Numerical simulation of electro-deposition process influenced by force convection and migration of ions

Electro-deposition process is one of the main steps in the LIGA procedure to fabricate microstructures. In this paper, one-dimensional modeling of Nickel electro-deposition process is implemented on Rayan and developed for simulation of time-dependence diffusion and migration of charge species with reduction reactions on the cathode surface. This model is proposed by considering governing equations on electro-kinetic phenomena consist of Nernst-Plank equation and Poisson's equation of electric potential. Transport of ions toward the cathode is considered based on the effect of convection, reaction rate, diffusion and migration. The numerical results cover two series of data consisting of effective diffusion layer thickness δeff and the transient current density. The effect of force convection and diffusion terms on effective diffusion layer δeff is validated by Ribeiro analytical model. The transient current densities for different applied voltages are in well agreement with Hyde and Compton's experimental model. Effect of every term on effective diffusion layer δeff is shown and we found that for velocity lower than vc = − 0.0005 cm s− 1, convection term does not have any influences on effective diffusion layer δeff . Moreover, the relationship between the applied voltages, current density, effective diffusion layer δeff and hydrodynamic velocity is proposed.