Experimental corroboration of the Mulheran-Blackman explanation of the scale invariance in thin film growth: the case of InAs quantum dots on GaAs(001)

TL;DR

This study experimentally confirms the Mulheran-Blackman theory explaining the scale invariance of island size distribution during early thin film growth, using InAs quantum dots on GaAs(001) and Voronoi cell analysis.

Contribution

It provides experimental evidence supporting the Mulheran-Blackman explanation of scale invariance in quantum dot formation, linking volume distributions to Voronoi cell areas.

Findings

Quantum dot volume distributions match Voronoi cell area distributions.

Experimental data supports the scale invariance theory.

Determined spatial correlation length among quantum dots.

Abstract

Mulheran and Blackman have provided a simple and clear explanation of the scale invariance of the island size distribution at the early stage of film growth [Phil. Mag. Lett. 72, 55 (1995)]. Their theory is centered on the concept of capture zone properly identified by Voronoi cell. Here we substantiate experimentally their theory by studying the scale invariance of InAs quantum dots (QDs) forming on GaAs(001) substrate. In particular, we show that the volume distributions of QDs well overlap the corrisponding experimental distributions of the Voronoi-cell areas. The interplay between the experimental data and the numerical simulations allowed us to determine the spatial correlation length among QDs.