Three-Dimensional Calculation of Current Distribution in Electrodeposition of Copper

"The three dimensional current distribution on the rectangular cathode is predicted using a boundary element method with a linear element of trigonal type. The effect of cell geometry and anode shape on current distribution is simulated. Calculated results compare well with experimental results. The proper combination of anode size and distance between electrodes increase the current uniformity.The importance of electrodeposition as a fabrication technology in the electronics industry is large and growing. The main advantages of this wet processing method, in comparison to other dry processing methods, lie in its high yield, rapid processing and low cost. In nearly every application of electrodeposition the pursuit of deposit uniformity, especially thickness uniformity, has been technically imperative. The thickness uniformity of the deposit depends largely on the current distribution over the cathode. The current distribution is primarily determined by the geometrical characteristics of the electrodes and the cell. Also the polarization at the electrode surface and the mass transfer affect the current distribution.The current distribution is an important consideration for those involved in designing electrochemical systems and electroplating systems in particular. Although it is important, the common practice in industry is to use trial and error method to design the cell that optimize the uniformity of current distributions in electroplating. The purpose of this paper is to illustrate the useof boundary element method to predict three-dimensional current distribution in rectangular cell.The calculation of the current distribution is possible by various numerical techniques, which include the finite difference method (FDM)1, the finite element method (FEM)2, and the boundary element method (BEM)3,4. These methods of the numerical calculation have various problems, respectively, but the BEM is considered to be the most efficient. This is due to the fact that the BEM has the advantage of solving field equations only on the surface of a calculation domain. A good comparison between the BEM and the FEM for the secondary current distribution in a Hull cell was made by Matlosz et al.5The fundamentals on the theory of current distribution in electroplating are well-established in the literature by a number of authors.6, 7, 8 However, a small fraction of these works have been specially addressed to three-dimensional analysis, and, mostly thel·10 have focused on the problem qualitatively rather than quantitatively.Extending the previous work to three-dimension, we developed the program for the quantitative calculation of 3-dimensional current distribution using a boundary element method with a linear element of trigonal type. Integrals with singularity from the fundamental solution have been analytically computed and it is shown in detail in the Iiterature11. This paper deals with the three dimensional current distribution for the electrode position of copper in a cubic type cell and the effect of anode shape, size and the distance between electrodes on current distribution is studied."