Analytical multi-step homogenization methodology for a stack of thin films in microelectronics

The manufacturing process causes silicon wafer curvature because of the thermomechanical mismatch between each layers and the substrate. This curvature depends on many factors such as the properties of the used materials (Young’s modulus, Poisson’s ratio, coefficient of thermal expansion), the process temperatures and the deposition route (intrinsic stress of each film). Wafer curvature has become critical, because the induced deflections lead to wafer handling issues or substrate breaking.The aim of this paper is to present a new analytical homogenization methodology to predict at production time scale the wafer curvature at any step of the process. The methodology takes into account the manufacturing process with the thermomechanical flow and the intrinsic stress. This will allow R&D engineers to estimate the curvature of new technology wafers before prototyping. Moreover, the results obtained with this methodology are validated with a comparison with a 2D axisymmetric model using the Finite Element Analysis (FEA).