On the size distribution in three-dimensional quantum-dot crystals

The size distribution function of nanodots in artificial three-dimensional (Si)Ge/Si and In(Ga)As/GaAs quantum dot crystals grown using templates with perfect periodicity is calculated. Pyramidal nanodots were modeled by cone-shaped clusters for which the Thomson formula was derived, which is necessary to determine the growth (dissolution) rate of clusters during Ostwald ripening. A comparison of the calculated curve with experimental histograms shows that the size distribution itself is formed during Ostwald ripening and is caused by features of Ge and InAs quantum-dot formation on preliminarily textured Si and GaAs substrates.