Phenomenological model of the quantum size effect on growth of nanosize towers in Pb/Si(111) and Pb/Cu(111)

In the growth and formation of nanoscaled structures on Pb/Si(111) and Pb/Cu(111), certain heights of the structures have increased stability, which leads to the formation of tower-like structures (nanotowers). Typically, such Pb nanotowers with even numbers of layers up to 8 are found to be stable, as well as towers with odd numbers of layers from 11 onwards. The stability of these preferred heights is due to the electronic structure dependent total energy, the so-called quantum size effect (QSE). We present here a simple phenomenological model describing the QSE on nanostructure growth. The basic model is a modification of the simultaneous multilayer growth model, relating the mass redistribution between different layers to Friedel-type surface energetics in order to capture the QSE. In the model, the structures consisting of even numbers of layers (4, 6, 8) and odd numbers of layers (11 and 13 onwards) are stable, and are shown to have tower-like morphology.