Multi-physics investigation of the influence of thermal stress on RF systems based on the bidirectional coupling method

Abstract System-in-Package (SiP), characterized by its compact structure and short design cycle, is widely used in wireless communication. As the critical components of SiP, radio frequency (RF) transmission lines are utilized to establish high-frequency signal circuits to connect the chip and external ports. With the increasing device power boosting, thermal management is a significant challenge for the SiP system. Therefore, comprehensive analysis of complex multi-physics environments is the foundational step for thermal management. In this paper, we proposed an electro-thermo-mechanical bidirectional coupling method at the cross-scale interface level to investigate the thermal reliability of transmission lines in RF SiP. Firstly, we developed the theoretical model for the bidirectional electro-thermo-mechanical coupling. Secondly, a predictive numerical model for the multi-physics bidirectional coupling in RF systems, utilizing silicon as the semiconductor and copper as the metal, was constructed. The bidirectional coupling mechanisms were primarily introduced through material properties. Microscopic analytical equations for various material properties were modified by using experimentally measured data. Temperature and strain variables were simultaneously incorporated for equation fitting. Finally, the obtained microscopic analytical equations were substituted into the multi-physics numerical model for the iterative calculation. We analyzed the RF performance changes of microstrip lines, strip lines and coplanar waveguides, over an ambient temperature range from 233.15 K to 398.15 K. In the bidirectional coupling framework, the impact of the stress feedback mechanism on system performance is closely associated with the boundary conditions, which is particularly evident during the warping process in actual packaging scenarios. The experimental validation in this study was based on S-parameters measured from fabricated coplanar waveguides at room temperature. Theoretical cross‑validation was performed for the electromagnetic loss model and the basic temperature rise analysis model. This study provides the foundation model for macroscopic control of RF performance through microscopic regulation of material properties.