Stable growth and kinetic roughening in electrochemical deposition.

Abstract

We studied kinetic roughening of copper which was electrodeposited at slow rates. The surfaces showed a unique scaling. In the shorter length regime, the interface width scaled with the length scale $L$ as ${L}^{\ensuremath{\alpha}}$ ($\ensuremath{\alpha}=0.87\ifmmode\pm\else\textpm\fi{}0.05$). In the longer length regime, the width scaled with the deposition time $t$ as ${t}^{\ensuremath{\beta}}$ ($\ensuremath{\beta}=0.45\ifmmode\pm\else\textpm\fi{}0.05$). The value of $\ensuremath{\alpha}+\frac{\ensuremath{\alpha}}{\ensuremath{\beta}}$, 2.8, is much larger than 2 predicted for the case where the growing direction is normal to the surface everywhere. The scaling behavior is interpreted as the result of enhanced growth of the protrusions owing to nonlocal Laplacian growth effect.