This Is AuburnElectronic Theses and Dissertations





Mondal, Debabrata

Type of Degree

PhD Dissertation


Mechanical Engineering

Restriction Status


Restriction Type

Auburn University Users

Date Available



With the growth of electronic packaging industries, ranging from automobiles to hand-held products, reliability is a major concern. Also, to keep pace with the increasing demand of end users for integration, miniaturization, light weight, high speed, and multi-functionality of portable electronic devices such as mobile phones, digital cameras, as well as personal digital assistant (PDA), electronic packaging industries are intended to manufacture packages of high density and smaller dimension. These packages consist of smaller solder interconnects with solder balls in each area and short distance between the solder balls. The reliability of smaller electronic packages is greatly affected by fundamental crystallographic configuration of beta-tin crystals in solder joints. Most of the studies in the field of mechanics of electronic packaging consider solder interconnects as isotropic material. However, solder alloys are highly anisotropic in terms of elastic modulus, rate-dependent plastic deformation behavior, and coefficient of thermal expansion. Hence, to predict the deformation behavior of solder joints in microelectronic packages more accurately, beta-tin crystallographic orientation needs to be considered in modeling and analysis of the deformation mechanics of solder interconnects. Solder joints provide mechanical support, electrical and thermal interconnection between packaging levels in microelectronics assembly systems. The proper functioning of these interconnections and the reliability of the electronic packages depend largely on the anisotropic mechanical properties of the solder joints. A few studies were conducted to investigate the effect of material orientation on lead free solder under the application of external shear loads. In addition, different crystallographic slip systems were incorporated in the modeling to assess the anisotropic deformation behavior of solder interconnects. However, no study has focused on the detailed analysis of beta-tin grain size and orientation on the overall deformation behavior of SAC solder joints. This research mostly involves several projects to define the deformation behavior of solder joints considering different grain size and orientation. Prior to that, experiments and simulations were conducted to evaluate anisotropic elastic stiffness matrix coefficients for SAC305. Because SAC alloys contain intermetallic particles and these intermetallic compounds (IMC) affect the overall deformation significantly. Therefore, investigations need to be carried out acknowledging that fact that SAC material domains contain explicit IMC particles which are embedded in anisotropic beta-tin matrix. In the first project, micromechanical behavior evolution of SAC305 lead free solder material was investigated using the nanoindentation technique and then micromechanical modeling was performed to evaluate the direction dependent elastic moduli. The dimensions of solder joints are typically in the sub-millimeter range. Hence, size effects must be taken into account when evaluating constitutive properties of lead-free solder joints. However, it is difficult to evaluate constitutive behavior by using traditional uniaxial tests for material samples that are so small. Thus, instrumented indentation or nanoindentation techniques have proven to be convenient in investigating mechanical properties such as elastic moduli and hardness of different materials. Samples of solder joints were collected from ball grid array packages. The samples were then cross sectioned and prepared for electron back-scatter diffraction (EBSD) experiments to record the orientations of the various single and multiple-grained solder balls. After characterization of the joint orientations, nanoindentation experiments were performed on individual grains with various material orientations to obtain the elastic moduli along different directions. Using the recorded experimental modulus data, calculations were performed to evaluate the elastic compliance and stiffness matrices, which incorporate the directional material properties. Next a micromechanical model with the presence of explicit nonspherical IMC particles was developed that takes inputs pertaining to individual constituents' mechanical properties and volume fractions. Then computations were performed to generate outputs in the form of effective properties of bulk solder. Studies show that IMC particles work as reinforcement agents to strengthen the overall mechanical behavior. The representative volume elements (RVE) were considered which contained all the constituents according to their volume fractions. Size, shape, and volume fractions of IMCs were determined from Scanning Electron Microscope – Focused Ion Beam (SEM-FIB) technology. Following the model with explicit IMC particles, another finite element model was generated with homogenized properties obtained from nanoindentation tests. Finally, stress-strain responses obtained from these two approaches were compared from the overall directional elastic moduli point of view. Almost 97% weight percentage is β-Sn which is a highly directional material in terms of elastic modulus (E) and coefficient of thermal expansion (CTE). In the second project, a physics-based crystal plasticity finite element (CPFE) model with homogenized SAC properties was used to explain the mesoscale deformation behavior of solder joints that have dimensions in the sub-millimeter range. A crystal plasticity theory-based subroutine was implemented in ABAQUS finite element (FE) software to forecast the effects of β-Sn crystal orientations on overall deformation behavior of SAC305 BGA solder joints. Since the crystal c-axis is the strongest axis in terms of elastic modulus, several finite element models were developed and run with varying c-axis orientation in the x-y plane to assess the effects of various slip systems on the deformation patterns. Since β-Sn is a crystalline material, deformation beyond the elastic limit is described by various atomic planes and directions, which are termed as slip systems together. Ten different slip families have been recognized in literature for β-Sn body-centered tetragonal (BCT) crystals. When external load is applied on solder balls, plastic deformation is dictated by the movement of dislocations and direction of deformation is defined by slip properties. Later in this project, solder joint models with multiple grains were developed and deformation behavior was explained under the application of mechanical shear. In the third project, a crystal plasticity-based DAMASK code was used to explain the mesoscale deformation behavior of polycrystal beta-tin samples. Analyzed polycrystalline beta-tin samples were obtained using Voronoi tessellation in NEPER with random grain orientations, which is the case for real samples. Tensile 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 tensile and shear loads along three orthogonal directions. 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. In this project, size effects were analyzed for polycrystal models subjected to both tensile and shear loads. In the fourth project, a data-driven machine learning (ML) model was developed to predict the mesoscale deformation behavior of single crystal SAC samples. The ML model was trained using a large number of solder stress-strain curves for various crystal orientations obtained using simulations performed with the crystal plasticity-based DAMASK code. The constants in the crystal plasticity (CP) code were first calibrated with experimental solder stress-strain data (both elastic and plastic regions) to obtain the model constants that describe the overall material deformation of SAC305 alloy from a crystallographic standpoint. For a single crystal SAC sample, there are an infinite number of possible orientations for uniaxial loading that can lead to an infinite number of different overall mechanical deformation behaviors. To account for this, a large number of CP simulations (15,000) were performed using the DAMASK code for samples with various single crystal orientations. A time-series based machine learning model was then trained on the simulated stress-strain plots for the 10,000 known orientations. The performance of the trained ML model was then evaluated by predicting the stress-strain behavior of a set of 2500 additional orientations that were not in the training set. The accuracy of the ML predictions was shown to be very good, so that the ML model can be used in the future without the need to perform computationally expensive and time-consuming CP simulations. In particular, the machine learning model can help to bypass the complicated pre-processing, computation, and post-processing aspects of numerical crystal plasticity modeling. In the final project, a comparison was made between the conventional modeling approach of package level solder joint reliability and the mesoscale method utilized throughout the significant part of this dissertation. At first, a plastic ball grid array package (PBGA) was created using CAD software SolidWorks and then the model was imported to ABAQUS finite element software for running simulations in both techniques. For the conventional technique, material properties of solder joints were assigned in terms of isotropic and homogeneous elastic properties and rate dependent plasticity using Anand model parameters. For mesoscale modeling, the solder joints’ properties were assigned in terms of anisotropic elastic stiffness matrix and beta-tin slip properties. Finally, a relative comparison was analyzed between the mesoscale simulation predictions and the conventional technique. In both approaches, elastic properties were considered for other package elements such as mold compound, die, die attachment adhesives, solder mask, substrate/PCB material and copper pad.