Coupling Characteristics of BGA Solder Balls at High Frequencies: A Simulation Study on Electromagnetic-Thermal-Mechanical Interactions Considering Skin and Proximity Effects

With the development of high-frequency and high-density System-in-Package (SiP) technologies, the coupling of electromagnetic, thermal, and mechanical stresses has become a significant reliability issue for packaging interconnect structures. This study investigates the electromagnetic-thermal-mechanical coupling problem of BGA solder balls in packaging interconnect structures, analyzing the multi-physics coupling characteristics under high-frequency conditions, as well as the impact of skin and proximity effects on current distribution and electromagnetic losses of the solder balls. The electromagnetic losses of the BGA were calculated at frequencies of 100 kHz and 5 GHz. Considering the influence of the temperature field on the material conductivity, a bidirectional electro-thermal coupling simulation was performed to obtain the temperature variation induced by electromagnetic losses. When the frequency increased from 100 kHz to 5 GHz, the electromagnetic losses caused the maximum temperature of the solder balls to rise by 18.5%. The temperature gradient was applied to the stress field to calculate the equivalent thermal stress of the solder balls, revealing that the thermal stress was primarily concentrated in the transition region between the solder ball and the pad. After optimizing the solder ball model, the thermal stress results became more accurate, and the maximum thermal stress at the transition between the solder ball and the pad decreased by 18.2%, indicating improved mechanical performance.