# Anand Model and Finite Element Analysis of Sn-0.3Ag-0.7Cu-3Bi Lead-Free Solder Joints in BGA Packages

## TL;DR

This study evaluates the mechanical behavior of a specific lead-free solder used in electronics under thermal stress, identifying key failure points and estimating its durability.

## Contribution

The study introduces a novel framework combining Anand model calibration and FEA to assess the reliability of Bi-doped SAC0307-3Bi solder joints in BGA packages.

## Key findings

- Stress concentration correlates with Distance to Neutral Point, with failure likely at the chip-side interface of corner joints.
- Creep strain accumulates in a step-wise pattern during thermal cycles, showing temperature sensitivity.
- Estimated fatigue life of SAC0307-3Bi solder joints is approximately 2239 cycles using the Syed model.

## Abstract

Bi-doped low-silver Sn-Ag-Cu solders are increasingly gaining attention in advanced electronic packaging due to their cost-effectiveness and enhanced mechanical properties. However, the thermo-mechanical reliability mechanisms of such modified solders, particularly Sn-0.3Ag-0.7Cu-3Bi (SAC0307-3Bi) within Ball Grid Array (BGA) assemblies, remain insufficiently understood. To address this gap, this research proposes a comprehensive assessment framework integrating constitutive parameter calibration with finite element analysis (FEA) to accurately characterize the mechanical behavior and fatigue durability of SAC0307-3Bi solder joints under cyclic thermal loads. The Anand viscoplastic parameters were first calibrated via the Norton creep law and virtual tensile tests. Subsequently, a 3D quarter-symmetry model was constructed to replicate thermal cycling conditions between 25 °C and 125 °C. Simulation data reveal a strong correlation between stress concentration and the Distance to Neutral Point (DNP), pinpointing the chip-side interface of the corner joint as the critical failure site. Moreover, creep strain was observed to accrue in a “step-wise” pattern, predominantly during the heating and cooling ramps, reflecting distinct temperature sensitivity. Utilizing the Syed model, the fatigue life was estimated at approximately 2239 cycles. These insights serve as a crucial benchmark for designing robust packages using Bi-doped, low-silver lead-free solders.