Scaling of the nucleation density for pulsed layer deposition

We discuss the logarithmic scaling of the nucleation density for pulsed laser deposition, discovered recently by Hinnemann et al. [Phys. Rev. Lett. 87, 135701 (2001)] in two dimensions. The logarithmic scaling is often observed in the upper critical dimension. We find that the nucleation density in one dimension also exhibits logarithmic scaling, implying that it is not a prerequisite for the upper critical dimension. The normalized island density also scales similarly both in one and two dimensions when plotted against the normalized coverage.