We develop a formalism for predicting morphology evolution during electrodeposition as a function of the deposition parameters, composition of the electrolyte, and the species being deposited. Our model explicitly couples the electrostatic fields and the metal cations and spectator ions of arbitrary concentrations. We first perform a mixed asymptotics analysis to predict the self-consistent, uniform, steady-state electrostatic, and concentration fields. Morphology evolution is analyzed within the framework of perturbation theory, where we linearize around the uniform, steady-state fields. We find that the surface is unstable at long length scales due to a diffusional instability, in agreement with previous results. Furthermore, we find that both increasing the deposition rate and the spectator ion concentration within the electrolyte at fixed deposition rate increases surface roughness, also in agreement with common experience. We provide an approximate analytical formula for the perturbation growth rates as a function of the spectator ion concentration. The formalism developed here provides a rigorous, self-consistent foundation upon which the effects of additives on surface morphology are analyzed in a companion paper.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Renewable Energy, Sustainability and the Environment
- Surfaces, Coatings and Films
- Materials Chemistry