The study of size effects in electronic structural components and solders is important when dimensions are being continually downsized. It is crucial to obtain a constitutive model that describes material behavior of electronic package solders at small scales. Ample studies are available to describe the deformation behavior of SAC alloys at bulk level. For instance, stress-strain, creep, and shear behaviors have been investigated for bulk SAC samples. Although solder joints are very small in dimensions, most researchers have not explained the solder deformation considering size effects. With further miniaturization of solder joints in high density packaging, the localized material behavior can influence significantly the overall system. For instance, knowledge of individual grain properties of a crystalline materials is essential in determining material behavior of miniaturized products.

Sn-Ag-Cu (SAC) alloys are the most widely used lead-free materials to fabricate solder interconnects in microelectronic packaging. For most of the SAC alloys, more than 95% weight percentage is β-Sn which is a highly anisotropic material in terms of elastic modulus (E) and coefficient of thermal expansion (CTE). Moreover, due to the crystalline nature of β-Sn material, plastic deformation beyond the elastic limit is described by various atomic planes and directions, which are termed as slip systems. Ten different slip families with 32 slip systems have been recognized for β-Sn body-centered tetragonal (BCT) crystals. When external loads are applied on solder joints, plastic deformation is dictated by the movement of dislocations and direction of deformation is defined by slip systems.

When structural components are miniature in dimensions, crystal plasticity theory can accurately predict the material response considering crystallographic deformation mechanisms. In this study, a crystal plasticity-based DAMASK code was used to explain the mesoscale deformation behavior of polycrystal beta-tin samples. Polycrystalline beta-tin samples were obtained using Voronoi tessellation in NEPER with random grain orientations, which is the case for real samples. Shear simulations were performed for a sample with reasonably large number of grains. The model was then calibrated with experimental stress-strain data for a reflowed SAC305 alloy to determine a set of beta-tin slip properties. Subsequently, multiple polycrystalline models were generated with varying number of Sn grains, and a spectral solver was used to determine the sample responses under shear loads on three orthogonal planes. Samples with large number of grains exhibited isotropic deformation behavior. However, samples with fewer number of grains demonstrated anisotropic behavior. This study determined the overall average grain size to sample size ratio at which isotropic behavior breaks down under the application of shear loads.

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