Bi-directional homogenization equivalent modeling for the prediction of thermo-mechanical properties of a multi-layered printed circuit board (PCB)

Abstract

Warpage of multi-layered printed circuit boards (PCB) during the reflow process is a serious problem which affects the reliability of solder ball connections between the PCB and the mounted semi-conductor packages in electronic devices. It is essential to predict the warpage of the PCB accurately; however, the complicated copper patterns in multi-layered PCBs render a full modeling analysis impossible due to the excessive computing time required. To overcome this problem, we have developed analytical equations of three Cu patterns (line, square, and grid) for the application of thermo-mechanical properties simply by equivalent modeling of Cu patterns. In the proposed equations, the effect of thermo-viscoelastic properties as well as the influence of surrounding layers such as woven glass fabric/BT (bismaleimide triazine), composite laminate (BT core), and photoimageable solder resist (PSR) were considered. To verify the developed equations, vibration tests based on the wave propagation approach were performed at various temperatures. Good agreement was observed between the equivalent model and the experimental results.