Transient Simulation of Diffusion-Limited Electrodeposition Using Volume of Fluid (VOF) Method

A numerical model utilizing the volume of fluid (VOF) method is proposed to simulate the transient shape changes of the deposit front, considering the diffusion-limited electrodeposition process. Modeling equations are proposed to accurately handle transport phenomena in both electrolyte (fluid) and deposit (solid). Transient evolutions of field structures, including flow, concentration, electric current density, and electric potential, are computed considering electrodeposited copper bumps. Two cases, including single cavity and multiple cavities, are studied. Based on the modeling results, the maximum height of the hump and the thickness of the deposited layer in each consecutive cavity decreases going from upstream to downstream. Conversely, the location of the maximum height of the hump remains unchanged in all cavities. Results are validated against available experiments.