Three-dimensional calculation of current distribution in electrodeposition on patterned cathode with auxiliary electrode

A three-dimensional model has been developed to predict the current distribution on a patterned cathode with an auxiliary electrode. The solution for the three-dimensional Laplace equation has been obtained by a boundary element method using a linear element of trigonal type. Integrals with singularity due to the fundamental solution have been analytically computed. This model suggests the optimum size of an auxiliary electrode, which minimizes the thickness variation through the entire area of the rectangular cathode for electrodeposition onto a lithographically patterned substrate.