Phase stability, phase transformations, and elastic properties of Cu 6 Sn 5 : Ab initio calculations and experimental re
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Among many Sn-based intermetallics, Cu6Sn5 ( and ⬘) is ubiquitous in modern solder interconnects. Using the published structural models of and ⬘ and also related structures, the total energies and equilibrium cohesive properties are calculated from first-principles employing electronic density-functional theory, ultrasoft pseudopotentials, and both the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange-correlation energy. The accuracy of our calculations is assessed through comparisons between theoretical results and experimental measurements for lattice parameters, elastic properties, and formation and transformation energies. The ambient-temperature experimental lattice constants of and ⬘ are found to lie between the LDA and GGA level calculated zero-temperature lattice constants. The Wyckoff positions in the structural models of and ⬘ agree very well with the ab initio results. The calculated formation energy of ⬘ lies between −3.2 and −4.0 kJ/mol, which is more positive by about 3 to 4 kJ/mol compared to reported experimental data obtained by solution calorimetry. Our systematic differential scanning calorimetry (DSC) experiments show that the ⬘ → transformation enthalpy is 438 ± 18 J/mol, which is about 66% higher than the literature value. In view of our DSC results on heating and cooling, the nature of ⬘ → and → ⬘ is discussed. Our experimental bulk modulus of and ⬘, and the heat of ⬘ → transformation agree very well with the ab initio total energy calculations at the GGA level. Based on these results, we conclude that other isotropic elastic moduli (Young’s modulus, shear, and Poissons ratio) of and ⬘ phases measured by pulse-echo technique are representative of their actual properties. The scatter in experimental elastic constants in the literature may be attributed to various factors, such as the measurement technique (pulse-echo versus nanoindentation), type of specimen (bulk, Cu6Sn5-layer in diffusion couple, thin-film), and anisotropy effects (particularly in Cu6Sn5-layer in diffusion couples).
I. INTRODUCTION
Due to the increasingly dense arrays of interconnects, the miniaturization of electronic packages, and the use of lead-free solders, there has been a renewed interest in soldering technology. The critical issues of a soldering technology are the wetting behavior and the dynamics of interfacial microstructure evolution during processing and in service.1 Therefore, it is of fundamental and practical interest to quantify the thermodynamic driving forces that govern these phenomena.
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Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2005.0371 3102
J. Mater. Res., Vol. 20, No. 11, Nov 2005
In addition, the phases that form in solder interconnects during fabrication and under normal service condition may affect the reliability of the devices through the following intrinsic properties: coefficient of thermal expansion (CTE), ductile/brittle transition, elastic and plastic pro
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