Anomalous scaling of the surface width during Cu electrodeposition

Kinetic roughening during thin film growth is a widely studied phenomenon, with many systems found to follow simple scaling laws. We show that for Cu electrodeposition from additive-free acid sulphate electrolyte, an extra scaling exponent is required to characterize the time evolution of the local roughness. The surface width w(l,t) scales as t(beta(loc))lH, when the deposition time t is large or the size l of the region over which w is measured is small, and as t(beta+beta(loc)) when l is large or t is small. This is the first report of such anomalous scaling for an experimental ( 2+1)-dimensional system. When the deposition current density or Cu concentration is varied, only beta(loc) changes, while the other power law exponents H and beta remain constant.