Optimization of Cathode Shielding in Cell Design Using Computer Simulation

This paper describes a straightforward numerical method for solving the Laplace equation to optimize the design of an electroplating cell by placement of the anode, cathode and cathode shields to achieve a uniform deposit thickness on a flat cathode in a cell tailored for a specific purpose. The method uses an iterative finite-difference algorithm to calculate the deposit thickness distributions for selected sets of cell geometry parameters so that the effect of changes in these parameters can be seen, thus allowing the optimum set of geometric parameters to be selected. The algorithm shows how sub-optimum geometry leads to either over-shielding or under-shielding and where the optimum cell geometry lies between these two conditions. The Tafel slope for the reaction, the exchange current density and the electrolyte conductivity are also considered. However, these factors have considerably less of an effect on the deposit distribution than do the geometric cell design parameters. This paper demonstrates the universality of Prentice’s numerical method by allowing the parametrization as illustrated with an exemplary symmetrical electrochemical cylindrical cell. Such a geometry is of utmost relevance in semiconductor manufacturing. Achieving a uniform deposit by optimization of cell design can lead to a significant reduction of subsequent corrective procedures such as chemical mechanical planarization commonly employed in the semiconductor industry.