Morphological instability during steady electrodeposition at overlimiting currents

TL;DR

This paper analyzes how extended space-charge regions influence the morphological stability of electrodes during steady electrodeposition at overlimiting currents, combining numerical and analytical methods.

Contribution

It extends previous stability analysis by including the effects of extended space-charge density at high voltages, providing new analytical expressions for different voltage limits.

Findings

Extended space-charge significantly affects electrode stability.

Analytical expressions derived for low and high voltage limits.

Numerical solutions support the impact of space-charge on morphology.

Abstract

We present a linear stability analysis of a planar metal electrode during steady electrodeposition. We extend the previous work of Sundstrom and Bark by accounting for the extended space-charge density, which develops at the cathode once the applied voltage exceeds a few thermal voltages. In accordance with Chazalviel's conjecture, the extended space-charge region is found to greatly affect the morphological stability of the electrode. To supplement the numerical solution of the stability problem, we have derived analytical expressions valid in limit of low and high voltage, respectively.