Galerkin-based modal analysis on the vibration of wire-slurry system in wafer slicing using a wiresaw

Wiresaws have been widely used in industries to slice semiconductor ingots into thin wafers for semiconductor fabrication. However, the surface roughness of a wiresaw-sliced wafer is usually not uniform which can be a concern in the subsequent lapping and polishing processes. It is sometimes observed that poor surface finish can occur at the beginning and the end of sliced round wafers when contact spans are short. In this paper, the dynamics of a coupled wire/slurry non-conservative vibration system is analyzed according to the rolling-indenting floating machining mechanism of typical wiresaw processes. Basic approaches adopted are the linearization of the coupled nonlinear governing equations with respect to the equilibrium, Galerkin-based discretization of the distributed non-conservative system, and the subsequent modal analysis. For the purpose of model verification, a numerical scheme of direct-time integration to an alternative finite element (FE) semi-discretized system is performed using the one-step Newmark's method. The results from the eigenanalysis of the Galerkin-based model are presented. These simulation results indicate that the wire/slurry system consists of both real and paired complex eigenvalues, which correspond to the over-damped modes and other vibration modes of the system. Parametric studies show that the vibration displacement of the wire decreases when the contact span expands, which explains the typical distribution of the surface roughness of a round wiresawn wafer. From the parametric studies, the tension and bow angle of the wire are found to play important roles in the response of the wire. Finally, in order to reduce the differential saw damage caused by the vibration of the wire, adaptive vibration control strategies are proposed for the wiresaw slicing processes.