The application of rate equations to describe nucleation and growth on rough substrates: tin and lead on aluminium

The description of island nucleation and growth is an essential goal in thin film deposition. The shape and the distribution of stable islands in the first phases of growth determines a wide variety of film properties. Because of their mean-field nature rate equations are a powerful tool for the analysis of nucleation and growth phenomena if local properties of the substrate are of minor importance. Therefore, the rate equation theory is well established for flat, single crystalline surfaces but it can also be applied to substrates with well-defined defects as e.g. vicinal surfaces. This paper shall test the applicability of the rate equation theory for rough substrates. In this case, one expects the validity of a mean-field approach only if the diffusion length of a monomer is significantly larger than the extension of a typical surface feature. Therefore highly mobile species have to be considered. In the present study tin (Sn) and lead (Pb) were sputter-deposited on aluminium (Al) substrates with RMS roughnesses of about 20 nm. Since a distinctive island growth was observed and the island separation was in the mu m-range the above statement was presumed to be valid because of the high ratios of island separation/RMS roughness. The growth mode of the Sn and Pb-films on the AI-substrates was analyzed in the framework of the rate equation theory by varying the coverage and deposition rate. For both systems, Sn on AI and Pb on Al, the rate equation analysis yielded Stranski-Krastanov growth with the size of the critical nucleus in the range from 6 to 20 monomers. This result was independently checked by sputter-AES. A thin layer of Sn or Pb was detected between the islands. This wetting layer seems to be highly conformal with the polycrystalline Al according to topographic atomic force microscopic (AFM) measurements. These facts support the Stranski-Krastanov result. (C) 1999 Elsevier Science B.V. All rights reserved.