Modeling of Dendrite Formation as a Consequence of Diffusion-Limited Electrodeposition

Diffusion-controlled electrodeposition was investigated experimentally and by finite element method simulations of the concentration profile on microstructured band electrode arrays (MEA) and compared to existing theoretical approaches. The simulations revealed the establishment of a diffusion layer significantly larger than anticipated according to existing models for individual bands. The electrochemical depositions were simulated by extending the finite element method to allow the modeling of changing electrode geometries during growth by use of automated remeshing steps. As an ideal case of electroplating, thin films of copper electrodeposited onto MEA of gold on SiO 2 /Si wafers were studied as a benchmark system. The electrodeposition of ZnO on MEA following initial reduction of O 2 served as an example of a multi-step reaction. The simulations considered an increasing depletion of the reactant (O 2 in the case of ZnO, Cu 2+ in the case of Cu) toward the electrode bands and film growth limited by mass transport. The growth of experimentally observed dendrites and even their detailed size distribution over the whole array was precisely predicted by the simulations. An extended understanding of diffusion-controlled growth could be achieved and used to study the temporal development of electrochemical depositions, applicable also in complex geometries.