Mathematical modeling of electrodeposition

Mathematical modeling of electrodeposition is a process that yields information about the plating system of interest. The process consists of first determining the composition of the plating bath of interest by using thermodynamic information. The second step consists of specifying or determining the electrochemical reactions that occur on the electrodes and the chemical reactions that occur on the electrodes and in the bath. The third step consists of specifying the governing equations (material balance equations) for the concentrations of the species in the bath. Next, reaction-rate expressions must be specified for the electrochemical reactions that occur at the electrodes. Finally, the geometry of the plating bath must be specified. Since the material balance equations for species in the bath depends on fluid flow, the flow conditions in the tank must be specified. In some cases, the material balance equations for the concentration of species in the bath and the momentum balance equations for the fluid flow must be solved simultaneously because the electrodeposition process can give rise to density changes at the surface of the working electrode. These density changes cause the hydrodynamics in the bath to change. Sparging and stirring of the bath also affect the flow conditions at the work piece. The hydrodynamic effects are sometimes lumped together and described by a hydrodynamic boundary layer. Similarly, the mass-transfer effects in plating baths are often lumped together and represented by a diffusion layer. These concepts of boundary layers and diffusion layers have been used to simplify the mathematical modeling of electrodeposition.