ABSTRACT
We study a thin-film electrodeposition model that represents the relaxation of the deposited material by adatom diffusion on quenched crystal topographies and considers simple mechanisms of cation flux in the electrolyte. The results of numerical simulations with collimated flux and a rapid cation reduction in contact with the deposit relate the surface roughness and the adatom hop numbers with two model parameters. A comparison with the results of a collective diffusion model for vapor deposition shows differences in the surface morphologies but similarities in scaling relations, which suggest thermally activated (Arrhenius) forms for the parameters of the electrodeposition model and relate one of them to the applied current. Simulations with purely diffusive cation flux and possible pore formation in simple cubic lattices show the growth of self-organized structures with leaf shapes (dendrites) above a compact layer that covers the flat electrode. The thickness of this layer and the average dendrite size also obey scaling relations in terms of the model parameters, which predict that both sizes decrease with the applied current, in agreement with recent experimental studies. Under all flux conditions, an increase in adatom diffusivity with temperature implies an increase in the average sizes of low-energy surface configurations, independently of their particular shapes. Finally, we note that a previously proposed model for electrodeposition produced similar morphologies, but the quantitative relations for the characteristic sizes differ from those of the present model, which also advances with a consistent interpretation of temperature effects.
ABSTRACT
We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in 1+1 and 2+1 dimensions using a Euler discretization scheme and the replacement of (nablah)(2) by exponentially decreasing functions of that quantity to suppress instabilities. When applied to the equation in 1+1 dimensions, the method of instability control provides values of scaling amplitudes consistent with exactly known results, in contrast to the deviations generated by the original scheme. In 2+1 dimensions, we spanned a range of the model parameters where transients with Edwards-Wilkinson or random growth are not observed, in box sizes 8< or =L< or =128 . We obtain a roughness exponent of 0.37< or =alpha< or =0.40 and steady state height distributions with skewness S=0.25+/-0.01 and kurtosis Q=0.15+/-0.1 . These estimates are obtained after extrapolations to the large L limit, which is necessary due to significant finite-size effects in the estimates of effective exponents and height distributions. On the other hand, the steady state roughness distributions show weak scaling corrections and evidence of stretched exponential tails. These results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.
