A simple model for roughening in the instantaneous electrodeposition process

We introduce a very simple model for the instantaneous electrodeposition process that takes into account the kinetic roughening during the film growth. The main ingredients of the model are the characteristic time for the cation particles to attain their steady-state velocity and the choice of a velocity-dependent probability for the particles to relax on the substrate. The model is capable of reproducing the experimental results for the density current as a function of time for a fixed value of the external potential during the electrodeposition experiment, as well as typical voltammograms. The model was investigated through a suitable continuous Monte Carlo algorithm where the number of particles to be deposited in a Monte Carlo step (MCs) changes with time. For small values of the particle velocities the deposition is essentially described by a pure random deposition model, while for high values of velocity a dominant local relaxation process is assumed. At each MC we compute the surface width in order to determine the roughness of the surface. From the plots of the surface width versus time we found the growing (β), dynamic (z) and roughness (α) exponents for this model.