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

Abstract

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 oftower-like structures (nanotowers). Typically, such Pb nanotowers with even numbers oflayers up to 8 are found to be stable, as well as towers with odd numbers of layers from 11onwards. The stability of these preferred heights is due to the electronic structuredependent total energy, the so-called quantum size effect (QSE). We present here a simplephenomenological model describing the QSE on nanostructure growth. The basic model is amodification of the simultaneous multilayer growth model, relating the mass redistributionbetween different layers to Friedel-type surface energetics in order to capture the QSE. Inthe model, the structures consisting of even numbers of layers (4, 6, 8) and oddnumbers of layers (11 and 13 onwards) are stable, and are shown to have tower-likemorphology.