effective Potentials for Use in Molecular Quantum Mechanics. Phys. Rev. A. 1974, 10(5):1528-1540.
209 A. Zunger, M.L. Cohen. Density-Functional Pseudopotential Approach toCrystal Phase Stability and Electronic Structure. Phys. Rev. Lett. 1978, 41(1):53-56.
210 J.A. Appelbaum, D.R. Hamann. Self-Consistent Pseudopotential for Si. Phys. Rev. B. 1973, 8(4):1777-1780.
211 M. Schlüter, J.R. Chelikowsky, S.G. Louie, M.L. Cohen. Self-Consistent Pseudopotential Calculations for Si (111) Surfaces: Unreconstructed (1 X 1) and Reconstructed (2 X 1) Model Structures. Phys. Rev. B. 1975, 12(10):4200-4214.
212 D.R. Hamann, M. Schlüter, C. Chiang. Norm-Conserving Pseudopotentials. Phys. Rev. Lett. 1979, 43(20):1494-1497.
213 G.B. Bachelet, D.R. Hamann, M. Schlüter. Pseudopotentials That Work: From H to Pu. Phys. Rev. B. 1982, 26(8):4199-1228.
214 D. Vanderbilt. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B. 1990, 41(11):7892-7895
215 J.C. Slater. Wave Functions in a Periodic Potential. Phys. Rev. 1937, 51(10):846-851.
216 J.C. Slater. An Augmented Plane Wave Method for the Periodic Potential Problem. Phys. Rev. 1953, 92(3):603-608.
217 J. Korringa. On the Calculation of the Energy of a Bloch Wave in a Metal. Physica. 1947, 13(6-7):392-400.
218 W. Kohn, N. Rostoker. Solution of the SchrÖDinger Equation in Periodic Lattices with an Application to Metallic Lithium. Phys. Rev. 1954, 94(5):1111-1120.
219 O.K. Andersen. Linear Methods in Band Theory. Phys. Rev. B. 1975, 12(8):3060-3083.
220 E. Wimmer, H. Krakauer, M. Weinert, A.J. Freeman. Full-Potential Self-Consistent Linearized-Augmented-Plane-Wave Method for Calculating the Electronic Structure of Molecules and Surfaces: O2 Molecule. Phys. Rev. B. 1981, 24(2):864-875.
221 O.K. Andersen, T. Saha-Dasgupta. Muffin-Tin Orbitals of Arbitrary Order. Phys. Rev. B. 2000, 62(24):R16219-R16222.
222 P.E. Bl?chl. Projector Augmented-Wave Method. Phys. Rev. B. 1994, 50(24):17953-17979.
223 G. Kresse, D. Joubert. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B. 1999, 59(3):1758-1775.
224 C. Erginsoy, G.H. Vineyard, A. Englert. Dynamics of Radiation Damage in a Body-Centered Cubic Lattice. Phys. Rev. 1964, 133(2A):A595-A606.
225 A. Rahman. Correlations in the Motion of Atoms in Liquid Argon. Phys. Rev. 1964, 136(2A):A405-A411.
226 V. Vitek. Interatomic Potentials for Atomistic Simulations. Materials Research Society, 1996:20.
227 J.E. Lennard-Jones. Proc. R. Soc., London, 1924:441-463.
228 P.M. Morse. Diatomic Molecules According to the Wave Mechanics. Ii. Vibrational Levels. Phys. Rev. 1929, 34(1):57-64.
229 I.M. Torrens. Interatomic Potentials. Academic Press, 1972:197-199.
230 M. Sigalas, D.A. Papaconstantopoulos. Materials Theory and Modelling. J.Q. Broughton, P. Bristowe ,J.M. Newsam. Mater. Res. Soc. Symp. Proc., Pittsburgh, 1993, Materials Research Society:27.
231 R.A. Johnson. Relationship between Two-Body Interatomic Potentials in a Lattice Model and Elastic Constants. Phys. Rev. B. 1972, 6(6):2094-2100.
232冯端.结构与缺陷.科学出版社, 2000:31-76.
233 V. Gerold. Structure of Solids of Materials Science and Technology-a Comprehensive Treatment. VCH, 1993:23-29.
234 A.P. Sutton. Applied Sciences. H.O. Kirchner, L.P. Kubin ,V. Pontikis. Proceedings of NATO ASI on Computer Simulation in Materials Science, 1996, Kluwer Academic:163.
235 M.S. Daw, M.I. Baskes. Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and Other Defects in Metals. Phys. Rev. B. 1984, 29(12):6443-6453.
236 M.W. Finnis, J.E. Sinclair. A Simple Empirical N-Body Potential for Transition Metals. Philosophical Magazine A. 1984, 50(1):45-55.
237 R.A. Johnson. Analytic Nearest-Neighbor Model for Fcc Metals. Phys. Rev. B. 1988, 37(8):3924-3931.
238R.A. Johnson. Alloy Models with the Embedded-Atom Method. Phys. Rev. B. 1989, 39(17):12554-12559.
239 S.M. Foiles, M.I. Baskes, M.S. Daw. Embedded-Atom-Method Functions for the Fcc Metals Cu, Ag, Au, Ni, Pd, Pt, and Their Alloys. Phys. Rev. B. 1986, 33(12):7983-7991.
240 M. Manninen. Interatomic Interactions in Solids: An Effective-Medium Approach. Phys. Rev. B. 1986, 34(12):8486-8495.
241 M.I. Baskes. Modified Embedded-Atom Potentials for Cubic Materials and Impurities. Phys. Rev. B. 1992, 46(5):2727-2742.
242 M.I. Baskes, R.A. Johnson. Modified Embedded Atom Potentials for Hcp Metals. Modell. Simul. Mater. Sci. Eng. 1994, 2(1):147-163.
243 K.W. Jacobsen, J.K. Norskov, M.J. Puska. Interatomic Interactions in the Effective-Medium Theory. Phys. Rev. B. 1987, 35(14):7423-7442.
244 F.H. Stillinger, T.A. Weber. Computer Simulation of Local Order in Condensed Phases of Silicon. Phys. Rev. B. 1985, 31(8):5262-5271.
245 G.C. Abell. Empirical Chemical Pseudopotential Theory of Molecular and Metallic Bonding. Phys. Rev. B. 1985, 31(10):6184-6196.
246 J. Tersoff. New Empirical Approach for the Structure and Energy of Covalent Systems. Phys. Rev. B. 1988, 37(12):6991-7000.
247 D.W. Brenner. Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of Diamond Films. Phys. Rev. B. 1990, 42(15):9458-9471.
248 D.W. Brenner, D.H. Robertson, M.L. Elert, C.T. White. Detonations at Nanometer Resolution Using Molecular Dynamics. Phys. Rev. Lett. 1993, 70(14):2174-2177.
249 D.G. Pettifor, I.I. Oleinik. Analytic Bond-Order Potentials Beyond Tersoff-Brenner. I. Theory. Phys. Rev. B. 1999, 59(13):8487-8499.
250 I.I. Oleinik, D.G. Pettifor. Analytic Bond-Order Potentials Beyond Tersoff-Brenner. Ii. Application to the Hydrocarbons. Phys. Rev. B. 1999, 59(13):8500-8507.
251 N.-x. Chen, G.-b. Ren. Carlsson-Gelatt-Ehrenreich Technique and the M?bius Inversion Theorem. Phys. Rev. B. 1992, 45(14):8177-8180.
252 H.J. Monkhorst, J.D. Pack. Special Points for Brillouin-Zone Integrations. Phys. Rev. B. 1976, 13(12):5188-5192
253 T.H. Fischer, J. Alml?f. General Methods for Geometry and Wave Function Optimization. J. Phys. Chem. 1992, 96(24):9768-9774.
254 Y. Watanabe, Y. Fujinaga, H. Iwasaki. Lattice Modulation in the Long-Period Superstructure of Cu3sn. Acta Crystallogr., Sect. B: Struct. Sci. 1983, 39(3):306-311.
255 W. Burkhardt, K. Schubert. Uber Messingartige Phasen Mit as-Uerwandter Struktur. Z. Metallkd. 1959, 50:442-452.
256 R. Kubiak, M. Wolcyrz. Refinement of the Crystal Structures of Ausn4 and Pdsn4. Journal of the less-common metals. 1984, 97:265-269.
257 K. Schubert, H. Breimer, R. Gohle. Zuin Aufbau Der Systeme Gold-Indium, Gold-Zinn, Gold-Indium-Zinn and Gold-Zinn-Antimon. Z. Metallkd. 1959, 50(3):146-153.
258 K. Osada, S. Yamaguchi, M. Hirabayashi. An Ordered Structure of Au5sn. Trans. Jpn. Inst. Met. 1974, 15:256-260.
259J.-P. Jan, W.B. Pearson, A. Kjekshus, S.B. Woods. On the Structural ,Thermal, Electrical, and Magnetic Properties of Ausn. Can. J. Phys. 1963, 41:2252-2266.
260 J.P. Watt. Hashin-Shtrikman Bounds on the Effective Elastic Moduli of Polycrystals with Orthorhombic Symmetry. J. Appl. Phys. 1979, 50(10):6290-6295.
261 J.P. Watt. Hashin-Shtrikman Bounds on the Effective Elastic Moduli of Polycrystals with Monoclinic Symmetry. J. Appl. Phys. 1980, 51(3):1520-1524.
262 J.P. Watt, L. Peselnick. Clarification of the Hashin-Shtrikman Bounds on the Effective Elastic Moduli of Polycrystals with Hexagonal, Trigonal, and Tetragonal Symmetries. J. Appl. Phys. 1980, 51(3):1525-1531.
263 S.F. Pugh. Philos. Mag. 1954, 45:823.
264 J.F. Nye. Physical Properties of Crystals. Oxford University Press, 1985:423-425.
265 K.H. Prakash, T. Sritharan. Interface Reaction between Copper and Molten Tin–Lead Solders. Acta Mater. 2001, 49:2481–2489.
266 O.L. Anderson. J. Phys. Chem. Solids. 1963, 24:909.
267 E. Schreiber, O.L. Anderson, N. Soga. Elastic Constants and Their Measurements. McGraw-Hill, 1973:245-246.
268 D.R. Clarke. Materials Selection Guidelines for Low Thermal Conductivity Thermal Barrier Coatings. Surf. Coat. Technol. 2003, 163-164:67-74.
269 D.W. Brenner. The Art and Science of an Analytic Potential. Phys. Status Solidi B-Basic Solid State Phys. 2000, 217(1):23-40.
270 D.W. Brenner. Relationship between the Embedded-Atom Method and Tersoff Potentials. Phys. Rev. Lett. 1989, 63(9):1022-1022.
271 J. Tersoff. Chemical Order in Amorphous Silicon Carbide. Phys. Rev. B. 1994, 49(23):16349-16352
272 K.E. Khor, S. Das Sarma. Proposed Universal Interatomic Potential for Elemental Tetrahedrally Bonded Semiconductors. Phys. Rev. B. 1988, 38(5):3318-3322.
273 D. Conrad, K. Scheerschmidt. Empirical Bond-Order Potential for Semiconductors. Phys. Rev. B. 1998, 58(8):4538-4542.
274 F. Birch. Finite Strain Isotherm and Velocities for Single-Crystal and Polycrystalline Nacl at High Pressures and 300k. J. Geophys. Res. 1978, 83(B3):1257-1268.
275 K. Albe. Theoretical Study of Boron Nitride Modifications at Hydrostatic Pressures. Phys. Rev. B. 1997, 55(10):6203-6210.
276 V.E. Bondybey, M.C. Heaven, T.A. Miller. Laser Vaporization of Tin: Spectra and Ground State Molecular Parameters of Sn2. J. Chem. Phys. 1983, 78(6):3593-3598.
277 C. Jo, K. Lee. Semiempirical Tight Binding Method Study of Small Ge and Sn Clusters. J. Chem. Phys. 2000, 113(17):7268-7272.
278 C. Majumder, V. Kumar, H. Mizuseki, Y. Kawazoe. Small Clusters of Tin: Atomic Structures, Energetics, and Fragmentation Behavior. Phys. Rev. B.2001, 64:233405.
279 C. Majumder, V. Kumar, H. Mizuseki, Y. Kawazoe. Atomic and Electronic Structures of Neutral and Cation SnN (N = 2-20) Clusters: A Comparative Theoretical Study with Different Exchange-Correlation Functionals. Phys. Rev. B. 2005, 71(3):035401.
280 R.W.G. Wyckoff. Crystal Structures. Interscience, 1963:26ff.
281 C. Kittel. Introduction to Solid State Physics. Wiley, 1976:24-28.
282 C.S. Barrett, T.B. Massalski. Structure of Metals. McGraw-Hill, 1966:53-56.
283 C.J. Buchenauer, M. Cardona, F.H. Pollak. Raman Scattering in Gray Tin. Phys. Rev. B. 1971, 3(4):1243-1244.
284 E.A. Brandes. Smithells Metals Reference Book. Butterworths, 1983:156-157.
285 J. Thewlis, A.R. Davey. Thermal Expansion of Grey Tin. Nature (London, U. K.). 1954, 174:1011.
286 J. Ihm, M.L. Cohen. Equilibrium Properties and the Phase Transition of Grey and White Tin. Phys. Rev. B. 1981, 23(4):1576-1579.
287 J.A. Rayne, B.S. Chandrasekhar. Elastic Constants of Beta Tin from 4.2 K to 300 K. Phys. Rev. 1960, 120(5):1658-1663.
288 P.W. Bridgman. Proc. Am. Acad. Arts Sci. 1949, 77:189.
289 S.N. Vaidya, G.C. Kennedy. J. Phys. Chem. Solids. 1970, 31:2329.
290 L.A. Carapella, R. Hultgren. The Ferromagnetic Nature of the Beta Phase in the Copper-Manganese-Tin System. Trans. AIME. 1942, 147:232-242.
291 M. Liu, L.-G. Liu. Compressions and Phase Transitions of Tin to Half a Megabar. High Temp. - High Pressures. 1986, 18:79-85.
292 J. Moré. The Levenberg-Marquardt Algorithm: Implementation and Theory. Springer, 1978:1-3.
293 F. Seitz, D. Turnbull. Solid State Physics. Academic Press, 1956:25-27.
294 R.W. Hill, D.H. Parkinson. Philos. Mag. 1952, 43:309.
295J.C. Phillips. Vibration Spectra and Specific Heats of Diamond-Type Lattices. Phys. Rev. 1959, 113(1):147-155.
296 T.C. Cetas, J.C. Holste, C.A. Swenson. Heat Capacities from 1 to 30 K of Zn, Cd, Sn, Bi, and Y. Phys. Rev. 1969, 182(3):679-685.
297 T. Wolfram, G.W. Lehman, R.E. De Wames. Lattice Dynamics of White Tin. Phys. Rev. 1963, 129(6):2483-2489.