Validity of the Kardar-Parisi-Zhang equation in the asymptotic limit of metal electrodeposition

Differential stochastic equations describe the interface evolution of discrete growth models. However, only a few examples an available about the application of these equations to real systems. We show that the interface evolution during quasi-two-dimensional silver electrodeposition under ionic mass transport control approaches asymptotically the predictions of the Kandar-Parisi-Zhang (KPZ) equation. The interface evolves from an initial unstable regime to a stable one assisted by free convection. In this case, the nonlinear term in the KPZ equation becomes dominant leading to a ballistic deposit structure.