# Crossover from compact to branched films in electrodeposition with surface diffusion

## TL;DR

This paper models thin film electrodeposition, revealing a crossover from smooth to branched growth, and predicts how surface diffusion parameters influence film morphology, supported by simulations and scaling analysis.

## Contribution

It introduces a detailed model incorporating surface diffusion and adsorption dynamics, providing a scaling law for the film thickness at the crossover point.

## Key findings

- Compact wetting layer forms before branched growth
- Maximal layer thickness scales with diffusion parameter G
- Model predictions align well with numerical simulations

## Abstract

We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G>>1), a detachment probability epsilon<1 per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness z_c of that layer increases with G, but is weakly affected by epsilon. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts z_c ~ G^gamma, with gamma = 1/[2(1-nu)] = 0.43, where nu=0.30 is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness z_c can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter epsilon are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity.