Dynamic Scaling in Electrochemical Deposition

Static and dynamic scaling behavior in copper electrochemical deposition in the stable growth condition (non-bulk fractal growth) was studied by atomic force microscopy and numerical simulation. We found two distinct scaling regimes with roughness exponent α of 0.6 and 0.87α0.05 corresponding to the concentrations of the “brightener” organic additive higher and lower than 1 mℓ/ℓ, respectively. The rms surface width of the whole measured area of the surfaces in the former regime was smaller than that in the latter regime. For the latter rougher surface, we observed dynamic scaling behavior for longer length scales as well as the stationary scaling behavior for shorter length scales: surface width did not further increase with linear size of the area for longer length scales than a characteristic correlation length and increased as a power of deposition time with the dynamic exponent β of 0.45. The sum of α + (α/β) was larger than the value expected for KPZ local growth, 2. This was understood that in electrochemical deposition there is enhancement of growth at protrusions owing to non-local Laplacian field effect. The smoother (α =0.6) and the rougher (0.87) surfaces were reproduced by numerical solutions of KPZ + (the growth term proportional to height) for the shorter and the longer growth times, respectively. Bifurcation of the surface morphology is understood as a result of decrease of weight of the additional term owing to increase of the additive.