A Comparison of Analytical and Finite Element Analysis Methods for Determining the Equivalent Thickness of Large 4H-SiC Taiko Wafers

The production of large semiconductor wafers, such as 8” Si and wide band gap SiC substrates, presents challenges that require early-stage warpage control to prevent uncontrolled asymmetric warpage or wafer bifurcation. The taiko method, which involves creating a thicker ring region around the rim of the wafer, has been widely used to mitigate this issue. However, the manufacturing process for large Si and 4H-SiC wafers can still be challenging due to warping during finishing and processing. In this study, we investigate the concept of equivalent thickness for a front-side metalized taiko wafer. The equivalent thickness lies between the thickness of the central region and the annular region due to the influence of the ring region. We developed both an analytical approach and a finite element analysis (FEA) using ANSYS® software to model the equivalent thickness of taiko wafers. We investigated the curvature as a function of the stress of the metal layer, considering key design factors such as the substrate region thickness, thin metal film thickness, step height, and width of the annular ring region. By systematically varying the thickness of the central region of the taiko wafer, we investigated the curvature as a function of the stress in the metal induced by thermal loads in the linear regime. The aim of this study is to identify regularities and similarities with the Stoney equation and investigate the validity of the analytical approach for the case of a Si and 4HSiC substrate as well.