Topology optimization for unifying deposit thickness in electroplating process

Uniformity of deposited thickness in electroplating processes is vital to the realization of desirable surface qualities in many products. The thickness distribution of deposits is affected by numerous factors, such as the arrangement and shapes of auxiliary cathodes, anodes, and shields as well as the detailed configuration of the electroplating process. Deposit thickness reflects the amount of ions transported from anodes to cathodes, particularly to the object being plated, although auxiliary cathodes are sometimes placed to prevent excess plating in certain areas of the product, as are shields that impede current flow. This study presents a topology optimization method for achieving uniform deposition thickness, applied to the design of anodes placed in an electroplating bath. The proposed method is based on level set-based topology optimization and FEM is used to analyze the electrochemical field. The shapes and arrangement of anodes are expressed with respect to ion sources using level set functions. The uniformity of the current density on a cathode is employed as an objective function, since current density is nearly proportional to the thickness of the resulting electroplating. To stabilize the optimization process, the Kreisselmeier-Steinhauser function is used. The magnitude of the current density on the cathode is set as a constraint so that it does not fall below a certain value, to avoid lengthy plating times that would occur if the current density were too low. Numerical examples are presented to confirm the utility of the proposed method and the results demonstrate that the proposed method can obtain appropriate shapes and arrangements of anodes.