Roughness in the Kolmogorov-Johnson-Mehl-Avrami framework: extension to (2+1)D of the Trofimov-Park model

In this paper the reformulation of Trofimov-Park (TP) model, [V.I. Trofimov, Appl. Surf. Sci. 219 (2003) 93], of thin film roughness evolution during nucleation and growth of islands in case of simultaneous nucleation is presented. The calculation of TP restricted to one-dimensional triangular islands has been extended to both the one-dimensional elliptical case and to the pyramidal two-dimensional one. The kinetics of the interface width, w, and the height-height autocorrelation function G, through which the correlation length has been defined, have been estimated. Moreover, w(Theta) and xi(Theta), where Theta is the fraction of the covered substrate, if properly rescaled to the density of nuclei N and to the aspect ratio of islands, are universal functions that, for a conspicuous range of Theta, obey a power law with the exponent depending upon island shape. (c) 2005 Elsevier B.V. All rights reserved.